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# Optoelectronics & Photonics: Principles & Practices, 2nd edition

Published by Pearson (October 15, 2012) Â© 2013

**Safa O. Kasap**University of Saskatchewan

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For one-semester, undergraduate-level courses in Optoelectronics and Photonics, in the departments of electrical engineering, engineering physics, and materials science and engineering.

This text takes a fresh look at the enormous developments in electo-optic devices and associated materials.

- Numerous modern topics in photonics are included in all the chapters.
- There are Additional Topics that can be covered in more advanced courses, or in courses that run over two semesters.
- There are manyÂ new and solved problems within chapters, and manyÂ practical end-of-chapter problems that start from basic concepts and build-up onto advanced applications.
- Photographs, illustrations, and artwork are used, where appropriate, to convey the concepts as clearly as possible.
- Advanced or complicated mathematical derivations are avoided and, instead, the emphasis is placed on concepts and engineering applications.
- Â Useful and essential equations in photonics are given with explanations; and are used in examples and problems to give the student a sense of what are typical values.
- Emphasis is placed on practical or engineering examples; care has been taken to consider various photonics/optoelectronics courses at the undergraduate level across major universities.
- The Second Edition is supported by an extensive Power Point presentation for instructors. The Power Point has all the illustrations in color, and includes additional color photos. The basic concepts and equations are also highlighted in additional slides. There are also numerous slides with examples and solved problems. The readers who have purchased a copy of the book are allowed to use the Power Point slides in their research seminars, workshops, symposia and conferences.
- The Second Edition is supported by an extensive Solutions Manual for instructors. (Instructors need to contact the publisher with their course details.)
- Â For updated Errata, Resources for Instructors and Students, and information regarding the Second Edition please visit: http://photonics.usask.ca/

The second edition represents a total revision of the first edition, with numerous additional features and enhancements.

- All chapters have been totally revised and extended.
- Numerous modern topics in photonics have been added to all the chapters.
- There are Additional Topics that can be covered in more advanced courses, or in courses that run over two semesters.
- There are many more new examples and solved problems within chapters, and many more practical end-of-chapter problems that start from basic concepts and build-up onto advanced applications.
- Nearly all the illustrations and artwork in the first edition have been revised and redrawn to better reflect the concepts.
- Numerous new illustrations have been added to convey the concepts as clearly as possible.
- Photographs have been added, where appropriate, to enhance the readability of the book; and to illustrate typical modern photonic/optoelectronic devices.
- Chapter 7 on photovoltaics has been incorporated into Ch. 6 as an Additional Topic, which has allowed more photonics-related topics to be covered in Chapters 1-5
- Advanced or complicated mathematical derivations are avoided and, instead, the emphasis is placed on concepts and engineering applications.
- Â Useful and essential equations in photonics are given with explanations; and are used in examples and problems to give the student a sense of what are typical values.
- Cross referencing in the Second Edition has been avoided as much as possible without too much repetition, and to allow various sections and chapters to be skipped as desired by the reader.
- There is greater emphasis on practical or engineering examples; care has been taken to consider various photonics/optoelectronics courses at the undergraduate level across major universities.
- The Second Edition is supported by an extensive Power Point presentation for instructors. The Power Point has all the illustrations in color, and includes additional color photos. The basic concepts and equations are also highlighted in additional slides. There are also numerous slides with examples and solved problems. The readers who have purchased a copy of the book are allowed to use the Power Point slides in their research seminars, workshops, symposia and conferences (go to http://www.pearsonhighered.com/kasap ).
- The Second Edition is supported by an extensive Solutions Manual for instructors. (Instructors need to contact the publisher with their course details.)

**Chapter 1 Wave Nature of Light 3**

1.1 Light Waves in a Homogeneous Medium 3

A. Plane Electromagnetic Wave 3

B. Maxwellâ€™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 Snellâ€™s Law and Total Internal Reflection (TIR) 22

Example 1.5.1 Beam displacement 25

1.6 Fresnelâ€™s Equations 26

A. Amplitude Reflection and Transmission Coefficients (r and t ) 26

B. Intensity, Reflectance, and Transmittance 32

C. Goos-HÃ¤nchen 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 Fabryâ€“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 Fibersâ€”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

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