LIGHT MANIPULATION IN PHOTONIC CRYSTAL STRUCTURES AND THEIR APPLICATIONS PANKAJ KUMAR SAHOO

Transcription

1 LIGHT MANIPULATION IN PHOTONIC CRYSTAL STRUCTURES AND THEIR APPLICATIONS PANKAJ KUMAR SAHOO DEPARTMENT OF PHYSICS INDIAN INSTITUTE OF TECHNOLOGY DELHI OCTOBER 2017

2 Indian Institute of Technology Delhi (IITD), New Delhi, 2017

3 LIGHT MANIPULATION IN PHOTONIC CRYSTAL STRUCTURES AND THEIR APPLICATIONS by PANKAJ KUMAR SAHOO Department of Physics Submitted in fulfilment of the requirements of the degree of Doctor of Philosophy to the INDIAN INSTITUTE OF TECHNOLOGY DELHI OCTOBER 2017

4 Dedicated to my Parents

5 CERTIFICATE This is to certify that the thesis entitled, Light manipulation in photonic crystal structures and their applications", being submitted by Pankaj Kumar Sahoo, to the Indian Institute of Technology Delhi, New Delhi, for the award of degree of Doctor of Philosophy in the Department of Physics is a record of bonafide research work carried out by him under my supervision and guidance. He has fulfilled the requirements for the submission of the thesis, which to the best of my knowledge has reached the required standard. The material contained in the thesis has not been submitted in part or full to any other University or Institute for the award of any degree or diploma. Prof. Joby Joseph Department of Physics Indian Institute of Technology Delhi New Delhi October, 2017

6 Acknowledgements It is my immense pleasure to acknowledge all the people who have supported and encouraged me throughout the PhD period to accomplish my thesis. First of all, I would like to express my deepest gratitude and respect to my supervisor Prof. Joby Joseph for providing me the opportunity to work with him. He has been a great support in my academic as well as personal matter. I had access to him whenever I needed to discuss my problems. His knowledge and encouragement have led to the success of my PhD work. It is a great privilege to be his student. Thank you a lot Sir! I would also like to thank Mrs. Joseph for her care & advice that gave me moral support during my PhD. I would also like to express my gratitude to Prof. Anand Srinivasan of KTH, Stockholm for giving me the opportunity to work in the Electrum laboratory, Kista, Sweden under the Erasmus Mundus (India4EU II) scholarship program. My special appreciation to Dr. Bikash Dev Choudhury of KTH, Sweden for his support and for sharing his knowledge on clean room fabrication tools. I have learned quite a lot from him while working with him on the Color filter and ZnO nano funnel project. I would like to thank the members of my thesis SRC committee, Prof. Anurag Sharma, Dr. Kedar Khare and Prof. Ranjan Bose for their guidance. A sincere word of gratitude goes out to Prof. P. Senthil Kumaran, Prof. M. R. Shenoy and Prof. Kehar Singh who have always been a motivation and support to pursue Optics and Photonics as my research field. I am very thankful to all the members of Photonics Research Lab for their cooperation and encouragement. Dr. Arvind Kumar and Dr. Sanjay Kumar have always extended their support whenever I encountered any problem. I am very delighted to express my heartfelt thanks to

7 my seniors: Dr. Jolly Xavier, Dr. Manish Kumar & Dr. Samsheer Ali for their guidance and cooperation. A lot of thanks to Dr. Sarita Ahlawat for her support and encouragement. Specifically, her advice to pursue interdisciplinary research through the Living Science program is quite impressive. I thank Dr. Shereena, Jagadeesh, Amit Kapoor, Priyanka, Charu, Saraswati and Krishnendu for extending their friendship and support during my life at Photonics Research Lab. I thank Mandeep & Faiz as my special friends who have always supported me whenever I needed their help in academic as well as personal matters. Swagato deserves particular mention for his time and interaction in the lab. My research got another dimension when I and Swagato started working together on the GMR phase measurement. The period we worked together is the most interesting and eventful phase of my research. I truly appreciate Jaiyam Sharma, a PhD scholar at the University of Electro Communication, Japan for his MATLAB related help. Many thanks to Rawatji for his timely assistance and cooperation. During my stay in Sweden, I got the support of many people, especially Prof. Sebastian Lourdudoss, Alphonsa Lourdudoss, Dr. Himanshu Kataria, Nedim, Balaji, Dennis and Inese. My special thanks to Giri for his continuous support throughout my tenure in Sweden. His friendliness and welcoming attitude have been very helpful and encouraging. This acknowledgment would remain incomplete without thanking my friends from masters program: Ambarish, Varinder, Piyush, Naresh, Jeeban, Ramu and Parvinder who always gave me strength and support whenever I felt low. During my PhD studies I have got the opportunity to partially guide the master students: Kamal, Sagar, Jyoti, Mansi, Pragati, Sunaina & Sruthy in their project work. I value it as a rewarding experience and thank all of them. vi

8 Thanks are due to other friends of the Physics department of IIT Delhi and specially Divya & Pragati for their support and encourage. My sincere thanks to my Odia friends; Nilamani, Bikash, Sonu and Sushant for their continuous support during my stay in IIT Delhi. I would definitely like to acknowledge the funding from the Ministry of Human Resource Development, India and the one year financial support from the Erasmus Mundus (India4EU II) scholarship program. I would like to thank my sister Sandhya & brother Saroj for their support, they were always proud of my every little success. Also thanks to all my family members & relatives, specifically my brother-in-law Madan bhai, for supporting me throughout my PhD career. At last but not the least, I am deeply grateful to my mother and father for their love, care and all the sacrifice they made for my education. Their trust on my decisions to pursue a career of my choice, has pushed me forward in my research and to reach my goals. They have always given me the moral strength through all my difficult times. (Pankaj Kumar Sahoo) vii

9 Abstract This Ph.D. thesis is concerned with the design, fabrication and use of photonic crystal structures for various photonic applications. Basically one and two dimensional, periodic as well as aperiodic photonic crystal structures have been used in the thesis. Among 1D PhCs, guided mode resonance (GMR) structures which contain 1D gratings, has been discussed in details. The resonance condition to obtain GMR peak and its properties have been discussed. We have proposed a new method to tune the GMR peaks by azimuthal rotation of the GMR device. The azimuthal rotation takes in to account the conical diffraction of grating that leads to a different resonance condition compared to the classical diffraction case. Based on this principle we have proposed highly tunable wavelength filters that covers the visible to NIR spectrum with a tuning range of around 600nm. We have also developed a design procedure to design dual wavelength filters with complete control over the two GMR peak wavelength positions. Based on this design procedure, we have developed a dual wavelength filter for C-band wavelengths at 1310nm & 1550nm with high azimuthal angle tolerances of 20 degrees. In addition to these filter applications, we have developed an optical sensor based on the measurement of the phase of the GMR wavelength using a laser tuned Mach Zehnder interferometer. The GMR signal is interfered with a reference signal to produce fringe pattern on a CMOS camera and analyzed further to measure the phase shift. The purpose of our setup is, to detect the smallest possible changes in refractive index of various liquid and gaseous media. With our set up, we obtained a minimum refractive index change of 3.43 x 10-7 RIU with a sensitivity of 0.608π phase change per 10-4 RI change that outperforms the other phase based GMR sensors. We have proposed a theoretical model to viii

10 numerically calculate the phase shift of this GMR signal that is in good agreement with the experimental results. In addition to the GMR sensors, we present another technique for refractive index sensor using 1D phase gratings. The grating parameters are such that the 1 st order diffracted light travels at a diffraction angle of 90 o with respect to the 0 th order. The diffracted light which is along the direction of periodicity can further get diffracted from the grating and interfere with the 0 th order light. Under this condition, the π phase difference that arises between the two interfering beams results in a transmission dip. We tune this dip wavelength according to grating equation and got a sensitivity of the order of the grating period. Among the 2D PhCs we have studied both periodic and aperiodic array of silicon pillars. We have used 2D square lattice of Si pillars and created defects in it to design optical diode and wavelength division multiplexer to be used in optical circuits. We have proposed color filters based on aperiodic assembly of Si nanopillars embedded in PDMS. The details of fabrication and characterization of the proposed filters are discussed. The transmission spectra are in good agreement with the industrial requirement of color filters for image sensor and display applications. Finally we will present a new light trapping technique to reduce reflection loss as well as for light focusing at submicron scales in solar cells. We have fabricated hexagonal arrays of ZnO-funnel like structures on Si substrate by patterned growth of ZnO nanowires in a hydrothermal growth process. The working principle of these funnels is similar to that of a GRIN lens for light trapping and convergence. The optimized structure has average reflectivity close to 3% in the wavelength range of nm with possibility of confining incident light to few hundreds of nanometers. ix

11 स र यह प एच.ड. थ स स स न न फ ट सनक अन प रय ग क स ए फ ट सनक स स ट रचन ओ क सडज इन, सनर ण और उपय ग ब स त ह र त एक और द ड यम शनल, पररय सडक और थ ह अपररय सडक फ ट सनक स स ट रचन ओ क उपय ग थ र सकय गय ह १ ड फ ट सनक स स ट क ब च, १ ड ग र ट ग स व ल ग इड ड म ड र ज न स (ज.एम.आर.) स रचन ओ पर टववरण ट य गय ह ज.एम.आर. प क और उसक ग ण क प र प त करन क टलए र ज न स क टथ ट पर चच ह ई ह ज.एम.आर. टडव इस क अज म ल र शन द व र ज.एम.आर. प क क य न करन क टलए हमन एक नई टवट प रथ टव क ह अज म ल र शन म ग र ट ग क क टनकल टडफ र क शन क ध य न म रख ज ह ज क ल टसकल टडफ र क शन म मल क लन म अलग र ज न स क टथ ट द त ह इस टसद क आ र पर हमन अत यट क य न करन य ग य व वल ट ल र क प रथ व टकय ह ज टक टवट बल स एनआईआर थप क रम क ६०० एन.एम. क य टन ग स म क क र करत ह हमन एक ड य ल व वल ट ल र टडज इन करन क टलए टडज इन प रट य टवकटस क ह ज य टक ज.एम.आर. प क व वल पर प ण टनय त रण रख ह इस टडज इन प रट य क आ र पर, हमन २० टडग र क उच च एट म ल क ण लर स क स स -ब ड व वल, १३१०एन.एम. और १५५०एन.एम. क टलए हर व वल ट ल र क टवकटस टकय ह इन ट ल र अन प रय ग क अल व, हमन एक ल जर य न ड म क ज डर इ र र म र क उपय ग कर ह ए ज.एम.आर. व वल क ज क म प क आ र पर ऑटट कल स सर टवकटस टकय ह ज.एम.आर. टसग नल क टसम स क मर पर टफ र ज प न बन न क टलए एक रर र न स टसग नल क स इ र र टकय ज ह और ज क म पन क टलए आग क टवश ल षण टकय ज ह टवट न न रल और ग स य म टडय क र फ र टक व इ ड क स म सबस कम स व पररव न क प लग न हम र थ पन क उद द श य ह हम र स अप क स, हमन ३.४ x १०-७ आर.आई.य. क एक न य न म र फ र टक व इ ड क स पररव न प र प त टकय, टजसम प रट १०-४ आर.आई. पररव न क टलए ०.६०८π ज पररव न क स व नश ल प र प त ह ह, ज य टक अन य ज आ रर ज.एम.आर. स सर स ज य ह हमन x

12 एक स द ट क म डल क प रथ व टकय ह ज प रय ग त मक पररण म क स अच छ समझ म ज.एम.आर. टसग नल क ज ब ल व क स ख य त मक गणन कर ह ज.एम.आर. स सर क अट ररक त, हम १ ड ज ग र ट ग क उपय ग स र फ र टक व इ ड क स स सर क टलए एक और कन क प श कर ह ग र ट ग स क म न ड ऐस ह, क थ आड र टडफ र क ड ल इ र ऑड र क ब र ९० सडग र क टडफ र क शन क ण पर प र प ग कर ह यह टडफ र क ड ल इ ज प ररओड स क सदश र ह, ह ग र ट ग ब र टडफ र क ह कत ह और र ऑड र इट क थ इ र र कर कत ह इ पररसस थसत र, द इ र रर ग ब र क ब च उगन π ज अ तर क पररण र स एक ट सर शन ड प टमल ह हर ग र ट ग र करण क अन र इ ड प व वल क य न कर ह ह और ग र ट ग क प ररयड क र क दनश त प र प त क करत ह २ ड प ररओड स क ब च, हमन टसटलक न टपल लस क प ररय टडक और ऐटपर टडक सरण न क अध ययन टकय ह हमन २ ड टसटलक न टपल लस क थक व यर ल ट स क इथ म ल टकय ह और इ र टड क स बन क ऑटट कल सटक म इथ म ल ह न क टलए ऑटट कल ड य ड और व वल टडव न मल टल क सर क टडज इन टकय ह हर न प.ड.एर.ए. र एम ब ड ड टसटलक न न न सपल र क ऐपररय सडक अ ब पर आ ररत कलर सफल टर प रस त स त सकए ह प रस त स त सफल टर क सनर ण और क षण ण न क स रण पर चच क गई ह इर ज र और सडस ए क शन क स ए, कलर सफल टर क ट सर शन स प क ट ट, औद य सगक आ श यकत क थ अच छ र झ त र ह अ त र हर स लर स ल र ररफ ल क शन ल थस क कर करन क स ए और ल इ क सब- म इ न थक ल म क स त करन क स ए एक नई ल इ र टप ग क तकन क प श कर ग हर न टसटलक न ब ट ट पर ट क ऑक स इड-फ न क ह क ट ग न रसणय ट क क ह, ज एक हयड र रम ल ग र प रस य र ट क ऑक स इड न न व यस क प न ड ग र बन य गए ह इन नल क ल इ र टप ग ए ड कन वज न स क र प म क म करन व ल टसद एक ग र न ल स क सम न ह ऑटट म इज ड स रचन म ३००-१२०० एन.एम. क व वल स म म ३% क कर ब औस र फ ल टक टव प य ग य ह, ज य टक क छ स कड न न म र क थक ल म ल इ क स टम करन क स वन रख ह xi

13 Organization of Thesis Chapter 1 provides the preface and essential outline of the work content of the thesis. Starting with a brief introduction to the photonic crystal structures, we discuss the concept and origin of photonic bandgap. The classification of PhC structures like 1D, 2D, 3D & photonic crystal slab (PhCS) structures along with their dispersion characteristics is discussed. The defect states such as the point defects and line defects in 2D PhCs are explained which will be used in chapter 4 of the thesis. Then different mechanisms of light manipulation in PhC structures is discussed along with relevant applications in nanophotonic industry. Chapter 2 describes about the detailed study of the guided mode resonance (GMR) phenomenon and their applications in various fields of photonics. We provide a detailed study on the history of GMR structures, its resonance condition, properties and applications etc. Importantly, we will focus on the study of GMR structure under conical diffraction regime and derive the resonance condition under this conical mount. Based on this method, various photonic applications like wide wavelength range tunable filter, high angular tolerance dual wavelength filter etc. have been discussed. In addition to that, we will discuss about phase measurement of GMR signal in a laser tuned Mach Zhender Interferometer setup. Based on this phase measurement, an ultra-high sensitive refractive index senor has been proposed. A theoretical model to formulate the phase shift has been described. In chapter 3, we discuss about a high sensitive refractive index sensor using phase grating structure. After describing the principle of the working of the proposed sensor we xii

14 will optimize the grating parameters to obtain a good contrast dip in the transmission spectrum which can be tuned following the grating equation. The experimental details of the fabrication and characterization to measure the sensitivity is described. Finally the sensitivity is compared with other grating based refractive index sensors. In chapter 4, we describe about the design and fabrication of 2D periodic and aperiodic array of Si nano pillar (SiNPs) structures for various photonic applications. By incorporating defects in 2D PhCs, an optical diode and a dynamic wavelength division multiplexer (WDM) has been designed on the basis of third order nonlinear (Kerr) effect. The working principle of the designed structures and the corresponding results has been described. In addition to that, this chapter also demonstrates about stand alone transmission RGB color filters based on deterministically aperiodic SiNPs assembly embedded in a flexible PDMS host matrix. We will discuss about the technology development, design, electromagnetic simulations and optical characterization of the color filters. Chapter 5 reports about a new light trapping technique to simultaneously reduce reflection loss, as well as for light focusing at submicron scales for solar cell and image sensing applications. The details of the fabrication of these ZnO nanofunnels on Si substrate by hydrothermal growth process have been described. The mechanism of light trapping is explained which is basically the simultaneous effect of funneling effect due to the geometrical funnel shape and convergence of light due to GRIN lens effect. Then we will analyze the behavior of the measured reflectivity spectrum with the change in periodicity and compared xiii

15 the result with FDTD simulation. Finally we will discuss about the optimization parameters to minimize the reflectivity. Finally chapter 6 sums up the research work reported in the above chapters and presents the important conclusions of the thesis. The scope of future work in the area of guided mode resonance structure and biosensors have been discussed. The relevance of silicon nano structures in the field of solar cell (/photo voltaic) and image sensors have been summarized. The future scope of our RGB color filter in the field of image sensors has been discussed and summarized. The future possibility of investigations of the ZnO funnels for various applications has been mentioned. xiv

16 Contents List of figures xx List of tables xxx 1 Introduction Photonic bandgap Different photonic crystal structures Defects in photonic crystals Different ways of light manipulation in PhCs for various applications PhC based biosensor PhC based wavelength/color filter PhC fiber/waveguide PhC cavity based lasers PhC in all-optical circuits PhC as efficient light trappers and antireflection coating in solar or photovoltaic cells A different way of light manipulation in PhC slab: the guided mode resonance phenomenon Motivation and objective of thesis 24 xv

17 2 Guided mode resonance structures and their applications Historical Overview Principle of Guided mode resonance Resonance condition and Eigen value equation to find the GMR position Regions of GMR Effect of grating refractive index Effect of grating fill factor Effect of grating height Effect of polarization Guided Mode Resonance structure under conical diffraction Conical diffraction from a grating Guided mode resonance condition under conical diffraction Tunable Guided mode resonance filter Principle of operation Results and discussion Experiment Tunable guided mode resonance dual wavelength filter Principle of operation Experiment 51 xvi

18 2.5.3 Design considerations for dual wavelength filter in C-band Angular tolerance of the filter High sensitivity GMR optical sensor employing phase detection Theory and principle Experiment Results and Discussion Conclusion 76 3 High sensitivity refractive index sensor based on diffraction from phase gratings Introduction Theory and principle Experiment Results & discussion Conclusion 89 4 Silicon nanophotonic structures and their applications Introduction Optical diode using nonlinear polystyrene ring resonators in twodimensional silicon photonic crystal structure Proposed Structure of the PhC diode Principle of diode operation 96 xvii

19 4.2.3 Results and discussion Optically controlled wavelength division multiplexer using nonlinear asymmetric cavity in 2d photonic crystal Proposed Structure of WDM Principle of operation Results & discussion Nanopillar assemblies with correlated disorder for color filtering Proposed design of the color filter Design procedure for generating correlated disordered nanopillar assemblies Fabrication procedures Measurement and characterization Explanation of the phenomenon involved in the transmission /reflection spectrum Incident angle and polarization dependency Transverse light localization & focusing effect Scalability Comparison with periodic lattice case Conclusion 133 xviii

20 5 ZnO nanowire-enabled funneling effect for antireflection and light convergence applications Introduction Hydrothermal growth of ZnO funnels on patterned Si substrate Measurement and analysis of the reflection spectrum Optimization of funnel parameters to minimize reflectivity Conclusion Conclusion and future scope Important conclusions of the thesis Scope for future study 151 References 153 Appendix A: FDTD simulation method 166 Appendix B: Measurement of reflection and transmission spectrum by Perkin Elmer spectrometer 168 List of Publications 170 Author s Biography 172 xix

21 List of Figures Figure No. Figure Caption Page No. 1.1 At each interface of a 1D PhC, some part of the incident wave gets reflected and the other part is transmitted. These reflected parts interfere & form the bandgap wavelength Two types of distribution of energy at the zone boundary of the PhC which leads to the formation of band gap. One mode centers its maxima at high dielectric constant region and the other at low dielectric constant region Schematic diagram of 1D PhC with alternating layers of materials with different dielectric constants ε1 & ε2, with a spatial period a. We imagine that each layer is uniform and extends to infinity along the x and y directions. The periodicity is along the z direction Dispersion curve for 1D PhC for on-axis propagation, computed for three different cases of multilayer films, where each layer has a width 0.5a. Left: every layer has the same dielectric constant of = 13. Centre: the two layers alternate between of 13 and 12. Right: layers alternate between of 13 and Schematic diagram of 2D PhCs. (a) Square lattice of dielectric rods in air (b) Hexagonal lattice of air holes in a dielectric material. The dielectric constant of the material & air in both (a) & (b) is taken as 1 and 2 respectively. The height of the rods in (a) and the thickness of the slab in (b) are considered to be infinitely long Fabricated (a) AFM image of periodic dielectric waveguide in the form of 1D grating & (b) SEM image PhC slab that contains hexagonal air holes in a photoresist layer. Both have finite thickness in the vertical (z) direction. 9 xx

22 1.7 Simulated band diagram for PhC slab. (a) For a slab suspended in air without any substrate where the guided modes can be distinguished as even & odd modes, (b) for a slab placed on a substrate where the light cone is the union of the two light cones corresponding to air and substrate. The guided modes in this case cannot be classified as even and odd, hence there is no band gap for this structure (a) SEM image of 3D inverse opals & (b) simulated band diagram of inverse opals, showing both the complete band gap as well as the stop gap Point defect in 2D PhC (a) square lattice & (b) hexagonal lattice, with corresponding electric field profiles and band diagrams showing defect state in the bandgap Line defect in 2D PhC (a) square lattice & (b) hexagonal lattice, with corresponding electric field profiles and band diagrams showing defect state in the bandgap Spectral responsivities of the L, M, and S cones in human eyes General schematic diagram of a guided mode resonance structure consisting a subwavelength grating layer on top of a planar waveguide layer on a substrate Diffraction phenomenon in a grating showing the diffracted orders propagating in both reflection (cover) and transmission medium (substrate) Boundary conditions for the two polarizations of the electric field that decides the average refractive index of the grating layer The diffracted light that propagates in the waveguide, has a certain roundtrip phase that includes the phase associated with the Fresnel reflection at the two interfaces of the waveguide, the phase accumulated due to optical path travelled and the phase change of π 2 due to 32 diffraction. 2.5 Definition of TE & TM guided mode: For the TE component, the electric field of the diffracted light lies on the interface plane (XY-plane) of grating and waveguide and similarly for the TM component magnetic field lies on the interface plane. 35 xxi

23 2.6 At resonance, the propagation constant (β m ) of the guided wave is equal to the x-component (k x,m ) of diffracted light Effect of refractive index of the grating material on the GMR peak that shows an increase in the FWHM with the refractive index Effect of grating duty cycle on the GMR peak that shows a maximum FWHM for 50% duty cycle and gradually decreasing FWHM towards higher and lower duty cycle Effect of grating height on the GMR peak that shows an increase in the contrast of the GMR peak w.r.t. its sidebands Effect of light polarization on the GMR peak that shows two distinct GMR peaks corresponding to the two polarizations TE & TM Conical diffraction from a grating showing the diffracted orders lying on the surface of a cone such that their Y-components are equal to each other and also equal to the Y-component of the incident light vector GMR structure under conical mounting. (a) Perspective view showing the guided wave, which is the diffracted light having both the θ m & m components, (b) top view of the structure showing the longitudinal component (k ρ,m ) of the diffracted light that is equal to the propagation constant (β m ) of the guided mode and (c) side view showing the z- component of the diffracted light GMR peak position Vs. Azimuthal angle for the TE mode: The azimuthal angle is increased from 0 o to 90 o in steps of 10 o GMR peak position vs. Azimuthal angle for the TM mode: The azimuthal angle is increased from 0 o to 90 o in steps of 10 o Simulated GMR peak positions at different azimuthal angles for the TE mode Comparison between experiment and theory for the TE mode Comparison between experiment and theory for the TM mode. 49 xxii

24 2.18 Characterization of the fabricated GMR structure (a) Photograph of the GMR structure (b) AFM topography of the GMR structure (c) AFM measurements show grating depth to be 120 nm Schematic diagram of the experimental set up for azimuthal rotation of the sample Experimental GMR peak positions vs. azimuthal angle for different incident angle (θ) values for the TE mode Possible (θ ) pairs corresponding to 1550nm, for a GMR structure with Λ = 900 nm and d= 150 nm. The green circles are the (θ ) values corresponding to the GMR position at 1550nm Two independent paths in θ- space for 1310nm and 1550nm. (a) When the two paths don t intersect with each other, there is no common solution. (b) When they intersect with each other, the intersection point gives the angular coordinate at which dual filtering is possible at 1310nm &1550nm Simultaneous solutions for 1310nm & 1550nm with all the possible (a) θ and (b) values Transmission spectra for the dual wavelength filters corresponding to different grating period and waveguide thickness. These GMR parameters take only the allowed angular coordinates ( ) as shown in Fig All the above GMR filters produce two GMR peaks at 1310nm and 1550nm Tolerance regions in space for 1310nm & 1550nm. The two blue lines are for 1310nm and the red lines are for 1550nm. The intersection of these four lines gives an area indicated by red color patch which decides the angular tolerances Angular tolerance around 1310nm & 1550nm for different Λ and d values (a) tolerance in angle of incidence ( ) & (b) tolerance in azimuthal angle ( ) Solid angle tolerance (ΔΩ) plotted as a function of waveguide thickness (d) and grating period (Λ). 60 xxiii

25 2.28 When the four curves are parallel with each other, they form a larger intersection area at the intersection point. This leads to a higher tolerance in θ- space. Since the four curves are also almost parallel to the -axis, they provide higher azimuthal angle tolerance GMR peaks at 1310nm & 1550nm corresponding to the sharpest peak (yellow color peak in Fig. 2.27). This shows that the two GMR peaks are insensitive to the rotation of the GMR device from 20 o to 40 o. Thus it can act as azimuthal angle tolerant dual wavelength filter with a wavelength tolerance of 2nm around the two GMR peak values GMR structure explaining phase detection. The change in the phase (Φ r ) of the resultant complex wave (E r) is measured in response to surrounding RI change Experimental set up of Mach-Zehnder Interferometer to measure the phase shift of the GMR signal Schematic diagram of the 3D printed cuvette holder with perforated wall inside the chamber Image of the experimental set up Measurement of refractive index of sugar solution by Abbe refractometer Images of fringe pattern for different values of phase shift. The first pattern is when there is no change in phase. For the case of a finite phase shift, the shifted and the initial fringe pattern are indicated by green and red color (false color) respectively. The small white color arrow shows the direction of shift Plot of phase shift ( Φ) vs. RI change ( n) of the sensing medium for the GMR as well as non GMR signal. For the GMR signal both the numerically calculated (blue curve) and experimentally obtained (red) curve are shown, whereas for the non-gmr signal only the experimental curve (green curve that lies almost along the horizontal axis) is shown Phase curve of the GMR signal showing a rapid change in the phase value at the resonance peak wavelength of 632.8nm. Both amplitude reflectance and phase curves are shown. 75 xxiv

26 3.1 Diffraction from a phase grating when light is incident normally (θ = 0 o ) and the grating period is chosen such that the 1 st order diffracted light travels at an angle 90 o to the 0 th order transmitted light Transmission dip at 1550nm is obtained due to the destructive interference between T0 & D Sketch of the optimized structure: Si3N4 grating of height 250nm & period 1165nm over a planar Si waveguide of thickness 200nm on glass 82 substrate. 3.4 Transmission spectrum (green line) showing dip at 1550nm is obtained due to destructive interference between T0 & D2. The corresponding peak in the reflection spectrum (red line) is also shown in that figure Electric field profile plotted at three different wavelengths. In (a) at 1550nm, there is destructive interference between T0 & D2 in the cover region. (b) At 800nm, light is diffracted into the cover region. (c) At 1600nm, there is no diffraction, only 0th order propagates into the cover region AFM image of the fabricated grating. (a) Large area view, (b) data showing grating height 250 nm and period 1165 nm, (c) perspective view, (d) top view (a) Schematic diagram of the experimental set up to measure transmission spectrum of the sensor, (b) Actual image of the experimental set up Shift in the transmission dip due change in the refractive index of cover region: (a) Experiment, (b) Simulation Optical diode consists of two PhC ring resonators R1, R2 and two PhC wave guides below and above the two resonators. Forward & backward propagation directions are shown by arrow signs Band-diagram of 2D square lattice (inset) of cylindrical Si rods with radius 0.185a Transmission at point A in linear case for (a) Forward transmission & (b) Backward transmission. 96 xxv

27 4.4 Transmission in linear case is independent of propagation direction, because the dips for both the cases are at same frequency of (a), (b), (c) shows field propagation in forward direction. In linear case (a), a very negligible power reaches at port2, whereas in the nonlinear case (b, c) the power at port2 increases with increasing input power at port1. Similarly, (d), (e), (f) shows the field propagation in backward direction, where much lesser power reaches to port1, with increasing input power at port Forward and backward transmission spectra, where the dotted & solid lines correspond to linear and nonlinear case respectively. (a) As intensity increases the curve shifts towards left so output power at increases indicated by vertical arrows, (b) there is no shift of the curve with increase intensity so the dip is always at The thicker solid curves indicate more intense input light Variation of transmittance with input power for forward and backward propagation which is similar to the characteristics of a diode. The horizontal nature of the curve in low power region is clearly visible in the magnified image as shown in the inset Proposed structure of the WDM with empty coupler region Band-diagram of 2D square lattice of cylindrical Si rods with radius 0.18a Transmittance of the left cavity with empty coupler region comes out to be only WDM with randomly arranged Si rods in the coupler region. This increases the coupling efficiency by reducing the amount of input light getting reflected from the wall below the cavities due to photonic band gap Transmittance from output 1 and output 2 of the WDM shown in Fig (a) Schematic diagram of the color filter, with the Si NPs embedded in PDMS, (b) 2D pattern of the aperiodically arranged Si nanopillars Conceptual schematic diagram of the NP RGB color filters, applicable for CMOS image sensors. 112 xxvi

28 4.15 Text to ASCII converter to import coordinates to the Raith software (a) Schematic diagram of the fabrication steps of the Si NP on SI substrate. (b) Different samples after Si-etching by ICP. Each sample contains Si nanopillars on Si substrate with varying pillar diameters (a) Schematic diagram of the process of embedding Si nanopillars inside PDMS layer. (b) Image of the samples inside liquid PDMS before heating, (c) The PDMS containing samples are heated on a hot plate to make it hard, (d) Final image of a sample where Si NPs are embedded inside PDMS block after being peeled off from the Si substrate Undercut at the base of the Si nano pillars for easy peeling off from the substrate Tilted SEM images of the aperiodic silicon nanopillars array of height 1300nm for (a) Red (D=200nm), (b) Green (D=140nm) & (c) Blue (D=100nm) color 117 filters Camera captured image of the transmitted colors generated by the red, green & blue color filters, kept on a glass slide and illuminated from top by a white light source (LED torch light) Measured transmission spectra (denoted as T-) & reflection spectrum (denoted as R-) of the three R, G & B color filters. The measured wavelength range is kept at 350nm-800nm CIE (1991) color coordinates and gamut of our fabricated RGB color filters Simulated E-field intensity in the XZ cross-section of the green filter, whose transmission spectrum is shown in Fig. 4.21: (a) 1 st dip at 465nm (b) Peak at 525nm (c) 2 nd dip at 665nm. (The color scale bar shows the value of the E-field intensity in arbitrary unit) Various color filters kept on a glass slide and the images of the corresponding transmitted colors (violet to red) is captured by a camera on a white paper Plot of wavelength vs. diameter, for different colors corresponding to (a) the first dip position & (b) the second dip position. The wavelength in the vertical axis is the wavelength (nm) in Si. 123 xxvii

29 4.26 (a) Experimentally obtained transmission spectra of the original and the expanded (in toluene) green filter. (b) Simulated transmission spectra for the expansion and compression of the green filter Experimental transmission spectra for: (a) different incidence angles and (b) different polarization angles (a) NP filter patterns for different degrees of correlated disorders in the transverse cross sections. (b) The respective (simulated) electric field intensities at the bottom of the filters. The color scale bar represents E-field intensity in arbitrary unit (a) Schematic diagram of the RGB Bayer arrangement of our filter. (b) Corresponding simulated transmission spectra for RGB color filters of area 2.2 *2.2 µm 2 (c) Power profile of our RGB filter in Bayer arrangement at different peak wavelengths corresponding to different colors Transmission (simulated) spectra of the green filter, with different pixel areas Transmission spectra for the green color filter for two different incident angles (0 o & 30 o ) for filters with aperiodic and hexagonal periodic pillar arrangement Schematic diagram of the patterned PR mask on ZnO seed layer on Si substrate The patterned samples are placed in a glass wire (a) horizontally with the ZnO seeded surface either facing down or (b) slanted with the seeded surface facing inward the wall (a) Before the chemical reaction, the solution was transparent. (b) After some time the solution turns to milkish white color SEM images of the fabricated ZnO funnels on Si substrate. (a) sample-1; period=3000nm, hole D=1250nm, height=1450nm, (b) sample-2; period=2000nm, hole D=1000nm, height=1650nm & (c) sample-3; period=1500nm, hole D=850nm, height=1000nm Measured reflection spectra of the three samples compared with that of the bare Si surface. 140 xxviii

30 5.6 (a) Schematic diagram of the simulation model of the ZnO funnels generated through FDTD solutions. (b) Effective refractive index profile along the vertical cross-section of a single ZnO funnel unit Simulated reflection spectra of the three samples compared with that of the bare Si surface E-field profiles in ZnO-funnels for different wavelengths (a) < 368nm, (b) nm, (c) > 700nm XY cross section at 1100nm showing confinement of field at the base of the funnel Normal incidence (0 o ) reflection spectrum of the optimized structure showing average reflectivity of 3% and the maximum reflectivity at any wavelength is 7% Simulated reflection spectra of optimized structure: (a) Angle dependency; at 0 o, 30 o & 60 o and (b) Polarization dependency (0 o, 45 o & o ) Calculated effective RI at cross-sections of an individual ZnO funnel unit along the vertical direction (Z) (a) for the optimized structure and (b) when the funnels overlap with each other at the top. 147 A.1 The Yee Cell in FDTD method. 166 B.1 Schematic diagram of the spectrophotometer setup for transmission and reflection measurement. 168 xxix

31 List of Tables Table No. Table Title Page No. 2.1 Experimentally measured phase change with respect to RI change for both GMR & non-gmr position Resonant frequencies & Q factors of the two resonators Dependency of the dip positions on the pillar diameter of the fabricated NP color filters. 121 xxx