DESIGNS OF APPLICATION-SPECIFIC MICROSTRUCTURED OPTICAL FIBERS FOR
MID-IR PHOTONICS
AJANTA BARH
DEPARTMENT OF PHYSICS
INDIAN INSTITUTE OF TECHNOLOGY DELHI
OCTOBER 2015
© Indian Institute of Technology Delhi (IITD), New Delhi, 2015
DESIGNS OF APPLICATION-SPECIFIC MICROSTRUCTURED OPTICAL FIBERS FOR
MID-IR PHOTONICS
by
AJANTA BARH
DEPARTMENT OF PHYSICS
Submitted
in fulfillment of the requirements of the degree of Doctor of Philosophy
to the
INDIAN INSTITUTE OF TECHNOLOGY DELHI
OCTOBER 2015
Dedicated to my parents...
CERTIFICATE
This is to certify that the proposed thesis entitled DESIGNS OF APPLICATION- SPECIFIC MICROSTRUCTURED OPTICAL FIBERS FOR MID-IR PHOTONICS, being submitted by Miss. Ajanta Barh to the Department of Physics, Indian Institute of Technology Delhi, for the award of degree of Doctor of Philosophy, is a record of bonafide research work carried out by her. She has worked under our guidance and supervision and has fulfilled the requirements, which to our knowledge have reached the requisite standard for the submission of the thesis. The results contained in this thesis have not been submitted in part or full to any other University or Institute for the award of any degree or diploma.
Prof. Bishnu P. Pal Prof. R. K. Varshney
Department of Physics Department of Physics
Indian Institute of Technology Delhi Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016 INDIA Hauz Khas, New Delhi-110016 INDIA (Currently at Mahindra Ecole Centrale,
Hyderabad, INDIA)
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Acknowledgments
Fiber optics group (FOG) of the Department of Physics at IIT Delhi is a community, where everyone (students and faculties) maintains a friendly environment and makes life comfortable for others, always. They love science, work passionately, encourage and help each other, so one can easily find the inspiration for their work. Last four and half years, as a Ph. D. student in this vibrating group, has been a very exciting, enjoyable and enriching journey for me, and I find a great satisfaction in accomplishing my goal in the form of this thesis work. Throughout this ride, I have been supported, encouraged and accompanied by many people; and at this finishing line, I wish to express my sincere gratitude to each of them.
First and foremost, I wish to thank my Ph. D. supervisors, Prof. Bishnu P. Pal and Prof. R.
K. Varshney for their constant support, invaluable guidance, ceaseless encouragement, enthusiasm and inspiration throughout my entire doctoral studies at IIT Delhi. Prof. Pal has supported and guided me in every possible way he could. Every single meeting/discussion with him, not only added something new or valuable to my technical research work, but certainly helped me to shape myself as a better human being and a professional researcher.
Moreover, he constantly supervised me on technical writings and taught me how to improve the presentation skills in front of scientific community, how to appreciate the good scientific works of others and help others to build their own. Apart from academics, he was there for me in all sort of problems that I faced throughout. Prof. Varshney helped me with all possible support during the critical handling of various numerical programming and software. Also he helped me making some of my important decisions in course. I am deeply indebted to both of them for the freedom and flexibility they gave me to encourage my independent thinking and nurture new ideas in me.
Being a part of the FOG I feel very much fortunate and wish to convey my gratitude towards faculty members of this group, namely, Prof. K. Thyagarajan, Prof. Anurag Sharma, Prof. M. R. Shenoy, Prof. Arun Kumar, Prof. Ajit Kumar, Prof. B. D. Gupta, and past member Prof. A. K. Ghatak, for their encouragement during various stages of this period. I wish to thank Dr. D. Ranganathan for his encouragement at different stages of my IIT life. I am very much thankful to all the young colleagues, seniors and juniors of FOG, specially,
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Somnath da, Debjani di, Kanchan di, Umesh Sir, Dinesh sir, Akhilesh sir, Sachin sir, Ruchi di, Sarika di, Priya di, Roli, Satyendra, Manoj, Jitender, Babita, Saraswati, Divya, Surajit, Anand, Ramesh, Parvinder, Rana, Sugeet, Pragati, Ranjeet, Harshit, Vivek, Sruthi, Nabarun, Ravikant, Anisha for providing a healthy and fun environment for work in the group. A very special thanks to Somnath da, my senior, who nurtured me during my early Ph. D. days, taught me how to maintain balance between academic and personal life and always motivated me. I started my very first research problem with him. Another special thanks to Deepak, a non-academic member of my lab, for his ever helping hand in any critical issue.
I am fortunate to work with many international bodies during my Ph. D. Thanks to my supervisors and the projects under them such as, UKIERI, NRL-project, THz-project etc. I feel grateful to my Institute for always supporting and allowing me leave whenever necessary. I spent two months in City University London, UK, working under Prof. B. M. A.
Rahman. Special thanks to him for his warm hospitality and cooperation there. I wish to thank Prof. G. P. Agrawal, University of Rochester, USA, with whom I worked on few research problems in collaboration. I would like to thank Prof. I. D. Aggarwal, Dr. J.
Sanghera, Dr. L. B. Shaw from NRL for their support during our NRL related project work. I wish to thank Prof. Ajoy Kar from Heriot-Watt University, UK for inviting me to visit his research labs and arranging 4 days stay there. I wish to thank Dr. Jayanta K. Sahu from ORC, Southampton University, UK for arranging a one day tour to his various research labs there.
I am grateful to my dear friends and colleagues Koena, Sharbari, Pushpsen, Kasi, Soumen, Shahab, Nagesh, Ravi sir, Rajkumar da, Rupesh sir for their continuous support and help.
A very special thanks to Sourav, my best friend, for his continuous support, motivation and encouragement throughout my Ph. D. life especially during my hard times.
Last, but not the least, I would like to thank my family members, parents, grand-parents, brother (Riku) and sister (Ria) for their understanding, endless support and unconditional love.
AJANTA BARH
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Abstract
In recent years, eye safe mid-infrared (mid-IR) spectral range (2 ~ 10 µm) have assumed great importance owing to myriad potential applications ranging from non-destructive medical diagnostics to strategic applications in military/defense. In the present thesis, primary aim is to numerically design few all-fiber mid-IR wavelength specific components such as narrow (N)- and broad (B)-band light sources, high power fiber for large throughput and parabolic pulse generation, filter/sensor etc. by exploiting the versatility of microstructured optical fibers (MOFs). Chalcogenide (Ch) glasses (S-Se-Te) are chosen as base materials for MOFs owing to their characteristic broad transmission window (~ 2 – 12 μm) with low loss (~ 1 dB/m), strong nonlinear (NL) properties, and availability of mature fabrication technologies for such fibers. In this thesis NL parametric process of four wave mixing in the highly NL Ch-glass based MOFs has been extensively exploited by taking commercially available light sources as the pump, and through new fiber designs via tailoring of their zero-dispersion wavelength to match the pump wavelength. Arsenic sulphide (As2S3) and arsenic selenide (As2Se3) glasses are considered as the fiber base materials, whereas, air or thermally compatible borosilicate glass/polymers were assumed to fill the holes of microstructured cladding. As2S3-based MOFs are exploited to design a highly efficient N- band source at ~ 4.36 µm and a B-band source extending over 3 ~ 4.2 µm, covering the second low-loss atmospheric transmission window of earth. On the other hand As2Se3-based MOFs are exploited to design N-band source at ~ 6.45 µm and an ultra B-band source ranging from 5 ~ 6.3 µm, which is extremely utilitarian for medical surgery and molecular spectroscopy. Designs of two Ch-based MOF devices for high power light guidance are also reported. In one case, the novel concept of a microstructured core with uniform cladding was used to design an ultra large mode area fiber operable over 3 – 5 µm wavelength, which is capable of handling extremely high power with effective single mode operation. In the second case, design of a Ch-MOF based suitably up-tapered fiber, which can transform a high power Gaussian pulse to a parabolic pulse with perfectly linear chirp across its temporal profile, is reported. This linear chirp enhances its power carrying capacity by reducing its tendency towards nonlinear optical wave breaking. Going forward we have studied some features of Ch-based photonic band-gap fibers (PBGFs), where both high as well as low
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refractive index contrast MOFs are investigated. Furthermore, all-glass (low contrast) Ch- PBGF has been designed, and studied for the first time temperature (T) dependence of its band-gap for potential application as mid-IR wavelength filter/sensor. Theoretical results indicated that T-sensitivity as high as ~ 140 pm/°C should be feasible.
In parallel to the aforementioned studies, which form the main theme of the present thesis, some additional works were also studied on the emerging topic of silicon (Si) photonics. It is a relatively newer entry in the realm of optics and have a huge potential for integrated optical applications owing to their high transparency (1.1 ~ 7 μm), CMOS fabrication compatibility and suitable linear/nonlinear properties. A directional coupler-based polarization rotator (PR) is reported, which is made of one Si-strip and one Si-slot waveguides, which can rotate both the polarization states depending on its input conditions within a relatively short device length of only 100’s of μm, and it is also reversible in nature. Proposals for two designs of PR, one within the mid-IR range, and the other at the telecom wavelength window of 1.55 μm are made. The Si-slot waveguide is further exploited to design chip-scale trace gas sensor operable at mid-IR fingerprint regime. Since a very high confinement of electric field is achievable in the lower index region of slot waveguide, which can be filled by liquids or gases to significantly enhance the light-matter interaction, sensitivity of such a sensor can be significantly improved. As an example, we have proposed a sensor design, which should be able to efficiently detect hazardous NO2 gas in air down to 10’s of ppm level in just a few mm of the device length.
Contents
Certificate ... i
Acknowledgments ... iii
Abstract ... v
1. Introduction and background study ... 1
1.1 Light guiding via optical fiber ... 1
1.2 Guiding mechanism in standard step index fiber ... 2
1.3 Linear effects in optical fiber ... 4
1.3.1 Fiber losses... 4
1.3.2 Fiber dispersion ... 6
1.4 Nonlinear effects in optical fiber ... 9
1.4.1 Stimulated Raman scattering (SRS)... 10
1.4.2 Stimulated Brillouin scattering (SBS) ... 12
1.4.3 Self-phase modulation (SPM) ... 13
1.4.4 Cross-phase modulation (XPM) ... 14
1.4.5 Four wave mixing (FWM) ... 15
1.5 Introduction to microstructured optical fiber (MOF) ... 17
1.6 Modeling of MOFs ... 18
1.7 Guiding mechanisms in MOFs ... 20
1.7.1 Index guided MOF ... 20
1.7.2 Photonic bang-gap guided MOF ... 21
1.8 Emerging mid–IR photonics ... 23
1.8.1 Primary demands for mid-IR Photonics ... 24
1.8.2 Suitable waveguide materials for mid-IR ... 25
1.9 Organization of the thesis ... 27
2. All-fiber mid-IR narrow-band light source ... 37
2.1 Introduction ... 37
2.2 Routes for new wavelength generation at mid-IR ... 40
2.2.1 Rare earth and transition metal doped lasers ... 40
2.2.2 Semiconductor and quantum cascade lasers ... 41
2.2.3 Nonlinearity tailored mid-IR source generation ... 42
2.3 Theory of four wave mixing (FWM) ... 45
2.4 Modelling of Ch-glass based mid-IR sources ... 49
2.4.1 Mid-IR narrow (N)-band source at 4.36 µm ... 50
2.4.1.1 Proposed fiber design recipe ... 50
2.4.1.2 Wavelength translation via designed MOF ... 53
2.4.1.3 Band-width and signal tunability ... 55
2.4.1.4 Fabrication tolerances ... 57
2.4.2 Mid-IR N-band source at 6.45 µm ... 60
2.4.2.1 Proposed fiber design ... 61
2.4.2.2 Wavelength translation and signal amplification ... 63
2.4.2.3 Fabrication tolerances ... 65
2.5 Summary ... 67
3. Design of all-fiber broad-band light source at mid-IR ... 69
3.1 Introduction ... 69
3.2 FWM based B-band source generation ... 71
3.3 Modelling of Ch-MOF-based B-band sources ... 72
3.3.1 Mid-IR B-band source at 3 ~ 4.2 µm ... 73
3.3.1.1 Proposed design ... 73
3.3.1.2 Wavelength translation under no pump depletion and no loss ... 74
3.3.1.3 Wavelength translation with pump depletion and loss ... 76
3.3.2 Mid-IR B-band source at 5 ~ 6.3 µm ... 78
3.3.2.1 Proposed design ... 78
3.3.2.2 Wavelength translation and generated BW ... 79
3.4 Summary ... 82
4. Temporal parabolic pulse generation for high power light guidance at mid-IR ... 85
4.1 Challenges in high power light propagation ... 85
4.2 Breaking-free parabolic pulses (PPs) ... 87
4.3 Numerical investigation of PP generation in tapered MOF ... 88
4.3.1 Theory of self-similar propagation in normal GVD regime ... 89
4.3.2 Split-step Fourier method (SSFM) to solve NLSE ... 90
4.3.3 Proposed MOF structure for PP generation at mid-IR ... 92
4.3.4 Performance without higher-order GVD and loss ... 94
4.3.4.1 Dispersion and nonlinearity of proposed MOF ... 94
4.3.4.2 Optimization of fiber length ... 95
4.3.4.3 Study of pulse evolution through the UT-MOF ... 96
4.3.5 Effects of higher-order GVD and loss ... 97
4.3.6 Effects of launching parameters ... 100
4.3.6.1 Variation in input peak power (Ppeak) ... 100
4.3.6.2 Variation in input pulse width (τFWHM) ... 102
4.3.6.3 Performance under fixed input pulse energy (Epulse) ... 103
4.3.7 Fabrication tolerance of the proposed UT-MOF ... 105
4.4 Summary ... 106
5. Specialty large mode area fiber for high power beam delivery at mid-IR ... 107
5.1 Introduction ... 107
5.1.1 Applications of LMA fibers ... 108
5.1.2 Primary limitations of LMA fibers ... 109
5.2 Various proposed designs of LMA fibers ... 109
5.3 Progress in mid-IR applications ... 110
5.4 Proposed design of LMA fiber ... 111
5.4.1 Properties of proposed MCOF ... 112
5.4.2 Mode profiles and confinement loss ... 115
5.4.3 Dispersion characteristics of fundamental mode ... 119
5.4.4 Bending loss characteristics ... 120
5.5 Summary ... 122
6. Photonic band-gap engineering in Ch-glass based MOF at mid-IR ... 125
6.1 Photonic band-gap (PBG) in MOF structures ... 125
6.2 Various applications of PBG fibers ... 127
6.3 Numerical techniques to model the PBG fibers ... 127
6.4 PBG in high RI contrast Ch-MOF and its tunability ... 132
6.5 Presence of PBG in low RI contrast Ch-fiber structures ... 136
6.5.1 Band-gap analysis of Type-1 Ch-PBGF ... 137
6.5.2 Band-gap analysis of Type-2 Ch-PBGF ... 144
6.5.2.1 Effect of exchanging materials: Type-3 PBGF ... 148
6.6 Summary ... 151
Summary and future scope of work ... 153
7. On-chip silicon-photonics components for mid-IR applications ... 157
7.1 Introduction ... 157
7.2 Potential applications of Si-photonics ... 161
7.3 Numerical techniques to model the SOI WGs ... 162
7.4 SOI WGs as polarization sensitive devices ... 164
7.4.1 Proposed design and effect of structural parameters ... 165
7.4.2 Supermode analysis of the proposed PR ... 170
7.4.3 Study of mode propagation through the PR ... 171
7.4.4 Fabrication tolerances and band-width of operation ... 173
7.5 SOI based on-chip gas sensor at mid-IR ... 175
7.5.1 EFA-based sensing scheme ... 176
7.5.2 Aim and proposed structure ... 177
7.5.3 Results and discussion on NO2 sensing ... 180
7.6 Summary ... 183
8. SOI-based polarization rotator for the C-band telecom wavelength window... 185
8.1 Introduction ... 185
8.2 Proposed design and structural analysis ... 186
8.3 Supermodes of the proposed PR ... 189
8.4 Propagation study of polarized modes in PR ... 190
8.5 Tolerance study and band-width of operation ... 192
8.6 Summary ... 193
Summary and future scope of work on Si-photonics ... 195
References ... 197
Author’s biography ... 227
List of Figures
Fig. 1.1. Schematic diagram of the standard step index fiber along with its refractive index (n(r)) profile in radial (r) direction. Core radius is a. Core and cladding RI are nc and nclad,
respectively. 3
Fig. 1.2. Schematic energy level diagrams of degenerate and non-degenerate four wave mixing. Formation of new photon pair (signal and idler) can be thought of transition from a
virtual level. 16
Fig. 1.3. Schematic diagrams of the cross-section of MOF. White circles are air holes embedded on uniform silica matrix (grey color). (a) Solid core MOF. (b) Hollow (air) core
MOF. (Adapted from Joannopoulos et al. 2008). 17
Fig. 1.4. (a) SEM image of an index guided MOF. The grey regions are silica and black circles are air holes (curtsey: university of Bath). (b) Simulated fundamental mode pattern of
IG-MOF. 23
Fig. 1.5. (a) SEM image of an air core photonic band-gap MOF. White regions are made of silica and the black region are air holes. (b) Simulated fundamental mode field pattern of the
PBGF. (Adapted from Amezcua-Correa et al. 2006). 23
Fig. 1.6. The transmission spectra through Earth’s atmosphere in the wavelength range of 0.5 to 15 µm. Black arrows are indicating the position of absorption wavelengths of different molecules at this spectral range. (Adapted from Wikipedia 1). 25 Fig. 2.1. A schematic of the cross-sectional view of our proposed MOF. Cladding consists of hexagonally arranged 5 rings of air holes (white circles) embedded in As2S3 matrix (black background). Fiber core is formed by omitting an air hole from the centre. The radius of air holes in the second cladding ring is r2, whereas the radius of rest of the holes is r. Centre to centre separation between two consecutive holes is denoted as the pitch (Λ). 52 Fig. 2.2. Variation of confinement loss (αc) of the fundamental mode at signal wavelength with r2/r for 3 different values of P0 (1, 5 and 10 W). Inset showing the magnified version of
αc around r2/r = 1.15, where αc takes a value ~ 1.2 dB/m, which is almost constant for
different values of P0. 52
Fig. 2.3. Calculated total dispersion as a function of wavelength of the proposed MOF. λZD is 2.105 µm, which is quite close but slightly greater than λp (~ 2 µm). 53 Fig. 2.4. FWM phase matching curve for the proposed MOF. The wavelength that corresponds to the vertical dashed line represents the pump wavelength λp. 54 Fig. 2.5. Variation of (a) amplification factor (AF), (b) output power (Pout) of three waves along the fiber length (L). The vertical dashed line indicates the position of optimum L at which AFs crosses 20 dB limit (this is the maximum achievable AFs for Pi,in = 8 mW). 54 Fig. 2.6. Variation of maximum AFs with n2(λ) for P0 = 5 W and Pi,in = 8 mW. 55 Fig. 2.7. Variation of AFs around λs (4.36 µm) for P0 = 5 W, L = 1.36 m. 3-dB BW is ~ 16
nm. 56
Fig. 2.8. Variation of signal amplification factor (AFs) for different pump wavelengths (λp).
AFs gradually decreases for larger λs due to reduction in FWM efficiency. 57 Fig. 2.9. Variation of αc (Solid curve) and Aeff (dashed curve) with the generated λs. As λs
increases, Aeff increases and hence, confinement loss increases. 57 Fig. 2.10. Dependence of (a) generated signal and idler wavelengths, (b) signal amplification factor (AFs) on variation in r2 for fixed values of Λ and r. AFs remains > 19.7 dB for the
entire variation. 59
Fig. 2.11. Dependence of (a) generated signal and idler wavelengths, (b) signal amplification factor (AFs) on variation in r (Δr) for fixed values of Λ and r2. 59 Fig. 2.12. Dependence of (a) generated signal and idler wavelengths, and (b) signal amplification factor (AFs) on variation in Λ for fixed values of r and the ratio r2/r. 59 Fig. 2.13. Cross sectional view of proposed MOF. Cladding consists of 4 rings of hexagonally arranged PES filled holes (white circles) embedded in As2Se3 matrix (black).
Core is made of As2Se3 glass (central missing hole region). Radius of air holes lie in the 3rd cladding ring is r3, radius of rest of the holes is r, and separation between two consecutive
holes is pitch (Λ). 62
Fig. 2.14. Calculated total dispersion of the designed MOF whose λZD = 5.676 μm lies close
to the chosen λp. 62
Fig. 2.15. Analytically calculated AFs of generated signal around 6.46 µm for P0 = 5 W, L = 1 m and λp= 5.59 µm. Peak AFs and 3-dB BW become ~ 20 dB and 30 nm, respectively. 63 Fig. 2.16. Variation of AF of three waves along L including pump depletion and loss for P0 = 5 W, Pi,in = 15 mW. Maximum power coupling from pump to signal is taking place at L ~
1.44 m. 64
Fig. 2.17. Variation of output power around the generated λs (~ 6.46 µm). 3-dB BW is ~ 35
nm. 64
Fig. 2.18. (a) Variation in phase matching signal wavelength (λs), (b) variation in signal amplification factor (AFs) by varying Λ and r3 by ± 4% for fixed r, L, P0 and Pi,in. Solid and dashed curves correspond to the variation in Λ and r3, respectively. 66 Fig. 2.19. (a) Variation in phase matching signal wavelength (λs), (b) variation in signal amplification factor (AFs) by varying r by -1 to +4% for fixed Λ, r3, L, P0 and Pi,in. 66 Fig. 3.1. Cross section of the proposed MOF. Cladding consists of 4 rings of borosilicate rods (white circles) embedded in the As2S3 matrix (black background). Optimized MOF parameters are d/Λ = 0.5, Λ = 2.5 μm and r2 = 0.635 µm. 75 Fig. 3.2. Dispersion characteristics of As2S3 and borosilicate based solid core MOF for d/Λ = 0.5, Λ = 2.5 μm and r2 = 0.635 µm. (a) D (dashed curve) and β2 (solid curve) variation with operating wavelength (λ); λZD= 2.788μm. (b) Variation of β4 with λ. 75 Fig. 3.3. Variation of signal amplification factor (AFs) with signal wavelength (λs) for P0 = 10 W and L = 50 cm. For λp coinciding with λZD, the output spectrum becomes almost flat (red dashed). As λp shifts away from λZD (still in anomalous GVD regime), band-width as
well as fluctuation increases. 77
Fig. 3.4. Variation of (a) amplification factors (AF) and (b) output powers (Pout) with propagation length (L) of three waves for P0 = 10 W and Pi,in = 20 mW. The green, blue and red curves correspond to pump, idler and signal wavelengths, respectively. Optimum L
becomes ~ 52 cm. 77
Fig. 3.5. Variation of AFs around generated signal wavelengths for λp= 2.792 µm, P0 = 10 W, Pi,in= 20 mW and L = 52 cm. The 3-dB BW is extended over 3 ~ 4.2 μm. 78 Fig. 3.6. Cross-sectional view of the proposed MOF made of 4 rings of hexagonally arranged PES filled holes (white circles) embedded in an As2Se3 matrix (black background). 80 Fig. 3.7. Calculated total dispersion of the designed MOF. The 2nd λZD (= 5.676 µm) lies close
to λp. 80
Fig. 3.8. Variation of AF of output spectrum for different λp. As λp shifts away from λZD (=
5.676 µm), the BW increases at the cost of fluctuation in AF (red to blue curve). 81 Fig. 3.9. Variation of amplification factors (AF) of pump, signal and idler with fiber length (L) for one set of phase wavelengths with P0 = 10 W and Pi,in = 15 mW. The optimum L
becomes ~ 78 cm. 81
Fig. 3.10. Generated output spectrum for P0 = 10 W and λp = 5.61 µm. The three curves, red (dotted), green (solid) and blue (dashed) correspond to 3 different input idler powers, 20 mW, 15 mW and 10 mW, respectively. The 3-dB BW is extended from 5 ~ 6.3 µm. 82 Fig. 4.1. Schematic diagram of (a) un-chirped pulse, which transforms to a (b) up-chirped pulse with red shifted leading and blue shifted trailing part under the combine effect of SPM
and GVD. 86
Fig. 4.2. Optimum linearly UT-MOF where the taper-ratio is fixed such that the cross- sectional parameters at input (d0 and Λ0) increase by 1.05 times at the output (d1 and Λ1) of 1 m taper length. In both the cross-sections, the white circles represent air holes embedded in
As2S3 matrix (black color). 94
Fig. 4.3. The variation of (a) 2nd order GVD coefficient (β2), (b) NL parameter (γ) along the
length of the proposed UT-MOF. 95
Fig. 4.4. Neglecting loss and higher-order dispersion effects, variation of misfit parameter (M) with distance of propagation (L) through the proposed UT-MOF. The optimum length (Lopt) ~ 19 cm for which M attains its minimum value (0.0216). 96
Fig. 4.5. Evolution of an input Gaussian pulse (blue in color) to a parabolic pulse (red in color) after just 19 cm length of propagation through our proposed UT-MOF. Loss and TOD
are ignored here. 97
Fig. 4.6. Output PP profile (red dashed) fitted to an ideal PP (green solid) of same energy.
Input Gaussian pulse (blue dotted) is also shown for comparison. Inset shows the linear chirp
of output PP. 97
Fig. 4.7. The variation of β3 along the length of proposed UT-MOF. 98 Fig. 4.8. Normalized power of output pulse including the effect of TOD (red dotted) at L = 19 cm. It is also compared with output pulse for β3 = 0 (blue solid). Inset showing (a) chirp characteristics of two pulses, (b) difference in normalized power (∆P) of two pulses in %
(Green dashed). 99
Fig. 4.9. Normalized power of output pulse for loss (α) = 0 (blue solid curve) and α ≠ 0 (red dashed curve). Inset shows their chirp characteristics. For both the cases TOD is included. 99 Fig. 4.10. Variation of maximum normalized output power (Max-Pout) (solid curve) and misfit parameter (M) (dashed curve) as a function of fiber loss. 100 Fig. 4.11. Variation of (a) optimum MOF length (Lopt) (b) Misfit parameter (M) with input peak power (Ppeak). In (b), the solid curve corresponds to variation in M at proposed fiber length (L = 19 cm) and dashed curve corresponds to the L = Lopt for that particular Ppeak. 101 Fig. 4.12. Variation of (a) output pulse width (output τFWHM), (b) maximum normalized output power (Max-Pout) with input peak power (Ppeak). In both figures, solid curve and dashed curve correspond to the values at proposed fiber length (L = 19 cm) and at Lopt for
that particular Ppeak, respectively. 101
Fig. 4.13. Variation of (a) optimum MOF length (Lopt), (b) Misfit parameter (M) with input pulse width (input τFWHM). In (b), the solid and dashed curves correspond to variation in M for L = 19 cm and at L = Lopt for that particular input τFWHM, respectively. 102 Fig. 4.14. Variation of (a) normalized output pulse width (τNorm), (b) maximum normalized output power (Max-Pout) for different input pulse width (input τFWHM). In both the figures, solid curve and dashed curve correspond to the values at proposed fiber length (L = 19 cm) and at Lopt for that particular input τFWHM, respectively. 103
Fig. 4.15. Variation of (a) optimum MOF length (Lopt), (b) Misfit parameter (M) with input Ppeak for a fixed input pulse energy (input Epulse) of 0.2234 nJ. In (b), the solid and dashed curves correspond to variation of M for the proposed fiber length (L = 19 cm) and for L = Lopt
for corresponding set of input Ppeak and τFWHM, respectively. 104 Fig. 4.16. Variation of (a) τNorm, (b) Max-Pout for different input Ppeak. In both the figures, solid and dashed curves correspond to the values for the proposed fiber length (L = 19 cm) and for Lopt for corresponding set of input Ppeak and τFWHM, respectively. 104 Fig. 4.17. Dependence of misfit parameter (M) with variation in (a) initial hole diameter (d0) for fixed initial pitch (Λ0) and up-tapered ratio, (b) Λ0 for fixed d0 and up-tapered ratio, (c)
up-tapered ratio for fixed d0 and Λ0. 105
Fig. 5.1. Cross-section of our proposed LMA MCOF. Microstructured core consists of 4 rings of hexagonally arranged high index As20Se80 rods (white circles) embedded at the centre of Ge12.5As20Se67.5 matrix (black color), which also forms the uniform cladding. 113 Fig. 5.2. The variation of Aeff with pitch (Λ) for four different values of r (0.5 µm, 0.75 µm,
1.0 µm and 2.0 µm) at operating wavelength of 4.3 µm. 115
Fig. 5.3. The variation of V parameter of equivalent SIF with operating wavelength (λ) for three different values of r (0.5, 0.75 and 1.0 µm) and a fixed value of pitch (Λ = 35 µm). 115 Fig. 5.4. Fundamental mode field patterns of proposed MCOF at λ = 4.3 µm for three different values of r (= 1.5, 1.0 and 0.5 µm) and a fixed value of Λ (= 35 µm). In all the
figures, mainly the core region is shown. 116
Fig. 5.5. Variation of z component of pointing vector (Sz) for Λ = 35 µm and r = 0.5 µm. (a) Plot of Sz in x-y plane, (b) variation of Sz along y direction at x = 0. 118 Fig. 5.6. Modal field pattern of first HOM for Λ = 35 µm and r = 0.75 µm at λ ≈ 4 µm.(a) Pointing vector (Sz) in x-y plane (b) x-component of electric field (Ex) in x-y plane. 118 Fig. 5.7. Variation of mode effective area (Aeff) with operating wavelength (λ) for Λ = 35 µm.
The solid line and dashed line correspond to r = 0.5 µm and 1.0 µm, respectively. 119 Fig. 5.8. Dispersion characteristics of FM of proposed MCOF for Λ = 35 µm and r = 0.5 µm.
(a) Variation of dispersion coefficient (D) and (b) dispersion slope (SD) with wavelength. 120
Fig. 5.9. Variation of bending-loss (αb) with bend radius (Rb) of the proposed LMA fiber for
r = 0.5 µm, Λ = 35 µm and λ = 4.0 µm. 122
Fig. 6.1. Schematic cross-sectional diagram of a (a) Bragg fiber with 1-D periodicity in RI, (b) Hollow core PBG-MOF with 2-D periodicity in RI in the cladding. 126 Fig. 6.2. Schematic diagrams of dispersion (ω vs. k) curve for optical mode in a (a) homogeneous medium with continuous translational symmetry, (b) periodic lattice with discrete translational symmetry (like photonic crystal); white shaded regions correspond to
the band-gaps. 129
Fig. 6.3. Transverse refractive index profile of air-chalcogenide (As2S3) lattice structure, where circular air holes (pink color) are hexagonally arranged on As2S3 matrix (red color).
The diameter of air holes are d and the separation (center to center) between two consecutive
holes is pitch (Λ). 133
Fig. 6.4. (a) Plot of normalized frequency (Λ/λ) vs. wave-vector (k0). The blue and red curves correspond to band structures of fundamental TE and TM modes, respectively. The Г, M and K are the coordinates of k0. (b) First Brillouin Zone and the path of in-plane k-vector (kx and
ky) is shown. 133
Fig. 6.5. Variation of mid-gap wavelength (dashed) and band-gap width (solid circled) with lattice period (Λ) for fundamental (a) TE mode, (b) TM mode. 134 Fig. 6.6. Spectral dependence of refractive indices of 3 Ch-glasses (A, B and C) at mid-IR
range. 137
Fig. 6.7. Transverse RI profile of the proposed Type-1 Ch-PBGF. Size of low index defect core (central white region) is relatively larger than the size of other low index rods. 138 Fig. 6.8. Band diagram of Type-1 PBGF with ∆ ~ 12% and d/Λ = 0.9 for (a) βp = 0 and (b) βp
= 18, shaded blue region represents the BG of fundamental hybrid mode which appears
between 4th and 5th band. 138
Fig. 6.9. Variation of band-gap width (red solid-circled) and mid-gap wavelength (blue dashed) with separation between rods (Λ) for fundamental hybrid mode for βp = 18 and d/Λ=
0.9. 139
Fig. 6.10. Hybrid band-gap map for lowest order and 1st higher order BG for different βp
(green shaded regions). The red solid line represents the light line corresponding to the RI of the defect core region. Intersection region with the light line (surrounded by rectangular dashed line) gives the bound state solutions. Inset shows the cross-section of the proposed
PBGF. 139
Fig. 6.11. Transverse field profile of fundamental hybrid mode for βp = 17.5; x-polarized component. (a) Intensity profile, black arrow shows the polarization direction, (b)
polarization plot. 142
Fig. 6.12. Transverse intensity plots of 4-fold degenerate four higher order modes for βp = 17.5. Black solid arrows are showing their polarization directions. 143 Fig. 6.13. Transverse intensity plots of 2-fold degenerate fundamental modes for βp = 20.
Black solid arrows are showing their polarization directions. 143 Fig. 6.14. Spectral dependence of KT of two Ch-glasses, glass A (solid circled) and glass B
(dashed). 144
Fig. 6.15. Variation of gap-ratio (gap width/mid-gap) of lowest order BG with external temperature (T). The temperature sensitivity (ST) is calculated as ~ 11.4 pm/°C. 144 Fig. 6.16. Band diagram of Type-2 PBGF with ∆ ~ 24% and d/Λ = 0.9 for (a) βp = 0 and (b) βp = 11, shaded region represents the lowest order band-gap which appears between 4th and
5th band. 146
Fig. 6.17. Variation of band-gap width (blue solid) and mid-gap wavelength (red dashed) with separation between rods (Λ) for lowest order BG for βp = 11 and d/Λ = 0.9. 146 Fig. 6.18. Hybrid band-gap map for lowest order BG (green shaded regions) for different βp. The red solid line represents the light line corresponds to the RI of defect core. Overlap region of the band-gap map with the light line (shown as a dashed rectangle) corresponds to
the bound state solutions. 147
Fig. 6.19. Spectral dependence of the KT of glass A (solid circled line) and glass C (dashed
line). 147
Fig. 6.20. Variation of mid-gap wavelength (λ0) of lowest order BG with external temperature (T). The temperature sensitivity (ST) is calculated as ~ 82 pm/°C. 148 Fig. 6.21. (a) Transverse RI profile of proposed Type-3 Ch-PBGF made of glass A (low index matrix, white color) and glass C (high index red circular rods). Low index defect core (central white region) is formed by omitting the central rod. (b) Band diagram of Type-3 PBGF with ∆ ~ 24%, d/Λ = 0.9 and βp = 11. For same βp, here two BG appears (shaded regions) one between 1st and 2nd band (lowest order BG) and other between 5th and 6th band
(1st higher order BG). 149
Fig. 6.22. Hybrid band-gap map for lowest and 1st higher order BG (green shaded regions) for different βp. The red solid line represents the light line corresponding to the RI of defect core region. Intersection regions with the light line (surrounded by dashed Blue ellipses)
represent the bound state solutions. 149
Fig. 6.23. Variation of mid-gap wavelength (λ0) of lowest order BG (solid circles) and 1st higher order BG (dashed) with external temperature (T). The T-sensitivity (ST) for the two BGs are calculated as ~ 140 pm/°C and 111 pm/°C, respectively. 150 Fig. 7.1. Optical transmission through bulk silicon. Transmittance > 50% is possible for 2 to 3 mm thickness of sample over the wavelength range ~ 1.1 - 7 µm. (Adapted from
Almazoptics.com). 160
Fig. 7.2. Schematic cross-sectional views of a variety of possible SOI waveguides; (a) strip, (b) rib, (c) horizontal slot and (d) vertical slot waveguide. 160 Fig. 7.3. Schematic diagram of a 2-D cross-section of the proposed PR. We have assumed IR grade SiO2 as substrate, Si as core, and air as forming the cover and slot region. 167 Fig. 7.4. (a) Variation of effective indices (neff) of TE (solid-circled) and TM (dashed) modes with W2 for isolated slot WG. TE becomes fundamental for W2 > 500 nm (see dotted line).
(b) Variation of neff of TE in slot (solid) and TM in strip WG (dashed) with separation (S).
Circled region indicates the mode exchange regime, which appears for S ≈ 876 nm. Inset
shows the larger view. 167
Fig. 7.5. Variation of (a) neff, (b) coupling length (Lc) and hybridness of (c) quasi-TE in slot and (d) quasi-TM in strip, with W1 for three different values of S (= 800, 900, and 1000 nm).
The inset in (a) shows the larger view near the anti-crossing region. 169 Fig. 7.6. Variation of (a) phase matching W1 and (b) corresponding Cm and Lc with S. 170 Fig. 7.7. Amplitudes of H-filed components of the two supermodes, even (SM 1) and odd (SM 2), for phase matched PR. (a) Hx of SM 1, (b) Hy of SM 1, (c) Hx of SM 2, (d) Hy of SM
2. 171
Fig. 7.8. Variation of (a) intensity of TE-slot and TM-strip and (b) normalized power of TE- slot (red dashed) and TM-strip (blue solid) along the device length for TE mode input at slot
WG. 173
Fig. 7.9. Variation of (a) intensity of TM-strip and TE-slot and (b) normalized power of TE- slot (red dashed), TM-strip (blue solid), TM-slot (green solid), TE-strip (orange solid) and total power (black dash-dot) along the device length for TM mode input in strip WG. 173 Fig. 7.10. Tolerance study of Cm for variation in (a) W1 by ± 5 nm, (b) W2 by ± 2 nm and (c) Ws by ± 2 nm. (d) Variation of Cm with operating wavelength (λ). In all the plots, red solid and blue dashed curves correspond to Cm at Lc of corresponding modified structure and Cm at
proposed device length (L = 535.8 μm), respectively. 174
Fig. 7.11. (a) Schematic cross-sectional view of proposed Si-slot waveguide with gas as a cover and slot material and SiO2 as substrate. Inset shows the 2-D intensity profile of TE mode in slot WG. (b) 3-D power density profile of fundamental TE mode in the proposed slot WG structure. Evanescent field inside the low index slot region is quite high. 179 Fig. 7.12. Variation of EFF with the width of high index Si region (W); (a) for three different low index slot width (Ws = 100, 150, 200 nm) with fixed H = 0.6 μm, (b) for three different height (H = 0.5, 0.6, 0.7 µm) with fixed Ws = 150 nm. Dotted lines indicate the position of
maximum EFF. 181
Fig. 7.13. Variation of sensitivity (SS) with WG length (L) for Cg = 50 ppm; (a) for different η with fixed loss (α = 5 dB/cm), (b) for different α with fixed η = 0.4104. Dotted lines indicate the position of optimum L corresponds to the maximum SS. 181
Fig. 7.14. Variation of normalized output power (PN = Pout/Pin) at the end of Lopt = 8 mm over the absorption band of NO2 for three different values of Cg (10, 50, 100 ppm). 183 Fig. 7.15. Tolerance study of EFF (η) for variation in (a) Ws by ± 10%, (b) W by – 4% to +8% and (c) H by ± 10 %. All the calculations are made for the wavelength 3.4 µm. 183 Fig. 8.1. Schematic diagram of the 2-D cross-section of the proposed PR, where core is Si, substrate is SiO2, air constitute the material for the cover and slot material. 186 Fig. 8.2. Variation of (a) neff, (b) coupling length (Lc) and hybridness of quasi-TE (c) and quasi-TM (d) modes with W1 for three different values of S. Phase matching value of W1
shifts towards higher values for larger values of S. 188
Fig. 8.3. magnetic (H) -field components of the two supermodes (SMs) in the proposed PR, even (SM 1) and odd (SM 2); (a) Hx of SM 1, (b) Hy of SM 1, (c) Hx of SM 2, (d) Hy of SM
2. 189
Fig. 8.4. Variation of intensity (time average) of two modes, TE in slot and TM in strip WG along the device length for (a) TE-slot input and (b) TM-strip input. 191 Fig. 8.5. Variation of normalized power of four individual WG modes, TE-slot (red dashed), TM-strip (blue solid), TM-slot (green solid), TE-strip (orange solid) and total power (black dash-dot) along the device length for (a) TE-slot input and (b) TM-strip input. 191 Fig. 8.6. Fabrication tolerance of proposed PR. Variation of Cm with the change in (a) W1 by
± 10 nm, (b) W2 by ± 5 nm and (c) Ws by ± 4 nm. (d) Variation of Cm with operating wavelength. Red solid and blue dashed curves correspond to Cm at Lc of corresponding modified structures and Cm at proposed device length (L = 134.5 μm), respectively. 192
List of Acronyms
AF Amplification Factor
ASE Amplified Spontaneous Emission
BC Boundary Condition
BPM Beam Propagation Method BPP Beam Parameter Product
BW Band-Width
CMOS Complementary Metal–Oxide–Semiconductor
CW Continuous Wave
DCF Dispersion Compensating Fiber DD Dispersion Decreasing
DDF Dispersion Decreasing Fiber DFG Difference Frequency Generation
D-FWM Degenerate Four Wave Mixing
DL Differential Loss
DWDM Dense Wavelength Division Multiplexing
EDFA Erbium Doped Fiber Amplifier
EFA Evanescent Field Absorption EFF Evanescent Field Fraction EIM Effective Index Method
EM Electromagnetic
EME Eigenmode Expansion FDM Finite Difference Method FDTD Finite Difference Time Domain FEM Finite Element Method
FM Fundamental Mode
FMM Film Mode Matching
FSM Fundamental Space Filling Mode
FV Full Vector
FWHM Full Width at Half Maximum
FWM Four Wave Mixing
GNLSE Generalized Nonlinear Schrödinger Equation GVD Group Velocity Dispersion
HOM Higher Order Mode
IG-MOF Index Guided Microstructured Optical Fiber
IR Infrared
LMA Large Mode Area
MC Microstructured Core
MCOF Microstructured Core Optical Fiber
MM Multipole Method
MMF Multi-Mode Fiber
MOF Microstructured Optical Fiber NA Numerical Aperture
ND-FWM Non-Degenerate Four Wave Mixing
NL Nonlinear
NLSE Nonlinear Schrödinger Equation OPO Optical Parametric Oscillator OWB Optical Wave Breaking PBG Photonic Band-Gap
PBGF Photonic Band-Gap Fiber
PC Photonic Crystal
PCF Photonic Crystal Fiber PES Polyethersulfone
PML Perfectly Matched Layer
PP Parabolic Pulse
PR Polarization Rotator PWE Plane Wave Expansion
PWM Plane Wave Method
QCL Quantum Cascade Laser
RE Rare Earth
RI Refractive Index
SBS Stimulated Brillouin Scattering SCG Supercontinuum Generation SEM Scanning Electron Microscope SIF Step Index Fiber
SM Single-Mode
SMF Single-Mode Fiber
SOI Silicon-on-Insulator SPM Self-Phase Modulation SRS Stimulated Raman Scattering SSFM Split-Step Fourier Method
S-SSFM Symmetrized Split-Step Fourier Method SVEA Slowly Varying Envelop Approximation TAT Trans-Atlantic Telecommunication TE Transverse-Electric
THG Third Harmonic Generation TIR Total Internal Reflection
TM Transverse-Magnetic
TMM Transfer Matrix Method TOD Third Order Dispersion TPA Two Photon Absorption
UV Ultra Violet
VLSI Very Large Scale Integration WDM Wavelength Division Multiplexing
WG Waveguide
XPM Cross-Phase Modulation