LIGHT MANIPULATION IN PHOTONIC CRYSTAL STRUCTURES AND THEIR APPLICATIONS

PANKAJ KUMAR SAHOO

DEPARTMENT OF PHYSICS INDIAN INSTITUTE OF TECHNOLOGY DELHI

OCTOBER 2017

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

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

Dedicated to my Parents

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 - 110016

October, 2017

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

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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.

vii

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)

viii

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

ix

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 1st order diffracted

light travels at a diffraction angle of 90o with respect to the 0th order. The diffracted light

which is along the direction of periodicity can further get diffracted from the grating and

interfere with the 0th 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 300-1200nm with

possibility of confining incident light to few hundreds of nanometers.

x

सार

यह पीएच.डी. थीसिि सिसिन्न फोटोसनक अनपु्रयोगों के सिए फोटोसनक सिस्टि िंरचनाओ ंके सडजाइन, सनर्ााण और उपयोग िे िंबंसित

ह।ै र्िूतः एक और दो डायमेंशनल, पररयोसडक और िाथ ही अपररयोसडक फोटोसनक सिस्टि िंरचनाओ ंका उपयोग थीिीि र्ें सकया

गया ह।ै

१ डी फोटोसनक सिस्टि के बीच, १ डी गे्रट िंग्स वाले गाइडेड मोड रेजोनेंस (जी.एम.आर.) सिंरचनाओ िं पर टववरण टिया

गया ह।ै जी.एम.आर. पीक और उसके गणुों को प्राप्त करन ेके टलए रेजोनेंस की टथिटि पर चचाा हुई ह।ै जी.एम.आर. टडवाइस के

अजीमिुल रो ेशन द्वारा जी.एम.आर. पीक को ्यनू करन ेके टलए हमन ेएक नई टवटि प्रथिाटवि की ह।ै अजीमिुल रो ेशन में गे्रट िंग

के कोटनकल टडफै्रक्शन को ध्यान में रखा जािा ह ैजो क्लाटसकल टडफै्रक्शन मामले की िुलना में अलग रेजोनेंस की टथिटि दतेा ह।ै इस

टसद्ािंि के आिार पर हमन ेअत्यटिक ्यनू करन ेयोग्य वेवलेंि ट़िल् र का प्रथिाव टकया ह ैजो टक टवटिबल से एनआईआर थपेक्रम

के ६०० एन.एम. की ्यटूनिंग सीमा को किर करता ह।ै हमन ेएक ड्यलू वेवलेंि ट़िल् र टडजाइन करनेके टलए टडजाइन प्रटिया टवकटसि

की ह ैज्योंटक िो जी.एम.आर. पीक वेवलेंि पर पणूा टनयिंत्रण रखिा ह।ै इस टडजाइन प्रटिया के आिार पर, हमन े२० टडग्री के उच्च

एटिमिुल कोण ॉलरेंस के साि सी-बैंड वेवलेंि, १३१०एन.एम. और १५५०एन.एम. के टलए िोहरी वेवलेंि ट़िल् र को टवकटसि

टकया ह।ै इन टिल् र अनपु्रयोगों के अलावा, हमन ेएक लेजर ्यनू्ड मॉक जेंडर इिं रिेरोमी र का उपयोग करि ेहुए जी.एम.आर. वेवलेंि

के िेज के माप के आिार पर ऑटट कल सेंसर टवकटसि टकया ह।ै जी.एम.आर. टसग्नल को टसमोस कैमरा पर टफ्रिं ज पै ना बनान ेके

टलए एक ररिरेन्स टसग्नल के साि इिं रिेरे टकया जािा ह ैऔर िेज को मापन ेके टलए आगे का टवशे्लषण टकया जािा ह।ै टवटिन्न िरल

और गैसीय मीटडया के रेफे्रटक् वे इिंडेक्स में सबसे कम सिंिव पररविानों का पिा लगाना हमारी थिापना का उद्दशे्य ह।ै हमारे से अप के

साि, हमन े३.४ x १०-७ आर.आई.य.ु का एक न्यनूिम रेफे्रटक् व ेइिंडेक्स पररविान प्राप्त टकया, टजसमें प्रटि १०-४ आर.आई. पररविान

के टलए ०.६०८π िेज पररविान की सिंवेिनशीलिा प्राप्त होिा ह,ै ज्योंटक अन्य िेज आिाररि जी.एम.आर. सेंसर से ज्यािा ह।ै हमन े

xi

एक सैद्ािंटिक मॉडल का प्रथिाव टकया ह ैजो प्रयोगात्मक पररणामों के साि अच्छे समझौिे में जी.एम.आर. टसग्नल के िेज बिलाव

की सिंख्यात्मक गणना करिा ह।ै

जी.एम.आर. सेंसर के अटिररक्त, हम १ डी िेज गे्रट िंग के उपयोग से रेफे्रटक् वे इिंडेक्स सेंसर के टलए एक और िकनीक

पेश करिे हैं। गे्रट िंग्स के मानििंड ऐसे हैं, की िथ ा आडार टडफे्रक् ेड लाइ िेरोि ऑडार के िंबंि र्ें ९० सडग्री के टडफै्रक्शन कोण पर

प्रोपगेे करिाह।ै यह टडफे्रक् ेड लाइ जो पेररओडीसी ी की सदशा र्ें ह,ै िह गे्रट िंग िे िबुारा टडफे्रक् हो िकता ह ैऔर िरेोि ऑडार

िाइट के िाथ इिं रिेरे कर िकता ह।ै इि पररसस्थसत र्ें, दो इिं रिेररिंग बीर् के बीच उगन ेिािे π िेज अतंर के पररणार् से एक ट्ांिसर्शन

डीप टमलिा ह।ै हर् गे्रट िंग िर्ीकरण के अनिुार इि डीप वेवलेंि को ्यनू करिेहैं हैं और गे्रट िंग की पीररयड के िर् की िंिेदनशीिता

प्राप्त क करते हैं।

२ डी पेररओडीसी ी के बीच, हमने टसटलकॉन टपल्लसा के पीररयाटडक और ऐटपरोटडक सरणी िोनों का अध्ययन

टकया ह।ै हमन े२ डी टसटलकॉन टपल्लसा के थक्वायर लैट स का इथिेमाल टकया ह ैऔर इि र्ें टडिेक् ्स बनाके ऑटट कल सटका में

इथिेमाल होन ेके टलए ऑटट कल डायोड और वेवलेंि टडवीिन मल् ीटलेक्सर को टडजाइन टकय ेहैं । हर्ने पी.डी.एर्.एि. र्ें एम्बेडेड

टसटलकॉन नैनोसपल्िार के ऐपररयोसडक अिेंबिी पर आिाररत कलर सफल्टर प्रस्तासित सकए हैं। प्रस्तासित सफल्टर के सनर्ााण और िक्षण

िणान के सििरण पर चचाा की गई ह।ै इर्ेज िेंिर और सडस््िे ए्िीकेशन के सिए, कलर सफल्टर की ट्ांिसर्शन स्पेक्ट्ट्ा, औद्योसगक

आिश्यकता के िाथ अच्छे िर्झौते र्ें हैं। अतं र्ें हर् सोलर सेल र्ें ररफ्लेक्शन लोथस को कर् करन ेके सिए और लाइ को सब-

माइिोन थकेल में कें सित करन ेके सिए एक नई लाइ रैटपिंग की तकनीक पेश करेंगे। हर्ने टसटलकॉन िब्िटे्ट पर टििंक ऑक्साइड-फ़नि

की हके्ट्िागोनि िरसणयां िैटिके े की हैं, जो एक हयड्रोिेरमाल ग्रोि प्रसिया र्ें टििंक ऑक्साइड नैनोवायसा के प नाड ग्रोि िे बनाय ेगए

हैं। इन ़िनलों का लाइ रैटपिंग एिंड कन्वजेन्स के रूप में काम करन ेवाला टसद्ािंि एक ग्रीन लेंस के समान ह।ै ऑटट माइज्ड सिंरचना में

३००-१२०० एन.एम. की वेवलेंि सीमा में ३% के करीब औसि रेफ्लेटक् टव ी पाया गैया ह,ै ज्योंटक कुछ सैकडों नैनोमी र की थकेल

में लाइ को सीटमि करन ेकी सिंिावना रखिा ह।ै

xii

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

xiii

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

xiv

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.

xv

Contents

List of figures xx

List of tables xxx

1 Introduction 1

1.1 Photonic bandgap 1

1.2 Different photonic crystal structures 5

1.3 Defects in photonic crystals 12

1.4 Different ways of light manipulation in PhCs for various applications 15

1.4.1 PhC based biosensor 15

1.4.2 PhC based wavelength/color filter 17

1.4.3 PhC fiber/waveguide 19

1.4.4 PhC cavity based lasers 20

1.4.5 PhC in all-optical circuits 21

1.4.6 PhC as efficient light trappers and antireflection coating in solar or

photovoltaic cells 22

1.4.7 A different way of light manipulation in PhC slab: the guided mode

resonance phenomenon 23

1.5 Motivation and objective of thesis 24

xvi

2 Guided mode resonance structures and their applications 26

2.1 Historical Overview 26

2.2 Principle of Guided mode resonance 28

2.2.1 Resonance condition and Eigen value equation to find the GMR

position 32

2.2.2 Regions of GMR 36

2.2.3 Effect of grating refractive index 37

2.2.4 Effect of grating fill factor 37

2.2.5 Effect of grating height 38

2.2.6 Effect of polarization 40

2.3 Guided Mode Resonance structure under conical diffraction 41

2.3.1 Conical diffraction from a grating 41

2.3.2 Guided mode resonance condition under conical diffraction 42

2.4 Tunable Guided mode resonance filter 44

2.4.1 Principle of operation 45

2.4.2 Results and discussion 45

2.4.3 Experiment 48

2.5 Tunable guided mode resonance dual wavelength filter 49

2.5.1 Principle of operation 50

2.5.2 Experiment 51

xvii

2.5.3 Design considerations for dual wavelength filter in C-band 53

2.5.4 Angular tolerance of the filter 58

2.6 High sensitivity GMR optical sensor employing phase detection 63

2.6.1 Theory and principle 64

2.6.2 Experiment 67

2.6.3 Results and Discussion 72

2.6.4 Conclusion 76

3 High sensitivity refractive index sensor based on diffraction from phase

gratings 78

3.1 Introduction 78

3.2 Theory and principle 79

3.3 Experiment 85

3.4 Results & discussion 87

3.5 Conclusion 89

4 Silicon nanophotonic structures and their applications 90

4.1 Introduction 90

4.2 Optical diode using nonlinear polystyrene ring resonators in two-

dimensional silicon photonic crystal structure 92

4.2.1 Proposed Structure of the PhC diode 93

4.2.2 Principle of diode operation 96

xviii

4.2.3 Results and discussion 102

4.3 Optically controlled wavelength division multiplexer using nonlinear

asymmetric cavity in 2d photonic crystal 104

4.3.1 Proposed Structure of WDM 104

4.3.2 Principle of operation 106

4.3.3 Results & discussion 108

4.4 Nanopillar assemblies with correlated disorder for color filtering 109

4.4.1 Proposed design of the color filter 111

4.4.2 Design procedure for generating correlated disordered nanopillar

assemblies 112

4.4.3 Fabrication procedures 114

4.4.4 Measurement and characterization 117

4.4.50Explanation of the phenomenon involved in the transmission

/reflection spectrum 120

4.4.6 Incident angle and polarization dependency 125

4.4.7 Transverse light localization & focusing effect 127

4.4.8 Scalability 130

4.4.9 Comparison with periodic lattice case 132

4.4.10 Conclusion 133

xix

5 ZnO nanowire-enabled funneling effect for antireflection and light

convergence applications 134

5.1 Introduction 134

5.2 Hydrothermal growth of ZnO funnels on patterned Si substrate 136

5.3 Measurement and analysis of the reflection spectrum 139

5.4 Optimization of funnel parameters to minimize reflectivity 144

5.5 Conclusion 148

6 Conclusion and future scope 149

6.1 Important conclusions of the thesis 149

6.2 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

xx

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. 2

1.2 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. 4

1.3 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. 5

1.4 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 1. 6

1.5 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. 7

1.6 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

xxi

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. 10

1.8 (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. 12

1.9 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. 13

1.10 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. 14

1.11 Spectral responsivities of the L, M, and S cones in human eyes. 19

2.1 General schematic diagram of a guided mode resonance structure

consisting a subwavelength grating layer on top of a planar waveguide

layer on a substrate. 28

2.2 Diffraction phenomenon in a grating showing the diffracted orders

propagating in both reflection (cover) and transmission medium

(substrate). 29

2.3 Boundary conditions for the two polarizations of the electric field that

decides the average refractive index of the grating layer. 31

2.4 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

diffraction.

32

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

xxii

2.6 At resonance, the propagation constant (𝛽𝑚) of the guided wave is equal

to the x-component (𝑘𝑥,𝑚) of diffracted light. 36

2.7 Effect of refractive index of the grating material on the GMR peak that

shows an increase in the FWHM with the refractive index. 37

2.8 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. 38

2.9 Effect of grating height on the GMR peak that shows an increase in the

contrast of the GMR peak w.r.t. its sidebands. 39

2.10 Effect of light polarization on the GMR peak that shows two distinct GMR

peaks corresponding to the two polarizations TE & TM. 40

2.11 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. 41

2.12 GMR structure under conical mounting. (a) Perspective view showing the

guided wave, which is the diffracted light having both the 𝜃𝑚 & m

components, (b) top view of the structure showing the longitudinal

component (𝑘𝜌,𝑚) of the diffracted light that is equal to the propagation

constant (𝛽𝑚) of the guided mode and (c) side view showing the z-

component of the diffracted light. 43

2.13 GMR peak position Vs. Azimuthal angle for the TE mode: The azimuthal

angle is increased from 0o to 90o in steps of 10o. 46

2.14 GMR peak position vs. Azimuthal angle for the TM mode: The azimuthal

angle is increased from 0o to 90o in steps of 10o. 46

2.15 Simulated GMR peak positions at different azimuthal angles for the TE

mode. 48

2.16 Comparison between experiment and theory for the TE mode. 48

2.17 Comparison between experiment and theory for the TM mode. 49

xxiii

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. 51

2.19 Schematic diagram of the experimental set up for azimuthal rotation of

the sample. 52

2.20 Experimental GMR peak positions vs. azimuthal angle for different

incident angle (𝜃) values for the TE mode. 53

2.21 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. 54

2.22 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.

55

2.23 Simultaneous solutions for 1310nm & 1550nm with all the possible (a) 𝜃

and (b) values. 56

2.24 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. 2.23. All

the above GMR filters produce two GMR peaks at 1310nm and 1550nm. 57

2.25 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. 58

2.26 Angular tolerance around 1310nm & 1550nm for different Λ and d values

(a) tolerance in angle of incidence (∆) & (b) tolerance in azimuthal angle

(∆). 59

2.27 Solid angle tolerance (ΔΩ) plotted as a function of waveguide thickness

(d) and grating period (Λ). 60

xxiv

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. 61

2.29 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 20o to 40o. Thus it can

act as azimuthal angle tolerant dual wavelength filter with a wavelength

tolerance of 2nm around the two GMR peak values. 62

2.30 GMR structure explaining phase detection. The change in the phase (Φ𝑟)

of the resultant complex wave (�̃�𝑟) is measured in response to

surrounding RI change. 65

2.31 Experimental set up of Mach-Zehnder Interferometer to measure the

phase shift of the GMR signal. 67

2.32 Schematic diagram of the 3D printed cuvette holder with perforated wall

inside the chamber. 69

2.33 Image of the experimental set up. 70

2.34 Measurement of refractive index of sugar solution by Abbe refractometer. 71

2.35 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. 72

2.36 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. 73

2.37 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

xxv

3.1 Diffraction from a phase grating when light is incident normally (𝜃 = 0𝑜)

and the grating period is chosen such that the 1st order diffracted light

travels at an angle 90o to the 0th order transmitted light. 79

3.2 Transmission dip at 1550nm is obtained due to the destructive

interference between T0 & D2. 81

3.3 Sketch of the optimized structure: Si3N4 grating of height 250nm & period

1165nm over a planar Si waveguide of thickness 200nm on glass

substrate.

82

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. 83

3.5 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. 84

3.6 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. 85

3.7 (a) Schematic diagram of the experimental set up to measure

transmission spectrum of the sensor, (b) Actual image of the experimental

set up. 86

3.8 Shift in the transmission dip due change in the refractive index of cover

region: (a) Experiment, (b) Simulation. 88

4.1 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. 94

4.2 Band-diagram of 2D square lattice (inset) of cylindrical Si rods with

radius 0.185a. 95

4.3 Transmission at point A in linear case for (a) Forward transmission & (b)

Backward transmission. 96

xxvi

4.4 Transmission in linear case is independent of propagation direction,

because the dips for both the cases are at same frequency of 0.3211. 98

4.5 (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 port2. 99

4.6 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 0.3211

increases indicated by vertical arrows, (b) there is no shift of the curve

with increase intensity so the dip is always at 0.3211. The thicker solid

curves indicate more intense input light. 101

4.7 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. 102

4.8 Proposed structure of the WDM with empty coupler region. 105

4.9 Band-diagram of 2D square lattice of cylindrical Si rods with radius 0.18a. 105

4.10 Transmittance of the left cavity with empty coupler region comes out to

be only 0.4. 106

4.11 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. 107

4.12 Transmittance from output 1 and output 2 of the WDM shown in Fig. 4.11. 108

4.13 (a) Schematic diagram of the color filter, with the Si NPs embedded in PDMS, (b)

2D pattern of the aperiodically arranged Si nanopillars. 111

4.14 Conceptual schematic diagram of the NP RGB color filters, applicable for CMOS

image sensors. 112

xxvii

4.15 Text to ASCII converter to import coordinates to the Raith software. 114

4.16 (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. 115

4.17 (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. 116

4.18 Undercut at the base of the Si nano pillars for easy peeling off from the substrate. 117

4.19 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

filters.

117

4.20 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). 118

4.21 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. 118

4.22 CIE (1991) color coordinates and gamut of our fabricated RGB color filters. 119

4.23 Simulated E-field intensity in the XZ cross-section of the green filter, whose

transmission spectrum is shown in Fig. 4.21: (a) 1st dip at 465nm (b) Peak at

525nm (c) 2nd dip at 665nm. (The color scale bar shows the value of the E-field

intensity in arbitrary unit). 120

4.24 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. 122

4.25 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

xxviii

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. 124

4.27 Experimental transmission spectra for: (a) different incidence angles and

(b) different polarization angles. 126

4.28 (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. 128

4.29 (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 µm2 (c) Power profile of our RGB filter in Bayer arrangement at different

peak wavelengths corresponding to different colors. 130

4.30 Transmission (simulated) spectra of the green filter, with different pixel areas. 131

4.31 Transmission spectra for the green color filter for two different incident angles

(0o & 30o) for filters with aperiodic and hexagonal periodic pillar arrangement. 132

5.1 Schematic diagram of the patterned PR mask on ZnO seed layer on Si

substrate. 137

5.2 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. 138

5.3 (a) Before the chemical reaction, the solution was transparent. (b) After

some time the solution turns to milkish white color. 138

5.4 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. 139

5.5 Measured reflection spectra of the three samples compared with that of

the bare Si surface. 140

xxix

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. 141

5.7 Simulated reflection spectra of the three samples compared with that of

the bare Si surface. 141

5.8 E-field profiles in ZnO-funnels for different wavelengths (a) < 368nm, (b)

400-700nm, (c) > 700nm. 142

5.9 XY cross section at 1100nm showing confinement of field at the base of

the funnel. 143

5.10 Normal incidence (0o) reflection spectrum of the optimized structure

showing average reflectivity of 3% and the maximum reflectivity at any

wavelength is 7%. 145

5.11 Simulated reflection spectra of optimized structure: (a) Angle

dependency; at 0o, 30o & 60o and (b) Polarization dependency (0o, 45o &

90o).

146

5.12 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

xxx

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. 74

4.1 Resonant frequencies & Q – factors of the two resonators. 94

4.2 Dependency of the dip positions on the pillar diameter of the fabricated NP

color filters. 121