Chapter 1 Wave Nature of Light ................................. 3
1.1 Light Waves in a Homogeneous Medium ........................ 3
A. Plane Electromagnetic Wave .............................. 3
B. Maxwell's Wave Equation and Diverging Waves ............. 6
Example 1.1.1 A diverging laser beam ...................... 10
1.2 Refractive Index and Dispersion ........................... 10
Example 1.2.1 Sellmeier equation and diamond .............. 13
Example 1.2.2 Cauchy equation and diamond ................. 14
1.3 Group Velocity and Group Index ............................ 14
Example 1.3.1 Group velocity .............................. 17
Example 1.3.2 Group velocity and index .................... 17
Example 1.3.3 Group and phase velocities .................. 18
1.4 Magnetic Field, Irradiance, and Poynting Vector ........... 18
Example 1.4.1 Electric and magnetic fields in light ....... 21
Example 1.4.2 Power and irradiance of a Gaussian beam ..... 21
1.5 Snell's Law and Total Internal Reflection (TIR) ........... 22
Example 1.5.1 Beam displacement ........................... 25
1.6 Fresnel's Equations ....................................... 26
A. Amplitude Reflection and Transmission Coefficients
(rand t) ............................................... 26
B. Intensity, Reflectance, and Transmittance .............. 32
C. Goos-Hanchen Shift and Optical Tunneling ............... 33
Example 1.6.1 Reflection of light from a less dense
medium (internal reflection) ........................... 35
Example 1.6.2 Reflection at normal incidence, and
internal and external reflection ....................... 36
Example 1.6.3 Reflection and transmission atthe Brewster
angle .................................................. 37
1.7 Antireflection Coatings and Dielectric Mirrors ............ 38
A. Antireflection Coatings on Photodetectors and Solar
Cells .................................................. 38
Example 1.7.1 Antireflection coating on a
photodetector ....................................... 39
B. Dielectric Mirrors and Bragg Reflectors ................ 40
Example 1.7.2 Dielectric mirror ........................ 42
1.8 Absorption of Light and Complex Refractive Index .......... 43
Example 1.8.1 Complex refractive index of InP ............. 46
Example 1.8.2 Reflectance of CdTe around resonance
absorption ............................................. 47
1.9 Temporal and Spatial Coherence ............................ 47
Example 1.9.1 Coherence length of LED light ............... 50
1.10 Superposition and Interference of Waves ................... 51
1.11 Multiple Interference and Optical Resonators .............. 53
Example 1.11.1 Resonator modes and spectral width of a
semiconductor Fabry-Perot cavity ....................... 57
1.12 Diffraction Principles .................................... 58
A. Fraunhofer Diffraction ................................. 58
Example 1.12.1 Resolving power of imaging systems ...... 63
B. Diffraction Grating .................................... 64
Example 1.12.2 A reflection grating .................... 67
Additional Topics ......................................... 68
1.13 Interferometers ........................................... 68
1.14 Thin Film Optics: Multiple Reflections in Thin Films ...... 70
Example 1.14.1 Thin film optics ........................... 72
1.15 Multiple Reflections in Plates and Incoherent Waves ....... 73
1.16 Scattering of Light ....................................... 74
1.17 Photonic Crystals ......................................... 76
Questions and Problems .................................... 82
Chapter 2 Dielectric Waveguides and Optical Fibers ............ 95
2.1 Symmetric Planar Dielectric Slab Waveguide ................ 95
A. Waveguide Condition .................................... 95
B. Single and Multimode Waveguides ....................... 100
C. ТЕ and TM Modes ....................................... 100
Example 2.1.1 Waveguide modes ......................... 101
Example 2.1.2 l/number and the number of modes ........ 102
Example 2.1.3 Mode field width, 2w„ ................... 103
2.2 Modal and Waveguide Dispersion in Planar Waveguides ...... 104
A. Waveguide Dispersion Diagram and Group Velocity ....... 104
B. Intermodal Dispersion ................................. 105
C. Intramodal Dispersion ................................. 106
2.3 Step-Index Optical Fiber ................................. 107
A. Principles and Allowed Modes .......................... 107
Example 2.3.1 A multimode fiber ....................... 112
Example 2.3.2 A single-mode fiber ..................... 112
B. Mode Field Diameter ................................... 112
Example 2.3.3 Mode field diameter ..................... 113
C. Propagation Constant and Group Velocity ............... 114
Example 2.3.4 Group velocity and delay ................ 115
D. Modal Dispersion in Multimode Step-Index Fibers ....... 116
Example 2.3.5 A multimode fiber and dispersion ........ 116
2.4 N u merica I Apertu re ................................... 117
Example 2.4.1 A multimode fiber and total acceptance
angle ................................................. 118
Example 2.4.2 A single-mode fiber ........................ 118
2.5 Dispersion In Single-Mode Fibers ......................... 119
A. Material Dispersion ................................... 119
B. Waveguide Dispersion .................................. 120
C. Chromatic Dispersion .................................. 122
D. Profile and Polarization Dispersion Effects ........... 122
Example 2.5.1 Material dispersion ..................... 124
Example 2.5.2 Material, waveguide, and chromatic
dispersion ......................................... 125
Example 2.5.3 Chromatic dispersion at different
wavelengths ........................................ 125
Example 2.5.4 Waveguide dispersion .................... 126
2.6 Dispersion Modified Fibers and Compensation .............. 126
A. Dispersion Modified Fibers ............................ 126
B. Dispersion Compensation ............................... 128
Example 2.6.1 Dispersion compensation ................. 130
2.7 Bit Rate, Dispersion, and Electrical and Optical
Bandwidth ................................................ 130
A. Bit Rate and Dispersion ............................... 130
B. Optical and Electrical Bandwidth ...................... 133
Example 2.7.1 Bit rate and dispersion for a single-
mode fiber ......................................... 135
2.8 The Graded Index (GRIN) Optical Fiber .................... 135
A. Basic Properties of GRIN Fibers ....................... 135
B. Telecommunications .................................... 139
Example 2.8.1 Dispersion in a graded index fiber and
bit rate ........................................... 140
Example 2.8.2 Dispersion in a graded index fiber and
bit rate ........................................... 141
2.9 Attenuation in Optical Fibers ............................ 142
A. Attenuation Coefficient and Optical Power Levels ...... 142
Example 2.9.1 Attenuation along an optical fiber ...... 144
B. Intrinsic Attenuation in Optical Fibers ............... 144
C. Intrinsic Attenuation Equations ....................... 146
Example 2.9.2 Rayleigh scattering equations ........... 147
D. Bending losses ........................................ 148
Example 2.9.3 Bending loss for SMF 151 2.10 Fiber
Manufacture ........................................ 152
A. Fiber Drawing ......................................... 152
B. Outside Vapor Deposition .............................. 153
Example 2.10.1 Fiber drawing .......................... 155
Additional Topics ........................................ 155
2.11 Wavelength Division Multiplexing: WDM .................... 155
2.12 Nonlinear Effects in Optical Fibers and DWDM ............. 157
2.13 Bragg Fibers ............................................. 159
2.14 Photonic Crystal Fibers—Holey Fibers ..................... 160
2.15 Fiber Bragg Gratings and Sensors ......................... 163
Example 2.15.1 Fiber Bragg grating at 1550 nm ............ 167
Questions and Problems ................................... 167
Chapter 3 Semiconductor Science and Light-Emitting Diodes .... 179
3.1 Review of Semiconductor Concepts and Energy Bands ........ 179
A. Energy Band Diagrams, Density of States, Fermi-Dirac
Function and Metals ................................... 179
B. Energy Band Diagrams of Semiconductors ................ 182
3.2 Semiconductor Statistics ................................. 184
3.3 Extrinsic Semiconductors ................................. 187
A. n-Type and p-Type Semiconductors ...................... 187
B. Compensation Doping ................................... 190
C. Nondegenerate and Degenerate Semiconductors ........... 191
E. Energy Band Diagrams in an Applied Field .............. 192
Example 3.3.1 Fermi levels in semiconductors .......... 193
Example 3.3.2 Conductivity of л-Si .................... 193
3.4 Direct and Indirect Bandgap Semiconductors: E-k
Diagrams ................................................. 194
3.5 pn Junction Principles ................................... 198
A. Open Circuit .......................................... 198
B. Forward Bias and the Shockley Diode Equation .......... 201
C. Minority Carrier Charge Stored in Forward Bias ........ 206
D. Recombination Current and the Total Current ........... 206
3.6 pn Junction Reverse Current .............................. 209
3.7 pn Junction Dynamic Resistance and Capacitances .......... 211
A. Depletion Layer Capacitance ........................... 211
B. Dynamic Resistance and Diffusion Capacitance for
Small Signals ......................................... 213
3.8 Recombination Lifetime ................................... 214
A. Direct Recombination .................................. 214
B. Indirect Recombination ................................ 216
Example 3.8.1 A direct bandgap pn junction ............ 216
3.9 pn Junction Band Diagram ................................. 218
A. Open Circuit .......................................... 218
B. Forward and Reverse Bias .............................. 220
Example 3.9.1 The built-in voltage from the band
diagram ............................................ 221
3.10 Heterojunctions .......................................... 222
3.11 Light-Emitting Diodes: Principles ........................ 224
A. Homojunction LEDs ..................................... 224
B. Heterostructure High Intensity LEDs ................... 226
C. Output Spectrum ....................................... 228
Example 3.11.1 LED spectral linewidth ................. 231
Example 3.11.2 LED spectral width ..................... 232
Example 3.11.3 Dependence of the emission peak and
linewidth on temperature ........................... 233
3.12 Quantum Well High Intensity LEDs ......................... 233
Example 3.12.1 Energy levels in the quantum well ......... 236
3.13 LED Materials and Structures ............................. 237
A. LED Materials ......................................... 237
B. LED Structures ........................................ 238
Example 3.13.1 Light extraction from a bare LED chip .. 241
3.14 LED Efficiencies and Luminous Flux ....................... 242
Example 3.14.1 LED efficiencies .......................... 244
Example 3.14.2 LED brightness ............................ 245
3.15 Basic LED Characteristics ................................ 245
3.16 LEDs for Optical Fiber Communications .................... 246
3.17 Phosphors and White LEDs ................................. 249
Additional Topics ........................................ 251
3.18 LED Electronics .......................................... 251
Questions and Problems ................................... 254
Chapter 4 Stimulated Emission Devices: Optical Amplifiers
and Lasers .................................................... 265
4.1 Stimulated Emission, Photon Amplification, and Lasers .... 265
A. Stimulated Emission and Population Inversion .......... 265
B. Photon Amplification and Laser Principles ............. 266
C. Four-Level Laser System ............................... 269
4.2 Stimulated Emission Rate and Emission Cross-Section ...... 270
A. Stimulated Emission and Einstein Coefficients ......... 270
Example 4.2.1 Minimum pumping power for three-level
laser systems ...................................... 272
B. Emission and Absorption Cross-Sections ................ 273
Example 4.2.2 Gain coefficient in a Nd3+-doped glass
fiber .............................................. 275
4.3 Erbium-Doped Fiber Amplifiers ............................ 276
A. Principle of Operation and Amplifier Configurations ... 276
B. EDFA Characteristics, Efficiency, and Gain
Saturation ............................................ 280
Example 4.3.1 An erbium-doped fiber amplifier ......... 283
C. Gain-Flattened EDFAs and Noise Figure ................. 284
A. Gas Lasers: The He-Ne Laser ........................... 287
Example 4.4.1 Efficiency of the He-Ne laser ........... 290
4.5 The Output Spectrum of a Gas Laser ....................... 290
Example 4.5.1 Doppler broadened linewidth ................ 293
4.6 Laser Oscillations: Threshold Gain Coefficient and Gain
Bandwidth ................................................ 295
A. Optical Gain Coefficient g ............................ 295
B. Threshold Gain Coefficient gth and Output Power ....... 296
Example 4.6.1 Threshold population inversion for the
He-Ne laser ........................................ 299
C. Output Power and Photon Lifetime in the Cavity ........ 299
Example 4.6.2 Output power and photon cavity
lifetime тр(1 ...................................... 301
D. Optical Cavity, Phase Condition, Laser Modes .......... 301
4.7 Broadening of the Optical Gain Curve and Linewidth ....... 303
4.8 Pulsed Lasers: Q-Switching and Mode Locking .............. 307
A. Q-Switching ........................................... 307
B. Mode Locking .......................................... 310
4.9 Principle of the Laser Diode28 ........................... 311
4.10 Heterostructu re Laser Diodes ............................ 315
Example 4.10.1 Modes in a semiconductor laser and the
optical cavity length ................................. 320
4.11 Quantum Well Devices ..................................... 321
Example 4.11.1 A GaAs quantum well ....................... 323
4.12 Elementary Laser Diode Characteristics ................... 324
Example 4.12.1 Laser output wavelength variation with
temperature ........................................... 330
Example 4.12.2 Laser diode efficiencies for a sky-blue
LD .................................................... 330
Example 4.12.3 Laser diode efficiencies .................. 331
4.13 Steady State Semiconductor Rate Equations: The Laser
Diode Equation ........................................... 332
A. Laser Diode Equation .................................. 332
B. Optical Gain Curve, Threshold, and Transparency
Conditions ............................................ 335
Example 4.13.1 Threshold current and optical output
power from a Fabry-Perot heterostructure laser
diode .............................................. 336
4.14 Single Frequency Semiconductor Lasers .................... 338
A. Distributed Bragg Reflector LDs ....................... 338
B. Distributed Feedback LDs .............................. 339
C. External Cavity LDs ................................... 342
Example 4.14.1 DFB LD wavelength ...................... 344
4.15 Vertical Cavity Surface Emitting Lasers36 ................ 344
4.16 Semiconductor Optical Amplifiers ......................... 348
Additional Topics ........................................ 350
4.17 Superluminescent and Resonant Cavity LEDs: SLD and
RCLED .................................................... 350
4.18 Direct Modulation of Laser Diodes ........................ 351
4.19 Holography ............................................... 354
Questions and Problems ................................... 357
Chapter 5 Photodetectors and Image Sensors .................... 365
5.1 Principle of the pn Junction Photodiode .................. 365
A. Basic Principles ...................................... 365
B. Energy Band Diagrams and Photodetection Modes ......... 367
C. Current-Voltage Convention and Modes of Operation ..... 369
5.2 Shockley-Ramo Theorem and External Photocurrent .......... 370
5.3 Absorption Coefficient and Photodetector Materials ....... 372
5.4 Quantum Efficiency and Responsivity ...................... 375
Example 5.4.1 Quantum efficiency and responsivity ........ 378
Example 5.4.2 Maximum quantum efficiency ................. 379
5.5 The pin Photodiode ....................................... 379
Example 5.5.1 Operation and speed of a pin photodiode .... 383
Example 5.5.2 Photocarrier Diffusion in a pin
photodiode ................................. 383
Example 5.5.3 Responsivity of a pin photodiode ........... 384
Example 5.5.4 Steady state photocurrent in the pin
photodiode ............................................ 385
5.6 Avalanche Photodiode ..................................... 386
A. Principles and Device Structures ...................... 386
Example 5.6.1 InGaAs APD responsivity ................. 390
Example 5.6.2 Silicon APD ............................. 390
B. Impact Ionization and Avalanche Multiplication ........ 390
Example 5.6.3 Avalanche multiplication in Si APDs ..... 392
5.7 Heterojunction Photodiodes ............................... 393
A. Separate Absorption and Multiplication APD ............ 393
B. Superlattice APDs ..................................... 395
5.8 Schottky Junction Photodetector .......................... 397
5.9 Phototransistors ......................................... 401
5.10 Photoconductive Detectors and Photoconductive Gain ....... 402
5.11 Basic Photodiode Circuits ................................ 405
5.12 Noise in Photodetectors .................................. 408
A. The pn Junction and pin Photodiodes ................... 408
Example 5.12.1 NEP of a Si pin photodiode ............. 412
Example 5.12.2 Noise of an ideal photodetector ........ 412
Example 5.12.3 SNR of a receiver ...................... 413
B. Avalanche Noise in the APD ............................ 414
Example 5.12.4 Noise in an APD ........................ 414
5.13 Image Sensors ............................................ 415
A. Basic Principles ...................................... 415
B. Active Matrix Array and CMOS Image Sensors ............ 417
C. Charge-Coupled Devices ................................ 419
Additional Topics ........................................ 421
5.14 Photovoltaic Devices: Solar Cells ........................ 421
A. Basic Principles ...................................... 421
B. Operating Current and Voltage, and Fill Factor ........ 423
C. Equivalent Circuit of a Solar Cell .................... 424
D. Solar Cell Structures and Efficiencies ................ 426
Example 5.14.1 Solar cell driving a load .............. 428
Example 5.14.2 Open circuit voltage and short
circuit current .................................... 429
Questions and Problems ................................... 429
Chapter 6 Polarization and Modulation of Light ................ 441
6.1 Polarization ............................................. 441
A. State of Polarization ................................. 441
Example 6.1.1 Elliptical and circular polarization .... 444
B. Malus's Law ........................................... 444
6.2 Light Propagation in an Anisotropic Medium:
Birefringence ............................................ 445
A. Optical Anisotropy .................................... 445
B. Uniaxial Crystals and Fresnel's Optical Indicatrix .... 447
C. Birefringence of Calcite .............................. 450
D. Dichroism ............................................. 451
6.3 Birefringent Optical Devices ............................. 452
A. Retarding Plates ...................................... 452
Example 6.3.1 Quartz-half wave plate .................. 453
Example 6.3.2 Circular polarization from linear
polarization ....................................... 454
B. Soleil-Babinet Compensator ............................ 454
C. Birefringent Prisms ................................... 455
6.4 Optical Activity and Circular Birefringence .............. 456
6.5 Liquid Crystal Displays .................................. 458
6.6 Electro-Optic Effects .................................... 462
A. Definitions ........................................... 462
B. Pockels Effect ........................................ 463
Example 6.6.1 Pockels Cell Modulator .................. 468
C. Kerr Effect ........................................... 468
Example 6.6.2 Kerr Effect Modulator ................... 470
6.7 Integrated Optical Modulators ............................ 470
A. Phase and Polarization Modulation ..................... 470
B. Mach-Zehnder Modulator ................................ 471
C. Coupled Waveguide Modulators .......................... 473
Example 6.7.1 Modulated Directional Coupler ........... 476
6.8 Acousto-Optic Modulator .................................. 476
A. Photoelastic Effect and Principles .................... 476
B. Acousto-Optic Modulators .............................. 478
Example 6.8.1 AO Modulator ............................ 483
6.9 Faraday Rotation and Optical Isolators ................... 483
Example 6.9.1 Faraday rotation ........................... 484
6.10 Nonlinear Optics and Second Harmonic Generation .......... 485
Additional Topics ........................................ 489
6.11 Jones Vectors ............................................ 489
Questions and Problems ................................... 490
Appendices
Appendix A Gaussian Distribution ............................. 498
Appendix В Solid Angles ....................................... 500
Appendix С Basic Radiometry and Photometry .................... 502
Appendix D Useful Mathematical Formulae ...................... 505
Appendix E Notation and Abbreviations ......................... 507
Index ......................................................... 519
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