## Table of Contents

**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 (r and t ) 26

B. Intensity, Reflectance, and Transmittance 32

C. Goos-Hänchen 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 at the 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. TE and TM Modes 100

Example 2.1.1 Waveguide modes 101

Example 2.1.2 V-number and the number of modes 102

Example 2.1.3 Mode field width, 2wo 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 Numerical Aperture 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 n-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

4.4 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 Tph 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 Heterostructure 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 B Solid Angles 500

Appendix C Basic Radiometry and Photometry 502

Appendix D Useful Mathematical Formulae 505

Appendix E Notation and Abbreviations 507

Index 519