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Format: 1 online resource (810 pages)

Edition: 2nd ed

ISBN: 9783030206925

Series Statement: Springer Series in Optical Sciences Ser. v.225

Content: This heavily-illustrated text presents a systematic treatment of the radiation and propagation of transient electromagnetic and optical wave fields through causal, locally linear media which exhibit both temporal dispersion and absorption

Note: Description based on publisher supplied metadata and other sources , Intro -- Preface to the Second Revised Edition -- Preface to the First Edition -- Contents - Volume II -- Contents - Volume I -- 10 Asymptotic Methods of Analysis Using Advanced Saddle Point Techniques -- 10.1 Olver's Saddle Point Method -- 10.1.1 Peak Value of the Integrand at the Endpoint of Integration -- 10.1.2 Peak Value of the Integrand at an Interior Point of the Path of Integration -- 10.1.3 The Application of Olver's Saddle Point Method -- 10.2 Uniform Asymptotic Expansion for Two Mirror Image First-Order Saddle Points at Infinity -- 10.3 Uniform Asymptotic Expansion for Two First-Order Saddle Points -- 10.3.1 The Uniform Asymptotic Expansion for Two Isolated First-Order Saddle Points -- 10.3.2 The Uniform Asymptotic Expansion for Two Neighboring First-Order Saddle Points -- 10.3.3 The Transitional Asymptotic Approximation for Two Neighboring First-Order Saddle Points -- 10.4 Uniform Asymptotic Expansion for a First-Order Saddle Point and a Simple Pole Singularity -- 10.4.1 The Complementary Error Function -- 10.4.2 Asymptotic Behavior for a Single Interacting Saddle Point -- 10.4.3 Asymptotic Behavior for Two Isolated Interacting Saddle Points -- 10.5 Asymptotic Expansions of Multiple Integrals -- 10.5.1 Absolute Maximum in the Interior of the Closure of Dξ -- 10.5.2 Absolute Maximum on the Boundary of the Closure of Dξ -- 10.6 Summary -- Problems -- References -- 11 The Group Velocity Approximation -- 11.1 Historical Introduction -- 11.2 The Pulsed Plane Wave Electromagnetic Field -- 11.2.1 The Delta Function Pulse and the Impulse Response of the Medium -- 11.2.2 The Heaviside Unit Step Function Signal -- 11.2.3 The Double Exponential Pulse -- 11.2.4 The Rectangular Pulse Envelope Modulated Signal -- 11.2.5 The Trapezoidal Pulse Envelope Modulated Signal -- 11.2.6 The Hyperbolic Tangent Envelope Modulated Signal , 11.2.7 The Van Bladel Envelope Modulated Pulse -- 11.2.8 The Gaussian Envelope Modulated Pulse -- 11.3 Wave Equations in a Simple Dispersive Medium and the Slowly-Varying Envelope Approximation -- 11.3.1 The Dispersive Wave Equations -- 11.3.2 The Slowly-Varying Envelope Approximation -- 11.3.3 Dispersive Wave Equations for the Slowly-Varying Wave Amplitude and Phase -- 11.3.3.1 Induced Polarization Density Approach -- 11.3.3.2 Electric Displacement Field Approach -- 11.4 The Classical Group Velocity Approximation -- 11.4.1 Linear Dispersion Approximation -- 11.4.2 Quadratic Dispersion Approximation -- 11.5 Failure of the Classical Group Velocity Method -- 11.5.1 Impulse Response of a Double-Resonance Lorentz Model Dielectric -- 11.5.2 Heaviside Unit Step Function Signal Evolution -- 11.5.3 Rectangular Envelope Pulse Evolution -- 11.5.4 Van Bladel Envelope Pulse Evolution -- 11.5.5 Concluding Remarks on the Slowly-Varying- Envelope (SVE) and Classical Group Velocity Approximations -- 11.6 Extensions of the Group Velocity Method -- 11.7 Localized Pulsed-Beam Propagation -- 11.7.1 Mathematical Preliminaries -- 11.7.2 Paraxial Asymptotics -- 11.7.2.1 Pulsed Beam Evolution in the Nondispersive Case -- 11.7.2.2 Pulsed Beam Evolution in the Lossless Dispersive Case -- 11.8 The Necessity of an Asymptotic Description -- Problems -- References -- 12 Analysis of the Phase Function and Its Saddle Points -- 12.1 General Saddle Point Dynamics for Causally Dispersive Dielectrics -- 12.1.1 The Region About the Origin (|ω| ω0) -- 12.1.1.1 Case 1: The Lorentz-Type Dielectric (α1 > -- 0) -- 12.1.1.2 Case 2: The Debye-Type Dielectric (α1 < -- 0) -- 12.1.1.3 Case 3: The Transition-Type Dielectric (α1 = 0) -- 12.1.2 The Region About Infinity (|ω| ωm) -- 12.1.2.1 Case 1: The Debye-Type Dielectric (b0 =0) -- 12.1.2.2 Case 2: The Lorentz-Type Dielectric (b0 = 0) , 12.1.3 Summary -- 12.2 The Behavior of the Phase in the Complex ω-Plane for Causally Dispersive Materials -- 12.2.1 Single-Resonance Lorentz Model Dielectrics -- 12.2.1.1 Behavior Along the Real ω'-Axis -- 12.2.1.2 Limiting Behavior as |ω| →∞ -- 12.2.1.3 Behavior Along the Line ω'' = -δ -- 12.2.1.4 Behavior in the Vicinity of the Branch Points -- 12.2.1.5 Numerical Results -- 12.2.2 Multiple-Resonance Lorentz Model Dielectrics -- 12.2.2.1 Case 1: θp < -- θ0 -- 12.2.2.2 Case 2: θp > -- θ0 -- 12.2.3 Rocard-Powles-Debye Model Dielectrics -- 12.2.3.1 Behavior Along the Real ω'-Axis -- 12.2.3.2 Limiting Behavior as |ω| →∞ -- 12.2.3.3 Behavior Along the Imaginary Axis -- 12.2.3.4 Behavior in the Vicinity of the Branch Points -- 12.2.3.5 Numerical Results -- 12.2.4 Drude Model Conductors -- 12.2.4.1 Behavior Along the Real ω'-Axis -- 12.2.4.2 Limiting Behavior as |ω| →∞ -- 12.2.4.3 Behavior in the Vicinity of the Branch Points -- 12.2.4.4 Numerical Results -- 12.3 The Location of the Saddle Points and the Approximation of the Phase -- 12.3.1 Single Resonance Lorentz Model Dielectrics -- 12.3.1.1 The Region Removed from the Origin (|ω| ≥ω1) -- 12.3.1.2 The Region About the Origin (|ω| ≤ω0) -- 12.3.1.3 Determination of the Dominant Saddle Points -- 12.3.1.4 Comparison with Numerical Results -- 12.3.2 Multiple Resonance Lorentz Model Dielectrics -- 12.3.2.1 The Region Above the Upper Resonance Line (|ω| ≥ω3) -- 12.3.2.2 The Region Below the Lower Resonance Line (|ω| ≤ω0) -- 12.3.2.3 The Region Between the Upper and Lower Resonance Lines (ω0 < -- |ω| < -- ω3) -- 12.3.2.4 Determination of the Dominant Saddle Points -- 12.3.3 Rocard-Powles-Debye Model Dielectrics -- 12.3.4 Drude Model Conductors -- 12.3.4.1 The Region Removed from the Origin (|ω| ≥|ωz|) -- 12.3.4.2 The Region About the Origin (|ω| ≤|ωz|) -- 12.3.5 Semiconducting Materials , 12.4 Procedure for the Asymptotic Analysis of the Propagated Field -- 12.5 Synopsis -- Problems -- References -- 13 Evolution of the Precursor Fields -- 13.1 The Field Behavior for θ< -- 1 -- 13.2 The Sommerfeld Precursor Field -- 13.2.1 The Nonuniform Approximation -- 13.2.1.1 The Single Resonance Case -- 13.2.1.2 The Double Resonance Case -- 13.2.2 The Uniform Approximation -- 13.2.2.1 The Single Resonance Case -- 13.2.2.2 The Double Resonance Case -- 13.2.3 Field Behavior at the Wave-Front -- 13.2.4 The Instantaneous Oscillation Frequency -- 13.2.5 The Delta Function Pulse Sommerfeld Precursor -- 13.2.6 The Heaviside Step Function Pulse Sommerfeld Precursor -- 13.3 The Brillouin Precursor Field in Lorentz Model Dielectrics -- 13.3.1 The Nonuniform Approximation -- 13.3.1.1 Case 1: 1 < -- θ< -- θ1 -- 13.3.1.2 Case 2: θ= θ1 -- 13.3.1.3 Case 3: θ> -- θ1 -- 13.3.2 The Uniform Approximation -- 13.3.3 The Instantaneous Oscillation Frequency -- 13.3.4 The Delta Function Pulse Brillouin Precursor -- 13.3.5 The Heaviside Step Function Pulse Brillouin Precursor -- 13.4 The Brillouin Precursor Field in Debye Model Dielectrics -- 13.5 The Middle Precursor Field -- 13.6 Impulse Response of Causally Dispersive Materials -- 13.7 The Effects of Spatial Dispersion on Precursor Field Formation -- Problems -- References -- 14 Evolution of the Signal -- 14.1 The Nonuniform Asymptotic Approximation -- 14.2 Rocard-Powles-Debye Model Dielectrics -- 14.3 The Uniform Asymptotic Approximation -- 14.4 Single Resonance Lorentz Model Dielectrics -- 14.4.1 Frequencies Below the Absorption Band -- 14.4.2 Frequencies Above the Absorption Band -- 14.4.3 Frequencies Within the Absorption Band -- 14.4.4 The Heaviside Unit Step Function Signal -- 14.5 Multiple Resonance Lorentz Model Dielectrics -- 14.6 Drude Model Conductors -- Problems -- References , 15 Continuous Evolution of the Total Field -- 15.1 The Total Precursor Field -- 15.2 Resonance Peaks of the Precursors and the Signal Contribution -- 15.3 The Signal Arrival and the Signal Velocity -- 15.3.1 Transition from the Precursor Field to the Signal -- 15.3.2 The Signal Velocity -- 15.3.2.1 Signal Velocity in Single Resonance Lorentz Model Dielectrics -- 15.3.2.2 Signal Velocity in Multiple Resonance Lorentz Model Dielectrics -- 15.3.2.3 Signal Velocity in Drude Model Conductors -- 15.3.2.4 Signal Velocity in Rocard-Powles-Debye Model Dielectrics -- 15.4 Comparison of the Signal Velocity with the Phase, Group, and Energy Velocities -- 15.5 The Heaviside Step-Function Modulated Signal -- 15.5.1 Signal Propagation in a Single Resonance Lorentz Model Dielectric -- 15.5.2 Signal Propagation in a Double Resonance Lorentz Model Dielectric -- 15.5.3 Signal Propagation in a Drude Model Conductor -- 15.5.4 Signal Propagation in a Rocard-Powles-Debye Model Dielectric -- 15.5.5 Signal Propagation Along a Dispersive μStrip Transmission Line -- 15.6 The Rectangular Pulse Envelope Modulated Signal -- 15.6.1 Rectangular Envelope Pulse Propagation in a Single Resonance Lorentz Model Dielectric -- 15.6.2 Rectangular Envelope Pulse Propagation in a Rocard- Powles-Debye Model Dielectric -- 15.6.3 Rectangular Envelope Pulse Propagation in H2O -- 15.6.4 Rectangular Envelope Pulse Propagation in Salt-Water -- 15.7 Non-instantaneous Rise-Time Signals -- 15.7.1 Hyperbolic Tangent Envelope Signal Propagation in a Single Resonance Lorentz Model Dielectric -- 15.7.2 Raised Cosine Envelope Signal Propagation in a Single Resonance Lorentz Model Dielectric -- 15.7.3 Trapezoidal Envelope Pulse Propagation in a Rocard- Powles-Debye Model Dielectric -- 15.8 Infinitely Smooth Envelope Pulses , 15.8.1 Gaussian Envelope Pulse Propagation in a Single Resonance Lorentz Model Dielectric

Additional Edition: Erscheint auch als Druck-Ausgabe Oughstun, Kurt E. Electromagnetic and Optical Pulse Propagation Cham : Springer International Publishing AG,c2019 ISBN 9783030206918

Language: English