Chapter 1 Wave Nature of Light 19

1.1 Light Waves in a Homogeneous Medium 19

A. Plane Electromagnetic Wave 19

B. Maxwell’s Wave Equation and Diverging Waves 22

Example 1.1.1 A diverging laser beam 26

1.2 Refractive Index and Dispersion 26

Example 1.2.1 Sellmeier equation and diamond 29

Example 1.2.2 Cauchy equation and diamond 30

1.3 Group Velocity and Group Index 30

Example 1.3.1 Group velocity 33

Example 1.3.2 Group velocity and index 33

Example 1.3.3 Group and phase velocities 34

1.4 Magnetic Field, Irradiance, and Poynting Vector 34

Example 1.4.1 Electric and magnetic fields in light 37

Example 1.4.2 Power and irradiance of a Gaussian beam 37

1.5 Snell’s Law and Total Internal Reflection (TIR) 38

Example 1.5.1 Beam displacement 41

1.6 Fresnel’s Equations 42

A. Amplitude Reflection and Transmission Coefficients (r and t ) 42

B. Intensity, Reflectance, and Transmittance 48

C. Goos-H＆auml;nchen Shift and Optical Tunneling 49

Example 1.6.1 Reflection of light from a less dense medium (internal

reflection) 51

Example 1.6.2 Reflection at normal incidence, and internal and external

reflection 52

Example 1.6.3 Reflection and transmission at the Brewster angle 53

1.7 Antireflection Coatings and Dielectric Mirrors 54

A. Antireflection Coatings on Photodetectors and Solar Cells 54

Example 1.7.1 Antireflection coating on a photodetector 55

B. Dielectric Mirrors and Bragg Reflectors 56

Example 1.7.2 Dielectric mirror 58

1.8 Absorption of Light and Complex Refractive Index 59

Example 1.8.1 Complex refractive index of InP 62

Example 1.8.2 Reflectance of CdTe around resonance absorption 63

1.9 Temporal and Spatial Coherence 63

Example 1.9.1 Coherence length of LED light 66

1.10 Superposition and Interference of Waves 67

1.11 Multiple Interference and Optical Resonators 69

Example 1.11.1 Resonator modes and spectral width of a semiconductor

Fabry–Perot cavity 73

1.12 Diffraction Principles 74

A. Fraunhofer Diffraction 74

Example 1.12.1 Resolving power of imaging systems 79

B. Diffraction Grating 80

Example 1.12.2 A reflection grating 83

Additional Topics 84

1.13 Interferometers 84

1.14 Thin Film Optics: Multiple Reflections in Thin Films 86

Example 1.14.1 Thin film optics 88

1.15 Multiple Reflections in Plates and Incoherent Waves 89

1.16 Scattering of Light 90

1.17 Photonic Crystals 92

Questions and Problems 98

Chapter 2 Dielectric Waveguides and Optical Fibers 111

2.1 Symmetric Planar Dielectric Slab Waveguide 111

A. Waveguide Condition 111

B. Single and Multimode Waveguides 116

C. TE and TM Modes 116

Example 2.1.1 Waveguide modes 117

Example 2.1.2 V-number and the number of modes 118

Example 2.1.3 Mode field width, 2wo 119

2.2 Modal and Waveguide Dispersion in Planar

Waveguides 120

A. Waveguide Dispersion Diagram and Group Velocity 120

B. Intermodal Dispersion 121

C. Intramodal Dispersion 122

2.3 Step-Index Optical Fiber 123

A. Principles and Allowed Modes 123

Example 2.3.1 A multimode fiber 128

Example 2.3.2 A single-mode fiber 128

B. Mode Field Diameter 128

Example 2.3.3 Mode field diameter 129

C. Propagation Constant and Group Velocity 130

Example 2.3.4 Group velocity and delay 131

D. Modal Dispersion in Multimode Step-Index Fibers 132

Example 2.3.5 A multimode fiber and dispersion 132

2.4 Numerical Aperture 133

Example 2.4.1 A multimode fiber and total acceptance angle 134

Example 2.4.2 A single-mode fiber 134

2.5 Dispersion In Single-Mode Fibers 135

A. Material Dispersion 135

B. Waveguide Dispersion 136

C. Chromatic Dispersion 138

D. Profile and Polarization Dispersion Effects 138

Example 2.5.1 Material dispersion 140

Example 2.5.2 Material, waveguide, and chromatic dispersion 141

Example 2.5.3 Chromatic dispersion at different wavelengths 141

Example 2.5.4 Waveguide dispersion 142

2.6 Dispersion Modified Fibers and Compensation 142

A. Dispersion Modified Fibers 142

B. Dispersion Compensation 144

Example 2.6.1 Dispersion compensation 146

2.7