Lasers and Electro-optics

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1 Lasers and Electro-optics Second Edition CHRISTOPHER C. DAVIS University of Maryland III ^0 CAMBRIDGE UNIVERSITY PRESS

2 Preface to the Second Edition page xv 1 Electromagnetic waves, light, and lasers The laser Light and electromagnetic waves Some basic electromagnetic theory The polarization state of an electromagnetic wave Electromagnetic waves and their propagation through matter Spontaneous and stimulated transitions Lasers as oscillators The energy levels of atoms, molecules, and condensed matter Amplification at optical frequencies The relation between energy density and intensity The intensity of a beam of electromagnetic radiation in terms of photon flux Black-body radiation The relation between the Einstein A and B coefficients The effect of level degeneracy The ratio of spontaneous and stimulated transitions Problems 30 Further reading 31 References 31-2 Optical frequency amplifiers Introduction Homogeneous line broadening Inhomogeneous broadening Optical frequency amplification Optical frequency oscillation saturation The power output from a laser amplifier The electron oscillator model of a radiative transition The classical oscillator explanation for stimulated emission Problems 69 References 70

3 3 An introduction to two practical laser systems Introduction Three- and four-level lasers The ruby laser The helium-neon laser 79 References 84 4 Optical resonators containing amplifying media Introduction Optical resonators containing amplifying media The oscillation frequency Multimode laser oscillation Mode-beating The power output of a laser Optimum coupling Problems 107 References Laser radiation Introduction Diffraction Babinet's principle Two parallel narrow slits A single slit Two-dimensional apertures Laser modes Beam divergence The linewidth of laser radiation Coherence properties Interference Problems 130 References Control of laser oscillators Introduction Multimode operation Single-longitudinal-mode operation Mode-locking Methods of mode-locking Pulse compression Attosecond pulses 149 References Optically pumped solid-state lasers Introduction 153

4 7.2 Optical pumping in three- and four-level lasers Pulsed versus continuous-wave operation Threshold population inversion and the stimulated-emission cross-section Paramagnetic-ion solid-state lasers The Nd:YAG laser Continuous-wave operation ofthe Nd:YAG laser The Nd3+glass laser Geometrical arrangements for optical pumping High-power pulsed solid-state lasers Diode-pumped solid-state lasers Fiber lasers Relaxation oscillations (spiking) Rate equations for relaxation oscillation Undamped relaxation oscillations Giant-pulse (g-switched) lasers A theoretical description of the ^-switching process Problem 203 References Gas lasers Introduction Excitation schemes The argon-ion laser Pumping saturation in gas-laser systems Pulsed gas lasers Continuous-wave ion lasers "Metal"-vapor ion lasers Gas discharges for exciting gas lasers Rate equations for gas-discharge lasers Problem 228 References Molecular gas lasers I Introduction The energy levels of molecules Vibrations of a polyatomic molecule Rotational energy states Rotational populations The overall energy state of a molecule The carbon dioxide laser The carbon monoxide laser Other gas-discharge molecular lasers 251 References 251

5 10 Molecular gas lasers II Introduction Gas transport lasers Gas dynamic lasers High-pressure pulsed gas lasers Ultraviolet molecular gas lasers Photodissociation lasers Chemical lasers Far-infrared lasers Problem 274 References Tunable lasers Introduction The titanium-sapphire laser Organic dye lasers Calculation of threshold pump power in dye lasers Inorganic liquid lasers Free-electron lasers Problems 298 References Semiconductor lasers Introduction Semiconductor physics background Carrier concentrations Intrinsic and extrinsic semiconductors The p-n junction Recombination and luminescence Heterojunctions Semiconductor lasers The gain coefficient of a semiconductor laser Threshold current and power-voltage characteristics Longitudinal and transverse modes Quantum-well lasers Semiconductor laser structures Surface-emitting lasers Laser diode arrays and broad-area lasers Blue-green lasers Quantum cascade lasers Silicon lasers Modulation of semiconductor lasers Problems 356

6 Further reading 357 References Passive optical systems Introduction The propagation of rays and waves through isotropic media Simple reflection and refraction analysis Paraxial-ray analysis Non-imaging light collectors Generalized imaging systems The numerical aperture Apertures, stops, and pupils Vignetting Exact ray tracing and aberrations Chromatic aberrations Geometrical aberrations Spot diagram The modulation transfer function The use of impedances in optics Problems 406 References Periodic optical systems, resonators, and inhomogeneous media Introduction Plane waves in media with complex refractive indices Negative-refractive-index materials Structures with periodically varying dielectric properties The transfer matrix for a single slab Theetalon A thin metal film A stratified medium of multiple slabs Fiber Bragg gratings Analysis of multi-layer structures by impedance techniques Photonic crystals Periodic lens sequences The identical-thin-lens waveguide The propagation of rays in mirror resonators The propagation of rays in isotropic media with refractive-index gradients Media with a Gaussian radial index variation The propagation of spherical waves Problems 436 References The optics of Gaussian beams Introduction 438

7 15.2 Beam-wave solutions of the wave equation Higher-order modes Transformation of Gaussian beams by general optical systems The transformation of a Gaussian beam by a lens Gaussian beams in lens waveguides The propagation of a Gaussian beam in a medium with a quadratic refractive-index profile The propagation of Gaussian beams in media with spatial gain or absorption variations Propagation in a medium with a parabolic gain profile Gaussian beams in plane and spherical mirror resonators Symmetrical resonators Examples of resonator design Diffraction losses Unstable resonators Other beam waves Problems 478 References Optical fibers and waveguides Introduction Ray theory of cylindrical optical fibers Ray theory of a dielectric-slab guide The Goos-Hanchen shift Wave theory of the dielectric-slab guide P waves in the slab guide Dispersion curves and field distributions in a slab waveguide S waves in the slab guide Practical slab guide geometries Cylindrical dielectric waveguides Modes and field patterns The weakly guiding approximation Mode patterns Cutoff frequencies Multimode fibers Fabrication of optical fibers Dispersion in optical fibers Holey fibers Solitons Erbium-doped fiber amplifiers Coupling optical sources and detectors to fibers Problems 535 References 536

8 17 The optics of anisotropic media Introduction The dielectric tensor Stored electromagnetic energy in anisotropic media Propagation of monochromatic plane waves in anisotropic media The two possible directions ofd for a given wave vector are orthogonal Angular relationships involving D, E, H, k, and the Poynting vector S The indicatrix Uniaxial crystals Index surfaces Other surfaces related to the uniaxial indicatrix Huygenian constructions Retardation Biaxial crystals Intensity transmission through polarizer/waveplate/polarizer combinations The Jones calculus Mueller calculus Problems 578 References The electro-optic and acousto-optic effects and modulation of light beams Introduction to the electro-optic effect The linear electro-optic effect The quadratic electro-optic effect Longitudinal electro-optic modulation Transverse electro-optic modulation Electro-optic amplitude modulation Electro-optic phase modulation High-frequency waveguide electro-optic modulators Other high-frequency electro-optic devices Electro-absorption modulators Electro-optic beam deflectors Acousto-optic modulators Applications of acousto-optic modulators Construction and materials for acousto-optic modulators Problem 620 References Introduction to nonlinear processes Introduction Anharmonic potentials and nonlinear polarization Nonlinear susceptibilities and mixing coefficients Second-harmonic generation 629

9 19.5 The linear electro-optic effect Parametric and other nonlinear processes Macroscopic and microscopic susceptibilities Problem 638 References Wave propagation in nonlinear media Introduction Electromagnetic waves and nonlinear polarization Second-harmonic generation The effective nonlinear coefficient deff Phase matching Beam walk-off and 90 phase matching Second-harmonic generation with Gaussian beams Up-conversion and difference-frequency generation Optical parametric amplification Parametric oscillators Parametric-oscillator tuning Phase conjugation Optical bistability Practical details of the use of crystals for nonlinear applications Problems 680 References Detection of optical radiation Introduction Noise Detector performance parameters Practical characteristics of optical detectors Thermal detectors Detection limits for optical detector systems Coherent detection The bit-error rate Problems 733 References Coherence theory Introduction Square-law detectors The analytic signal Correlation functions Temporal coherence Spatial coherence Spatial coherence with an extended source 751

10 22.8 Propagation laws of partial coherence Propagation from a finite plane surface The van Cittert-Zernike theorem The spatial coherence of a quasi-monochromatic, uniform, spatially incoherent circular source Intensity-correlation interferometry Intensity fluctuations Photon statistics The Hanbury Brown-Twiss interferometer The Hanbury Brown-Twiss experiment with photon-count correlations Squeezed light 780 References Laser applications Optical communication systems Optical amplification and wavelength-division multiplexing Holography Medical applications of lasers Laser weapons Laser isotope separation Laser plasma generation and fusion 813 References 816 Appendix 1 Optical terminology 821 Appendix 2 The 5-function 824 Appendix 3 Black-body radiation formulas 826 Appendix 4 RLC circuits 828 Appendix 5 Storage and transport of energy by electromagnetic fields 831 Appendix 6 The reflection and refraction of a plane electromagnetic wave at a boundary between two isotropic media of different refractive indices 834 Appendix 7 The vector differential equation for light rays 837 Appendix 8 Symmetry properties of crystals and the 32 crystal classes 841 Appendix 9 Tensors 845 Appendix10 Bessel-function relations 848 Appendix 11 Green's functions 849 Appendix 12 Recommended values of some physical constants 852 Index 853

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