Contents. Part I Fundamentals of Lasers 1 Introduction... 3

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1 Contents Part I Fundamentals of Lasers 1 Introduction Basic Optics Introduction TheWaveEquation Linearly Polarized Waves Circularly and Elliptically Polarized Waves TheDiffractionIntegral DiffractionofaGaussianBeam Intensity Distribution at the Back Focal Plane of a Lens Two-Beam Interference Multiple Reflections from a Plane Parallel Film Modes of the Fabry Perot Cavity Problems Elements of Quantum Mechanics Introduction The One-Dimensional Schrödinger Equation The Three-Dimensional Schrödinger Equation Physical Interpretation of anditsnormalization DensityofStates Expectation Values of Dynamical Quantities TheCommutator Orthogonality of Wave Functions Spherically Symmetric Potentials TheTwo-BodyProblem The Hydrogen-Like Atom Problem Problems xi

2 xii Contents 4 Einstein Coefficients and Light Amplification Introduction TheEinsteinCoefficients AbsorptionandEmissionCrossSections LightAmplification The Threshold Condition Line Broadening Mechanisms Natural Broadening Collision Broadening Doppler Broadening Saturation Behavior of Homogeneously and Inhomogeneously Broadened Transitions Quantum Theory for the Evaluation of the Transition RatesandEinsteinCoefficients Interaction with Radiation Having a Broad Spectrum Interaction of a Near-Monochromatic Wave with an Atom Having a Broad Frequency Response More Accurate Solution for the Two-Level System Problems Laser Rate Equations Introduction TheTwo-LevelSystem TheThree-LevelLaserSystem TheFour-LevelLaserSystem Variation of Laser Power Around Threshold OptimumOutputCoupling Problems Semiclassical Theory of the Laser Introduction Cavity Modes PolarizationoftheCavityMedium First-Order Theory Higher Order Theory Optical Resonators Introduction Modes of a Rectangular Cavity and the Open Planar Resonator Spherical Mirror Resonators The Quality Factor The Ultimate Linewidth of a Laser ModeSelection TransverseModeSelection LongitudinalModeSelection

3 Contents xiii 7.7 PulsedOperationofLasers Q-Switching Techniques for Q-Switching Mode Locking Modes of Confocal Resonator System Modes of a General Spherical Resonator Problems Vector Spaces and Linear Operators: Dirac Notation Introduction TheBraandKetNotation Linear Operators TheEigenvalueEquation Observables The Harmonic Oscillator Problem TheNumberOperator The Uncertainty Product The Coherent States TimeDevelopmentofStates TheDensityOperator The Schrödinger and Heisenberg Pictures Problems Quantum Theory of Interaction of Radiation Field with Matter Introduction Quantization of the Electromagnetic Field The Eigenkets of the Hamiltonian The Coherent States Squeezed States of Light Transition Rates The Phase Operator Photons Incident on a Beam Splitter Single-Photon Incident on a Beam Splitter MovingMirrorinOneArm Problems Properties of Lasers Introduction LaserBeamCharacteristics Coherence Properties of Laser Light Temporal Coherence Spatial Coherence Some Laser Systems Introduction

4 xiv Contents 11.2 RubyLasers Neodymium-Based Lasers Nd:YAGLaser Nd:GlassLaser Titanium Sapphire Laser TheHe NeLaser TheArgonIonLaser The CO 2 Laser DyeLasers Problems Doped Fiber Amplifiers and Lasers Introduction TheFiberLaser Basic Equations for Amplification in Erbium-Doped Fiber GaussianApproximation GaussianEnvelopeApproximation Solutions Under Steady State FiberLasers Minimum Required Doped Fiber Length Threshold LaserOutputPower SlopeEfficiency Erbium-Doped Fiber Amplifier TransparencyPower Mode Locking in Fiber Lasers Non-linear Polarization Rotation Mode Locking Using Non-linear Polarization Rotation Semiconductor Saturable Absorbers Problems Semiconductor Lasers Introduction Some Basics of Semiconductors EVersusk Optical Gain in Semiconductors DensityofStates Probability of Occupancy of States InteractionwithLight JointDensityofStates AbsorptionandEmissionRates LightAmplification GainCoefficient Electron Hole Population and Quasi-Fermi Levels GaininaForward-Biasedp njunction

5 Contents xv Laser Oscillation HeterostructureLasers Quantum Well Lasers JointDensityofStates Materials LaserDiodeCharacteristics Vertical Cavity Surface-Emitting Lasers (VCSELs) Problems Optical Parametric Oscillators Introduction Optical Non-linearity ParametricAmplification Singly Resonant Oscillator Doubly Resonant Oscillator Frequency Tuning Phase Matching Problems Part II Some Important Applications of Lasers 15 Spatial Frequency Filtering and Holography Introduction Spatial Frequency Filtering Holography Problems Laser-Induced Fusion Introduction The Fusion Process The Laser Energy Requirements The Laser-Induced Fusion Reactor Light Wave Communications Introduction CarrierWaveCommunication Analog Modulation Digital Modulation OpticalFibersinCommunication TheOpticalFiber WhyGlassFibers? Attenuation of Optical Fibers NumericalApertureoftheFiber Multimode and Single-Mode Fibers Single-ModeFiber Spot Size of the Fundamental Mode

6 xvi Contents 17.10PulseDispersioninOpticalFibers Dispersion in Multimode Fibers MaterialDispersion Dispersionand Bit Rate DispersioninSingle-Mode Fibers Dispersion and Maximum Bit Rate in Single-ModeFibers Problems Lasers in Science Introduction Second-Harmonic Generation StimulatedRamanEmission Intensity-Dependent Refractive Index LasersinChemistry LasersandEtherDrift Lasers and Gravitational Waves RotationoftheEarth Photon Statistics Lasers in Isotope Separation Separation Using Radiation Pressure Separation by Selective Photoionization or Photodissociation Photochemical Separation Problems Lasers in Industry Introduction ApplicationsinMaterialProcessing LaserWelding Hole Drilling Laser Cutting OtherApplications Laser Tracking Lidar LasersinMedicine Precision Length Measurement Laser Interferometry and Speckle Metrology Homodyne and Heterodyne Interferometry Holographic Interferometry Laser Interferometry Lithography Speckle Metrology VelocityMeasurement LasersinInformationStorage Bar Code Scanner Problems

7 Contents xvii The Nobel Lectures Production of coherent radiation by atoms and molecules Charles H. Townes Quantum electronics A.M. Prochorov Semiconductor lasers NikolaiG.Basov PassionforPrecision Theodor W. Hänsch Appendix A. Solution for the Harmonic Oscillator Equation B. The Solution of the Radial Part of the Schrödinger Equation C.TheFourierTransform D. Planck s Law E.TheDensityofStates F. Fourier Transforming Property of a Lens G. The Natural Lineshape Function H. Nonlinear polarization in optical fibers References and Suggested Reading Index

Lasers and Electro-optics

Lasers and Electro-optics Second Edition CHRISTOPHER C. DAVIS University of Maryland III ^0 CAMBRIDGE UNIVERSITY PRESS Preface to the Second Edition page xv 1 Electromagnetic waves, light, and lasers 1