Optical Signal Processing

1. Introduction.- 1.1 Why Optical Signal Processing?.- 1.2 Signal Processing: Tools and Applications.- 1.3 Arrangement of the Book.- 1.3.1 Guide for Selective Use of the Book.- 1.3.2 Note on References.- 2. Optics Fundamentals.- 2.1 Maxwell's Equations.- 2.2 Boundary Conditions.- 2.3 Snell's Laws.- 2.4 Total Internal Reflection and Optical Tunneling.- 2.5 Transmission Lines.- 2.6 Reflection and Transmission Coefficients for Electromagnetic Waves.- 2.6.1 Normal Incidence: ?i = 0.- 2.6.2 General Case.- 2.7 Group and Phase Velocity.- 2.7.1 Poynting Vector, Ray Velocity, Phase Velocity, and Group Velocity.- 2.7.2 Goos-Hanchen Effect.- 2.8 Gaussian Beam Propagation.- 2.9 Geometrical Optics.- 2.9.1 Eikonal Equation.- 2.9.2 Matrix Formulation of Geometrical Optics.- 2.9.3 Gaussian Optics Including Lenses.- 2.9.4 Optical Fiber.- 2.10 Gradient Optical Fiber.- 2.11 Integrated Optics and Step-Index Optical Fibers.- 2.11.1 Electromagnetic Waveguide Solutions.- 2.11.2 Parallel Plate Waveguide: TE Solution.- 2.11.3 Integrated Optics Problem.- 2.11.4 Multimode Group Delay in a Dielectric Waveguide.- 2.11.5 Cylindrical Waveguide.- 2.11.6 Stepped-Index Optical Fiber.- 2.12 Propagation in Anisotropic Media.- 2.12.1 Wave Vector Surface, Phase Velocity Surface, and Ray Velocity Surface.- 2.12.2 Double Refraction.- 2.13 Electro-optic Effect.- 2.13.1 General Discussion.- 2.13.2 Kerr Effect.- 2.13.3 Indirect Electro-optic Effect.- 2.14 The Acousto-optic or Elasto-optic Effect.- 2.14.1 Acousto-optic Coefficients.- 2.14.2 Acousto-optic Interaction: Thin Grating.- 2.14.3 Acousto-optic Interaction: Thick Grating.- 2.14.4 Acousto-optic Interaction Including Light Polarization: Isotropic Solids.- 2.14.5 Bragg Acousto-optic Interaction: Light Polarization Included.- 2.14.6 Bragg Diffraction: Anisotropic Case.- 2.15 Magneto-optics.- 2.15.1 Polarization and the Jones Matrix.- 2.15.2 Optical Activity.- 2.15.3 Magneto-optics: The Faraday Effect, the Voigt Effect and the Kerr Effect.- 2.16 Wave Equation with Source and Boundary.- 2.16.1 Diffraction.- 2.16.2 Solution of the Scalar Wave Equation with Source and Boundary.- 2.16.3 Solution of the Vector Wave Equation with Source and Boundary.- 2.17 Fourier Optics.- 2.17.1 Holography.- Problems.- 3. Signal Processing Fundamentals.- 3.1 Analog Signals and Systems.- 3.1.1 Linear Systems.- 3.1.2 Fourier Transforms and Frequency Response.- 3.1.3 Examples.- 3.1.4 Hilbert Transform and Causality.- 3.1.5 Time-Variant Systems.- 3.2 Discrete Systems.- 3.2.1 Examples.- 3.2.2 Sampling Theorem and Aliasing.- 3.2.3 Frequency Response of a Discrete Time Filter.- 3.3 Noise and Stochastic Processes.- 3.3.1 Linear Systems with Stochastic Input.- 3.3.2 Matched Filters.- 3.3.3 Matched Filters from the Point of View of Maximum Output.- 3.3.4 Matched Filtering of Stochastic Signals.- 3.3.5 Noise and Stochastic Processes: Discrete.- 3.3.6 Matrix Methods.- 3.3.7 Matched Filters: Discrete Case.- 3.4 Filters.- 3.5 Adaptive Filters.- 3.5.1 Linear Mean Squares Estimation.- 3.5.2 Least Mean Squares Adaptive Filters.- 3.5.3 Lattice Filters.- 3.6 Power Spectra Estimation.- 3.6.1 MA Model.- 3.6.2 AR Model.- 3.6.3 ARMA Model.- 3.7 Kalman Filtering.- 3.7.1 State-Space Formulation.- 3.7.2 The Kalman Filter.- 3.7.3 Solution of the Ricatti Equation with Constant Coefficients.- 3.7.4 Square Root Filtering.- 3.8 Two-Dimensional Signal Processing.- 3.8.1 Analog Signals and Systems.- 3.8.2 Linear Systems.- 3.8.3 The Fourier Transform and the Spatial Frequency Response.- 3.8.4 Examples of Fourier Transformation, Imaging, etc..- 3.8.5 Space-Variant Systems.- 3.8.6 Discrete Signals and Matrix Representation.- 3.9 Stochastic Processes: Multidimensional.- 3.9.1 Point Source.- 3.9.2 Partially Coherent Source Distribution.- 3.9.3 Coherent Source.- 3.9.4 Effect of a Mask.- 3.9.5 General Case.- 3.9.6 Coherency Matrix.- 3.10 The Ambiguity Function, Wigner Distribution Function and Triple Correlation.- 3.10.1 The Ambiguity Function.- 3.10.2 Wigner Distribution Function.- 3.10.3 Two-Dimensional Ambiguity and Wigner Distribution Functions.- 3.10.4 Triple and Higher-Order Correlations.- Problems.- 4. Introduction to SAW and CCD Technology.- 4.1 History of CCD and SAW Devices.- 4.1.1 Charge Coupled Devices.- 4.1.2 Surface Acoustic Waves.- 4.2 Why SAWs Became Popular and Useful in the 1960s.- 4.2.1 Bulk Ultrasound Devices.- 4.2.2 Advantages of SAWs.- 4.2.3 SAW Devices.- 4.3 Charge Coupled Devices.- 4.4 Magneto-Static Waves.- 4.4.1 MSW Field Equations and Dispersion Relations.- 4.4.2 MSW Devices.- 4.5 ACT Devices.- 4.6 Comparison of Technologies.- 4.6.1 SAW Technology.- 4.6.2 Bulk Ultrasound Devices.- 4.6.3 Charge Coupled Devices.- 4.6.4 Acoustic Charge Transport.- 4.6.5 Acousto-optics.- 4.6.6 Digital Devices: IC/VHSIC.- Appendices.- A. Matrices.- A.1 The Hamilton-Cayley Theorem.- A.2 Some Definitions.- A.3 Matrix Inversion.- A.4 Gaussian Elimination Method.- A.5 Successive Orthogonalization of a Matrix.- A.6 Circulant Matrices and Fourier Matrices.- A.7 Pseudo-Inverse, Singular-Value Decomposition, Overdetermination and Principle of Least Squares: Kalman Filtering.- A.8 Coordinate Transformation.- B. Orthogonal Functions and Polynomials.- B.1 Sturm-Liouville Equation.- B.2 Fourier Series.- B.3 Hypergeometric Series.- B.4 Legendre Polynomials.- B.5 Hermite Polynomials.- B.6 Laguerre Polynomials.- B.7 Generalized Laguerre Polynomials.- B.8 Chebyshev Polynomials.- B.9 Bessel Functions.- C. Principle of Stationary Phase.- D. Vectors.- D.1 Important Results.- D.2 Green's Theorem: Scalar.- D.3 Green's Theorem: Vector.- E. Symmetry Properties of Different Coefficients in Crystal Classes.- References.