Introduction |
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1 | (3) |
1 Optical plane waves in an unbounded medium |
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4 | (30) |
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1.1 Introduction to optical plane waves |
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4 | (10) |
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1.1.1 Plane waves and Maxwell's equations |
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4 | (3) |
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a The y-polarized plane wave |
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5 | (1) |
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b The x-polarized plane wave |
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6 | (1) |
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1.1.2 Plane waves in an arbitrary direction |
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7 | (2) |
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1.1.3 Evanescent plane waves |
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9 | (1) |
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1.1.4 Intensity and power |
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9 | (1) |
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1.1.5 Superposition and plane wave modes |
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10 | (3) |
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a Plane waves with circular polarization |
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10 | (1) |
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b Interference of coherent plane waves |
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10 | (1) |
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c Representation by summation of plane waves |
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11 | (2) |
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1.1.6 Representation of plane waves as optical rays |
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13 | (1) |
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1.2 Mirror reflection of plane waves |
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14 | (3) |
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1.2.1 Plane waves polarized perpendicular to the plane of incidence |
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14 | (1) |
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1.2.2 Plane waves polarized in the plane of incidence |
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15 | (1) |
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1.2.3 Plane waves with arbitrary polarization |
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15 | (1) |
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15 | (1) |
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1.2.5 Ray representation of reflection |
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15 | (1) |
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1.2.6 Reflection from a spherical mirror |
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16 | (1) |
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1.3 Refraction of plane waves |
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17 | (11) |
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1.3.1 Plane waves polarized perpendicular to the plane of incidence |
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17 | (2) |
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1.3.2 Plane waves polarized in the plane of incidence |
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19 | (1) |
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1.3.3 Properties of refracted and transmitted waves |
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20 | (2) |
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a Transmission and reflection at different incident angles |
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20 | (1) |
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b Total internal reflection |
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21 | (1) |
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c Refraction and reflection of arbitrary polarized waves |
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21 | (1) |
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d Ray representation of refraction |
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21 | (1) |
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1.3.4 Refraction and dispersion in prisms |
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22 | (3) |
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a Plane wave analysis of prisms |
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22 | (2) |
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24 | (1) |
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c Thin prism represented as a transparent layer with a varying index |
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24 | (1) |
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1.3.5 Refraction in a lens |
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25 | (12) |
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a Ray analysis of a thin lens |
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25 | (2) |
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b Thin lens represented as a transparency with varying index |
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27 | (1) |
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1.4 Geometrical relations in image formation |
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28 | (2) |
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1.5 Reflection and transmission at a grating |
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30 | (1) |
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1.6 Pulse propagation of plane waves |
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31 | (1) |
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32 | (2) |
2 Superposition of plane waves and applications |
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34 | (19) |
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2.1 Reflection and anti-reflection coatings |
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34 | (3) |
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2.2 Fabry-Perot resonance |
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37 | (6) |
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2.2.1 Multiple reflections and Fabry-Perot resonance |
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37 | (2) |
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2.2.2 Properties of Fabry-Perot resonance |
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39 | (2) |
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2.2.3 Applications of the Fabry-Perot resonance |
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41 | (5) |
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a The Fabry-Perot scanning interferometer |
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41 | (1) |
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b Measurement of refractive properties of materials |
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42 | (1) |
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c Resonators for filtering and time delay of signals |
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43 | (1) |
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2.3 Reconstruction of propagating waves |
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43 | (3) |
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2.4 Planar waveguide modes viewed as internal reflected plane waves |
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46 | (5) |
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2.4.1 Plane waves incident from the cladding |
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46 | (2) |
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2.4.2 Plane waves incident from the substrate |
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48 | (1) |
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a Incident plane waves with sin-1 (n, I ns) < Os < r /2 |
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48 | (1) |
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b Incident plane waves with 0 Os < sin-1(nc/ns) |
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48 | (1) |
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2.4.3 Plane waves incident within the waveguide: the planar waveguide modes |
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48 | (2) |
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2.4.4 The hollow dielectric waveguide mode |
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50 | (1) |
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51 | (2) |
3 Scalar wave equation and diffraction of optical radiation |
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53 | (20) |
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3.1 The scalar wave equation |
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54 | (1) |
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3.2 The solution of the scalar wave equation: Kirchhoff's diffraction integral |
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55 | (16) |
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3.2.1 Kirchhoff's integral and the unit impulse response |
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57 | (1) |
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3.2.2 Fresnel and Fraunhofer diffractions |
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57 | (1) |
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3.2.3 Applications of diffraction integrals |
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58 | (7) |
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a Far field diffraction pattern of an aperture |
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58 | (2) |
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b Far field radiation intensity pattern of a lens |
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60 | (2) |
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c Fraunhofer diffraction in the focal plane of a lens |
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62 | (3) |
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d The lens viewed as a transformation element |
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65 | (1) |
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3.2.4 Convolution theory and other mathematical techniques |
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65 | (10) |
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a The convolution relation |
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66 | (1) |
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b Double slit diffraction |
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66 | (1) |
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c Diffraction by an opaque disk |
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67 | (1) |
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67 | (1) |
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67 | (4) |
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71 | (2) |
4 Optical resonators and Gaussian beams |
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73 | (36) |
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4.1 Integral equations for laser cavities |
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74 | (1) |
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4.2 Modes in confocal cavities |
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75 | (11) |
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4.2.1 The simplified integral equation for confocal cavities |
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75 | (2) |
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4.2.2 Analytical solutions of the modes in confocal cavities |
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77 | (1) |
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4.2.3 Properties of resonant modes in confocal cavities |
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78 | (5) |
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a The transverse field pattern |
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78 | (1) |
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b The resonance frequency |
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79 | (1) |
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c The orthogonality of the modes |
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79 | (1) |
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d A simplified analytical expression of the field |
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80 | (1) |
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81 | (1) |
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81 | (1) |
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g The line width of resonances |
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82 | (1) |
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4.2.4 Radiation fields inside and outside the cavity |
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83 | (3) |
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a The far field pattern of the TEM modes |
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84 | (1) |
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b A general expression for the TEMlm Gaussian modes |
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84 | (1) |
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c An example to illustrate confocal cavity modes |
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85 | (1) |
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4.3 Modes of non-confocal cavities |
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86 | (5) |
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4.3.1 Formation of a new cavity for known modes of confocal resonator |
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86 | (2) |
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4.3.2 Finding the virtual equivalent confocal resonator for a given set of reflectors |
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88 | (1) |
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4.3.3 A formal procedure to find the resonant modes in non-confocal cavities |
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89 | (2) |
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4.3.4 An example of resonant modes in a non-confocal cavity |
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91 | (1) |
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4.4 The propagation and transformation of Gaussian beams (the ABCD matrix) |
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91 | (16) |
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4.4.1 A Gaussian mode as a solution of Maxwell's equation |
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92 | (2) |
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4.4.2 The physical meaning of the terms in the Gaussian beam expression |
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94 | (1) |
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4.4.3 The analysis of Gaussian beam propagation by matrix transformation |
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95 | (2) |
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4.4.4 Gaussian beam passing through a lens |
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97 | (1) |
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4.4.5 Gaussian beam passing through a spatial filter |
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98 | (2) |
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4.4.6 Gaussian beam passing through a prism |
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100 | (2) |
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4.4.7 Diffraction of a Gaussian beam by a grating |
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102 | (1) |
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4.4.8 Focusing a Gaussian beam |
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103 | (1) |
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4.4.9 An example of Gaussian mode matching |
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104 | (1) |
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4.4.10 Modes in complex cavities |
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105 | (1) |
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4.4.11 An example of the resonance mode in a ring cavity |
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106 | (1) |
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107 | (2) |
5 Optical waveguides and fibers |
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109 | (39) |
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5.1 Introduction to optical waveguides and fibers |
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109 | (3) |
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5.2 Electromagnetic analysis of modes in planar optical waveguides |
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112 | (1) |
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5.2.1 The asymmetric planar waveguide |
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112 | (1) |
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5.2.2 Equations for TE and TM modes |
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112 | (1) |
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5.3 TE modes of planar waveguides |
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113 | (8) |
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5.3.1 TE planar guided-wave modes |
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114 | (1) |
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5.3.2 TE planar guided-wave modes in a symmetrical waveguide |
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115 | (2) |
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5.3.3 The cut-off condition of TE planar guided-wave modes |
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117 | (1) |
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5.3.4 An example of TE planar guided-wave modes |
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118 | (1) |
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5.3.5 TE planar substrate modes |
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119 | (1) |
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5.3.6 TE planar air modes |
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119 | (2) |
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5.4 TM modes of planar waveguides |
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121 | (5) |
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5.4.1 TM planar guided-wave modes |
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121 | (1) |
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5.4.2 TM planar guided-wave modes in a symmetrical waveguide |
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122 | (1) |
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5.4.3 The cut-off condition of TM planar guided-wave modes |
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123 | (1) |
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5.4.4 An example of TM planar guided-wave modes |
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123 | (1) |
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5.4.5 TM planar substrate modes |
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124 | (1) |
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5.4.6 TM planar air modes |
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125 | (1) |
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5.4.7 Two practical considerations for TM modes |
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126 | (1) |
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5.5 Guided waves in planar waveguides |
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126 | (9) |
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5.5.1 The orthogonality of modes |
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126 | (1) |
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5.5.2 Guided waves propagating in the y-z plane |
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127 | (1) |
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5.5.3 Convergent and divergent guided waves |
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127 | (1) |
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5.5.4 Refraction of a planar guided wave |
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128 | (1) |
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5.5.5 Focusing and collimation of planar guided waves |
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129 | (2) |
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129 | (1) |
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129 | (1) |
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c The Fresnel diffraction lens |
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130 | (1) |
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5.5.6 Grating diffraction of planar guided waves |
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131 | (3) |
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5.5.7 Excitation of planar guided-wave modes |
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134 | (1) |
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5.5.8 Multi-layer planar waveguides |
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135 | (1) |
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135 | (7) |
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5.6.1 The effective index analysis |
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136 | (4) |
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5.6.2 An example of the effective index method |
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140 | (1) |
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5.6.3 Channel waveguide modes of complex structures |
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141 | (1) |
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5.7 Guided-wave modes in optical fibers |
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142 | (4) |
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5.7.1 Guided-wave solutions of Maxwell's equations |
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142 | (2) |
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5.7.2 Properties of the modes in fibers |
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144 | (1) |
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5.7.3 Properties of optical fibers in applications |
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145 | (1) |
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146 | (1) |
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146 | (2) |
6 Guided-wave interactions |
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148 | (28) |
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6.1 Review of properties of the modes in a waveguide |
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149 | (1) |
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6.2 Perturbation analysis |
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150 | (3) |
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6.2.1 Derivation of perturbation analysis |
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150 | (2) |
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6.2.2 A simple application of perturbation analysis: perturbation by a nearby dielectric |
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152 | (1) |
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6.3 Coupled mode analysis |
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153 | (10) |
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6.3.1 Modes of two uncoupled parallel waveguides |
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153 | (1) |
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6.3.2 Modes of two coupled waveguides |
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154 | (1) |
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6.3.3 An example of coupled mode analysis: the grating reflection filter |
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155 | (5) |
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6.3.4 Another example of coupled mode analysis: the directional coupler |
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160 | (3) |
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163 | (1) |
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6.5 Super modes of two parallel waveguides |
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163 | (6) |
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6.5.1 Super modes of two well-separated waveguides |
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164 | (1) |
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6.5.2 Super modes of two coupled waveguides |
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164 | (2) |
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6.5.3 Super modes of two coupled identical waveguides |
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166 | (4) |
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a Super modes obtained from the effective index method |
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166 | (2) |
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b Super modes obtained from coupled mode analysis |
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168 | (1) |
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6.6 Directional coupling of two identical waveguides viewed as super modes |
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169 | (1) |
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6.7 Super mode analysis of the adiabatic Y-branch and Mach-Zehnder interferometer |
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170 | (5) |
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170 | (1) |
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6.7.2 Super mode analysis of a symmetric Y-branch |
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171 | (2) |
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171 | (2) |
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173 | (1) |
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6.7.3 Super mode analysis of the Mach-Zehnder interferometer |
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173 | (2) |
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175 | (1) |
7 Passive waveguide devices |
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176 | (20) |
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7.1 Waveguide and fiber tapers |
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176 | (1) |
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176 | (10) |
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7.2.1 The Y-branch equal-power splitter |
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177 | (1) |
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7.2.2 The directional coupler |
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177 | (1) |
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7.2.3 The multi-mode interference coupler |
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178 | (4) |
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182 | (4) |
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7.3 The phased array channel waveguide frequency demultiplexer |
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186 | (2) |
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7.4 Wavelength filters and resonators |
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188 | (7) |
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188 | (1) |
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189 | (1) |
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7.4.3 The ring resonator wavelength filter |
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189 | (5) |
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a Variable-gap directional coupling |
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190 | (1) |
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b The resonance condition of the couple ring |
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191 | (1) |
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192 | (1) |
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d The free spectral range and the Q-factor |
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192 | (2) |
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7.4.4 The ring resonator delay line |
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194 | (1) |
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195 | (1) |
8 Active opto-electronic guided-wave components |
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196 | (23) |
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8.1 The effect of electro-optical χ |
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197 | (3) |
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8.1.1 Electro-optic effects in plane waves |
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197 | (1) |
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8.1.2 Electro-optic effects in waveguides at low frequencies |
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198 | (2) |
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198 | (1) |
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199 | (1) |
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8.2 The physical mechanisms to create Δχ |
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200 | (11) |
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200 | (5) |
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202 | (1) |
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203 | (1) |
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c The III-V compound semiconductor waveguide |
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203 | (2) |
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8.2.2 &dELTA;&CHI;" in semiconductors |
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205 | (6) |
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a Stimulated absorption and the bandgap |
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205 | (1) |
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b The quantum-confined Stark effect, QCSE |
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206 | (5) |
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8.3 Active opto-electronic devices |
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211 | (4) |
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8.3.1 The phase modulator |
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211 | (1) |
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8.3.2 The Mach-Zhender modulator |
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212 | (1) |
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8.3.3 The directional coupler modulator/switch |
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213 | (1) |
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8.3.4 The electro-absorption modulator |
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214 | (1) |
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8.4 The traveling wave modulator |
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215 | (2) |
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217 | (2) |
Appendix |
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219 | (6) |
Index |
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225 | |