Anti-Stokes Raman conversion in silicon waveguides

Transcription

1 Anti-Stoke Raman converion in ilicon waveguide R. Clap, V. Raghunathan, D. Dimitropoulo, and B. Jalali Optoelectronic Circuit and Sytem Laboratory Univerity of California, Lo Angele Lo Angele, CA Abtract: The firt obervation of parametric down-converion in ilicon i reported. Converion from 154.3nm to 138.8nm i achieved uing a CW pump laer at 147 nm. The converion occur via Coherent Anti-Stoke Raman Scattering (CARS) in which two pump photon and one Stoke photon couple through a zone-center optical phonon to an anti-stoke photon. The maximum meaured Stoke/anti-Stoke power converion efficiency i The value depend on the effective pump power, the Stimulated Raman Scattering (SRS) coefficient of bulk ilicon, and waveguide diperion. It i hown that the power converion efficiency i a trong function of phae mimatch inide the waveguide. 3 Optical Society of America OCIS code: (3.737) Waveguide; (5.314) Integrated optoelectronic circuit; (5.448) Optical amplifier. Reference and Link 1. Jame B. Kuo and Shih-Chia Lin, Low voltage SOI CMOS VLSI circuit and device, John Wiley and Son, Incorporated, 1, ISBN M. Cardona, G. Guntherodt, Light Scattering in Solid II, in Topic in Applied Phyic, Vol. 5. Chapter 4, Coherent and Hyper-Raman Technique, by H. Vogt. (Springer-Verlag, Berlin, 198). ISBN M.C. Ho, K. Ueaka, Michel Marhic, Y. Akaaka, L.G. Kazovky, -nm-bandwidth Fiber Optical Amplifier Combining Parametric and Raman Gain, J. Lightwave Technol. 19, (1). 4. M.E. Marhic, K.K.-Y. Wong, and L.G. Kazovky, Propect for CW Fiber OPA and OPO, Proceeding CLEO (Optical Society of America, Wahington, D.C., 3) CTuA1. 5. J.K. Chee, J-M Liu, Polarization-Dependent Parametric and Raman Procee in a Birefringent Optical Fiber, IEEE J. Quantum Electron. 6, (199). 6. Y.R. Shen, N. Bloembergen, Theory of Stimulated Brillouin and Raman Scattering, Phy. Rev. A 137, A1787-A185 (1964). 7. E. Golovchenko, P. V. Mamyhev, A. N. Pilipetkii, E.M. Dianov, Mutual Influence of the Parametric Effect and Stimulated Raman Scattering in Optical Fiber, IEEE J. Quantum Electron. 6, (199). 8. P.A. Temple, C.E. Hathaway, Multiphonon Raman Spectrum of Silicon, Phy. Rev. A 7, (1973). 9. J.M. Ralton, R.K. Chang, Spontaneou-Raman-cattering efficiency and timulated cattering in ilicon, Phy. Rev. B, (197). 1. R. Clap, D. Dimitropoulo, Y. Han, B. Jalali, Obervation of Raman emiion in ilicon waveguide at 1.54 µm, Opt. Expre 1, () R. Clap, D. Dimitropoulo, V. Raghunathan, Y. Han, B. Jalali, Obervation of Stimulated Raman Scattering in Silicon Waveguide, Opt. Expre 11, (3) D. Dimitropoulo, B. Houhmand, R. Clap, B. Jalali, Coupled-mode theory of the Raman effect in Silicon-On-Inulator waveguide, Optic Letter 8() (3). 13. J.J. Wynne, Optical Third-Order Mixing in GaA, Ge, Si, and InA, Phy. Rev (1969). (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 86

2 14. H.K. Tang, C.S. Wong, T.K. Lang, I.E. Day, S.W. Robert, A. Harpin, J. Drake, M. Aghari, Optical diperion, two-photon aborption and elf-phae modulation in ilicon waveguide at 1.5 µm wavelength, Appl. Phy. Lett. 3, (). 15. Spectra-Phyic Telecom: Model RL5 Raman Fiber Laer Specification. 1. Introduction The tudy of nonlinear optical material ha been driven in recent year by the need of optically active device that can be monolithically integrated into optoelectronic circuit. Silicon offer the capability of optoelectronic integration via Silicon-On-Inulator (SOI) technology [1]. The major limitation of ilicon, in thi context, ha been the lack of mechanim for light generation, amplification, and wavelength converion. Hence, the tudy of optical nonlinearitie in ilicon waveguide i of importance to determine the feaibility of realizing SOI-baed optoelectronic circuit, with both paive and active optical functionality. Coherent Anti-Stoke Raman Scattering (CARS), Parametric Wavelength Converion (PWC), and Optical Parametric Amplification (OPA) are well-known nonlinear optical procee [, 3]. PWC and OPA have been extenively invetigated in optical fiber in the context of broadband ignal amplification, or a wavelength-converion mechanim [4,5]. The theory that govern thee phenomena ha been fully developed in the pat [6]. Conidering only the χ (3) component of the optical interaction and auming no pump power depletion, a detailed theory decribing the interaction of Stoke and anti-stoke wave via SRS and Four Wave Mixing (FWM) ha been developed [7]. The preent ituation involve interaction of three field: the pump, the Stoke, and the anti-stoke (a-stoke) field, at wavelength (frequencie) λ p (ω p ), λ S (ω S ), λ as (ω as ), repectively. Thee field interact inide a SOI waveguide via the third-rank nonlinear tenor of ilicon (χ (3) ). In what follow, for the ake of implicity and to accurately decribe the condition of the experiment performed, it will be aumed that the a-stoke field, E as, ha zero value at the front facet of the waveguide. The incoming field will be the pump, E P (TE mode), and the Stoke, E S (TM mode). In general, the χ (3) tenor ha two contribution. The firt i the electronic, non-reonant component, χ (3) NR, which i nearly intantaneou in repone and hence broadband, and which account for uch effect a elf-phae modulation (SPM) and FWM. The econd i the Raman component, χ (3) R(Ω=ω p -ω S ) which account for SRS. The χ (3) R(Ω) component ha a trong pectral dependence, with a reonant peak at Ω=Ω, the frequency of ocillation of zone-center optical phonon in ilicon. The element χ (3) R(Ω) ha therefore the pectral ignature of the Raman-active phonon mode of vibration of the crytal lattice. Thi implie that there i a repone time aociated with thi component, which correpond to the phonon de-phaing lifetime. In the cae of firt order Raman cattering from ilicon at room temperature, where only zone-center optical phonon are involved, the bandwidth i ~ 15 GHz. Thi correpond to a repone time of about 1 p. In thi paper we demontrate, for the firt time, Stoke to anti-stoke wave-converion in ilicon waveguide. A detailed preentation of the experimental reult will be given, plu a qualitative decription of the phyic involved. The wavelength-converion phenomenon i reminicent of coherent anti- Stoke generation (CARS) under quai-phae-matching condition. Wavelength converion ha important implication for optical communication, in particular for optical packet routing. In the following ection, a brief theoretical review of SRS and Stoke/anti-Stoke wave coupling in ilicon will be preented. The reult that are relevant to the experimental condition of the preent work will be highlighted, followed by the decription of the experimental work in Section 3. (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 863

3 t. Background The pontaneou and timulated Raman cattering in bulk ilicon and in the viible region of the pectrum have been tudied in the pat [8, 9]. Recently, our group ha reported the firt obervation of pontaneou [1] and timulated [11] Raman cattering in integrated ilicon waveguide. In addition, we have performed a detailed coupled-mode analyi of SRS in ilicon waveguide [1]. The waveguide ued in our previou meaurement and in the current etup were fabricated parallel to [ 11 ] direction on a ilicon [ 1] urface, due to the favorable cleaving property of ilicon in thi orientation. Thi geometry lend itelf to a coordinate ytem ( x, y, z) rotated with repect to the crytallographic axe by 45 o around the [ 1] axi. In thi ytem, the waveguide i oriented along the z-axi, the TM mode i linearly polarized along the Y-axi, and the TE mode along the X-axi. The tenorial nature and ymmetry propertie of χ (3) R(Ω) in ilicon are inherited from the pontaneou Raman tenor, and i carried in the three Raman tenor component, R i, which in the preent coordinate ytem are written a [1], 1 1 t t t 1 1 R1 = 1 ; R = 1 ; R = The aniotropic cattering efficiency, S(Ω), defined a the percentage of cattered radiation per unit of olid angle, per unit length, i related to the Raman tenor a follow S( Ω) = S o ( Ω) n= 1,,3 eˆ R where ê i, ê are the polarization of the incident and cattered radiation, repectively. S o (Ω) i a contant of proportionality that contain the material parameter. The value of S(Ω) at the peak Raman hift (Ω=15.6 THz) wa meaured to be 4.1 x 1-7 cm -1 Sr 1 [1]. For the timulated Raman effect in bulk material, the gain coefficient g, i obtained from the pontaneou efficiency following reference [9]. The relevant parameter for SRS and FWM in ilicon can be ummarized a, n eˆ i, 1 (1) () Ω = ω ω ; g ( Ω p R = π χ ) = 4 hω n = i 4π χ = (3) NR Ω ω /( c = 15.6 THz, 8π c ω p S( Ω ( ω )( N + 1) ω (3) R 8 ( Ω ) ω /( c cm / W, k) = k) 9 ) cm / W. (3.1) (3.) (3.3) Where N i the Boe occupation factor (.1 at room temperature), n i the refractive index, and ω i the FWHM of the pontaneou Raman line-hape. Equation (3.) define the Raman uceptibility, χ 3 R. In Eq. (3.3), the value of χ (3) NR i the χ 11 component of the nonlinear uceptibility tenor [13, 14]. For a waveguide along the Z-axi, the amplitude of (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 864

4 the Y-axi component (TM mode) of the anti-stoke field, E as (z), i related to the initial amplitude of the Y-axi component (TM mode) of the Stoke field, E So, by [7] i( k + RI ) z / inh Az p EaS ( z) = i e (R + ig ( Ω)) I p ESo. (4) A Where I p i the effective pump intenity and k i the phae mimatch between pump, Stoke and anti-stoke wave, defined a, k = k TE p k Note that in Eq. (5), the phae difference take into account the two different polarization mode in the waveguide (TE and TM ) and therefore, waveguide-induced birefringence will play a crucial role in the efficiency of Stoke to anti-stoke converion. The coefficient A, in Eq. (4), i given by [7] TM S k TM as A = (R + ig ( Ω)) I ( k ) ( k ). (6) Note that A i in general a complex number. It real part i reponible for an exponential gain in the a-stoke wave [7]. The imaginary part of A reult in an ocillatory behavior of the a-stoke converion efficiency, along the waveguide direction, z. A will be hown in Figure 1, it alo manifet itelf a a characteritic inc dependence of the a-stoke power on the phae mimatch. From Eq. (4) and (6), two regime can be clearly identified, k k >> << p 4R + g 4R + g ( Ω) I ( Ω) I The firt cae correpond to an SRS dominated regime in which the large phae mimatch diminihe the FWM efficiency. In thi regime, the Stoke ignal i exponentially amplified with pump power and waveguide length, and the generated a-stoke wave i negligible. The econd cae correpond to a nearly phae-matched condition, in which the anti-stoke ignal i linearly amplified via the FWM effect. Thi proce deplete the pump wave, effectively uppreing the exponential SRS gain. With the value given in Eq. (3) for the nonlinear coefficient in ilicon, and auming an effective pump power of.7 W inide the waveguide, the value of the threhold that define thee two regime i 4R + g ( Ω) I p =.1 cm. (8) Therefore, to operate the waveguide a an amplifier, the amplitude of k mut be larger than.1 cm -1, wherea to realize efficient wavelength converion, the phae mimatch mut have much maller amplitude than.1 cm -1. Figure 1 how the Stoke to anti-stoke converion efficiency v. k, calculated uing Eq. (4). The efficiency ha a inc dependence on k, for all value larger than the threhold defined in Eq. (8). At the threhold value, k =.1 cm -1, the converion efficiency i approximately.5 %. For k maller than 1 cm -1, the maximum efficiency drop by at leat two order of magnitude, compared to the phaematched condition. From thi figure, it i evident that in the SRS regime the anti-stoke converion efficiency i not a ingle-valued function of k. Furthermore, the lower the converion efficiency i, the wider the range of value of k that can fit it. p p.,. 1 (5) (7) (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 865

5 -1 Stoke/a-Stoke efficiency (Log 1 ) K (cm -1 ) Fig. 1- Converion efficiency, calculated from Eq. (4) uing an effective pump power of.7 W at the input facet of the waveguide. The meaured efficiency in the experiment i Figure i a plot of the real part of the coefficient A, relative to the value of the Raman gain, g, a a function of the phae mimatch parameter, k, according to Eq. (6). The plot depict the uppreion of the exponential SRS gain a the phae-matched condition ( k = cm -1 ) i reached. It i alo clear that the gain uppreion i negligible for abolute value of the phae mimatch lower than 1 cm -1. Alo noticeable i the regime for mall, poitive value of k (~ 1 cm -1 ) in which the gain coefficient i larger than that of pure SRS. Thi behavior ha been predicted in ilica fiber and ha been attributed to Modulation Intability [7]. 1 Re(A)/g (Ω ) K (cm -1 ) Fig. - Ratio of effective gain relative to SRS Raman gain, calculated from Eq. (6). (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 866

6 3. Experimental etup The experimental etup depicted in Fig. 3 i imilar to the etup ued to meaure pontaneou Raman emiion and SRS in ilicon waveguide [1, 11]. The pump ued i a CW, cacaded- Raman-cavity (CRC) fiber laer (Spectra Phyic), operating at a wavelength of 147 nm. The ignal laer i an External-Cavity-Diode-Laer (ECDL, New Focu), tuned in the Stoke domain from 1535 nm to 155 nm. Waveguide PBS (1.8 cm) TE F(147 nm) TM P(TM) Pump 147. nm VOA ECDL PC OSA Fig. 3 Experimental etup ued for oberving CARS in ilicon. F.- Pump laer filter. PBS.- Polarizing beam plitter. P(TM).- Polarizer to collect the TM mode from SOI waveguide. OSA.- Optical Spectrum Analyzer. ECDL.- External Cavity Diode Laer, to ue a a ignal, with a can range from 1535 to 155 nm. VOA.- Variable Optical Attenuator. The Polarizing-Beam-Splitter (PBS) i ued to couple the pump and ignal laer into the waveguide, in a cro-polarization cheme. The pump laer i coupled into the TE mode and the ignal laer i coupled into the TM mode. In order to meaure the converion efficiency between the Stoke and the a-stoke ignal, a Variable Optical Attenuator (VOA) i placed after the ECDL. Only the TM mode i collected at the waveguide output. No filter for the reidual pump and ignal beam i neceary, ince the a-stoke ignal i collected by an Optical Spectrum Analyzer (OSA). The total pump-to-waveguide coupling lo i 6.1 db coniting of 3dB lo due to the PBS, 1dB due to the pump filter, and.1db of coupling lo into the waveguide. Fabry-Perot fringe from the cavity formed between the two facet of the waveguide (which are not AR coated), are mall in amplitude compared to the oberved pectral ignature of the CARS effect. Therefore, thee fringe are irrelevant for the reult preented in the following ection. The waveguide had a cro ection of 5.4 µm and wa fabricated along the [ 11 ] direction of ilicon [11]. 4. Reult Figure 4 how the anti-stoke pectra meaured a a function of the Stoke laer wavelength. There i a clear peak at 138.8nm of anti-stoke emiion when the Stoke laer i tuned to 154.3nm. The latter correpond to the peak of the pontaneou Raman emiion in ilicon. The nature of the weaker feature in Fig. 4 mot likely correpond to the wavelengthdependent character of the phae-matching parameter, k, in the SOI waveguide. Further analyi will be carried out in the future, conidering other polarization configuration of the experiment, to determine the ymmetry propertie of thee reonance. (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 867

7 Fig. 4 Plot of the a-stoke pectra collected for a given value of the ignal (Stoke wavelength). The z-axi repreent the Stoke/a-Stoke converion efficiency, normalized to unity. Note the clear appearance of two atellite reonance, a mentioned in the text. Figure 5 how the a-stoke power, integrated acro the anti-stoke pectrum ( nm), a a function of the pump power effectively coupled into the waveguide (red triangle). The blue diamond correpond to counter-propagating pump and Stoke ignal in the waveguide. The relative lack of a-stoke emiion in the counter propagating condition undercore the importance of phae matching. In thi cae ( k= cm -1 ), any a-stoke ignal would be due to down-converted pontaneou Stoke emiion. Alo hown in the figure i the meaured power when the Stoke laer i off (croe). The relative abence of power in thi cae i an unambiguou indication that the meaured a-stoke ignal i that of down-converted Stoke ignal. The figure alo how the reult for the a-stoke power obtained from Eq. (4) (olid line) uing k ~ -7 cm -1. The fact that the theoretical fit pan everal value of a-stoke power reduce the range of k value that match the meaured data. Nonethele, it hould be treed that the above procedure will not be contrued a an accurate meaurement of k. The latter can be achieved uing procedure imilar to thoe outlined in reference [14]. (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 868

8 a-stoke Power (nw) 1 5 a-stoke Forward a-stoke c-propagation Stoke off Theory Pump Power (W) Fig. 5.- Integrated a-stoke power ignal v. pump power, with the Stoke ignal power fixed. The integration i carried out from 133 to 1333 nm in the a-stoke pectra (Fig. 4). The red triangle how clearly the a-stoke amplification due to Stoke parametric down-converion. The blue diamond correpond to counter-propagating pump and Stoke ignal in the waveguide. The croe are the down-converted, pontaneou a-stoke ignal. The Stoke ignal wa et at nm and 3 µw of input power. The fit with Eq. (4) wa performed uing A = i. Thi correpond to k ~ -7 cm -1. Figure 6 how the integrated power in the a-stoke domain a a function of the Stoke wavelength, λ. The peak hown at the center of the Raman frequency hift (154.3 nm) indicate that the oberved parametric down converion ha the pectral characteritic of Stimulated Raman emiion in ilicon, a expected from Eq. (4). Note that at high pump power, the data appear to how a double-peak pectrum. The reaon for thi i that at high power, the pump laer exhibit a double-peak pectral line-hape. Thi i a well known artifact of CRC fiber laer, and i well documented by the manufacturer [15]. To obtain the down-converion efficiency, the a-stoke integrated power wa meaured a a function of the Stoke ignal power, for different value of pump power. The reult i hown in Fig. 7. (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 869

9 a-stoke Power (pw) W.61 W.5 W.3 W.3 W Signal wavelength (nm) Fig. 6.- Spectral dependence of the a-stoke integrated power (a in Fig. 4), againt Stoke wavelength, for different value of pump power. The olid line are lorentzian fit to the data. Data fluctuation at high pump power in the region cloe to the Raman reonance (154.3 nm) i mot likely due to Fabry-Perot effect from the waveguide facet [11]. a-stoke Power (pw) W.4 W. W.3 W Stoke Power (uw) Fig. 7. Stoke to a-stoke converion efficiency. The Stoke power wa varied uing the VOA hown in Fig. 3. The efficiency, defined a the lope of the plot hown, increae with pump power, a expected from Eq. (4). (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 87

10 From the lope in Fig. 7, the maximum Stoke/anti-Stoke power converion efficiency meaured for thi particular waveguide i found to be 1 1-5, for an effective pump power of.7 W. Referring to Fig. 1, the horizontal line how the meaured converion efficiency relative to the phae mimatch parameter. Becaue of the ocillatory nature of the curve, an accurate etimation of the phae-mimatch, baed on the meaured CARS efficiency, i not poible when the efficiency i low. Specifically, the value of k that match the meaured converion efficiency are in the range -55 to -1 cm -1. Next, an Erbium-Doped-Fiber-Amplifier wa introduced in the etup, to amplify the Stoke ignal up to mw. The reult i an effective ignal power of about 5 mw inide the waveguide, leading to a maximum a-stoke ignal oberved of 55 nw, a hown in Fig. 8. a-stoke Power (nw) Pump Power (W) Fig. 8. Maximum amount of a-stoke ignal obtained, at nm. It wa obtained by increaing the Stoke ignal power up to ~ 5 mw effectively coupled into the waveguide. 4. Concluion Thi paper ha reported the firt obervation of coherent anti-stoke Raman cattering in ilicon. Specifically, we have demontrated coherent parametric wavelength converion from nm to nm. Thi wa achieved uing a 147nm CW pump with ~nm linewidth. The bandwidth over which the converion occur correpond to that of the Raman proce. Including the pump broadening effect, thi bandwidth i 35GHz in the preent experiment. The bandwidth may be increaed uing multiple pump, uitably paced in wavelength. The meaured Stoke / anti-stoke power converion efficiency i The relatively low converion efficiency can be attributed to the non-phae-matched condition in the preent waveguide. With proper deign of waveguide diperion, converion efficiency can be dratically increaed, leading to ilicon baed, all-optical wavelength converter, uitable for optical packet witched network. (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 871

11 Acknowledgment Thi work wa upported by the MTO office of the Defene Advance Reearch Project Agency (DARPA). The author would like to thank Dr. Jag Shah for hi upport. (C) 3 OSA 3 November 3 / Vol. 11, No. / OPTICS EXPRESS 87