Nonlinear integrated photonics on silicon and gallium arsenide substrates

Transcription

1 Univerity of Central Florida Electronic Thee and Diertation Doctoral Diertation (Oen Acce) Nonlinear integrated hotonic on ilicon and gallium arenide ubtrate 2014 Jichi Ma Univerity of Central Florida Find imilar work at: htt://tar.library.ucf.edu/etd Univerity of Central Florida Librarie htt://library.ucf.edu Part of the Electromagnetic and Photonic Common, and the Otic Common STARS Citation Ma, Jichi, "Nonlinear integrated hotonic on ilicon and gallium arenide ubtrate" (2014). Electronic Thee and Diertation htt://tar.library.ucf.edu/etd/4729 Thi Doctoral Diertation (Oen Acce) i brought to you for free and oen acce by STARS. It ha been acceted for incluion in Electronic Thee and Diertation by an authorized adminitrator of STARS. For more information, leae contact lee.doton@ucf.edu.

2 NONLINEAR INTEGRATED PHOTONICS ON SILICON AND GALLIUM ARSENIDE SUBSTRATES by JICHI MA B.S. Tinghua Univerity 2006 M.Sc. Tinghua Univerity 2008 A diertation ubmitted in artial fulfillment of the requirement for the degree of Doctor of Philoohy in the College of Otic and Photonic at the Univerity of Central Florida Orlando, Florida Summer Term 2014 Major Profeor: Saan Fathour

3 2014 Jichi Ma ii

4 ABSTRACT Silicon hotonic i nowaday a mature technology and i on the verge of becoming a blooming indutry. Silicon hotonic ha alo been urued a a latform for integrated nonlinear otic baed on Raman and Kerr effect. In recent year, more futuritic direction have been urued by variou grou. For intance, the realm of ilicon hotonic ha been exanded beyond the well-etablihed near-infrared wavelength and into the mid-infrared (3 5 µm). In thi wavelength range, the omnireent hurdle of nonlinear ilicon hotonic in the telecommunication band, i.e., nonlinear loe due to two-hoton abortion, i inherently nonexitent. With the lack of efficient light-emiion caability and econd-order otical nonlinearity in ilicon, heterogeneou integration with other material ytem ha been another direction urued. Finally, everal aroache have been rooed and demontrated to addre the energy efficiency of ilicon hotonic device in the near-infrared wavelength range. In thi diertation, theoretical and exerimental work are conducted to extend alication of integrated hotonic into mid-infrared wavelength baed on ilicon, demontrate heterogeneou integration of tantalum entoxide and lithium niobate hotonic on ilicon ubtrate, and tudy two-hoton hotovoltaic effect in gallium arenide and lamonicenhanced tructure. Secifically, erformance and noie roertie of nonlinear ilicon hotonic device, uch a Raman laer and otical arametric amlifier, baed on novel and reliable waveguide iii

5 technologie are tudied. Both near-infrared and mid-infrared nonlinear ilicon device have been tudied for comarion. Novel tantalum-entoxide- and lithium-niobate-on-ilicon latform are develoed for comact microring reonator and Mach-Zehnder modulator. Thirdand econd-harmonic generation are theoretical tudied baed on thee two latform, reectively. Alo, the two-hoton hotovoltaic effect i tudied in gallium arenide waveguide for the firt time. The effect, which wa firt demontrated in ilicon, i the nonlinear equivalent of the hotovoltaic effect of olar cell and offer a viable olution for achieving energy-efficient hotonic device. The meaured ower efficiency achieved in gallium arenide i higher than that in ilicon and even higher efficiency i theoretically redicted with otimized deign. Finally, lamonic-enhanced hotovoltaic ower converter, baed on the two-hoton hotovoltaic effect in ilicon uing ubwavelength aerture in metallic film, are rooed and theoretically tudied. iv

6 To my arent, Sui Ma and Huaihong Zhu; and my wife, Si Chang v

7 ACKNOWLEDGMENT I would acknowledge my Ph.D. advior, Dr. Saan Fathour, for hi trut in me, which manifeted in hi offer for a graduate reearch aitant oition along with financial uort throughout my tudie. He i alway willing to dicu with me on my reearch in the field of integrated hotonic. I have learned not only knowledge, but more imortantly, the way to analyze and olve roblem from him. Furthermore, he haen to be more than a Ph.D. advior. Hi guidance and mentorhi, which wa not limited to tudie and reearch, heled me to raie my awarene and creativity level. Next, I would like to thank my committee member, Dr. David Hagan, Dr. Guifang Li and Dr. Robert Peale, for their valuable time, interet and uggetion on my reearch. Many thank go to my colleague in the reearch grou, Dr. Payam Rabiei, Dr. Saeed Khan, Jeff Chile, and Ahutoh Rao for their friendhi, hel and dicuion. At lat and mot imortantly, my ecial thank go to my wife, Si Chang, who bring joy to my life. vi

8 TABLE OF CONTENTS LIST OF FIGURES... x LIST OF TABLES... xiv LIST OF ACRONYMS/ABBREVIATIONS... xv CHAPTER 1: INTRODUCTION... 1 CHAPTER 2: MID-INFRARED NONLINEAR SILICON PHOTONICS Overview Waveguide Technologie for Mid-IR Silicon Photonic Mid-IR Silicon Raman Laer Background of Silicon Raman Laer/Amlifier Analytical Modeling of Mid-IR Silicon Raman Laer Pum-to-Stoke RIN Tranfer of Mid-IR Silicon Raman Laer Exerimental Reult on Mid-IR Silicon Raman Laer Mid-IR Nonlinear Silicon Photonic Uing the Kerr Effect Mid-IR Continuum Generation Source Mid-IR Otical Parametric Amlifier Vertical-Cavity Silicon Raman Amlifier Background Deign of Mirror Reflectivitie CHAPTER 3: NOISE FIGURE IN SILICON OPTICAL PARAMETRIC AMPLIFIERS Background Noie Figure of Near-IR a-si OPA Noie Figure of Mid-IR c-si OPA vii

9 CHAPTER 4: HYBRID WAVEGUIDE TECHNOLOGY ON SILICON Background Ta2O5-on-Si Integrated Photonic LiNbO3-on-Si Waveguide and Micro Reonator Nonlinear Integrated Photonic in LiNbO3 and Ta2O5-on-Si Waveguide Third-Harmonic Generation in Ta2O5-on-Si Second-Harmonic Generation in LiNbO3-on-Si CHAPTER 5: TWO-PHOTON PHOTOVOLTAIC EFFECT IN GALLIUM ARSENIDE Background Model Exerimental Reult on TPPV Effect in GaA CHAPTER 6: PLASMONIC-ENHANCED SILICON PHOTOVOLTAIC DEVICES Background Plamonic-Enhanced Solar Cell Uing Non-Sherical Nanoarticle Plamonic-Enhanced Two-Photon Photovoltaic Power Converter Uing Nanoaerture Structure CHAPTER 7: FUTURE WORK Active Coherent Beam-Combining via Mid-infrared Silicon Raman Laing Alication of VCSRA a Image Pre-Amlifier Radio-Frequency and high-seed Characterization of the LiNbO3 Electro-otic Modulator Exerimental Demontration of Harmonic Generation in LiNbO3 and Ta2O5-on Silicon Waveguide Power Efficiency of the Two-hoton Photovoltaic Effect in Gallium Arenide viii

10 APPENDIX: FABRICATION STEPS AND SIMULATION CODES FOR GAAS/ALGAAS HETEROJUNCTION DIODES A.1 Fabrication Ste and Recie for GaA/AlGaA Heterojunction Diode A.2 COMSOL Code for Simulation of the Two-hoton Photovoltaic Effect in GaA/AlGaA Heterojunction Diode LIST OF REFERENCES ix

11 LIST OF FIGURES Figure 1-1: Organization of the diertation Figure 2-1: TPA and the aociated FCA for near-ir um Figure 2-2: (a) Three waveguide technologie of ilicon hotonic at mid-ir baed on novel fabrication technique: SOS, SON, and all-ilicon waveguiding latform. (b) SEM image of the fabricated waveguide for the three latform Figure 2-3: Linear roagation lo characterization of the SOS waveguide uing (a) the FP method and (b) the cut-back method Figure 2-4: Schematic of the exerimental mid-ir etu ued to characterize the ilicon-on-nitride and ASOP (uended membrane) waveguide Figure 2-5: FP interference fringe at wavelength of 3.39 μm obtained by tuning the temerature of the chi for (a) SON waveguide and (b) all-ilicon uended membrane waveguide Figure 2-6: (a) Schematic of the tudied mid-ir ilicon Raman laer; (b) Otical mode rofile (TE) at um (to) and the Stoke (bottom) wavelength in the SOS waveguide with air tocladding having rib width of 2 µm, rib height of 2 µm and lab height of 1 µm. The calculation are obtained from a commercial numerical mode olver (BeamPROP by RSoft) Figure 2-7: (a) Intenity ditribution of um and Stoke wave with I in = 200 MW/cm 2. R l = R r = R l = R r = 30%, α = α = 0.5 db/cm and L = 2 cm were aumed. The inet how the inutoutut characteritic of the Raman laer; (b) Threhold intenity veru cavity length for variou outut facet reflectivitie and roagation loe and for R l = 10%, R r = R l = 90% Figure 2-8: Converion efficiency veru cavity length L and outut facet reflectivity R r for two roagation lo value and two um intenitie Figure 2-9: Maximum converion efficiency veru um intenity for four different roagation lo value Figure 2-10: (a) RIN tranfer ectra for mid-ir SRL umed at 50, 75, 100 and 200 MW/cm 2 and (b) the device low frequency RIN tranfer veru um intenity for four roagation lo value. Modal arameter: L = 1.20 cm, R r = 38%, α = 0.5 db/cm (otimized deign for I in = 100 MW/cm 2 ), D = 120 /(nm km) Figure 2-11: Set-u ued for mid-ir Raman laing in bulk ilicon Figure 2-12: Sontaneou Raman emiion a a function of um ower x

12 Figure 2-13: Meaured ignal at 3.4 µm from a 1-inch-thick bulk ilicon amle coated with dielectric mirror deigned for Raman laing at thi wavelength and umed with a nanoecond OPO at a wavelength of 2.88 µm Fig. 2-14: Inut/outut ectra of continuum generation in an SOS waveguide at um intenity of 96 GW/cm 2. The inet lot the broadening factor veru um intenity Figure 2-15: Schematic of VCSOA howing co-directionally roagating mode (left) and counter-directionally roagating mode oeration (right) Figure 2-16: Signal gain veru RTS for um intenity of 400 kw/cm 2 and for R BS = 0.9, R BP = 0.9, R TP = Figure 3-1: Real and imaginary art of the nonlinear coefficient γ(ω) including the Raman contribution. The effective area of the waveguide i aumed to be 0.07 µm Figure 3-2: Linear NF ectra of near-ir a-si OPA umed at wavelength of 1550 nm with a eak intenity of 500 MW/cm 2. The noie ource contribute to the total NF, i.e., hoton fluctuation and PTN are modeled earately. For the NF ectra calculation excluding the Raman effect (dahed line), Im{γ(Ω)} = 0. The linear lo of the waveguide i 2 db/cm Figure 3-3: Gain and total NF ectra of near-ir a-si OPA with linear roagation loe of 2 db/cm and 4 db/cm. Raman ucetibility i included Figure 3-4: Pum-to-ignal RIN tranfer ectra for mid-ir c-si OPA with linear roagation loe of 1, 3 and 5 db/cm. The OPA i umed at a wavelength of 3.4 µm with a eak intenity of 3 GW/cm Figure 3-5: Linear NF ectra of mid-ir c-si OPA umed at wavelength of 3.4 µm with a eak intenity of 3 GW/cm 2. The noie ource contribute to the total NF, i.e., hoton fluctuation and RIN tranfer are modeled earately: (a) α = 1 db/cm and (b) α = 3 db/cm Figure 3-6: (a) Gain and total NF ectra of mid-ir c-si OPA with linear roagation loe of 1 db/cm and 3 db/cm; and (b) NF evolution at the maximum gain Figure 4-1: Tyical range of effective area and minimum radii for negligible (< ~ 0.1 db) bending lo at 90 bend are hown for different waveguide technologie. n denote the rough refractive index contrat between core and cladding of the waveguide Figure 4-2: The roceing te of the rooed SORM waveguide fabrication technique Figure 4-3: The SEM cro-ection image of the fabricated device: (a) ridge and (b) channel waveguide Figure 4-4: (a) To-view high-magnification otical microcoe image of a fabricated ringreonator with inut and outut bent bu waveguide. (b) TE tranmiion ectrum of a xi

13 device with 300-µm diameter and for variou couling trength and the fitted ectrum around 1550 nm Figure 4-5: (a)-(d) Proce te for the fabrication of LiNbO 3-on-Si wafer; (e) Picture of ucceful bonding of a 3-inch Y-cut LiNbO 3 wafer bonded to a 4-inch ilicon wafer; (f)- (j)the rooed roce te of elective oxidation of tantalum to form ubmicron LiNbO 3 ridge waveguide on ilicon Figure 4-6: (a) Cro ection of the waveguide tructure at one arm of the modulator and imlitic RF electric field rofile in the LiNbO 3 active region. (b) SEM image of cro ection of a fabricated LiNbO 3-on-ilicon waveguide Figure 4-7: (a) Tranmiion ectrum of a microreonator with 300 µm diameter for the TE mode around 1550 nm wavelength. The reonance linewidth i 2.7 GHz; (b) Alied awtooth electrical ignal and the meaured modulation reone of a 6-mm-long Mach-Zehnder modulator Figure 4-8: (a) Dierion of Ta 2O 5 waveguide for THG; (b) The otical mode of fundamental TE 11 (um at 1550 nm) and higher-order TE 15 (ignal at 517 nm) of a deigned waveguide that atifie the hae-matching condition. The height of the channel waveguide i 1.2 µm Figure 4-9: (a) Dierion lot of LiNbO 3 waveguide for SHG; (b) The otical rofile of fundamental TM (um at 1550 nm) and TE (ignal at 775 nm) mode of a deigned waveguide that atifie the hae-matching condition correonding to the croover in (a): Ridge width: 2.31 µm, lab height 1560 nm, ridge height 600 nm Figure 5-1: (a) Two-hoton abortion (TPA) in GaA at wavelength of 976 and 1550 nm; (b) Waveguide lo with and without TPA. The carrier generated in GaA by TPA are in rincile available for hotovoltaic converion (free-carrier abortion ha been ignored in thi imlified diagram) Figure 5-2: An electronic-hotonic integrated circuit fully owered by an off-chi laer ource uing the TPPV effect Figure 5-3: Schematic of the deigned GaA/AlGaA waveguide with a -i-n junction diode Figure 5-4: Set u for characterization of the TPPV effect in the -i-n junction diode Figure 5-5: (a) I-V characteritic of the diode at wavelength of 976 nm for three different inut ower. (b) The correonding P-V characteritic of the diode from numerical imulation (olid line) and exeriment (circle, triangle and quare) Figure 5-6: (a) I-V characteritic of the hallow-etched device at wavelength of 976 nm for three different inut ower. (b) The electrical ower generated on a 1 kω load reitance for both etch deth xii

14 Figure 5-7: (a) I-V characteritic of the hallow-etched device at wavelength of 976 nm for three different inut ower. (b) The electrical ower generated on a 1 kω load reitance for both etch deth Figure 5-8: Theoretical tudy of the maximum oible electrical ower generation veru couled otical ower for three different device length of 1, 2, and 5 cm Figure 6-1: (a) Normalized field of urface lamonic reonance in three different nanoarticle hae with identical urface area and 20 nm thicknee on ilicon ubtrate; (b) Reonance wavelength and maximum field enhancement factor veru ide length in the triangular (rim-haed) nanoarticle with 20 nm thicknee Figure 6-2: Electric field enhancement rofile for 1 V/m incident field on a triangular nanoarticle. The incident E-field olarization i horizontal: (a) To-view at ilicon-metal interface; (b) Cro-ection view along the horizontal triangle ide in (a); (c) 1-D lot along the dahed line in (b) Figure 6-3: Schematic of rooed lamonic-enhanced olar cell with lateral -i-n junction and nanorim atterned nanoarticle Figure 6-4: (a) Geometry and dimenion of the C-haed aerture tudied; (b) ower throughut veru metal layer thickne for the five tranmiion mode conidered in thi tudy Figure 6-5: Prooed lamonic-enhanced TPPV ower converter uing an array of C-haed aerture Figure 7-1: Prooed coherent beam-combining technique uing a ilicon Raman laer umed by an array of QCL Figure 7-2: (a) To-view chematic. The MMI length i ~770 μm. Inut arm are 1 mm long to accommodate 950 μm heater (not hown); (b) and (c) Induced inut hae difference via aroriate biaing of hae hifter to achieve coherently-combined beam at the outut waveguide Figure 7-3: The rooed mid-ir imaging ytem uing VCSRA array a re-amlifier Figure 7-4: Electrode deign to achieve imedance match in RF tranmiion line. The electrode can be laced further away from each other without increaing the V π value of the EO modulator Figure 7-5: The exerimental et u for demontration of SHG in LiNbO 3-on-ilicon and THG in Ta 2O 5-on-ilicon xiii

15 LIST OF TABLES Table 2-1: DBR deign for the to and bottom mirror of a mid-ir VCSRA Table 3-1: Summary of otical roertie of three different tye of ilicon waveguide Table 6-1: Material roertie ued in thi tudy xiv

16 LIST OF ACRONYMS/ABBREVIATIONS 3PA CMOS CW DBR EO FCA FOM FP FWM GSG ICP IRCM LED LHS LIDAR LOCOS MMI MWIR MZ Three-hoton abortion Comlementary Metal-Oxide-Semiconductor Continuou wave Ditributed Bragg reflector Electro-otic Free-carrier abortion Figure of merit Fabry-Perot Four-wave mixing Ground-ignal-ground Inductively-couled-lama Infrared countermeaure Light-emitting diode Left-hand ide Light detection and ranging Local oxidation of ilicon Multimode interferometer Mid-wave infrared Mach-Zehnder xv

17 NF NIR OPA OPO OSA PECVD PPC QCL RF RHS RIE RIN SEM SHG SNR SOI SON SOS SPM SRL SRS TEC Noie figure Near-infrared Otical arametric amlifier Otical arametric ocillator Otical ectrum analyzer Plama-enhanced chemical vaor deoition Photovoltaic ower converter Quantum cacade laer Radio frequency Right-hand ide Reactive ion etching Relative intenity noie Scanning-electron microcoy Second-harmonic generation Signal-to-noie ratio Silicon-on-inulator Silicon-on-nitride Silicon-on-ahire Self-hae modulation Silicon Raman laer Stimulated Raman cattering Thermoelectric cooler xvi

18 THG TPA TPPV VCSOA VCSEL VCSRA Third-harmonic generation Two-hoton abortion Two-hoton hotovoltaic Vertical-cavity emiconductor otical amlifier Vertical-cavity urface-emitting laer Vertical cavity ilicon Raman amlifier xvii

19 CHAPTER 1: INTRODUCTION Silicon i an ideal candidate for building hotonic device due to it low linear lo in the 1.2 to 6.5 μm wavelength range. Silicon hotonic, alo known a grou IV hotonic, i the tudy and alication of hotonic ytem which ue ilicon a the main otical medium [1]. It ha attracted ignificant attention in recent year with the aim of realizing low-cot, high-eed otoelectronic comonent for data and telecommunication alication, uch a high-eed otical interconnect [ 2 ], otical router and ignal roceor [ 3 ], and long-range telecommunication [4]. It ha been hown that ilicon waveguide are caable of contructing mot of the comonent of a hotonic data tranmiion ytem on a ingle chi. Additionally, comlex electronic-hotonic integrated circuit can be created by integrating thee comonent together with comlementary metal-oxide-emiconductor (CMOS) electronic [5]. The field of ilicon hotonic ha been the toic of active reearch for everal year in the near-infrared (near-ir or NIR) wavelength range, i.e., from 1.1 to around 2 µm. The advantage of integrated ilicon hotonic device for near infrared data communication alication are well-known, and a large amount of otical comonent are commercially available at the imortant 1300 and 1550 nm range. A review can be found elewhere [1]. However, although thee wavelength are convenient for telecommunication, obviouly they are not uitable for all alication. Mid-wave infrared (MWIR, alo known a mid-ir), defined vaguely a the wavelength range anning 3 to 5 or ometime 2 to 6 µm, rereent another array of alication, where ilicon hotonic lay an imortant role. Hitorically, the need for ource oerating in thi range ha been rimarily driven by military alication uch a wind Light 1

20 Detection and Ranging (LIDAR), remote chemical and biological ening and infrared countermeaure (IRCM). Over the at decade, uch ource have alo found ue in thermal imaging [6], chemical bond ectrocoy which an from the viible to 20 µm [7], ga ening [8] including CO2 (4.6 µm), NOx (6.5 µm), CO (4.2 µm) and SOx (7.3 µm), environmental monitoring and atronomy. Silicon hotonic, however, ha an inherent roblem at near-infrared wavelength: ignificant otical lo under high-ower uming. Although ilicon i tranarent and ha low roagation loe, at high intenitie it begin to aborb light due to two-hoton abortion (TPA). TPA create free carrier that, in turn, can aborb more ignificantly through free-carrier abortion (FCA) [ 9]. A an indirect band-ga emiconductor, ilicon ha a low intrinic recombination rate of free carrier. Conequently, the free-carrier oulation quickly grow u, reulting in huge otical lo. However, thi roblem i no longer eriou when the wavelength of the incident light exceed ~2.2 µm (the threhold for TPA to occur). It ha been exerimentally hown that TPA and the abortion of free carrier can be decreaed to negligible level by going to longer hoton wavelength [10]. A a reult, ilicon i an excellent nonlinear otical crytal in the MWIR range. It i attracting great interet becaue it offer the oibility of integrating a variety of aive and active comonent on a ingle chi, a well a exloiting an inherent tranarency and trong nonlinear otical effect in the MWIR region. Silicon ha everal additional attractive roertie, uch a a large thermal conductivity and high-oticaldamage threhold. In the at, the mid-infrared (mid-ir) wavelength range wa a roblematic region for hotonic due to lack of coherent ource and integrated otical waveguide. Recently, although 2

21 there are till ome miing iece uch a high-bandwidth modulator, tunable filter and otical element of comlex fiber/waveguide-couled hotonic ytem, the landcae ha begun to change a lot. Inexenive ingle-mode quantum cacade laer (QCL), exloiting electronic wavefunction engineering at an unrecedented level of ohitication, are now available commercially all the way down to below 4 µm [11]. Single-mode fiber are now available at wavelength u to 6 µm [ 12 ], o are mid-ir hotodetector that oerate at near roomtemerature with a bandwidth of above 1 GHz (Boton Electronic Cororation). Thee comonent make it oible to build efficient mid-infrared device and give hoe to on-chi alication. A new kind of integrated hotonic i being born. Future reearch will focu on integrated room-temerature active and aive device uch a waveguide, amlifier, reonator, witche, modulator and otical arametric device. All of thee will hel to realize on-chi otoelectronic ytem. A major art of thi diertation i devoted to everal aect of mid-ir ilicon hotonic waveguide technology and nonlinear otical effect in them. The erformance of nonlinear device oerating baed on third-order nonlinearity (χ (3) ) cannot in rincile comete with device baed on econd-order nonlinearity (χ (2) ) for mot alication. Silicon i a centroymmetric crytal and hence χ (2) doe not exit in the material. A hybrid latform, which enjoy the advantage of ilicon hotonic (CMOS comatibility and low-lo and tightly confined waveguide), and ue a econd-order nonlinear material in the waveguide core region intead of ilicon i deired. Lithium niobate (LiNbO3) in one of the bet candidate due to it high χ (2) value. Indeed, tandard LiNbO3 waveguide are regarded a the bet choice for electro-otical modulator in the hotonic indutry with imreively high modulation bandwidth u to 100 GHz [ 13 ]. LiNbO3 modulator definitely offer higher 3

22 erformance in term of modulation bandwidth, modulation deth and inertion lo over ilicon otical modulator [1]. The challenge for thi hybrid aroach lie in the fabrication of reliable LiNbO3-on-ilicon wafer and low-lo ubmicron ridge or channel waveguide on the wafer. Thee roblem are addreed here and the demontrated latform can alo an ideal candidate for integrated χ (2) nonlinear otic, uch a econd-harmonic generation. Two-hoton hotovoltaic (TPPV) effect i an energy harveting technique baed on TPA. It i a nonlinear equivalent of the conventional ingle-hoton hotovoltaic effect in olar cell. It wa firt demontrated in ilicon a a carrier wee-out technique that not only eliminate the nonlinear loe without electrical ower diiation but alo generate electrical ower at the ame time [14]. The TPPV effect ha otential alication in hotovoltaic ower converter (PPC) and elf-owered remote enor in fiber-otic network [15]. The TPPV effect i not retricted to ilicon. It i alo alicable to III-V emiconductor. It i exected to be even tronger in gallium arenide (GaA), a tudied here for the firt time, and indium hohide (InP) [16]. The ower efficiency of the PPC baed on the TPPV effect can alo be enhanced by the lamonic effect of ubwavelength aerture, a tudied in thi work. 4

23 Figure 1-1: Organization of the diertation. The organization of thi diertation i deicted in Fig Theoretical model are develoed and exerimental work are conducted to tudy and tet the erformance of nonlinear integrated hotonic device on ilicon and GaA ubtrate. In Chater 2, mid-ir nonlinear ilicon hotonic device baed on Raman (ilicon Raman amlifier/laer) and Kerr effect (otical arametric amlifier (OPA) and continuum generation ource) are theoretically tudied. Chater 3 numerically invetigated the noie figure (NF) ectra of near-ir amorhou ilicon (a-si) and mid-ir crytalline ilicon (c-si) OPA. In Chater 4, two novel waveguide technologie, Ta2O5-on-Si and LiNbO3-on-Si, baed on newly demontrated fabrication technique, are introduced and their otential alication in nonlinear integrated hotonic uch a harmonic generation are rooed and theoretically invetigated. Chater 5 focue on the TPPV effect in GaA, which i exected to be more efficient than in ilicon and thu can be utilized in elf-owered otoelectronic chi and PPC. Chater 6 reent the theoretical tudy of lamonic-enhanced ilicon hotovoltaic device including olar cell with nanoarticle and 5

24 two-hoton PPC uing nanoaerture tructure. The final chater how the idea on future reearch direction for nonlinear integrated hotonic device on ilicon and III-V emiconductor ubtrate. 6

25 CHAPTER 2: MID-INFRARED NONLINEAR SILICON PHOTONICS 2.1 Overview The econd-order otical ucetibility i abent in ilicon becaue the material i in the form of a centroymmetric crytal. Alternatively, third-order nonlinearity in ilicon ha been exloited and aggreively tudied in the lat decade. More recently, ilicon hotonic ha been urued in the mid-ir regime with a hot of civilian and military alication. Otical Raman amlification at 3.4 µm [17,18], four-wave mixing (FWM) and arametric amlification at ~2.2 µm [ 19, 20 ], ilicon-on-ahire (SOS) waveguide at 4.5 µm [ 21 ], ilicon-on-inulator waveguide at 3.39 µm [22] and SOS grating couler at 2.75 µm [23] are ome of the recent develoment in the emerging field of mid-ir ilicon hotonic. The nonlinear abortion rocee in near-ir ilicon hotonic device include TPA (in which two hoton can imultaneouly get aborbed and excite an electron out of the valance band and into the conduction band), free-carrier abortion (FCA) induced by TPA, a well a higher order nonlinear roce uch a three-hoton abortion, which can occur at very high intenitie. Thee rocee have been found to create additional lo mechanim for otical wave interacting with each other in ilicon. Therefore, the efficiency of the nonlinear rocee i ignificantly reduced. TPA and the generation of free carrier in ilicon for near-ir um are hown in Fig The oulation of free carrier build u raidly becaue of their long lifetime in ilicon a an indirect band-ga material, cauing hoton to be lot through FCA. The rate of two-hoton 7

26 generation i much larger for higher energy um hoton due to the number of available electron tate in both the valence band and the conduction band. V. Raghunathan et al. tudied the tranmiion through a ilicon amle at two um wavelength, 2.09 µm and µm [10]. The maximum tranmiion wa around 53% becaue the ilicon amle i double-ided olihed and the reflection lo er facet i around 29%. The enhanced nonlinear loe at 2.09 µm due to TPA and FCA and the abence of thee loe at µm are clearly illutrated in Ref. [10]. Figure 2-1: TPA and the aociated FCA for near-ir um [24]. Abortion by TPA-induced free carrier i a broadband roce that comete with the Raman or FWM gain. TPA ha been hown to be negligible from the oint of view of um deletion. Thi i reaonable becaue the TPA coefficient in ilicon, β, i relatively mall (about 0.5 cm/gw) comared with the Raman gain coefficient at 1550-nm wavelength. The magnitude of the TPA-induced FCA deend on free carrier concentration and the effective recombination lifetime for free carrier. In order to make the nonlinear rocee more efficient, a lot of effort 8

27 ha been ut on minimizing the carrier concentration in the near-ir regime. Active carrier wee-out uing -i-n junction diode and hort ule uming have been rooed a mean to mitigate thi roblem [1]. Three-hoton abortion (3PA) might be more roblematic at the mid-ir than the near- IR becaue of the quare-wavelength (λ 2 ) deendence of the free-carrier cattering cro-ection. However, the three-hoton abortion coefficient, γ, i quite mall. Meaured in the range from 2300 nm to 3300 nm with a 200 f uled laer, γ ha a eak value of cm 3 /GW 2 [25]. If the um wavelength i above 3300 nm, or the um intenity i jut a few hundred MW/cm 2, which i enough for timulated Raman cattering and FWM to take lace, three-hoton abortion i virtually negligible. 2.2 Waveguide Technologie for Mid-IR Silicon Photonic A reliable low-lo otical waveguide technology i of great imortance for any integrated hotonic latform. The ilicon-on-inulator (SOI) latform i generally not uitable for the mid-ir becaue the bottom cladding material, ilicon dioxide (SiO2), i loy over the µm and above 3.6 µm wavelength. My colleague and I have been develoing novel waveguide latform and unique fabrication technique to exand the realm of ilicon hotonic into the Mid-IR wavelength. Figure 2-2 illutrate the three latform we have demontrated o far: ilicon-on-ahire (SOS), ilicon-on-nitride (SON) [26] and all-ilicon otical latform (ASOP) [27]. 9

28 Sahire ha high tranmittance over the broad 1 to 5 µm range [28]. Therefore, iliconon-ahire (SOS) wafer can be ued for both mid- and near-ir hotonic. SOS waveguide were firt rooed by Soref et al. [28] and then demontrated by Hochberg et al. [21]. However, fabricating ubmicron waveguide uing electron-beam (e-beam) lithograhy reult in oor idewall roughne and high roagation lo. We have been develoing a unique SOS waveguide fabrication technology-local oxidation of ilicon (LOCOS) of microelectronic fabrication [29]. Thi method not only moothen the idewall roughne, but alo hrink the lateral dimenion of the waveguide (ee the canning-electron microcoy image for SOS waveguide in Fig. 2-2(b)). Therefore, the technique can beat the reolution limit of conventional micron-ize mak aligner and achieve ubmicron waveguide. Figure 2-2: (a) Three waveguide technologie of ilicon hotonic at mid-ir baed on novel fabrication technique: SOS, SON, and all-ilicon waveguiding latform. (b) SEM image of the fabricated waveguide for the three latform [26,27]. 10

29 The linear roagation lo α of the SOS waveguide at wavelength of 1550 nm wa firt characterized uing the Fabry-Perot (FP) method (Fig. 2-3(a)). Interference fringe can be oberved in the tranmiion ectrum of the waveguide a FP cavity i formed by the two facet of the waveguide. α wa then extracted from the modulation deth of the FP fringe: 1 1+ P min / Pmax α = log R (2.1) L 1 Pmin / Pmax where Pmin and Pmax are the minimum and maximum ower in the FP fringe, L i the length of the waveguide, and R=(1-neff) 2 /(1+neff) 2 i the reflectivity of the waveguide facet, where neff i the effective index of the waveguide calculated in COMSOL TM. Another convenient and accurate way to meaure the linear roagation lo of the waveguide i the cut-back method. The ower tranmiion of L-hae waveguide with different length wa meaured with a hotodetector and α wa extracted from the leat-quare linear fit of the data obtained (Fig. 2-3(b)). The radiu of curvature of the L-haed waveguide i 1 mm, which i large enough to ignore any bending lo. The meaured lo in the SOS waveguide i 12.1 db/cm uing the FP method and 13.4 db/cm uing the cut-back method at wavelength of 1550 nm. The high roagation lo can be exlained by the aluminum generation from chemical interaction between ilicon and ahire at high temerature, a well a dilocation caued by the large difference in the thermal exanion coefficient and lattice contant of the two material. 11

30 Figure 2-3: Linear roagation lo characterization of the SOS waveguide uing (a) the FP method and (b) the cut-back method. One challenge in roceing SOS wafer i achieving high-quality waveguide facet becaue olihing ahire i extremely difficult. Although the roblem can be alleviated by artial dicing of ahire ubtrate at the very firt roceing te and ubequent cleaving along the dicing mark, the quality of the olihed facet of SOS waveguide i till wore than thoe of SOI waveguide. Moreover, the tranmiion window of SOS technology i limited by the tranmittance of ahire for wavelength above 5 µm. In order to make olihing eaier and obtain the larget oible tranmiion window, i.e., the low-lo tranmiion window of ilicon ( µm), two alternative to SOS technology, SON and ASOP have been develoed. The SON latform wa achieved by bonding a ilicon die to a SOI die coated with a ilicon nitride layer uing a in-on-gla layer and ubequent removal of the SOI ubtrate [26], becaue SON wafer are not commercially available in the market. The ASOP latform wa realized by direct bonding of an inverted SOI die to a bulk ilicon die with trenche on it [27]. 12

31 The detail of the fabrication rocee of thee two novel waveguide technologie are tated in Ref. [26] and [27], reectively. The meaurement et-u for charactering the SON and ASOP waveguide at mid-ir wavelength i hown in Fig The device were teted uing a Newort 3.39-µm HeNe laer with a continuou-wave (CW) outut ower of 2 mw. The laer wa couled through a ZnSe objective len (5 mm focal length) into a mid-ir ingle-mode ZBLAN (a family of glae with a chemical comoition of ZrF4-BaF2-LaF3-AlF3-NaF) otical fiber from IRPhotonic, and then into the waveguide. The outut of the chi wa couled into a lead elenide (PbSe) amlified detector (model# PDA20H from Thorlab) through a mid-ir multimode metal halide fiber. The FP fringe were obtained by weeing the temerature of the chi uing a thermoelectric cooler (TEC) controller, a mid-ir tunable laer are not yet available. The temerature wa canned at a eed of 0.1 C/ec. The ignal-to-noie ratio (SNR) wa further enhanced by mechanically choing the laer at 700 Hz and uing a lock-in amlifier to detect the modulated ignal. Figure 2-5 reent the FP interference fringe recorded from the fabricated waveguide. The calculated lo (uing Eq. (2.1)) of SON waveguide and ASOP (uended membrane) waveguide are 5.2 db/cm [26] and 2.8 db/cm [27], reectively. 13

32 HeNe laer Choer controller 700 Len Choer Ref Photo detector Mid-IR SM fiber Ocillocoe Lock-in TEC Mid-IR MM fiber Waveguide Figure 2-4: Schematic of the exerimental mid-ir etu ued to characterize the ilicon-on-nitride and ASOP (uended membrane) waveguide [26]. Figure 2-5: FP interference fringe at wavelength of 3.39 μm obtained by tuning the temerature of the chi for (a) SON waveguide [26] and (b) all-ilicon uended membrane waveguide [27]. 14

33 2.3 Mid-IR Silicon Raman Laer Background of Silicon Raman Laer/Amlifier Hitorically, achieving otical gain and/or laing in ilicon ha been one of the mot challenging target in ilicon hotonic becaue bulk ilicon ha an indirect electronic band tructure and therefore ha a very low light emiion efficiency, i.e., low band-to-band radiative electron-hole recombination rate. Alternatively, Raman cattering and timulated emiion ha been urued. The Raman effect i the inelatic cattering of a hoton. When light i cattered from an atom, molecule or crytal, a mall fraction of the cattered light i cattered by an excitation, with the cattered hoton having a frequency different from, and uually lower than, the frequency of the incident hoton. The timulated Raman cattering (SRS) roce actually i a combination of a Raman roce with timulated emiion. It can be decribed a the interaction of the incoming um with the vibration in the medium to efficiently timulate the creation of Stoke hoton. The Raman hift, i.e., the frequency difference between the um and Stoke wave of ingle-crytal ilicon i 15.6 THz. Obervation of Raman emiion in ilicon wa firt reorted in 2002 [30]. Both forward and backward ontaneou Raman cattering from SOI waveguide were meaured at 1.54 µm with a 1.43 µm um. In 2004, timulated Raman cattering wa ued to demontrate light amlification and laing in ilicon [ 31 ]. However, becaue of the nonlinear otical lo aociated with TPA-induced free-carrier abortion (FCA), laing wa limited to uled bia oeration. A continuou-wave ilicon Raman laer (SRL) baed on low-lo SOI rib waveguide, 15

34 umed at 1550 nm wavelength, wa demontrated in 2005 [32]. TPA-induced FCA in ilicon wa ignificantly reduced by introducing a revere-biaed -i-n diode traddling the SOI waveguide. The laer cavity wa formed by coating the facet of the ilicon waveguide with multilayer dielectric film, whoe reflectivitie were deigned uing the FP reonance. Other reearch on near-ir ilicon Raman laer/amlifier include uing ilicon ring reonator intead of conventional ingle-a-umed ilicon Raman amlifier to reonantly enhance the externally alied um ower [33], and injecting the um ower into a urrounding cladding intead of directly into the ilicon core, which ignificantly increaed the maximum achievable total gain of ilicon Raman amlifier [34]. Alo, fourth quadrant biaing of the traddling diode have been rooed and demontrated to achieve energy harveting in ilicon Raman amlifier [14]. Mid-infrared ilicon Raman amlifier wa firt demontrated in 2007 [17]. Becaue of the high lo of SiO2 at mid-infrared wavelength, a 2.5-cm-long bulk ilicon ingot wa ued a the active medium and umed with 5 n ule at 2.88 µm. The two facet of the ilicon amle were coated with broadband anti-reflection coating to revent incurring Frenel reflection loe. Two dichroic beam-litter and a ectrometer were ued a filter to earate the trong reidual um from the weak amlified Stoke ignal. The time-reolved Stoke ignal wa detected uing a cooled indium arenide (InA) detector. A gain of 12 db wa reorted for a ignal at 3.4 µm wavelength. The behavior of Raman amlified Stoke ignal and coherent anti-stoke Raman cattered ignal in reence of a noiy um wa tudied [18]. It wa exerimentally determined that the Raman amlification roce of the weak inut toke beam by a noiy um ource 16

35 follow L-haed ditribution. The ditribution of ule energy of 3000 um ule wa found to follow a mean centric ditribution, uch a a Gauian or a Rician ditribution. Simultaneouly, the Raman gain exerienced by the Stoke beam wa meaured. The oberved ditribution clearly follow an L-haed extreme value tatitical behavior, highlighted by the high robability of the large outlier in the extended tail of the ditribution. Thi i attributed to the inherently noiy um ource ued in the exeriment (Q-wtiched Nd-YAG laer umed Otical Parametric Ocillator). Under the aumtion of undeleted um, the evolution of the Raman Stoke intenity I along the roagation direction z i decribed a: di dz = g I I (2.2) R where I i the um intenity, and gr i the Raman gain coefficient, determined from the value of the third order Raman ucetibility χ (3) [17]: 6πµ g = 0 (3) R χ λnn (2.3) Equation (2.3) tell u that the Raman gain coefficient i roortion to 1/λ. The gain coefficient meaured in the near infrared (1550 nm) i in the range of 10~20 cm/gw [35]. So at the Stoke wavelength of 3.4 µm, the Raman gain coefficient i exected to be 4.5~9 cm/gw. It ha been found in Raman amlification exeriment in bulk crytal that the Raman gain cale down fater than the invere wavelength caling a redicted by theory [36]. 17

36 2.3.2 Analytical Modeling of Mid-IR Silicon Raman Laer SRL were firt demontrated in the near-ir regime [31,32]. The work were followed by everal imulation on Raman laer and amlifier [37,38,39,40,41]. The longet wavelength exerimentally reorted in the near-ir i a cacaded laer oerating at µm [42]. Cacaded Raman laer u to 3 µm and umed at 1.55 µm have been tudied baed on fully numerical method [39]. Here, an analytical model for mid-ir SRL i develoed for the firt time. The model can be ued to avoid time-conuming fully numerical imulation in the deign and analyi of the device. The model i validated by comaring it with numerical olution of couled-wave equation, and i ued to redict the erformance of the laer. With the abence of TPA and FCA at above 2.2 µm, the couled-wave equation for Raman laing lend themelve to analytical olution, a develoed here. Thi i in contrat to near-ir wavelength where achieving accurate analytical olution i difficult, if not imoible, and hence fully numerical imulation are uually emloyed [37,38,39,40,41]. The model i alicable to variou ilicon waveguide configuration a well a bulk ilicon, coated or uncoated with dielectric or integrated mirror, rovided that the redicted um intenitie are achievable in ractice. Figure 2-6(a) how the chematic of the SRL analyzed in thi work in which the inut um i injected from the left-hand ide (LHS) and the outut Stoke i from the right-hand ide (RHS). A dicued later, a device in which the outut i from the LHS wa alo tudied but exhibited very imilar erformance. In either cae, the device conit of a ilicon waveguide of length L, whoe facet are coated with multilayer dielectric film. A continuou wave (CW) um laer () at wavelength λ i couled into the LHS (l) of the cavity and the outut Stoke 18

37 () wavelength λ i exited from the RHS (r) via timulated Raman cattering. The reflectivitie of the left and right mirror at λ and λ are Rl, Rr, Rl and Rr, reectively. A tyical micron-ize ridge waveguide with the geometry decribed in the cation of Fig. 2-6 wa analyzed. Figure 2-6(b) how the TE otical mode roagating in the SOS waveguide at both the um and the Stoke wavelength. The effective core area of the waveguide i ~3 µm 2. The overla of the two mode, Γ, i calculated to be cloe to unity (99.75%). The overla integral, Γ, i included in the following model for comletene. However, it value i aumed to be 1 for the reent micron-ize ridge waveguide. It i noted that Γ could be coniderably maller than unity in ubmicron waveguide. Figure 2-6: (a) Schematic of the tudied mid-ir ilicon Raman laer; (b) Otical mode rofile (TE) at um (to) and the Stoke (bottom) wavelength in the SOS waveguide with air to-cladding having rib width of 2 µm, rib height of 2 µm and lab height of 1 µm. The calculation are obtained from a commercial numerical mode olver (BeamPROP by RSoft) [43]. A mentioned, TPA and FCA are negligible at mid-ir wavelength. By alo neglecting ontaneou Raman cattering at and above threhold, the evolution of the forward (+) and 19

38 backward ( ) roagating um and Stoke intenitie are governed by the following couledwave equation [37] ± di λ + = α Γ ( + ), ± gr I I (2.4a) I dz λ ± ± di + = α + Γ ( + ) ± gr I I (2.4b) I dz ± where gr i the Raman gain coefficient, α and α are the linear roagation loe at λ and λ, reectively. The correonding boundary condition are I I I + (0) = (1 R ( L) = R + I (0) = R I ( L) = R r I l I + + r l ) I ( L), (0), in ( L), + R l I (0), (2.5) where Iin i the inut um intenity. Equation (2.4) and (2.5) might be conidered to be imilar to the couled-wave equation and boundary condition of near-ir Raman fiber laer (RFL). Although everal analytical and numerical model for RFL have been ublihed [44-49], each ha it own hortcoming for the reent cae, a follow. F. Lelingard et al. imlified the numerical algorithm for olving the equation by tranforming the two-oint boundary value roblem into an initial value roblem, but the olution wa till fully numerical [44]; The analytical olution develoed by J. Zhou et al. aumed ingle a um, i.e., anti-reflection coated mirror [45]; Other analytical model develoed for RFL aume zero left-mirror reflectivity at the um wavelength (a imlifying valid aumtion becaue of the low index of ilica) [46,47,48,49]; Z. Qin et al. made the further imlifying aumtion of zero reidual um ower reflected back to 20

39 the inut end [46]; S. A. Babin et al. not only aumed zero left-mirror reflectivity but alo aumed that the outut ower increae linearly with the inut [47]. However, none of thee model are alicable to ilicon Raman laer becaue a coniderable amount of um ower reflect back and forth between the right- and left-hand ide mirror into the cavity. Indeed, a variety of dielectric coated mirror, with different reflectivitie at um and Stoke wavelength are commonly conidered in ilicon Raman laer. Therefore, in thi work, nonzero left- and right- mirror reflectivitie at both um and Stoke wavelength are included in the modeling of Raman laer, for the firt time, to account for ilicon and other high-index material cae (the imlet examle may be uncoated air-ilicon interface with reflectivity of ~30% at both um and Stoke). Thi will require develoing a more comlicated mathematical treatment of the roblem, a reented here. Comment hould be made regarding the other nonlinear rocee that may influence the erformance of SRL. Stimulated Brillouin Scattering (SBS) reent a eriou roblem in RFL. However, SBS can be ignored in SRL a the Brillouin cattering coefficient for ilicon i two order of magnitude maller than the Raman gain coefficient [50]. 3PA and aociated freecarrier effect are alo negligible becaue the correonding coefficient for ilicon i very mall [25]. Degenerate FWM between the um and the generated Stoke wave can be dicarded a the hae matching condition cannot be atified due to the large difference of the interacting wavelength. Therefore, only SRS i conidered in Eq. (2.4). Thi aumtion i conitent with reviou work on SRL [37,39,40]. The above differential equation with the boundary condition can be olved numerically by collocation. However, an initial gue i uually required for numerical method. In our cae, 21

40 thi gue i difficult to find becaue zero Stoke intenity i alway a oible olution even when the um intenity i above laing threhold. Therefore, an analytical olution to thi boundary-value roblem i develoed. The reented olution can be utilized not only a an initial gue for numerical olver but alo a a fully-analytical model. G 2 1/ 2 Firt, the geometric mean intenity 1/ + I ( I I and the gain factor, =,, ) + z) = 1/ 2ln I, ( z) / I ( ) are defined [44,45,46,47,48,49]. I and I are contant, i.e., they, (, z are indeendent of z. A a reult, Eq. (2.4) and (2.5) can then be rewritten in term of I, and G,(z). A linear deendence of G,(z) on z i alo aumed, i.e., G ( z) = G (0) + z[ G ( L) G (0)] / L. (2.6) Thi linear aumtion imlie that the um delete exonentially in both forward and backward direction. The validity of thi linear deendency aumtion wa confirmed by comarion with fully numerical olution (Fig. 2.5). Baed on the above, the threhold intenity of the ilicon Raman laer i obtained a I th 2δ αδ(1 Rle )( e Rle ) =, (2.7) αl αl g (1 R )(1 e )(1 + R e ) R l δ r δ where δ = αl + / 2ln(1/ R ), (2.8a) 1 r δ = αl + / 2ln(1/ R R ) (2.8b) 1 l r are lo factor of the um and Stoke wave due to linear roagation lo and mirror tranmiion loe. By defining 22

41 L, above threhold, I can be olved from inh[ G, ( z)] inh[ G, (0)] ( z) = L, (2.9) G ( L) G (0),, I 1/ 2 = δ /[2g L ( L)]. (2.10) 1 R obtained from Conequently, the geometric mean intenity and gain factor of the Stoke wave are I 1/ 2 = λ G (0) δ ] /[2g λ L ( L)], (2.11) [ 0 R 1/ 2 G ( z) = G (0) α z 2g I L ( z). (2.12) + G,(z) and G,(L) are eaily obtained from Eq. (2.5). Finally, the intenity ditribution for the um and Stoke wave are R I ± 1/ 2, ( z) = I, ex[ ± G, ( z )], (2.13) and the outut of the laer at the Stoke wavelength on the RHS of the waveguide in Fig. 2-4(a) i finally I out + = ( 1 R ) I ( L). (2.14) r An equation imilar to Eq. (2.14) can be eaily obtained if the laer outut beam i at the LHS, i.e., the cae where the laer outut and inut beam are counterroagating. The above general model wa alied to ecific examle. In all the following numerical and analytical olution, a um wavelength of 2.88 µm i ued [17,18]. The correonding Stoke wavelength i 3.39 µm according to ilicon otical honon energy. The exerimentally etimated Raman gain coefficient gr of 9 cm/gw at thee wavelength wa emloyed [17]. 23

42 A non-coated 2-cm long-cavity wa firt analytically modeled by auming that reflectivitie at both um and Stoke wavelength were 30%. Fully numerical imulation to couled-wave equation wa alo carried out for thi ecial cae by uing the reult from the analytical method a guee for the initial olution. Figure 2-7(a) reent the comarion between the analytical and numerical olution. The intenity ditribution of the um and Stoke wave in the laer cavity for an inut intenity of Iin = 200 MW/cm 2 are lotted uing both method. Such um intenitie can be attained in ractice by olid-tate mid-ir laer (e.g., otical arametric ocillator) [17,18]. Alo hown in the inet of Fig. 2-7(a) i the inut-outut (light-light) characteritic of the laer. It i clearly evident that the reult have excellent agreement. The validity of the model wa rigorouly teted under other boundary condition examle not reented here. Meanwhile, the analytical model i roved to be much fater than the traditional numerical way of olving thi et of equation. For examle, the time conumed for lotting the inet of Fig. 2-7(a) i 200 time fater than numerical imulation. Therefore, our analytical model can be confidently ued a a convenient and efficient tool in deign and otimization of mid-ir SRL. The reult of Fig. 2-7(a) alo ugget that at mid-ir wavelength, where TPA and FCA are negligible, it i oible to um a non-coated CW SRL above threhold with a reaonable um intenity of around 100 MW/cm 2. It i reminded that CW near- IR SRL are not achievable at any um intenity without uing aroriate mirror coating on to of emloying the carrier wee-out technique to reduce the carrier lifetime [32]. 24

43 (a) (b) Figure 2-7: (a) Intenity ditribution of um and Stoke wave with I in = 200 MW/cm 2. R l = R r = R l = R r = 30%, α = α = 0.5 db/cm and L = 2 cm were aumed. The inet how the inut-outut characteritic of the Raman laer; (b) Threhold intenity veru cavity length for variou outut facet reflectivitie and roagation loe and for R l = 10%, R r = R l = 90% [43]. Uing the decribed analytical model, it i eay to analyze mid-ir SRL and otimize their deign arameter. Indeed, achieving all the following reult would have been extremely challenging and time-conuming baed on fully numerical model. Figure 2.7(b) how the threhold intenity a a function of L for different right facet reflectivitie and two different linear roagation loe of 0.5 and 2.0 db/cm. Unlike near-ir SRL that have no laing threhold outide a limited range of length [40], mid-ir ilicon waveguide cavitie can lae for any given length if enough um ower i available. Alo, it i evident that for fixed reflectivitie, there i an otimum length, where the laing threhold reache a minimum. Thi i more remarkable at the higher tudied roagation lo (2.0 db/cm), a an otimum length of < ~ 1 cm can be recognized. 25

44 Figure 2.8 how the influence of the cavity arameter, length and facet reflectivitie, on the energy converion efficiency of the laer, defined a Iout/Iin. Generating each 3D lot in Fig. 2-8 wa achieved in about 10 minute with a tyical dekto PC (with a 3 GHz Intel(R) Core(TM)2 Duo CPU), while it can take day to make imilar lot baed on fully numerical method. However, our analytical model offer an efficient way to otimize the deign of mid-ir SRL. In thi cae, L and Rr could be otimized under certain um intenitie. For linear roagation lo of α = α = 0.5 db/cm, maximum converion efficiencie of 55.8% and 45.1% are obtained at inut intenitie of Iin = 200 and 100 MW/cm 2, reectively (Fig. 2-8(a) and (c)). Such high converion efficiency have been reviouly etimated baed on fully numerical imulation and indicate that ilicon Raman laer in the mid-ir can attain erformance comarable to near-ir fiber Raman laer [39]. The laer efficiency, however, dro quickly for device with the higher lo, i.e., α = α = 2.0 db/cm. The maximum converion efficiency obtained are 30.5% and 13.5% at inut intenitie of Iin = 200 and 100 MW/cm 2, reectively (Fig. 2-8(b) and (d)). The otimum length are below 0.4 cm in thee two cae. Further increaing the length will reult in higher laing threhold and lower loe efficiency at the ame time. Nonethele, thee rediction indicate a key advantage of mid-ir laer, a comact laer cavitie can be demontrated. In comarion, u to 5 cm length are required at near-ir wavelength [32]. It i noted that even more comact device can be enviioned uing ring reonator Raman laer, a reorted in the near-ir [50]. However, the tudy of uch laer i beyond the coe of thi work. The maximum converion efficiencie achievable for four roagation lo value are lotted veru um intenity in Fig For device with the lowet lo, i.e., α = α =

45 db/cm, the maximum oible converion efficiency i ~73%. Thi could be conidered a a ractical limit for the efficiency of a mid-ir SRL auming extremely low-lo ilicon waveguide. Puming the laer with intenitie above 200 MW/cm 2 i unneceary in thi cae a it could hardly imrove the converion efficiency. For device with higher lo, i.e., α = α = 1.0 or 2.0 db/cm, the converion efficiency ha not yet reached aturation at an intenity of 500 MW/cm 2. The minimum achievable laing threhold for the four roagation lo value are recognizable by the interection of the curve with the x-axi. Figure 2-8: Converion efficiency veru cavity length L and outut facet reflectivity R r for two roagation lo value and two um intenitie [43]. 27

46 Figure 2-9: Maximum converion efficiency veru um intenity for four different roagation lo value [43]. It i noted that unlike Raman amlifier whoe gain deend on whether a co- or counterroagating cheme i emloyed [40], our tudie on mid-ir SRL ugget that there i little deendency of the device converion efficiency on the roagation direction of the um and the outut Stoke wave. Thi difference between Raman amlifier and laer can be attributed to the fact that the aymmetric imact of the nonuniform um ditribution along the waveguide i more ronounced in amlifier whoe Stoke ignal i tyically aed a ingle time through the waveguide-a ooed to laer whoe Stoke outut wave exerience everal roundtri in the cavity Pum-to-Stoke RIN Tranfer of Mid-IR Silicon Raman Laer The Rician ditribution of um amlitude fluctuation ha been hown to have a ignificant imact on the ule-to-ule gain tatitic of mid-ir Raman amlifier [18]. Similarly, the relative intenity noie (RIN) tranferred from the intability of the um ource to the outut Stoke can have a ignificant imact on the erformance of mid-ir SRL. The RIN 28

47 tranfer ha been theoretically and exerimentally tudied in Raman fiber laer [51], and ha been numerically imulated in near-ir ilicon Raman amlifier and laer [52,53,54]. In thi aer, the imact of RIN tranfer on the erformance of mid-ir SRL i invetigated for the firt time. Unlike the above model for the light-light characteritic, the governing equation for RIN tranfer in SRL do not lend themelve to analytical olution. To etimate the effect of RIN tranfer from the um to the Stoke outut, the noie comonent at angular frequency Ω in the um noie ectrum i conidered. The intenity fluctuation of the um and the Stoke ± wave, normalized to the average intenitie, are rereented by m (z) and m ± (z), reectively: ± ± ± I ( z, t) = I ( z)[1 + m ( z)ex( iωt)], (2.15a) I ± ± ± ( z, t) = I ( z)[1 + m ( z)ex( iωt)], (2.15b) ± where I (z) and I ± (z) ± are time-indeendent average intenitie. m (z), m ± (z) are comlex ± ± value atifying m ( z), m ( z) << 1. The inut um i aumed to be modulated by a inuoidal function at angular frequency Ω, i.e., I = I [ 1+ m ex( iωt)], where min i a mall real number. The different value of um and Stoke grou velocitie, v and v, hould be accounted for imilar to Raman amlifier [52,53]. Thi lead to reduced RIN tranfer: I I ± 1 ± ± + ± z v t I I in in in ± λ + = α I gr ( I + I ) I, (2.16a) λ ± 1 ± ± + ± R z v t ± + = α I + g ( I + I ) I. (2.16b) 29

48 Subtituting Eq. (2.15) into Eq. (2.16) and (2.5) and neglecting higher order fluctuation term, a total of eight couled differential equation and eight boundary condition can be obtained. Thi i a omewhat more comlicated roblem comared to the only four [52] or ix (to account for carrier denity noie [53]) equation and boundary condition that ought to be olved for ilicon Raman amlifier. The equation for teady tate oeration and correonding boundary condition can be obtained by relacing I ±, in Eq. (2.4) and (2.5) with I ±, and olved uing the analytical model mentioned above. The other four couled equation and four boundary condition that decribe the mall fluctuation on the um and Stoke wave along tranmiion length z are derived a: dm dz ± iω ± λ + + m g R ( I m + I m ), (2.17a) v λ = dm dz ± iω ± + + m ± g R ( I m + I m ), (2.17b) v = I + (0) m m ( L) = m m ( L) = m (0) = (1 R ( L), + m (0) = m (0), ( L). l ) I in m in + R l I (0) m (0), (2.18) Equation (2.17) and (2.18), together with the teady-tate equation, can be numerically olved uing the collocation method, from which the RIN tranferred from the um to the Stoke i calculated a T RIN + m ( L, Ω) ( Ω) = 2 m in 2. (2.19) 30

49 The RIN tranfer in a SRL with a linear waveguide lo of 0.5 db/cm and for an otimized um intenity of 100 MW/cm 2, i.e., L = 1.20 cm, Rr = 38% (auming Rl = 10% and Rr = Rl = 90%), wa numerically evaluated. Noie frequencie ranging from zero to ten of gigahertz were included. The grou velocity at the um wavelength in Eq. (2.16(a)) and (2.17(a)) wa calculated a v = c/neff, where c i the eed of light in vacuum and neff i the effective index of the ilicon waveguide at um wavelength. The grou velocity at the Stoke wavelength wa obtained from v = 1/[(λ λ)d + 1/v], where D = 120 /(nm.km) i the local grou-velocity dierion in ilicon calculated by the Sellmeier equation. Thi material dierion dominate the waveguide dierion in the tudied large cro-ection waveguide. Thi wa validated by RSoft calculation and i conitent with reviou work [52,53,54]. Finally, min = 0.01 i aumed in our imulation but even higher value for thi quantity change the following calculation inignificantly. Figure 2-10(a) reent the um-to-stoke RIN tranfer ectrum for um intenitie of 50, 75, 100 and 200 MW/cm 2. It i evident that the RIN tranfer remain contant at low frequencie, then tart to ocillate at the free-ectral range (FSR) of the laer cavity, i.e., Δυ = c/(2neff L) = 3.6 GHz. The oberved trong ocillation at higher frequencie ugget that laer ource with RIN ectra no wider than a few GHz are required for uming mid-ir laer with cavity length of ~ 1 cm. The low-frequency tranferred RIN, a well a the magnitude of the high-frequency ocillation, dro a the um ower increae. Thi i conitent with theoretical and exerimental RIN tranfer ectrum of Raman fiber laer [51]. The low-frequency RIN tranfer for the SRL could be above 12 db when umed at 50 MW/cm 2, and dro to below 1 db at a um intenity of 200 MW/cm 2. 31

50 Reult very cloe to Fig. 2-10(a) were obtained for the cae in which the laer outut and the inut um are counterroagating. Thi differ from Raman amlifier that how a higher RIN bandwidth for the coroagation cheme a comared with the counterroagation cheme [52]. (a) (b) Figure 2-10: (a) RIN tranfer ectra for mid-ir SRL umed at 50, 75, 100 and 200 MW/cm 2 and (b) the device low frequency RIN tranfer veru um intenity for four roagation lo value. Modal arameter: L = 1.20 cm, R r = 38%, α = 0.5 db/cm (otimized deign for I in = 100 MW/cm 2 ), D = 120 /(nm km) [43]. Figure 2-10(b) ummarize the low-frequency RIN tranfer veru um intenity under different roagation lo value. The RIN tranfer oberved goe to infinity right below the laing threhold and decreae with increaing um intenity. Alo evident i the noticeable increae in the low-frequency RIN tranfer with increaing roagation lo. Unlike near-ir SRL, in which the RIN tranfer i trongly affected by FCA [53], the RIN tranfer in mid-ir laer i mainly determined by the linear roagation lo and the um intenity. Therefore, uming at well-above laing threhold and reducing the linear lo of ilicon waveguide are two crucial requirement for decreaing the RIN tranfer in mid-ir SRL. 32

51 2.3.4 Exerimental Reult on Mid-IR Silicon Raman Laer No exerimental work on mid-ir SRL ha yet been reorted to the bet of our knowledge. It i, nonethele, mentioned that demontration of 3.4 µm mid-ir SRL ha been attemted by u. We firt oberved ontaneou Raman emiion in an uncoated 1-inch thick bulk ilicon uing the laer ytem of CREOL Nonlinear Otic Grou. The et-u i hown in Fig The um laer (2.88 µm) wa an otical arametric ocillator (OPO) oerating under uled condition with a ule width of 11~14 and reetition rate of 10 Hz. The viible ource wa ued for otical alignment uroe only. The olarization of the beam from OPO wa et to the vertical direction uing the Babinet-Soleil comenator o that the tranmittance of the monochromator reached it maximum. A ingle CaF2 lano-convex len wa ued to focu the um into the ilicon amle. At the outut end another CaF2 lano-convex len wa ued a the imaging len. A monochromator wa ued to filter the reidual um, leaving only the Raman emiion at the Stoke wavelength. The Stoke wave wa detected uing a cooled gold doed germanium detector and oberved with an ocillocoe. 33

52 Figure 2-11: Set-u ued for mid-ir Raman laing in bulk ilicon. No Raman laing wa oberved becaue the amle wa not coated, and more imortantly, the cavity hoton lifetime of the FP cavity τ i around 70 (1/τ = - 1/2(vg/L)log(R1R2)) for lole cavity, where vg i the grou velocity, L i the length of the cavity, and R1, R2 are reflectivitie of the facet), much longer than the ule width of the OPO. However, an increae in the outut ower after the filter wa oberved when the ilicon amle i laced in the ath, which indicated that ontaneou Raman cattering wa taking lace inide ilicon. The increae in the outut ower i roughly etimated a the generated Stoke ignal. The reult i hown in Fig (only forward cattering). The loe efficiency of the ontaneou Raman emiion i etimated to be The fluctuation in the outut ower might be exlained by extreme value tatitic in ilicon. 34

53 Figure 2-12: Sontaneou Raman emiion a a function of um ower. Later we had the 1-inch thick bulk ilicon coated with aroriately deigned dielectric mirror and tried the ame exeriment at UCLA, uing VIBRANT IR Model 2731 otical arametric ocillator by OPOTEK, Inc. a the um ource, which ha a ule width of ~ 5 n, much longer than the cavity hoton lifetime a well a the Raman reone time of ilicon (~3 [55]). Although ontaneou Raman emiion wa certainly oberved and the bulk device wa erha at or lightly above threhold (Fig. 2-13), the low average ower and the oor beam quality of the emloyed um ource revented definite and undiutable confirmation of laing. It i our belief that otical waveguiding would alleviate ome of thee iue rovided that lowlo mid-ir ilicon waveguide and efficient couling cheme are imultaneouly emloyed. 35

54 Figure 2-13: Meaured ignal at 3.4 µm from a 1-inch-thick bulk ilicon amle coated with dielectric mirror deigned for Raman laing at thi wavelength and umed with a nanoecond OPO at a wavelength of 2.88 µm. 2.4 Mid-IR Nonlinear Silicon Photonic Uing the Kerr Effect Third-order nonlinear ucetibility (χ (3) ) baed on Kerr effect i eecially imortant in ilicon a it exhibit a wide variety of henomena uch a four-wave mixing (FWM) and elfhae modulation (SPM) [1, 56]. Among other, two of the ueful nonlinear functionalitie that have been urued in the near-ir in SOI waveguide are wavelength converion and arametric amlification (baed on FWM) and continuum generation (baed on SPM). Demontrating thee two functionalitie on SOS waveguide in the mid-ir range i rooed here. At near-ir, a figure of merit (FOM), defined a n2(λ)/βtpaλ (n2 i the nonlinear coefficient and βtpa i the TPA coefficient), i often ued to comare the trength of the Kerr effect and the nonlinear abortion. However, FOM may be irrelevant at > 2.2 μm, ince βtpa 0. Intead, the conventional nonlinear arameter, γ = 2πn2(λ)/Aeffλ [57] will lay a dominant role (Aeff i the effective waveguide area). Not only the Kerr effect i omewhat weaker in the mid-ir 36

55 [ 58,59], but alo the larger λ (comared to near-ir) reduce γ. Nonethele, due to lower nonlinear loe (TPA and FCA), FWM on SOI waveguide erform better at ~ 2.2 μm when comared to ~ 1.5 μm [19,20]. n2 at > 2.35 μm i not yet meaured to the bet of our knowledge. Theoretical calculation were ublihed that redict n2 value of 3.67 to cm 2 /GW for λ varying from 3.39 to 4.26 μm [60] Mid-IR Continuum Generation Source Continuum generation i formed when everal nonlinear rocee act together uon a um beam in order to caue ectral broadening of the original um beam, wherea the atial coherence uually remain high. The ectral broadening i uually accomlihed by roagating otical ule through a trongly nonlinear device. A lot of tudie on continuum generation in guided-wave tructure, uch a ingle-mode fiber [ 61] or hotonic-crytal fiber [ 62] have been reorted. Thee tudie ugget that continuum generation can be achieved at low otical ower and hort roagation ditance, if the guiding medium ha tunable dierion roertie and high nonlinear reone. Although efficient continuum generation i hown in reviou tudie on PCF, it ue in on-chi integration alication i limited by the large roagation length required for inducing large ectral broadening. An alternative mean to overcome thi limitation i ilicon waveguide, which have everal unique roertie that can be emloyed to achieve on-chi uercontinuum generation [63]. Becaue ilicon waveguide have mall tranvere dimenion, their dierion roertie are governed mainly by the waveguide dierion. A a reult, tunable dierion roertie can 37

56 be achieved by carefully deigning the tranvere waveguide dimenion. In addition, becaue of high otical confinement in ilicon waveguide due to the high index contrat between ilicon and the urrounding media (uch a SiO2), large otical intenitie are achieved inide the guiding layer. Furthermore, ilicon ha higher material nonlinearity. Thee advantage make the effective nonlinear coefficient in ilicon waveguide everal order higher than that in a lowconfinement otical fiber. The grou-velocity dierion (GVD) ha a great imact on nonlinear ule roagation. The efficiency of continuum generation i greatly enhanced if the inut ule i launched in the anomalou dierion regime, near the zero-grou velocity dierion (ZGVD) oint. Silicon ha ignificant normal dierion over it tranarent ectral region beyond 1.2 µm. However, the dierion introduced by mode confinement rovided by waveguide geometry can be ued to comenate for the material dierion. The wavelength deendence of β2 i illutrated clearly in Ref. [64]. By changing the ize and aect ratio of a rectangular SOI waveguide, the ZGVD oint can be deigned to lie anywhere from 1.2 µm to beyond 3 µm. It i alo hown that quai- TE mode are more enitive to the waveguide width, while quai-tm mode are more enitive to the waveguide height. A good exlanation to thi henomenon i the GVD for a mode i determined by the boundarie where the electric field i dicontinuou. There are everal tudie on continuum generation at near-ir wavelength in SOI waveguide [1,56]. It ha been hown that TPA i the main redicament for achieving high brocading factor [65]. It i hence exected that higher broadening can be mot likely oberved in the mid-ir. For λ0 = 3.85 μm, a channel SOS waveguide with a width of 0.9 μm and height a 0.5 μm wa deigned uing a commercial beam roagation method olver (BeamPROP). The 38

57 ectral broadening of a 80 f tranform-limited inut ule in thi SOS waveguide and with an otimized length of 0.5 cm wa calculated by numerically olving the nonlinear Schrödinger equation uing an in-houe Matlab code. A 3-dB broadening factor of u to 6 i redicted (Fig. 2-14) for a um intenity of 200 GW/cm 2, which i below the threhold damage of ilicon for ub-icoecond ule width [66]. The redicted broadening factor are indeed higher than thoe in SOI waveguide in the near-ir [65]. Fig. 2-14: Inut/outut ectra of continuum generation in an SOS waveguide at um intenity of 96 GW/cm 2. The inet lot the broadening factor veru um intenity Mid-IR Otical Parametric Amlifier FWM-baed arametric amlification ha a large gain bandwidth (uually ten of nanometer or even more), which i a ignificant advantage over timulated Raman amlification. However, unlike the Raman-baed device that are only enitive to the um intenity, arametric amlifier require hae matching to achieve wideband oeration, i.e., the 39

58 device mut oerate in the anomalou dierion regime that can be achieved by dierion engineering via roer waveguide deign. Succeful arametric gain and wavelength converion have been demontrated around the communication wavelength of 1.55 µm and in the µm range [19,20]. According to the dierion calculation baed on numerical imulation of waveguide effective indice uing BeamPROP by RSoft, broad band ( µm) anomalou dierion can be achieved in 1.5-µm-wide and 0.5-µm-high SOS waveguide. In Section 3.3, the gain and noie figure (NF) of a mid-ir ilicon OPA umed at 3.4 µm are imulated numerically. 2.5 Vertical-Cavity Silicon Raman Amlifier Background Our rooed idea of vertical-cavity ilicon Raman amlifier (VCSRA) arie from vertical cavity emiconductor otical amlifier (VCSOA), which are in rincile verticalcavity urface-emitting laer (VCSEL) oerated below laing threhold. A a background, it ha to be mentioned that VCSEL have been tudied extenively for ue in fiber-otic network and otical interconnect due to it comatibility with low-cot wafer cale fabrication and teting method [67]. A review of VCSEL i beyond the coe of thi work and can be found elewhere. VCSOA are FP amlifier that hare the ame fabrication advantage a VCSEL. A an alternative to fiber amlifier, VCSOA are intereting device for a wide range of alication in otical communication ytem [67]. VCSOA have been demontrated at all imortant 40

59 telecommunication wavelength including 980 nm, 1300 nm and 1550 nm [68]. The verticalcavity deign give VCSOA everal advantage over in-lane device uch a higher couling efficiency to otical fiber, olarization indeendent gain, mall form factor, and oibility of fabricating 2-D array on wafer. The rooed VCSRA i imilar in deign to a VCSOA. It i comoed of a gain region andwiched between two ditributed Bragg reflector (DBR) which allow the gain to build u, a hown in Fig Different from VCSOA, in VCSRA, Raman cattering i ued a the gain mechanim for ignal amlification intead of timulated emiion. Thi mean unlike VCSOA that are uually electrically umed, VCSRA are otically umed. The entire tructure i undoed, which imlifie roceing and minimize otical loe. VCSRA have two mode of oeration: co-directionally roagating (reflection mode) and counter-directionally roagating (tranmiion mode), a illutrated in Fig Figure 2-15: Schematic of VCSOA howing co-directionally roagating mode (left) and counter-directionally roagating mode oeration (right). 41

60 VCSRA can oerate at both near- and mid-infrared. Demontration of mid-ir Raman amlification in a iece of uncoated bulk ilicon wa mentioned in Section 2.1. Proer deign of the DBR will hel booting the total ignal gain Deign of Mirror Reflectivitie Deign of mirror reflectivitie i crucial in the deign of VCSRA. If the reflectivitie are too low, there will not be enough feedback to reach ufficient gain. However, if the mirror reflectivitie are too high, the device tart to lae. Therefore, the reflectivitie hould be jut low enough o that laing threhold i not reached when the amlifier i otically umed. Similar to mid-ir ilicon Raman laer, the couled-mode equation that govern the evolution of forward (+) and backward (-) roagating intenitie at um () and ignal () wavelength in the FP cavity of a VCSRA are a follow: di di ± S ± P / dz = ± g R R ( I S + P + I P / dz = g λ / λ ( I ) I + S ± αi + I S ) I ± ± P αi Given the to (T) and bottom (B) mirror reflectivitie, the boundary condition for Mode 1 are: ± P (4.1) I I I I P + P + S S ( L) = (1 R (0) = R (0) = R BS I BP P I S ( L) = (1 R TP ) I (0) (0) TS ) I Pin Sin + R + R while the boundary condition for Mode 2 are: I I I I + P P + S S (0) = (1 R ( L) = R (0) = R BS I I S ( L) = (1 R BP + TP P ) I ( L) (0) TS ) I Pin Sin + R TS + R I + TP P TS I I + S I BP P + S ( L) ( L) (0) ( L) 42 (4.2) (4.3)

61 L i the length of the cavity. In order to achieve tanding wave in the cavity at both um and ignal (Stoke) wavelength, L ha to be a multile of both λs (3.39 µm) and λp (2.88 µm). Here we aume L = 949 µm = 960λS = 1130λP. We identified CaF2 (refractive index n1 = 1.42) and ZnSe (refractive index n2 = 2.44) for to and bottom DBR. Due to the large index contrat between CaF2 and ZnSe, DBR deign for Mode 2 i more difficult. Thi i becaue the counterdirectionally roagating mode require high reflectivity (>0.9) at λs (or λp) and much lower reflectivity at λp (or λs) for the to (or bottom) mirror, which i imoible to achieve when the bandwidth of the DBR i too large, a the frequency hift between the two wave i only 15.6 THz. Uing material with lower index contrat for DBR deign i a oible olution. Here we circumvent the roblem by chooing the co-directionally roagating mode (Mode 1). We et RBS=0.9, RBP=0.9, RTP=0.2, and RTS a a variable. In Fig the ignal gain i lotted veru RTS at um intenity of 400 kw/cm 2. RTS hould be ket below 50% in order to avoid oerating too cloe to the laing threhold. Table 2-1 ummarie the DBR deign for the to and bottom mirror. The ignal gain obtained i 4.5 db. Figure 2-16: Signal gain veru RTS for um intenity of 400 kw/cm 2 and for R BS = 0.9, R BP = 0.9, R TP =

62 Table 2-1: DBR deign for the to and bottom mirror of a mid-ir VCSRA. Mirror To Bottom Material ZnSe/CaF2 CaF2/ZnSe Number of air Layer thickne dcaf2 = µm; dcaf2 = µm; dznse = µm dznse = µm Reflectivitie RTS = 0.454; RTP = RBP = 0.917; RBS =

63 CHAPTER 3: NOISE FIGURE IN SILICON OPTICAL PARAMETRIC AMPLIFIERS 3.1 Background There ha been ignificant rogre in the develoment of ilicon-hotonic-baed otical arametric amlifier and wavelength converter baed on the Kerr effect [69]. However, imilar to SRL dicued in reviou chater, ignificant nonlinear lo mechanim of TPA-induced FCA caued by the high otical intenitie required for nonlinear interaction, have limited the erformance and efficiency of thee nonlinear device [10]. Several method, imilar to thoe alied to SRL, have been rooed to mitigate thi drawback. Firt, active carrier wee-out uing -i-n junction diode and hort-ule uming can artially reduce FCA [21]; econd, ilicon hotonic ha been urued in the mid-ir regime uing otical um at wavelength above the TPA threhold wavelength of 2.2 µm [10] (Recent develoment in the emerging field of mid-ir ilicon hotonic were dicued in detail in Chater 2); Third, amorhou ilicon (a- Si) ha hown romie for large arametric amlification and efficient wavelength converion due to it large nonlinear figure of merit (FOM = n2/βtpaλ, where βtpa i the TPA coefficient and n2 i the nonlinear refractive index) at telecom wavelength [70]. Nonlinear coefficient a large a 2000 (W.m) -1 [71] and FOM of ~5, which i more than 7 time higher than that of the SOI waveguide [ 72 ] are reorted. Material degradation due to um exoure can limit the erformance, although it ha been claimed that otical tability ha been greatly imroved recently and no degradation of the nonlinear arameter ha been oberved at eak um 45

64 intenity a high a 2 GW/cm 2 [72]. FWM gain of 26.5 db [73] and converion efficiency of 12 db [74] have been demontrated exerimentally in hydrogenated a-si nanowire. One of the main concern in the deign of nonlinear hotonic device i the noie figure (NF), which imair the device erformance. Several tudie on the noie characteritic of ilicon Raman amlifier [75, 76], SRL [ 77, 78], and near-ir c-si OPA [ 79] have been reorted. The ignal-to-noie ratio (SNR) of mid-ir c-si arametric wavelength converter ha been tudied in Ref. [80]. However, the noie originating from the um laer wa excluded from the calculation and the waveguide wa aumed to be lole. Thi chater aim at full characterization of the ignal NF ectrum in both near-ir a-si and mid-ir c-si OPA. Main noie ource, i.e., hoton fluctuation due to gain and lo in the medium and um tranferred noie (PTN), are accounted for and numerically imulated. Secifically, the following aect of a-si and mid-ir c-si OPA are tudied here for the firt time. Firt, a-si ha a broad band Raman ectrum centered at 480 cm -1 (~ 14.4 THz) [81]. The effect of the comlex Raman nonlinearity on the roce of FWM cannot be ignored in the analyi of gain and NF of a-si OPA. Second, unlike near-ir c-si OPA, in which the um laer RIN i not a effective a the ASE of the EDFA, mid-ir c-si OPA are uually umed with otical arametric ocillator (OPO) or high ower uled laer (e.g., Er:YAG laer) intead of EDFA. Therefore, um ASE noie doe not exit but the RIN of the um laer will be tranferred to the ignal and the final NF of the amlifier will be increaed. Thu, the PTN mut be analyzed uing a different numerical model. 46

65 3.2 Noie Figure of Near-IR a-si OPA Unlike c-si whoe Raman ectrum eak at a frequency hift of 15.6 THz and ha a fullwidth at half-maximum (FWHM) of only 105 GHz [41], a-si i le orderly in it atomic arrangement and hence ha a broad Raman band centered at 14.4 THz [81]. When high um ower and large gain bandwidth are conidered, the effect of Raman nonlinearity on the arametric amlification roce become non-negligible. Both the gain and NF ectra will be modified due to the comlex Raman ucetibility. Raman-induced quantum-limited NF and aymmetric um noie tranfer in fiber OPA have been analytically tudied [82]. However, in a-si OPA, where nonlinear loe (TPA and FCA) are reent, achieving accurate analytical olution become difficult, if not imoible. In thi aer, the imact of Raman nonlinear ucetibility on the erformance of near-ir a-si OPA i invetigated for the firt time. In reviou tudie of c-si OPA, the conventional nonlinear arameter γ0 = 2πn2/Aeffλ i alway aumed to be contant over the telecommunication band (where λ i the um wavelength and Aeff i the effective waveguide area). Here, a frequency deendent nonlinear arameter i defined: ( ) = 2πn2 ( Ω) λaeff γ Ω / (3.1) (3) 2 where n ( Ω ) = 3χ ( Ω) /(4ε n ) i the frequency deendent nonlinear refractive index (ε0 i the 2 0 0c ermittivity of free ace and c i the eed of light). The third-order ucetibility χ (3) (Ω) i comoed of the nonreonant (or electronic) ucetibility χ (3) NR, which i a delta function in the time domain and a contant in the frequency domain, and the reonant (or Raman) ucetibility 47

66 (3) χ ( Ω), which i a time-delayed reone and varie over the bandwidth of interet [82]. R The real art of the Kerr nonlinearity in a-si:h waveguide can be found in ublihed meaurement [71]. It hould be noted that the γ reorted in thi reference i the um of the nonreonant nonlinearity and the reonant nonlinearity at zero frequency hift. The broad band Raman gain rofile gr(ω) of a-si i reviouly characterized too [81]. It maximum value i etimated to be ~4.735 cm/gw from Fig. 1 of Ref. [81], given the Raman gain coefficient of c-si at wavelength of 1550 nm (20 cm/gw). The imaginary art of γ(ω) equal to gr(ω)/2 if the um and the ignal wave are co-roagating and co-olarized [82]. The real art of γ(ω) i then calculated uing Kramer-Kronig tranformation for the arallel Raman ucetibility [83]: (3) ( 3) 1 Im[ χ R R ( Ω)] = P dω π Ω ( Ω )] Re[ χ (3.2) Ω where P denote the rincile art of the integral and i etimated to be in the cae of a- Si. Figure 3-1 how the real and imaginary art of γ(ω) of the waveguide tudied later, including the Raman contribution. Auming the um intenity i much higher than the ignal intenity, the couled-mode equation that decribe the evolution of the um, ignal and idler amlitude along the waveguide including the effect of the Raman ucetibility are a follow [84]: da / dz = 1/ da / dz = 1/ + i + i FCA 2( α + α ( z) ) A 2 ( γ 0 + iβtpa /(2Aeff )) A A FCA 2( α + α ( z) ) A ( γ + γ ( Ω) + iβ / A ) 0 + iγ ( Ω) A 2 A ex( i kz) * i TPA eff A 2 A (3.3a) (3.3b) 48

67 da / dz = 1/ i + i FCA 2( α + αi ( z) ) Ai ( γ + γ ( Ω) + iβ / A ) 0 + iγ ( Ω) A 2 A ex( i kz) * TPA eff A 2 A i (3.3c) Here, α i the linear roagation lo of the waveguide, βtpa i the TPA coefficient, Aj (j =,,i) i the electrical field amlitude of the three wave in unit of W 1/2, α FCA j ( z) = ( λ /1.55) τ β A /(2E A ), where τeff i the effective carrier lifetime, j eff TPA E i the hoton energy at um wavelength. Ω = ωi - ω = ω - ω i the frequency deviation from the um wavelength. Δk = k + ki - 2k = β2ω 2 i the hae mimatch between the three wave, where kj i the roagation contant at frequency ωj and β2 i the grou velocity dierion coefficient. eff Nonlinear coefficient γ (W -1 m -1 ) Real art Imaginary art Frequency hift (THz) Figure 3-1: Real and imaginary art of the nonlinear coefficient γ(ω) including the Raman contribution. The effective area of the waveguide i aumed to be 0.07 µm 2 [85]. 49

68 To etimate the total NF of ilicon OPA, the noie induced by hoton fluctuation in the material and the noie induced by the noie of the um ource are calculated earately. In the reence of nonlinear TPA and FCA loe, the above couled-mode equation do not have analytical olution a in otical fiber. Therefore, the model in Ref. [82] cannot be alied to a- Si OPA. Here, the noie model in [75] and [79] for linear otical amlifier i ued. Ideally, when lo or gain i reent in a waveguide, Langevin noie ource mut be added to the roagation equation (e.g., Eq. 3.3) in order to maintain the equilibrium value of the field amlitude along the waveguide length. Thi emi-claical aroach ha been urued in Raman fiber laer, where there exit no nonlinear lo and analytical olution are oible [86]. However, in the reent cae, the reulting equation do not lend themelve to analytical olution, ince nonlinear loe are reent and hence the noie term do not have exlicit z- deendent exreion. Intead, a fully quantum-mechanical noie model i ued here. In thi aroach Eq. 3.3 are olved under teady tate condition without including the noie term and then the aroach decribed in the following i ued to include the noie term in the roagation equation of the quantum-mechanic annihilation oerator [75,79]. In a ingle-mode ilicon OPA, the ignal wave roagating along the waveguide exerience both arametric gain g(z) and loe determined by γ'(z): daˆ dz g( z) γ ( z) = aˆ 2 2 (3.4) where â i the hoton annihilation oerator of the ignal field. The oerator i normalized + according to the commutation relation [ a ˆ, ˆ ] = 1 where a + â i the hoton creation oerator of the ignal field. The gain and lo arameter g(z) and γ'(z) can be numerically olved from the 50

69 couled mode equation (3.3a)-(3.3c). The Langevin noie ource for gain and lo are derived on the rincile of commutator + conervation, i.e., d[ aˆ, aˆ ]/ dz = 0, and are given by the oerator g ˆ γ ( z) N ˆ, + ( z) N g and l reectively [75]. The commutator of the noie ource oerator are delta function. Eq. (3.4) i now rewritten taking into account the noie ource: daˆ dz g( z) γ ( z) = aˆ g( z) Nˆ + g + γ ( z) Nˆ l (3.5) The analytical olution of Eq. (3.5) i given by: 1 aˆ ( z) = ex z 1 dz ex 2 0 z z z [ g( z) γ ( z)] dz aˆ (0) [ g( z ) γ ( z )] dz ( ˆ + g( z) N ( z) + γ ( z) Nˆ ( z) ) g l (3.6) The analyi of noie in a-si OPA i more comlicated than that of c-si OPA due to the frequency deendent nonlinear coefficient. Eq. (3.3a)-(3.3c) are firt olved numerically. The numerical olution, i.e., the ditribution of the three wave along the a-si waveguide (z direction) are then ued to calculate the gain and lo arameter g(z) and γ'(z). The mean outut hoton number No i evaluated from the firt term on the right ide of Eq. (3.6): N o 1 = ex z [ g( z) γ ( z)] dz (3.7) 0 2 and the hoton number fluctuation induced by gain and lo in the FWM roce are given by: N N L L = g( z)ex [ g( z' ) γ ( z )] dz dz (3.8a) 0 z g L L = γ ( z)ex [ g( z' ) γ ( z )] dz dz (3.8b) 0 z i 51

70 Auming the inut hoton number at the ignal wavelength i large enough, the NF induced by hoton fluctuation can be calculated a [75,79]: NF = ( N + N + N ) / N. (3.9) f o At near-ir, an EDFA i uually ued a the um ource. The ASE noie of the EDFA i tranferred to the ignal during the arametric amlification roce. The RIN of the um laer (before getting amlified by the EDFA) can alo imact the erformance of the a-si OPA. However, the availability of low noie laer at telecom wavelength with RIN below -160 db/hz make the contribution of um-to-ignal RIN tranfer negligible. The cae for mid-ir OPA i comletely different, a will be dicued in the Section 3.3. To calculate the ignal variation due to the ower variation of the inut um ΔPin, the outut ignal Pout = A (z=l) 2 i aumed to be linearly deendent on the mean inut um ower Pin = A(z=0) 2, if ΔPin i mall. Conequently, the quadratic fluctuation term can be neglected: P out in in g l o ( P ) = G( P ) P ( z = 0) + B P (3.10) where G(Pin) i the ignal gain a a function of inut um ower, and B i the loe of Pout at Pin. The analytical exreion of B can be found in Ref. [87] for lole waveguide. However, B mut be calculated numerically in a-si waveguide due to the reence of linear and nonlinear loe. If the quantum noie of the um ource a well a the ASE-ASE beating term are neglected and only the um-ase beating noie i conidered, the linear NF increae (after detection) contributed by the noiy um i given by [87]: 2 2B Pinn ( GA 1) NF = (3.11) um 2 G( P ) P ( z = 0) where n i the oulation inverion factor of the EDFA and GA i the gain of the EDFA. It i 52 in in

71 noticed that B i roortional to P (z = 0), therefore ΔNFum i linearly deendent on the inut ignal ower, while ΔNFf doe not have ignal deendence. The total NF of a-si OPA i finally obtained by NF = NF f + NF um (3.12) Table 3-1 ummarize the linear and nonlinear otical roertie of near-ir c-si, near-ir a-si and mid-ir c-si waveguide emloyed in thi work. It i noted that, unlike c-si, the nonlinear otical roertie of a-si:h uch a βtpa and γ(ω) trongly deend on the fabrication roce, i.e., it comoition (hydrogen content) or atomic arrangement. γ0 a high a 2000 W -1 m - 1 [72] and βtpa a low a 0.08 cm/gw [88] have been reorted for a-si waveguide. However, unfortunately they cannot be achieved imultaneouly. Nonlinear arameter γ0 = 1200 W -1 m -1 and βtpa = 0.25 cm/gw [71] are ued in the following imulation a they rovide the highet nonlinear FOM (~ 5) reorted to date. The tudied waveguide are 500 nm wide and 220 nm high and have an effective area Aeff = 0.07 µm 2. The length of the device i 2 cm. The grou velocity dierion (GVD) of the waveguide i et to be 200.km -1.nm -1, which lead to a large gain bandwidth of > 200 µm (Fig. 3) and thu more aarent Raman-induced noie. Although the linear lo of a-si waveguide are higher than c-si waveguide, the roagation loe a low a 3.2 ± 0.2 db/cm for the TE mode and 2.3 ± 0.1 db/cm for the TM mode have been reorted for ubmicron (200 nm 500 nm) a-si wire waveguide [ 89 ]. Free-carrier lifetime in the icoecond range have been meaured [90]. Here, the device are aumed to be umed with a eak intenity of 500 MW/cm 2 at wavelength of 1550 nm. In the imulation of PTN contribution to the NF, n = 1.5 and GA = 50 are ued a tyical near-ir laer have 1-10 mw of outut ower before amlification. The inut ignal ower i aumed to be 10 µw. 53

72 Table 3-1: Summary of otical roertie of three different tye of ilicon waveguide. c-si (near-ir) a-si (near-ir) c-si (mid-ir) n 2 (m 2 /W) α (db/cm) < 0.2 > 2 ~ 1 β TPA (cm/gw) τ eff ~ n ~ -- FOM ~ 5 -- Linear noie figure PF w/o Raman PTN w/o Raman PF with Raman PTN with Raman Wavelength ( µm) Figure 3-2: Linear NF ectra of near-ir a-si OPA umed at wavelength of 1550 nm with a eak intenity of 500 MW/cm 2. The noie ource contribute to the total NF, i.e., hoton fluctuation and PTN are modeled earately. For the NF ectra calculation excluding the Raman effect (dahed line), Im{γ(Ω)} = 0. The linear lo of the waveguide i 2 db/cm [85]. Figure 3-2 how the linear NF ectrum of a-si OPA umed at 1550 nm. The NF ectrum without Raman effect, i.e., γ(ω) = γ0 or Im{γ(Ω)} = 0, i alo lotted for comarion. A illutrated, the NF contribution from gain and lo fluctuation i greater than the PTN 54

73 contribution, o that it can be treated a the dominant noie ource in a-si OPA, when the inut ignal ower i mall. It i hown that when the Raman effect i taken into account, the NF ectra for both gain and lo fluctuation and PTN become aymmetric due to the real and imaginary art of the Raman ucetibility. For ignal wavelength that are longer than the um wavelength (Stoke ide or negative frequency hift), the NF ectrum are lightly modified when Raman-induced noie i conidered. For ignal wavelength horter than the um wavelength (anti-stoke ide or oitive frequency hift), the NF i evidently increaed comared to the NF without Raman, eecially at the gain edge (Fig. 3). Similar reult have been obtained in lole fiber OPA [82]. In thi aer, for the firt time, linear and nonlinear loe, a well a the comlex third order ucetibility are all conidered at the ame time Gain (db) Noie figure (db) Gain (α = 2 db/cm) Noie figure (α = 2 db/cm) Gain (α = 4 db/cm) Noie figure (α = 4 db/cm) Wavelength ( µm) Figure 3-3: Gain and total NF ectra of near-ir a-si OPA with linear roagation loe of 2 db/cm and 4 db/cm. Raman ucetibility i included [85]. In Fig. 3-3, the gain and total NF ectra are lotted in logarithmic cale. For linear lo a low a 2 db/cm, wideband otical gain (maximum 30 db) i obtained with a NF of ~ 5 db at 55

74 wavelength from 1.48 µm to 1.65 µm. The aymmetry of the gain ectrum i obviou due to the Raman gain on the Stoke ide and Raman lo on the anti-stoke ide. The NF increae harly to above 20 db at the gain edge on the anti-stoke ide. Although the gain at wavelength ~ 1.47 µm i till high (10 db or more), the overall erformance of the OPA i oor becaue of the high NF. Therefore, oeration of the a-si OPA i limited by the NF for ignal frequencie larger than the um frequency. Linear lo of 4 db/cm i alo conidered becaue low linear lo and high nonlinear FOM may not be achieved imultaneouly. It i clear that for OPA with higher roagation lo, the gain i lower and the NF i lightly higher over the gain bandwidth. 3.3 Noie Figure of Mid-IR c-si OPA TPA and FCA vanih in the mid-ir regime in c-si. Although 3PA and aociated freecarrier effect are coniderable for um intenitie of a few GW/cm 2 in the wavelength range of 2300 nm 3300 nm [25,91], in our cae, the um laer wavelength i aumed to be 3.4 µm. Since thi um hoton energy i below one third of ilicon indirect band-ga, 3PA-induced nonlinear loe are negligible for mall ignal intenitie. Alo, although the Kerr effect i weaker in the mid-ir, and the larger λ further reduce the conventional nonlinear arameter γ, FWM on SOI waveguide erform better at ~2.2 µm when comared to ~ 1.5 µm due to lower nonlinear loe [19]. n2 = cm 2 /GW wa meaured at 2.35 µm [55] and theoretical calculation were ublihed that redict different n2 value (3.67 to cm 2 /GW for λ varying from 3.39 to 4.26 µm [60]). The latter are the value ued in thi work. 56

75 Noie ource in mid-ir c-si OPA are imilar to thoe in a-si OPA. Modeling of hoton fluctuation in mid-ir c-si OPA i much eaier becaue βtpa, α FCA (z), and γ(±ω) in Eq. (3.3a)-(3.3c) can be imly et to be zero. The nonlinear coefficient γ i aumed to be real and contant over the frequency range of interet becaue the Raman gain ectrum of c-si ha a har eak at a frequency hift of 15.6 THz and the common bandwidth of c-si OPA i only a few THz. However, the PTN of mid-ir c-si OPA hould be modeled differently becaue mid- IR otical amlifier are not commercially available. Mid-IR high ower ource uch a uled laer and OPO have low beam quality and high intenity fluctuation. Therefore, the RIN tranferred from um to ignal hould be analyzed intead of the ASE noie of the um. The noie comonent at angular frequency ω in the um noie ectrum i conidered. A inuoidal noie term i introduced on the um, ignal and idler amlitude: A ( z, t) = A ( z) + A ( z, t) = A ( z)[1 + δ ( z)ex( iωt)] (3.13) j j j j where A j (z) (j =,,i) are time-indeendent average intenitie, δj(z) are time-indeendent comlex value that atify δj(z) << 1. The different value of um, ignal and idler grou velocitie, v, v and vi hould be accounted for, eecially for high modulation frequencie (> 1 GHz). The couled-mode equation including grou velocitie and neglecting nonlinear loe a well a Raman contribution are a follow: j j A / z + 1/ v A / t = (1/ 2) α A + iγ A A (3.14a) 2 A / z + 1/ v A / t = (1/ 2) αa * i 2 + 2iγ A + iγa A ex( i kz) 2 A (3.14b) 57

76 ) ex( 2 2) (1/ / 1/ / 2 * 2 kz i A A i A A i A t A v z A i i i i i + + = + γ γ α (3.14c) Subtituting Eq. (3.13) into Eq. (3.14) and neglecting higher order fluctuation term, the roagation equation for the um, ignal and idler amlitude modulation are obtained: ) (2 2) (1/ / / * 2 2 A A A A i A v A i z A + + = γ α ω (3.15a) ) )ex( 2 ( ) ( 2 2) (1/ / / * * 2 * * 2 kz i A A A A A i A A A A A A A A i A v A i z A i i = γ γ α ω (3.11b) ) )ex( 2 ( ) ( 2 2) (1/ / / * * 2 * * 2 kz i A A A A A i A A A A A A A A i A v A i z A i i i i i i i = γ γ α ω (3.11c) The RIN tranfer i then calculated a the ratio of the ignal RIN at the outut of the OPA and the um RIN at the inut of the OPA: ( ) ( ) 2 2 * * 2 2 * * 2 2 ) ( (0) (0) (0) (0) (0) ) ( ) ( ) ( ) ( (0) (0) / ) ( ) ( L A A A A A A L A L A L A L A P P L P L P T RIN + + = = (3.12) The linear NF increae due to um-to-ignal RIN tranfer i given by [70]: hc P T RIN NF RIN um um 2 / 0) ( λ = (3.13) where h i the Planck contant. Similar to near-ir a-si OPA, the PTN contribution to the total NF i alo linearly deendent on the inut ignal ower. In order to atify the hae matching condition required by OPA, an SOS waveguide i deigned by dierion engineering to achieve wideband anomalou dierion (D > 0). The SOS 58

77 waveguide i 1.5 µm wide and 0.5 µm high and exhibit D of km -1.nm -1 in the wavelength range of µm. The um wavelength i fixed at 3.4 µm. Due to the abence of nonlinear loe, increaing the um ower will alway increae the gain of the OPA. The limiting factor, therefore, become the damaging threhold of ilicon intead of the um deletion due to FCA. Otical gain of ~30 db i eaily obtained at a eak um intenity of 3 GW/cm 2 auming the waveguide linear lo i 1 db/cm and the length of the waveguide i 3 cm (Fig. 3-6(a)). RIN Tranfer (db) α = 1 db/cm α -60 = 3 db/cm α = 5 db/cm Frequency (Hz) Figure 3-4: Pum-to-ignal RIN tranfer ectra for mid-ir c-si OPA with linear roagation loe of 1, 3 and 5 db/cm. The OPA i umed at a wavelength of 3.4 µm with a eak intenity of 3 GW/cm 2 [85]. Figure 3-4 reent the modulation frequency deendent um-to-ignal RIN tranfer for waveguide loe of 1, 3 and 5 db/cm at the wavelength of µm, where the gain eak (Fig. 3-6(a)). RIN tranfer remain contant at low frequencie, and then tart to ocillate at > 10 GHz. The oberved trong ocillation at higher frequencie ugget that laer ource with RIN 59

78 ectra no wider than 10 GHz are required for uming mid-ir c-si OPA. The RIN value of the ignal at lower frequencie could be about 5 ~ 10 db higher than that of the um for waveguide with linear lo of 5 db/cm, and the ituation i even wore for waveguide with lower roagation loe (larger arametric gain). Figure 3-5(a) and (b) reent the linear NF ectrum of mid-ir c-si OPA for roagation loe of 1 db/cm and 3 db/cm, reectively. Noie ource including gain and lo fluctuation and low-frequency um-to-ignal RIN tranfer are both taken into account. No data on the RIN of mid-ir laer i currently available. The um RIN ued in the following imulation i -140 db/hz, auming mid-ir OPO or uled laer have imilar noie erformance a tyical near-ir um laer, whoe RIN i 20 db wore than near-ir laer ued in otical communication [76]. It i evident that for mid-ir c-si OPA with linear lo of 1 db/cm (Fig. 3-5(a)), the noie induced by hoton fluctuation i jut lightly above the wellknown 3 db NF limit for an ideal OPA, while the noie tranferred from the um ource i much higher, which lead to a total NF of well above 10 db at the gain edge (Fig. 3-6(a)). In OPA with linear lo of 3 db/cm (Fig. 3-5(b)), the um-to-ignal RIN tranfer dominate over the noie induced by gain and lo fluctuation. 60

79 10 8 Photon fluctuation RIN tranfer Total Linear noie figure Linear noie figure Wavelength ( µm) (a) Photon fluctuation RIN tranfer Total Wavelength ( µm) (b) Figure 3-5: Linear NF ectra of mid-ir c-si OPA umed at wavelength of 3.4 µm with a eak intenity of 3 GW/cm 2. The noie ource contribute to the total NF, i.e., hoton fluctuation and RIN tranfer are modeled earately: (a) α = 1 db/cm and (b) α = 3 db/cm [85]. In Fig. 3-6(a), the gain and NF ectra of the mid-ir c-si OPA are lotted in logarithmic cale. Unlike near-ir a-si OPA, in which higher amlification alway lead to lower NF, in mid-ir c-si OPA, the gain and NF are both higher for lower roagation lo at large frequency hift (around the maximum gain). Thi i becaue the RIN tranfer increae with increaing gain 61

80 a illutrated in Fig Thi limit the erformance of low-lo mid-ir c-si OPA for large bandwidth oeration. In Fig. 3.6(b), the maximum gain and NF of maximum gain are lotted veru eak um intenity. It i hown that there i no gain aturation a in near-ir c-si OPA [79] becaue of the abence of TPA and FCA. For linear noie of 1 db/cm, the NF of maximum gain kee increaing when the um intenity increae due to the high um-to-ignal RIN tranfer which i the dominant noie ource. For linear lo of 3 db/cm, the noie figure of maximum gain i almot contant (< 10 db), for um intenitie ranging from a few hundred MW/cm 2 to 5 GW/cm 2. Thi originate from the mutual influence of hoton fluctuation (which decreae with increaing um intenity) and um-to-ignal RIN tranfer (which increae with increaing um intenity). 62

81 Gain (db) Gain (α = 1 db/cm) Noie figure ( α = 1 db/cm) Gain (α = 3 db/cm) Noie figure ( α = 3 db/cm) Noie figure (db) Maximum gain (db) Wavelength ( µm) (a) Gain (α = 1 db/cm) Noie figure ( α = 1 db/cm) Gain (α = 3 db/cm) Noie figure ( α = 3 db/cm) Pum intenity (GW/cm ) (b) Figure 3-6: (a) Gain and total NF ectra of mid-ir c-si OPA with linear roagation loe of 1 db/cm and 3 db/cm; and (b) NF evolution at the maximum gain [85]. The gain and NF ectra of near-ir a-si OPA (Fig. 3-3) and mid-ir c-si OPA (Fig. 3-6(a)) are quite different from thoe of near-ir c-si OPA reviouly tudied in Ref. [79]. Near- IR c-si OPA umed with uled laer have a maximum gain of ~ 10 db, even when the carrier wee-out technique i alied. Further increaing the um ower will reult in lower gain and higher NF at the ame time due to the intenity-deendent nonlinear loe. In contrat, in near-ir a-si OPA and mid-ir c-si OPA, > 30 db gain can be eaily achieved and no Noie figure of maximum gain (db)

82 aturation of the gain i oberved with um intenity u to a few GW/cm 2. Slight aymmetry aear in the gain ectrum of a-si OPA due to the Raman-effect-induced gain and lo. The NF ectrum of near-ir c-si OPA (Fig. 3 in [79]) i more or le ymmetric with reect to the um wavelength (light aymmetry come from the wavelength deendence of FCA). The NF i around 10 db for mall frequency detuning and dro to below 6 db at the gain edge. However, in near-ir a-si OPA, the NF i only about 5 db on the Stoke ide due to the low nonlinear loe, but increae harly at the gain edge on the anti-stoke ide. The NF ectrum of mid-ir c-si OPA i trictly ymmetric with reect to the um wavelength. However, unlike near-ir c-si OPA in which the NF contribution from gain and lo fluctuation i the dominant noie ource, the NF of mid-ir c-si OPA might be dominated by the um-to-ignal RIN tranfer. Large gain and mall NF cannot be achieved at the ame time becaue the RIN tranfer increae with increaing gain. 64

83 CHAPTER 4: HYBRID WAVEGUIDE TECHNOLOGY ON SILICON 4.1 Background The rimary target for ilicon hotonic ha been low-cot otical telecommunication comonent and integrated circuit, e.g., otical tranceiver for Ethernet and data center alication. Meanwhile, ilicon hotonic ha been alo urued a a latform for integrated nonlinear otic. Silicon i a centroymmetric crytal and hence the econd-order otical ucetibility (χ (2) ) i virtually nonexitent in the material. Alternatively, the third-order nonlinearity (χ (3) baed effect) ha been exloited. However, the erformance of nonlinear device oerating baed on χ (3) effect cannot in rincile comete with device baed on χ (2) effect for mot alication. In thi chater, in collaboration with my colleague, a novel hybrid latform [92] i demontrated that not only enjoy the mentioned advantage of ilicon hotonic (comatible with CMOS roce of microelectronic, low-lo and tightly confined waveguide), but alo ue a econd-order nonlinear material in the waveguide core region intead of ilicon. The choice of the material i LiNbO3, which ha one of the highet χ (2) value among nonlinear otical material. The ingle-crytalline LiNbO3 alo ha large electrootic (EO) coefficient (r33 = 31 m/v and r13 = 8 m/v), wide tranarency wavelength window (0.4 to 5 µm), and large intrinic bandwidth [93,94]. Indeed, tandard LiNbO3 waveguide are widely regarded a the bet vehicle for electrootic modulation in the hotonic indutry with imreively high modulation bandwidth (u to 100 GHz [13]). LiNbO3 modulator definitely offer higher 65

84 erformance (in term of modulation bandwidth, modulation deth and inertion lo) comared to ilicon otical modulator [1]. The challenge for thi hybrid aroach i how to make reliable LiNbO3-on-Si wafer and low-lo ubmicron ridge/channel waveguide on them. LiNbO3 waveguide are traditionally formed by diffuion of titanium, the roce of annealed roton exchange or imlantation of doant (e.g., oxygen ion) in bulk wafer [95]. Any of thee rocee can only lightly alter the refractive index of the material, i.e., the index contrat of the obtained trie waveguide i rather mall (0.1 to 0.2) and hence the guided mode are weakly confined. In EO modulator, thi hortcoming lead to large device croection (width of everal micron) and hence large half-voltage length-roduct, Vπ.L, of 10 to 20 V.cm deending on modulation frequency and characteritic imedance [13,96]. Large croection waveguide alo imlie the need for high-ower ource to achieve high otical denity for the onet of otically-induced χ (2) nonlinearity. Furthermore, weakly-confined waveguide mean that their bending lo become ignificantly high for mall radii. Several year of effort in develoing dry or wet etching recie for LiNbO3 have not been ucceful in achieving ubmicron waveguide with mooth and vertical idewall. We enviion an alternative aroach that circumvent directly etching the hard dielectric material and intead form the ridge on another index-matched material. Oxide of refractory metal, uch a tantalum, niobium and titanium, have refractive indice cloe to that of LiNbO3 (2.1 to 2.2) and are tranarent over a very large range of otical wavelength. Figure 4-1 ummarize the minimum achievable bending radiu and waveguide core ize of different waveguide technologie including our novel LiNbO3-on-ilicon latform. It i obviou that uing thi 66

85 technology, the waveguide dimenion and bending radiu of LiNbO3 device can be reduced by one to two order of magnitude comared with traditional LiNbO3 waveguide technologie. Figure 4-1: Tyical range of effective area and minimum radii for negligible (< ~ 0.1 db) bending lo at 90 bend are hown for different waveguide technologie. n denote the rough refractive index contrat between core and cladding of the waveguide [92]. 4.2 Ta2O5-on-Si Integrated Photonic It ha been mentioned in Section 4.1 that our novel LiNbO3-on-ilicon latform i baed on etchle ridge formation technology uing index-matched material. In thi work, the emloyed refractory metal i tantalum (Ta), whoe oxide (Ta2O5) ha a refractive index very cloe to that of LiNbO3. Before demontration of LiNbO3 device and in collaboration with my colleague, Ta2O5-on-ilicon waveguide and microring reonator were demontrated firt [97]. Previouly, Ta2O5 waveguide have been demontrated uing tandard lithograhy and RIE [98,99]. However, the roagation lo of the fabricated waveguide i high. Here my 67

86 colleague and I develoed a novel method baed on elective oxidation of refractory metal (SORM) [97]. Intead of aying a lot of effort in develoing dry etching recie for Ta2O5 to achieve ubmicron waveguide with mooth idewall, in our aroach, the ridge waveguide i formed without the need of etching Ta2O5. Figure 4-2 how the fabrication roce of Ta2O5 waveguide. Firt, the refractory metal (Ta) i deoited uing a uttering tool on a ilicon ubtrate with a SiO2 buffer layer (grown by thermal oxidation) on to. Next, 400-nm-thick SiO2 i deoited on the tantalum urface by lama-enhanced chemical vaor deoition (PECVD) a a mak layer. The SiO2 layer i then atterned by electron-beam (e-beam) lithograhy to oen a narrow ubmicron lot in the mak. The amle i then laced in a furnace with oxygen flow at high temerature (520 C) to electively convert Ta into Ta2O5 in the exoed region of the SiO2 mak. A volume exanion of ~2 during oxidation mut be conidered during the mak deign. In the ubequent te, the SiO2 layer i removed and the remaining Ta layer i etched away and a channel waveguide i formed. It i noted that ince Ta can be etched highly electively comared to Ta2O5, the tantalum etching te doe not introduce any roughne in the waveguide layer. Finally, 1.5-µmthick SiO2 i deoited on to of the waveguide uing PECVD a a cladding layer. Ridge waveguide and ridge and channel ring reonator were alo fabricated. The ga with of the ring reonator i controlled by the oxidation time. The SEM image for the fabricated ridge and channel waveguide are hown in Fig. 4-3(a) and (b), reectively. 68

87 Figure 4-2: The roceing te of the rooed SORM waveguide fabrication technique [97]. Figure 4-3: The SEM cro-ection image of the fabricated device: (a) ridge and (b) channel waveguide [97]. Ta2O5 micro-ring reonator were fabricated uing the SORM technology in order to validate the new fabrication method. The microcoe image of a fabricated micro-ring reonator with inut and outut bent bu waveguide i hown in Fig. 4-4(a). The tranmiion ectrum of the TE mode of the Ta2O5 ring reonator for different ga width i hown in Fig. 4-4(b). The 69

88 roagation lo of the waveguide and the couling trength were extracted by curve fitting to tandard ring-reonator theorie. The roagation lo i 9.5 db/cm in a 300-µm diameter device. The lo i accetable a an initial reult conidering that comarable value (8.5 db/cm) are reorted in the literature for much wider waveguide (18-µm wide). The unloaded quality factor of the reonator, Q, i etimated to be ~ and the unloaded finee i 30. Figure 4-4: (a) To-view high-magnification otical microcoe image of a fabricated ring-reonator with inut and outut bent bu waveguide. (b) TE tranmiion ectrum of a device with 300-µm diameter and for variou couling trength and the fitted ectrum around 1550 nm [97]. 4.3 LiNbO3-on-Si Waveguide and Micro Reonator The fabrication method that allow achieving ubmicron LiNbO3 i waveguide on ilicon ubtrate comromie of two key rorietary technologie: (a) Thermal bonding of ubmicron thin film of LiNbO3 on ilicon; and (b) an etchle technique to achieve low-lo ridge waveguide, which ha been decribed in detail in Section

89 The demontrated fabrication te are reented in Fig. 4-5 [92]. The bonding roce tart with ion imlantation of a LiNbO3 wafer to high doe of He + ion. A ilicon wafer i coated by a ~2-µm-thick SiO2 buffer layer. The two wafer are then olihed and brought into contact at room temerature. After the room-temerature initial bonding, a heating roce at 200 C i emloyed to imrove the bonding. During the heating roce, the imlanted ion form a very high-reure He ga in the imlanted layer that force the crytal to be liced reciely at the eak oition of the imlanted ecie. Figure 3(e) how an image of a 3 thin film of bonded to a 4 ilicon wafer with no evidence of cracking or other bonding iue. After wafer boning, the ridge waveguide are fabricated uing the SORM method mentioned in Section 4.2. A 30-nm layer of SiO2 i firt deoited on LiNbO3-on-Si wafer a a diffuion barrier to revent out-diffuion of oxygen from LiNbO3 in the Ta oxidation te. Then, Ta i deoited on LiNbO3 thin film. A PECVD SiO2 mak i then atterned on Ta by e-beam lithograhy for elective oxidation of Ta at 520 C. After oxidation, a comoite rib-loaded waveguide i formed coniting of Ta2O5 ridge layer and LiNbO3 lab layer. The mak layer i ubequently removed, the remaining non-oxidized tantalum layer i dry-etched in RIE uing a chlorine-baed recie. The device i then covered with SiO2 for aivation. In the end, for fabrication of EO modulator (Mach-Zehnder (MZ) interferometer-baed or Ring-reonatorbaed), metal electrode are added to the device uing tandard fabrication technique. Figure 4-6(a) illutrate the cro ection of the waveguide tructure at one arm of the modulator with RF electric field in the LiNbO3 active region. The correonding SEM image of the fabricated waveguide i hown in Fig. 4-6(b). 71

90 (a) Ion imlantation LiNbO 3 (b) SiO 2 deoition on Si ubtrate SiO 2 Silicon (c) Wafer bonding LiNbO 3 SiO 2 Silicon (d) Heating LiNbO 3 SiO 2 Silicon ~400 nm ~2000 nm (e) Samle bonded wafer Y-cut LiNbO 3 Si (f) Tantalum deoition (g) SiO 2 mak with e-beam lithograhy (h) SiO 2 mak with e-beam lithograhy (i) Mak removal and Ta etching (j) SiO 2 aivation Tantalum LiNbO 3 SiO 2 Silicon SiO 2 SiO 2 Tantalum LiNbO 3 SiO 2 Silicon SiO 2 Ta SiO 2 Ta 2 O 5 Ta LiNbO 3 SiO 2 Silicon 900 nm SiO Ta 2 2 O 5 Ta 2 O 5 LiNbO 3 LiNbO 3 SiO 2 SiO 2 Silicon Silicon 400 nm 400 nm Figure 4-5: (a)-(d) Proce te for the fabrication of LiNbO 3-on-Si wafer; (e) Picture of ucceful bonding of a 3-inch Y-cut LiNbO 3 wafer bonded to a 4-inch ilicon wafer; (f)-(j)the rooed roce te of elective oxidation of tantalum to form ubmicron LiNbO 3 ridge waveguide on ilicon [92]. Figure 4-6: (a) Cro ection of the waveguide tructure at one arm of the modulator and imlitic RF electric field rofile in the LiNbO 3 active region. (b) SEM image of cro ection of a fabricated LiNbO 3-on-ilicon waveguide [92]. An imortant advantage of the ubmicron, tightly-confined waveguide i that the electrode can be laced much cloer to the waveguide without ignificant abortion of light by the metallic electrode. Thi reduce the voltage needed to obtain the ame electric field for EO modulation. According to imulation, the ga between the electrode can be a mall a 4 μm 72

91 without overla between the highly-confined otical mode and the electrode. Thi i maller by a factor of 5 comared to traditional LiNbO3 EO modulator [92]. The meaurement reult of the fabricated device are reented in Fig The loaded Q of the ring reonator i (Fig. 4-7(a)), which i over an order of magnitude higher than reviou reult [100]. The linear roagation lo i around 5 db/cm. The the MZ modulator were characterized by alying a awtooth modulation voltage at 1 khz on a device with 7 µm ga between the electrode. The meaured Vπ i 6.8 V, which correond to a (half-wave voltage-length) of 4 V cm for 6-mm-long electrode, much lower than Vπ L of diffuion-baed modulator [101]. The extinction ratio of the modulator i aroximately 20 db. Figure 4-7: (a) Tranmiion ectrum of a microreonator with 300 µm diameter for the TE mode around 1550 nm wavelength. The reonance linewidth i 2.7 GHz; (b) Alied awtooth electrical ignal and the meaured modulation reone of a 6-mmlong Mach-Zehnder modulator [92]. The exerimental reult we got o far confirm that the LiNbO3-on-Si latform i quite romiing for a hot of alication uch a otical communication, otical ening, nonlinear hotonic and quantum otic. 73

92 4.4 Nonlinear Integrated Photonic in LiNbO3 and Ta2O5-on-Si Waveguide A dicued before, ilicon hotonic ha been urued a a latform for integrated nonlinear otic. However, the econd-order ucetibility i nonexitent in ilicon. Although the third-order nonlinearity of ilicon ha been aggreively tudied in the lat decade [41], nonlinear loe due to TPA and FCA at high otical intenitie limit the erformance of the χ (3) device. The two latform decribed in Section 4.2 and 4.3 are ideal candidate for integrated χ (2) and χ (3) nonlinear otic, rovided that the roagation loe of the fabricated waveguide are reaonably low Third-Harmonic Generation in Ta2O5-on-Si For certain alication (e.g., green light generation from infrared ource via thirdharmonic generation (THG), which cannot be realized in ilicon waveguide becaue the generated viible light will be aborbed by ilicon), χ (3) material are ueful. Comared with other χ (3) material that have been tudied by reearcher, uch a chalcogenide glae and Hydex, Ta2O5 ha a comarable nonlinear refractive index (n2 = ), relatively higher refractive index (~2.2) and higher damage threhold. Therefore, the Ta2O5-on-Si waveguide technology i an attractive latform in thi regard and worth uruing. R. Y. Chen et al. have reorted THG in loy (8.5 db/cm) and wide Ta2O5 waveguide uing high-ower femtoecond laer [102]. The reduction of the waveguide dimenion in our ubmicron waveguide, a well a the low loe exected in the etchle fabrication technique, make it oible to demontrate THG in Ta2O5 waveguide uing CW ource like high-ower EDFA. 74

93 The hae-matching condition for THG i n3ω = nω, i.e., the effective refractive indice for the um and the third-harmonic ignal hould be identical. Thi can be achieved by dierion engineering of the waveguide. The calculation hown in Fig. 4-8 are baed on numerical imulation of waveguide effective indice uing a commercial beam roagation method olver (COMSOL). The refractive indice of bulk Ta2O5 at the um (1550 nm) and the third-harmonic ignal (517 nm) are meaured by an elliometer. The TE15 mode at 517 nm i ued along with the fundamental TE11 mode at 1550 nm to achieve hae matching. The lower order mode of the waveguide at 517 nm (e.g., TE13 mode), which have larger overla integral with TE11 mode at 1550 nm, are not feaible in thi cae becaue our Ta2O5 obtained by Ta oxidation i quite dierive. 75

94 Figure 4-8: (a) Dierion of Ta 2O 5 waveguide for THG; (b) The otical mode of fundamental TE 11 (um at 1550 nm) and higher-order TE 15 (ignal at 517 nm) of a deigned waveguide that atifie the hae-matching condition. The height of the channel waveguide i 1.2 µm Second-Harmonic Generation in LiNbO3-on-Si The erformance of nonlinear device oerating baed on χ (3) effect cannot in rincile comete with device baed on χ (2) effect for mot alication uch a quantum otic. With the ubmicron LiNbO3 waveguide technology reented in Section 4.3, dierion engineering become oible through the geometrical deign of the ridge waveguide. Thi i a big advantage comared with traditional LiNbO3 integrated otic technology. The key to high converion efficiency in econd-harmonic generation (SHG) i fulfilling the hae matching condition, i.e., n2ω = nω. The aniotroy of LiNbO3 can be exloited to atify thi condition. Two hoton olarized along the ordinary axi (TM11 mode) can be hae-matched to a econdharmonic hoton along extraordinary axi (TE11 mode). It i known a Tye I SHG. Similar to 76

95 the THG cae, a waveguide with lab (LiNbO3) height of 1560 nm, ridge (Ta2O5) width of 2.31 µm and ridge height of 600 nm i deigned to atify the hae-matching condition (Fig. 4-9). Figure 4-9: (a) Dierion lot of LiNbO 3 waveguide for SHG; (b) The otical rofile of fundamental TM (um at 1550 nm) and TE (ignal at 775 nm) mode of a deigned waveguide that atifie the hae-matching condition correonding to the croover in (a): Ridge width: 2.31 µm, lab height 1560 nm, ridge height 600 nm. 77

96 CHAPTER 5: TWO-PHOTON PHOTOVOLTAIC EFFECT IN GALLIUM ARSENIDE 5.1 Background Photovoltaic i the roce of converting light into electricity uing olar cell. Nowaday, it i a raidly growing and increaingly imortant technology develoed for reolving the global energy crii. Two-hoton hotovoltaic (TPPV) effect i harveting the energy of the hoton lot to TPA. The effect i a nonlinear equivalent of the conventional (ingle-hoton) hotovoltaic effect widely ued in olar cell. The TPPV effect wa firt demontrated in ilicon [14]. Although the main uroe wa to eliminate the nonlinear lo in ilicon waveguide by decreaing the carrier lifetime, at the ame time, electrical energy wa harveted from the ilicon hotonic device. In Ref. [14], the electron-hole collection efficiency of the roce reached ~40% and i nearly indeendent of the couled otical intenity from 5 to 150 MW/cm 2. It i alo roved by imulation the maximum generated electrical ower can go above 40 mw in a 1-cm-long device umed with an otical intenity of 150 MW/cm 2. Thi reaonable ower efficiency make it oible to utilize the energy harveted through the TPPV effect to uly the electrical ower on-chi. Energy harveting (or negative electrical ower diiation) baed on TPPV effect in ilicon ha been demontrated in Raman amlifier [103], arametric wavelength converter [69], and electrootical modulator [104]. 78

97 In rincile, every two hoton lot only to TPA generate one electron-hole air in the emiconductor material and thee hotogenerated carrier are available for hotovoltaic converion into electrical ower. Figure 6-1(a) how the TPA roce at the two articular wavelength tudied here, 976 nm and 1550 nm. Figure 6-1(b) how a imlified chematic on how nonlinear abortion along the waveguide (due to TPA at high otical intenitie) i different than linear abortion at low intenitie. FCA i ignored in thi imlified diagram. Figure 5-1: (a) Two-hoton abortion (TPA) in GaA at wavelength of 976 and 1550 nm; (b) Waveguide lo with and without TPA. The carrier generated in GaA by TPA are in rincile available for hotovoltaic converion (free-carrier abortion ha been ignored in thi imlified diagram) [105]. One oible alication of the TPPV i elf-owered otoelectronic chi. Figure 6-1 how the chematic of an electronic-hotonic integrated circuit that i fully owered by an offchi laer ource [16]. It hould be mentioned that only a mall fraction of the ignal i aborbed by TPA while mot of the light i aed through the waveguide. Thi mean the otical tranmiion of the hotonic device can till be meaured and characterized while at the ame 79

98 time the hotodetector or the ening circuitry can be driven by the electrical ower harveted through the TPPV effect. Another oible alication of the TPPV effect i remote ower delivery. Sometime enor ued for temerature or reure meaurement are intalled in critical environment (e.g., in coal mine) where otential danger or hazard exit if the enor are owered electrically (e.g., uing coer cable). Photovoltaic ower converter (PPC) baed on the TPPV effect could be oibly alied in uch cae. Figure 5-2: An electronic-hotonic integrated circuit fully owered by an off-chi laer ource uing the TPPV effect. The TPPV effect i not retricted to Si. It i alo alicable to III-V emiconductor. TPA wa oberved exerimentally in GaA and the TPA coefficient β reorted at 1.3 µm in GaA i 70 cm/gw, much higher than in Si (3.3 cm/gw) [106]. Thu, the TPPV effect i exected to be 80

99 tronger in GaA. It ha been reorted that at wavelength of 1.3 µm, the maximum ower efficiency for GaA i a high a 9%, achieved at otical intenitie of below 5 MW/cm 2 [16]. 5.2 Model Figure 5-3 illutrate how TPPV can be realized in a ingle-mode GaA/AlGaA waveguide uing a -i-n junction diode. The emloyed device reemble a tandard edgeemitting laer but without any active (quantum well) region. A theoretical model i develoed to decribe the TPPV effect in the GaA/AlGaA waveguide with vertical -i-n heterojunction diode hown in Fig Although a one-dimenional (1D) model i enough for imulation of the conventional olar cell, a 2D aroach i alied here conidering the otical intenity ditribution of the guided mode. The junction cro ection i in the x-y lane and light i roagating along the z-direction. Taking into account the lo due to nonlinear abortion (TPA and FCA), the otical intenity I(z) roagating along the waveguide i governed by: 2 di( z) / dz = αi ( z) βi ( z) α I( z) (5.1) where α i the linear roagation lo and β i the TPA coefficient. αfca i the FCA coefficient calculated by αfca = ΔN (λ/2) 2 (cm -1 ), where ΔN i the free carrier concentration in cm -3 and λ i the wavelength in µm [107]. ΔN deend on otical intenity I(z) and bia voltage V and i calculated numerically. FCA 81

100 Figure 5-3: Schematic of the deigned GaA/AlGaA waveguide with a -i-n junction diode. The 2D numerical model i develoed in COMSOL TM Multihyic module. Different from imulation of homojunction diode, the model ue the drift-diffuion aroach in combination with Poion equation [108]. The teady tate current continuity equation for electron (Jn) and hole (J) are [109]: J = qr qg (5.2) n SRH n J = qr + qg (5.3) n SRH ε ψ ) = q( n + N D N ) (5.4) ( A where q i the electron charge, ε i the dielectric ermittivity, and n are the hole and electron denitie, ND and NA are the ionized donor and accetor concentration. ψ i the electrotatic otential. RSRH rereent the Shockley-Read-Hall recombination. Auming the tra energy level i located at the middle of the band ga, the rate i given by [109]: 82

101 R SRH 2 n ni = τ ( + n ) + τ ( n + n ) n i i (5.5) where ni i the intrinic carrier denity. τn and τ are electron and hole bulk recombination lifetime, reectively. The carrier hotogeneration rate from TPA i [14]: G = G = βλi 2 ( z) / hc (5.6) n 2 where h i the Planck contant and c i the eed of light in vacuum. The large dynamic range of the carrier concentration, eecially in the vicinity of the heterojunction interface, make the numerical olver difficult to converge. Therefore, the current denity function are exreed in term of the Fermi level for electron (ϕn) and hole (ϕ) [109]: J J n = µ n( dφ / dz) (5.7) n n = µ ( dφ / dz) (5.8) where µn and µ are the electron and hole mobilitie, reectively. τn and τ in bulk GaA are on the order of 10-8, about two order of magnitude maller than thoe in bulk ilicon. In GaA/AlGaA waveguide, the effective free carrier lifetime τeff can be even maller when the urface recombination at the idewall dominate over the bulk recombination. τeff of 250 i reorted for a 2.4 µm 0.8 µm GaA/Al0.8Ga0.2A ridge waveguide [110]. In thi work, τeff i aumed to be 100 a good agreement between numerical imulation and exerimental data i achieved under thi aumtion (Fig. 5-5(b) and Fig. 5-7(b) in Section 5.3). Thi value i reaonable conidering the idewall roughne induced by the dry 83

102 etching roce, which might accelerate the urface recombination. Table 6.1 ummarie the other arameter and material roertie ued in the imulation. Table 6-1: Material roertie ued in thi tudy. Parameter Unit GaA Al0.15Ga0.85A εr (976 nm) εr (1550 nm) ni cm µn cm 2 /(V) µ cm 2 /(V) me m mh m Eg ev Χ ev In Table 6-1, εr i the relative ermittivity, me and mh are the effective ma of electron and hole, reectively. m0 = kg i the electron ma. Eg i the energy bandga, and Χ i the electron affinity. Equation (5.2)-(5.4), (5.7) and (5.8) are firt olved auming no otical inut and zero bia voltage. Then the inut ower i increaed from zero in mall te (1 mw) and the olution from a reviou te i ued a the initial condition for the next one. After olving the Fermi level at a certain otical intenity, imilar method for arameter wee i alied to can the bia voltage V from 0 V to 1.2 V in te of V. The revere-bia cae can be calculated in the ame way but i not conidered in thi tudy a the junction diode mut be biaed in the fourth quadrant (current Ic < 0 and V > 0) in order to achieve energy harveting. From the current denity J = Jn + J rovided by COMSOL, the total current Ic i then calculated by integrating J over the waveguide length L. 84

103 At lat, the ohmic lo of the electrode and the contact mut be included. A erie reitance R in the circuit will reduce the harveted electrical ower and might oibly lower the hort-circuit current if R i exceively high. In order to model thi effect, the Ic deendence on the bia voltage V i firt nonlinearly fitted to an exonential function: I c ( V ) = A + Bex[ qv /( nkt)] (5.9) where k i the Boltzmann contant and T i the room temerature (300 K). A and B are fitting arameter. Then, the final current collected, taking into account the erie reitance R in the circuit, i numerically olved from the following equation: q( V + IcR ) Ic ( V ) = A + B ex[ ] (5.10) nkt 5.3 Exerimental Reult on TPPV Effect in GaA The junction diode in Fig. 5-3 wa fabricated uing CREOL cleanroom facility. The heterotructure in Fig. 5-3 were grown by molecular beam eitaxy. The negative electrode (a 15-nm-thick chromium layer lu a 200-nm-thick gold layer) wa firt deoited on the bottom of the wafer uing a thermal evaorator. The uroe of the chromium layer i to make better adheion between the gold layer and the bottom of the ubtrate. Then the waveguide were atterned by ultraviolet hotolithograhy uing negative hotoreit NR PY. A 17-µmwide taer wa added at the outut end of the waveguide. Thi make it eaier to add robe from to and ha little influence on the TPPV effect a the otical intenity in the taer i low. After hotolithograhy, another 300-nm-thick gold layer wa deoited on to of the amle and then the hotoreit wa removed by acetone. The to gold layer after lift-off erved a both the 85

104 oitive electrode and the mak for GaA etching. In the end, the GaA/AlGaA multilayer tructure wa etched uing an inductively-couled-lama (ICP) reactive ion etcher (RIE) from Plama-Therm. The 4.2-µm-dee dry etching wa divided into three te and a few econd of wet etching wa erformed in the middle in order to remove the reidue. The length of the waveguide i 4.5 mm after cleaving. Figure 5-4 how the et u for characterization of the TPPV effect in the fabricated junction diode. Otical ower (from a high-ower diode laer at 976 nm or from an erbiumdoed fiber amlifier (EDFA) at 1550 nm) i couled into the intrinic GaA layer through a lened-fiber. The linear roagation lo α of the waveguide i meaured by cut-back method and i etimated to be 7 db/cm at 976 nm and around 18 db/cm at 1550 nm. The high linear lo at 1550 nm can be exlained by the mode leakage into the n + -GaA ubtrate a the AlGaA bottom cladding layer i only 1 µm thick. In order to reduce the mode leakage and increae the ower efficiency of the device at thi longer wavelength (1550 nm), the bottom cladding layer ha to be thicker than 2 µm, according to the mode rofile and comlex refractive index calculated by COMSOL. The current-voltage (I-V) characteritic of the fabricated waveguide diode were meaured with a curve-tracer at variou couled um ower and wavelength. 86

105 Figure 5-4: Set u for characterization of the TPPV effect in the -i-n junction diode. TPPV in GaA wa firt invetigated at 976 nm wavelength. In thi cae, (down to the center of the intrinic AlGaA to cladding). Figure 5-5(a) how the meaured I-V characteritic at three different laer diode ower. The TPPV effect i oberved when the device i biaed in the fourth quadrant of it I-V characteritic, i.e., the carrier generated by TPA are wet out by the built-in field of the -i-n junction. The current meaured i a combination of the hotocurrent (from TPA), the minority carrier diffuion current and the recombination current including both bulk and urface recombination. The ower-voltage (P-V) characteritic of the diode at three different um ower are hown in Fig. 5-5(b). Evidently, over 200 µw of electrical ower can be cavenged from thi device. The olid line how the numerical imulation reult baed on the theoretical model in Section 5.2 for comarion. It i clear that the imulation reult how excellent agreement with exerimental reult when the diode i biaed in the fourth quadrant of it P-V characteritic. R and β are treated a fitting arameter in the imulation and are etimated to be around 700 Ω and 40 cm/gw, reectively. 87

106 The β obtained here i comarable to the value reorted in reference [106,107]. It hould be mentioned that the device ha alo been teted before annealing. At um ower of 55 mw, the generated electrical ower i only half of that harveted from an annealed device. Thi indicate that annealing alleviate the ohmic lo remarkably and i crucial in fabrication of hotovoltaic device. U to 9% ower efficiency, excluding the couling lo, i theoretically redicted in long (everal centimeter), low-lo GaA waveguide [16]. The rather low wall-lug efficiency oberved here i attributed to high linear roagation lo due to fabrication imerfection, a well a the high erie reitance at the contact. Figure 5-5: (a) I-V characteritic of the diode at wavelength of 976 nm for three different inut ower. (b) The correonding P-V characteritic of the diode from numerical imulation (olid line) and exeriment (circle, triangle and quare). Figure 5-6(a) how the I-V characteritic of a imilar device, which ha the ame multilayer tructure a in Fig. 5-3, but an etch deth of 1.0 µm (down to the center of the AlGaA cladding layer), alo characterized at wavelength of 976 nm. The hallow-etched device ha two advantage comared with the reviou dee-etched one. Firt, the GaA core layer i 88

107 not etched o the cattering lo of the otical mode i le and the urface recombination i weakened; econd, the to contact gold layer i thicker due to le etching time in the roce, which decreae R by about 200 Ω. However, the generated hotocurrent, a well a the harveted electrical ower are le than thoe of the dee-etched device becaue of the exitence of a huge lab mode, which reult in low otical intenity in the waveguide core. Moreover, the hoton generated in the lab cannot be efficiently collected by the circuit. Figure 5-6(b) reent the electrical ower harveted from a load reitance of 1 kω (without bia), for both etch deth. Thi reemble the cae of a elf-owered electronic-hotonic integrated circuit mentioned in Section 5.1. Figure 5-6: (a) I-V characteritic of the hallow-etched device at wavelength of 976 nm for three different inut ower. (b) The electrical ower generated on a 1 kω load reitance for both etch deth. Next, TPPV in GaA wa tudied at the telecommunication wavelength of 1550 nm. The I-V and P-V characteritic meaured at three different inut ower are hown in Fig. 5-7(a) and (b), reectively. Once more, good agreement between the numerical modeling and the 89

108 exerimental reult i oberved. β i etimated to be 17 cm/gw at thi wavelength, in accordance with the value reorted in Ref [107], and i till much higher than that in ilicon (0.7 cm/gw at 1550 nm). 230 µw of electrical ower i generated at inut ower of 90 mw. Figure 5-7: (a) I-V characteritic of the hallow-etched device at wavelength of 976 nm for three different inut ower. (b) The electrical ower generated on a 1 kω load reitance for both etch deth. Figure 5-8: Theoretical tudy of the maximum oible electrical ower generation veru couled otical ower for three different device length of 1, 2, and 5 cm. 90

109 Figure 5-8 reent the imulated maximum oible generated electrical ower veru inut ower for three different waveguide length. Negligible ohmic lo of the contact, a well a low linear roagation lo of 1 db/cm are aumed in thi imulation. Such low α i achievable in micron ize waveguide if the bottom cladding layer i deigned to be thicker and the fabrication rocee, eecially the dry etching recie are otimized. 12 mw of electrical ower can be harveted at inut ower of 150 mw in a 5-cm long device, i.e., a ower efficiency of 8% i theoretically redicted in thi cae. At higher inut ower, a light increae in the loe i clearly viible in all three line, a well a in Fig. 5-6(b). Thi doe not haen in ilicon (Fig. 5 of Ref [14]) due to the high FCA lo in ilicon waveguide. In GaA, the carrier recombination lifetime i two order of magnitude maller than in ilicon. Although the hotogenerated carrier recombine fater before they are collected by the circuit, at the ame time, the otical lo due to FCA i greatly reduced. Further increaing the length of the waveguide can only lightly imrove the ower efficiency a the otical intenity i not high enough after the light roagate a certain ditance along the waveguide and get aborbed gradually. 91

110 CHAPTER 6: PLASMONIC-ENHANCED SILICON PHOTOVOLTAIC DEVICES 6.1 Background Photovoltaic (or olar) cell are undoubtedly one of the mot romiing green technologie for alleviating the energy crii facing the human civilization in the coming decade. Bulk ilicon olar cell with μm thicknee currently dominate the olar cell market. Recently, enhancement of hotovoltaic effect uing urface lamon olariton ha been rooed and demontrated a an alternative method to achieve cot-effective thin-film Si olar cell [111]. In thee device, conventional olar cell are covered with metallic (uually ilver or gold) nanoarticle. The nanoarticle are elf-aembled by thin film (10-20 nm) metal deoition followed by coalecing metal article via thermal annealing. Deending on the deoited thickne and annealing condition, colloidal iland with nm height and diameter are elf-formed [112]. Thee ubwavelength nanoarticle are caable of enhancing the hotocurrent generation in olar cell via lamonic effect. Two mechanim have been rooed to exlain the imroved erformance [111,113]: (a) the iminged light can reonantly coule into the localized urface lamon of the conduction electron in the nanoarticle. The curved urface of the article alie a retoring force on the reonantly driven electron and near-field amlification occur in the high-index material (Si); (b) imultaneouly, light cattering via the metallic nanoarticle occur, which 92

111 lead to enhanced light traing. A a reult, thin film olar cell enhanced by lamonic can be demontrated. Baed on the dicued lamonic enhancement of hotogeneration via metallic nanoarticle, Stuart and Hall demontrated an u to 18-fold hotocurrent enhancement at around 800 nm in 165 nm thick ilicon-on-inulator (SOI) hotodetector [114]. Yu and coworker have more recently hown enhanced erformance of hotodetector (u to 80%) at about 500 nm wavelength [112]. The ame grou ha ued gold nanoarticle and reorted more than 8% increae in ower efficiency of lamonic olar cell a comared with conventional olar cell without nanoarticle [ 115]. Pillai et al. have alied the ame technique and demontrated increae in hotocurrent generation in 1.25 μm thick SOI olar cell [111]. Finally, it i noteworthy that lamonic-enhanced hotovoltaic effect ha been tudied in material other than Si (e.g., GaA), a review of which can be found elewhere [113]. 6.2 Plamonic-Enhanced Solar Cell Uing Non-Sherical Nanoarticle Subwavelength metal nanoarticle are trong catterer of light at wavelength near the lamon reonance. For herical ubwavelength article, the cattering and abortion croection follow the metal olarizability given by [116]: ε ε m α = 3V, (6.1) ε + 2ε m where V i the nanohere volume, ε i the dielectric function of the article and εm i the dielectric function of the embedding medium. The olarizability ha a reonant enhancement 93

112 when ε+2εm i a minimum. Thi i called Fröchlin condition and the aociated mode i called the diole urface lamon of the nanoarticle. For metal with low interband abortion, the dielectric function can be decribed by Drude model. Uing εm = 11.9 for Si, the diole urface lamon reonance of a ilver herical nanoarticle embedded in Si can be analytically calculated. It ha been hown that red-hifting and broadening of the lamonic reonance occur a a function of hae and ize in non-ymmetrical nanoarticle [117]. However, the analytical model i not alicable to analyze thee non-herical tructure and numerical imulation are required. Here, the CST Microwave Studio for 3-D electromagnetic (EM) imulation i ued. To confirm the validity of our imulation, herical nanoarticle with 10 nm diameter embedded in Si were firt tudied. A reonance wavelength of 730 nm wa obtained which i in cloe agreement with the 720 nm analytical value. Normalized Field (a.u.) Radiu = 37nm Length of ide=65nm Length of ide=100nm Circle Triangle Square Wavelength (nm) (a) Reonance wavelength (nm) 1,200 1,000 Enhancement Wavelegth Side length of triangle (nm) (b) Field enhancement factor Figure 6-1: (a) Normalized field of urface lamonic reonance in three different nanoarticle hae with identical urface area and 20 nm thicknee on ilicon ubtrate; (b) Reonance wavelength and maximum field enhancement factor veru ide length in the triangular (rim-haed) nanoarticle with 20 nm thicknee. 94

113 The normalized electric field ectra for circular, quare and triangular ilver nanoarticle on Si ubtrate are hown in Fig. 6-1(a). The reonant wavelength are at 935, 1032 and 1064 nm, reectively. The reonance wavelength of the circular and quare cae are longer than the herical cae, but they remain horter than Si bandga. It i clear that triangular (rim-haed) nanoarticle rovide the furthet reonance hift. The reonant wavelength can be increaed to above Si bandga (~1200 nm) by further increaing the ide length of the triangle at the exene of decreaed lamonic enhancement factor a reented in Fig. 6-1(b). The imulated electric field at 1064 nm wavelength normalized to an incident value of 1 V/m are lotted in Fig. 6-2(a) and (b). The enhanced field inide ilicon i about two order of magnitude (~98 time) tronger than the incident field. Thi i evident from the field veru device deth, along the dahed line of Fig. 6-2(b), lotted in Fig. 6-2(c). Figure 6-2: Electric field enhancement rofile for 1 V/m incident field on a triangular nanoarticle. The incident E-field olarization i horizontal: (a) To-view at iliconmetal interface; (b) Cro-ection view along the horizontal triangle ide in (a); (c) 1- D lot along the dahed line in (b). Uing the triangular nanoarticle that give the larget redhift of reonance, a oible cheme of lamonic-enhanced olar cell i deicted in Fig Lateral -i-n junction i alied here intead of the reviouly demontrated vertical -n junction becaue -i-n olar cell can demontrate enhanced efficiencie [118] a carrier tranort i dominated by drift in the intrinic 95

114 region of the diode. The hotogenerated carrier are accelerated out of the intrinic region before they recombine and hence cloe to ideal quantum efficiency i exected [ 119 ]. Furthermore, wavy finger doed region are included in our deign uch that each nanoarticle i cloely urrounded by - and n-doed region. Thi allow the lamonic region of each nanoarticle be ituated in the middle of the drift region of the -i-n diode ath overlaing with it. The rooed cheme (Fig. 6-3) not only enhance the collection efficiency of the device but alo reduce the ohmic lo of the intrinic region in carrier tranort. Figure 6-3: Schematic of rooed lamonic-enhanced olar cell with lateral -i-n junction and nanorim atterned nanoarticle. 6.3 Plamonic-Enhanced Two-Photon Photovoltaic Power Converter Uing Nanoaerture Structure The TPPV effect dicued in Chater 5 i the nonlinear equivalent of the hotovoltaic effect of olar cell. A reviouly mentioned in Section 5.1, one oible alication i PPC that tranform otical ower into electrical ower. The difference between a PPC and a olar cell i that the otical ource in the cae of a PPC i the outut of a laer or a high-ower lightemitting diode (LED) delivered to the PPC via otical fiber or free ace. 96

115 PPC baed on conventional hotovoltaic and comound emiconductor are available [120]. The diadvantage of uing uch a conventional cheme i that the device are bulky and they uffer from elf-heating. TPPV effect i a viable olution, eecially for nanohotonic alication where local ower generation on an integrated chi i demanded. The TPPV device demontrated o far [14] rely on otical waveguide for enhancing otical intenity (>10 MW/cm 2 ). However, the linear lo of ubmicron waveguide (required to achieve uch high intenitie with reaonable otical ower) remain too high to date for the reent CW alication. Another roblem i that very long waveguide (~10 cm) are required to aborb and convert all the otical energy into electrical ower [16]. Plamonic-enhanced TPPV in Si i rooed here to achieve ultracomact and highly-efficient nanohotovoltaic ower converter. Subwavelength aerture can be alied to hotovoltaic ower converter whoe inut i the beam of a narrow linewidth light-emitting diode or a laer ource focued into the aerture. C-haed ingle aerture have certain advantage over other oible configuration uch a lit and circular aerture due to their comact tructure, which doe not require the reence of array or extenive corrugation. My colleague and I tudied the otical roertie of C-haed ubwavelength aerture in metallic (ilver) film on ilicon ubtrate in the wavelength range of µm [121]. 97

116 Figure 6-4: (a) Geometry and dimenion of the C-haed aerture tudied; (b) ower throughut veru metal layer thickne for the five tranmiion mode conidered in thi tudy [121]. The geometrical dimenion for the deigned C-haed aerture are illutrated in Fig. 6-4(a). In Fig. 6-4(b), the ower throughut (PT) of the aerture, which i defined a the ratio of the total ower at the exit urface to that iminging uon the hyical area of the aerture [122], wa calculated and lotted veru metal layer thickne for five different tranmiion mode at their eak wavelength. The tranmiion mode include one evanecently couled urface lamon (ESCP) mode, one thickne indeendent urface lamon (SP) mode, and FP cavity mode. The number of the FP cavity mode increae with increaing thickne of the metal layer. Detailed hyical exlanation on thee mode can be found in Ref. [121]. A PT of ~7 i redicted for FP1 mode at the telecommunication wavelength of 1.55 µm. The highet PT of 12 i redicted for the ame mode at wavelength of 1.92 µm. 98

117 It hould be mentioned that the above aroache are not ower efficient in reality becaue the PT in the imulation are normalized to the area of the aerture, not the real illuminated area. Enhancement of extraordinary tranmiion ha been reviouly reorted when eriodic array of quare-haed nanoaerture are comared with ingle nanoaerture [123]. Thu, further enhancement i exected in array of our C-haed aerture too. Such a rooed cheme i deicted in Fig. 6-5 and i worth uruing a a future direction reearch. Figure 6-5: Prooed lamonic-enhanced TPPV ower converter uing an array of C- haed aerture. 99

118 CHAPTER 7: FUTURE WORK 7.1 Active Coherent Beam-Combining via Mid-infrared Silicon Raman Laing Quantum cacade laer (QCL) are able to deliver otical ower in a wide wavelength range (3.5 to 150 μm) and are conidered a good candidate for mid-ir integrated hotonic alication. A ingle QCL, however, cannot rovide very high ower. Indeed, roomtemerature and CW oeration i limited due to the heating of the active region at high current denitie. Beam-combining can be alied to imly add u the ower of everal laer, while keeing the beam quality of a ingle emitter. Coherent beam-combining can be achieved by everal cheme including aroache baed on a common reonator, evanecent or leaky wave, elf-organizing or uermode, active feedback and nonlinearitie (hae conjugation) [124]. One cheme for coherent beam combining of laer ource i otical nonlinearitie. One aroach theoretically uggeted in 1986 i uing SRS in otically nonlinear media [125]. Mid- IR SRL have been theoretically modeled and exerimentally attemted in Section 2.3. Here, a novel hotonic circuit i rooed to ractically demontrate thi idea via Mid-IR ilicon Raman laing. The chematic of the rooed technique i illutrated in Fig

119 Figure 7-1: Prooed coherent beam-combining technique uing a ilicon Raman laer umed by an array of QCL. The otical outut of N indeendent QCL at λ are combined to um a Raman laer on SOS uing a multimode interferometer (MMI) on SOS. The deign of a 10 1 MMI oerating at 4.6 μm i reented in Fig In order to obtain coherent combining of the inut beam, aroriate hae difference among the 10 inut ought to be reerved. A tyical calculated inut hae rofile i hown in Fig. 7-2(b). Thee choice of hae difference lead to the evident beam-combing at the MMI outut hown in Fig. 7-2(c). The required hae hift (Fig. 7-2(b)) can be introduced at the inut waveguide by the thermo-otic effect via microheater. Such Mid-IR MMI may find alicator beyond the reent beam-combiner, e.g., ower litter, arrayed-waveguide grating and hotodetector array. 101

120 Figure 7-2: (a) To-view chematic. The MMI length i ~770 μm. Inut arm are 1 mm long to accommodate 950 μm heater (not hown); (b) and (c) Induced inut hae difference via aroriate biaing of hae hifter to achieve coherentlycombined beam at the outut waveguide. The actual coherent beam-combining i mediated by Raman laing in the hown cavity in Fig. 7-1, which i reonant at the coherent Stoke wavelength of λ. The Bragg wavelength of the chematically hown integrated ditributed Bragg reflector (DBR1 and DBR2) i deigned to be at λ, while the combined um ower of QCL at λ i not reflected by the inut DBR1 and can feed the SRS roce. DBR3 only reflect λ to boot the um intenity in the cavity. The DBR can be achieved in ractice by fabricating uniform grating waveguide on SOS. The advantage over that aive technique i that the common cavity i on ilicon and hence the QCL can be off-the-helf comonent (no anti- or high-reflection coating needed). Wavelength tunability i a major advantage of the Raman laer aroach. 102

121 7.2 Alication of VCSRA a Image Pre-Amlifier In Section 2.5, the idea of VCSRA i rooed and the deign of the to and bottom mirror ha been reented. Here we rooe a novel mid-ir imaging ytem uing VCSRA a re-amlifier (Fig. 4-3). The imaging ytem conit of a um laer that allow canning of the beam, a dichroic beam litter that can efficiently tranmit the um and reflect the Stoke beam and hence combine the two beam, a len array for focuing both the um and the ignal into the VCSRA, which re-amlifie the ignal, and a hotodiode (PD) array. Each hotodiode correond to a ixel on the creen. Figure 7-3: The rooed mid-ir imaging ytem uing VCSRA array a re-amlifier. 103

122 The work that will be conducted in the future include the deign of laer beam canning, len array and hoto diode array, a well a theoretical tudie on the NF of the VCSRA conidering the cavity effect. 7.3 Radio-Frequency and high-seed Characterization of the LiNbO3 Electro-otic Modulator The high-eed modulation roertie of the LiNbO3 EO modulator in Section 4.3 have been characterized by meauring the S21 arameter of the modulated ignal uing a network analyzer. The device are functional u to a few GHz [92]. However, the data obtained wa not good enough for full characterization of the modulation roertie and extraction of the modulation bandwidth. Below are the uggeted way to imrove the erformance of the EO modulator at radio frequencie (RF): 1. RF-termination of the electrode i eential in characterization of high-eed modulator. Thi can be realized by adding a 50-Ω reitor to the end of the tranmiion line and connecting it to the chi by a ground-ignal-ground (GSG) robe or through wire bonding. 2. Benzocyclobutene (BCB) can be ued intead of SiO2 for aivation of the device. The dielectric contant BCB i lower (~2.65) comared with SiO2 (~3.9) and ha no frequency deendence for frequencie from 1 khz to 20 GHz. Moreover, BCB can be eaily coated uing inner and the urface flatne of the cladding layer i better than 104

123 that of deoited SiO2. Therefore, better RF erformance of the EO modulator i exected uing BCB a the material for cladding. 3. Imedance matching i of great imortance in achieving high modulation bandwidth in RF ytem. So far, we have been focuing on achieving lower Vπ value by lacing the oitive and negative electrode a cloe to each other a oible (4 µm ditance [92]). Thi make it quite difficult to achieve imedance matching with the current deign a the electrode on the tranmiion line, grown by electrolating, are alo too cloe to each other. The electrode deign hown in Fig. 7-4 not only take the advantage of our highly-confined otical waveguide but alo rovide flexibility in the tranmiion line deign. The fabrication of uch electrode require additional hotolithograhy (image reveral i required if oitive hotoreit i emloyed) and lift-off te. Figure 7-4: Electrode deign to achieve imedance match in RF tranmiion line. The electrode can be laced further away from each other without increaing the V π value of the EO modulator. 105

124 4. High-eed hoto receiver with bandwidth of 10 GHz or higher i needed for RF characterization. 7.4 Exerimental Demontration of Harmonic Generation in LiNbO3 and Ta2O5-on Silicon Waveguide SHG in LiNbO3-on-ilicon and THG in Ta2O5-on-ilicon ha been theoretically tudied in Section 4.4. The hae-matching condition required by SHG and THG can be achieved by conducting dierion engineering in the geometry deign of the ridge waveguide. Alo, attainability of mall cro-ection uing the novel technologie reented in Chater 4 imlie the required intenity for the onet of the deired nonlinearity can be achieved with much lower otical ower. Figure 7-5 how the exerimental et u for demontration of SHG in LiNbO3- on-ilicon and THG in Ta2O5-on-ilicon. The outut ectrum can be eaily meaured with an otical ectrum analyzer (OSA). Viible light can be generated on ilicon from infrared ource baed on thi cheme. 106

125 Figure 7-5: The exerimental et u for demontration of SHG in LiNbO 3-on-ilicon and THG in Ta 2O 5-on-ilicon. 7.5 Power Efficiency of the Two-hoton Photovoltaic Effect in Gallium Arenide The TPPV effect i conidered a a viable olution for achieving energy-efficient integrated hotonic device. It ha been theoretically redicted in Section 5.3 that the ower efficiency of the TPPV effect in GaA at wavelength of 1550 nm can reach 8% (Fig. 5-8) or even higher auming low linear roagation lo, zero ohmic lo at the contact and long enough device. In order to imrove the erformance of the TPPV device at wavelength of 1550 nm, firt of all, the bottom cladding layer (intrinic AlGaA) ha to be thick enough to avoid mode 107