Optics, Optoelectronics and Photonics

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1 Optics, Optoelectronics and Photonics Engineering Principles and Applications Alan Billings Emeritus Professor, University of Western Australia New York London Toronto Sydney Tokyo Singapore

2 v Contents Preface xiii Chapter 1 Basic optical principles Introduction Geometric optics Snell's law and refracted rays The matrix approach to translation of ray in material of constant refractive index The matrix description of ray refraction at a plane interface 5, The matrix description of a simple composite optical system The matrix description of refraction at a spherical surface, when the paraxial assumption applies The matrix description of refraction by a lens The matrix description of simple optical systems containing lenses The imaging properties of a thin lens Real and virtual images The matrix description of other refracting components The matrix description of reflecting elements Polarization The nature of unguided optical traveling waves The Jones calculus The Brewster effect Coherence and incoherence Diffraction Anisotropy and non-linearity 32 v

3 vi Contents Chapter 2 Fourier optics Fourier integrals in optics Introduction to Fourier integrals The Fourier integral in one and two dimensions The representation of a propagating wave as the superposition of uniform plane waves Fresnel and Fraunhofer diffraction Examples of Fraunhofer diffraction patterns Fourier transformations performed by thin lenses Focal plane transformations for a thin lens The propagation of gaussian beams The impulse response of optical components and systems, and ) the use of the optical propagator function The optical propagator function *F The quasi-fourier transforming properties of a lens when the object is not in the front focal plane The input-output relationship for a system using a point source with a transparency and a lens The quasi-fourier transform of transparency placed between a lens and its output focal plane 64 Chapter 3 Diffraction gratings and holography' Introduction to holography The thin holographic diffraction grating The general thin hologram The thin transmission hologram using a uniform plane wave reference beam Holograms of three-dimensional objects The angular spectrum of hologram output Thick holographic amplitude modulated gratings Reading thick amplitude gratings The Bragg effect Thick phase modulated gratings The diffraction efficiency of gratings, and the coupled wave equations Thick holograms The hologram of a two-dimensional object, and the Fourier hologram Fourier holography Computer-generated holograms Computer-generated Fourier transform holograms 100 Chapter 4 Optical materials and their properties Tensor preliminaries Introduction Summation notation Tensor transformation rules 110

4 Contents vii Tensor description of optical and electrical properties of materials The influence of crystal symmetry and thermodynamics upon tensor components Natural optical birefringence Fresnel's equations Uniaxial materials Applications of natural birefringence Controlled birefringence The source and nature of controlled birefringence The electro-optic or Pockels effect The transverse switching modulator The longitudinal switching modulator Bulk phase and amplitude modulators Transit time limitations of bulk modulators Optical activity Eigenmodes and eigenvectors of waves propagating in anisotropic materials 135 Chapter 5 Guided optical waves Introduction to waveguiding Solution to Maxwell's equations for isotropic planar waveguides Modes in slab isotropic waveguides Transverse electric modes in isotropic slab waveguides ТЕ modes in the symmetrical isotropic slab waveguide TM modes in the symmetrical isotropic slab waveguide Mode cut-off conditions for isotropic multimode symmetrical guides ТЕ modes in the asymmetric isotropic slab waveguide TM modes in asymmetric isotropic slab waveguides General classification of waveguide modes and waveguide field distributions Normalized modes and orthogonality Propagation in rectangular dielectric waveguides Propagating modes in anisotropic slab waveguides Propagation in optical fibers The modal approach to propagation in an isotropic step index fiber Modes in step index fiber when the wave is weakly confined Modal dispersion in weakly guiding multimode fibers Dispersion in single-mode weakly guiding fibers The soliton in non-linear fibers Birefringent fibers and polarization-maintaining fibers 171 Chapter 6 Coherent optical sources Introduction to lasers Stimulated and spontaneous emission 176

5 viii Contents The gain of optical medium with inverted population Methods of pumping to obtain population inversion The Fabry-Perot cavity Threshold population inversion for lasing Lasing frequencies The rate equations for the four-level laser Homogeneous and inhomogeneous lasers Comparison between three-level and four-level lasers Examples of gas lasers The HeNe laser The C0 2 laser The ion laser Modes of laser operation The Q-switched laser The mode-locked laser The single-mode laser Examples of solid state lasers The ruby laser The Nd-YAG laser and the Nd-glass laser The color center laser Semiconductor diode lasers The hetero-junction laser The external cavity laser The surface-emitting diode laser Fiber lasers The soliton laser The erbium doped fiber amplifier (EDFA) The free electron laser 208 Chapter 7 Optical detection Methods of optical detection Detectors that operate as direct energy converters Hybrid detectors that operate as indirect energy converters Detectors that operate as energy controllers rather than energy converters Cathode emission photodetectors Single-stage cathode emitters The photomultiplier The semiconductor photodiode The pn junction photodetector The Schottky barrier photodiode The pin photodiode The semiconductor avalanche detector The operating wavelength and temporal response of photodetectors The operational wavelengths of photodetectors The temporal response of photodetectors The noise performance of photodetectors Thermal noise 230

6 Contents Sources of noise in photodetectors The noise performance of direct photodetectors The noise performance of photodetectors in indirect detection modes 233 Chapter 8 Non-linear optics Introduction Material non-linearity second order in the optical electric field Second harmonic polarization waves produced by optical waves passing through a non-linear optical material Polarization waves for KDP and its isomorphs Launching second harmonic electromagnetic waves An extraordinary second harmonic wave launched by an ordinary fundamental wave in a KDP crystal An ordinary second harmonic wave launched by a combination of an ordinary fundamental wave and an extraordinary fundamental wave in a KDP crystal Second harmonic waves launched in materials for which X 323 is non-zero Phase-matching the second harmonic generator Temperature-matching Angle-matching Polarization waves for the parametric amplifier Launching an electromagnetic wave at Щ due to inputs at a>i and щ Phase-matching parametric amplifiers Temperature-matching Angle phase-matching Degenerate four-wave mixing, using the Kerr effect Phase conjugation produced by the photorefractive effect Two-wave mixing using photorefractive materials Phase-conjugate mirrors and their applications The optical properties of the phase-conjugate mirror Applications of phase-conjugate mirrors 267 Chapter 9 Coupled wave and other waveguide devices Introduction to waveguide devices Coupling between modes in slab waveguides Devices based on coupling between modes in a single slab guide Devices based upon coupling between modes in multiple slab guide structures Coupled wave equations for mullimode slab waveguide structures The general form of the coupled wave equations for co-directional and contra-directional coupling between ТЕ modes The coupled wave equations for co-directional coupling in a symmetrical isotropic two-waveguide structure 277 ix

7 x Contents Coupling between modes in a single corrugated isotropic slab waveguide Slab waveguide devices based on interaction between acoustic and optical waves Coupling between modes in a single anisotropic slab waveguide Coupling between modes in channel guides Specific examples of waveguide devices Coupled wave directional couplers Electro-optic coupled wave modulators Interferometric electro-optic modulators Traveling wave modulators Mode conversion and control Corrugated waveguide devices Acousto-optic modulators, deflectors and switches Waveguide amplifiers and frequency converters Multiple quantum well materials and their application in waveguide devices Integrated optics 310 Chapter 10 Optical sensors Introduction to fiber sensors Interferometry with and without the use of fibers Sources of physical change to the transmission properties of intrinsic fiber sensors Sources of physical change to the transmission properties of sensing elements incorporated in hybrid fiber sensors Optical gyroscopes The Sagnac effect Non-fiber optical gyroscopes The biasing and sensitivity of the ring laser gyroscope The multi-oscillator ring laser gyroscope Fiber gyroscopes The phase-conjugate fiber gyroscope 330 Chapter 11 Optical computing and processing Optical computing and optics in computing The distinction between digital and non-digital computers and computing Analog optical computing and analog optical processors The optically addressed spatial light modulator (SLM) The electrically addressed spatial light modulator Matrix-vector multiplication, matrix-matrix multiplication, and other linear algebraic processes using optical systolic arrays Fourier transform computation Pattern recognition using a matched filter Read-only memory 349

8 Contents xi Page-oriented holographic memory (POHM) Adaptable phase-conjugate three-dimensional memory Optical neural networks Digital computer architectures and their relevance to optical computing Systolic array processing Wavefront array processing The use of optics in hybrid digital computers The intra-chip, inter-chip and inter-subsystem communication problem Clock distribution Data communication at intra-chip, inter-chip and board-toboard level Electro-optic and opto-electric transducers Optically sampled analog-to-digital conversion Optical digital computing Optical bistability Ultra-fast optical storage and optical logic elements 370 Appendix A Fourier transforms 373 Appendix В The optical propagator operator *P 377 AppendixC Tensor transformations 379 Appendix D Tensor components and crystal classes 385 Appendix E Diagonalizing second order tensors 391 Index 397

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