Electromagnetic Pulse Propagation in Casual Dielectrics: (v. 16 Springer Series on Wave Phenomena)

This research monograph presents a systematic treatment of the theory of the propagation of transient electromagnetic fields (such as optical pulses) through dielectric media which exhibit both dispersion and absorption. The work divides naturally into two parts. Part I presents a summary of the fundamental theory of the radiation and propagation of rather general electromagnetic waves in causal, linear media which are homogeneous and isotropic but which otherwise have rather general dispersive and absorbing properties. In Part II, we specialize on the propagation of a plane, transient electromagnetic field in a homogeneous dielectric. Although we have made some contributions to the fundamental theory given in Part I, most of the results of our own research appear in Part II. The purpose of the theory presented in Part II is to predict and to explain in explicit detail the dynamics of the field after it has propagated far enough through the medium to be in the mature-dispersion regime. It is the subject of a classic theory, based on the research conducted by A. Sommerfeld and L.

Table of Contents:
I: Fundamental Theory.- 1. Introduction.- 1.1. Motivation.- 1.2. History of Previous Research.- 1.3. Organization of the Book.- I: Fundamental Theory.- 2. Fundamental Field Equations in a Temporally Dispersive Medium.- 2.1. Fundamental Field Equations in a Temporally Dispersive Medium.- 2.1.1. Temporal Frequency Domain Representation of the Field and Medium Properties.- 2.1.2. Complex Time-Harmonic Form of the Field Quantities.- 2.2. Electromagnetic Energy and Energy Flow in a Temporally Dispersive Medium.- 2.2.1. Poynting's Theorem and the Conservation of Energy.- 2.2.2. The Energy Density and Evolved Heat in a Dispersive and Absorptive Medium.- 2.2.3. Complex Time-Harmonic Form of Poynting's Theorem.- 2.3. The Harmonic Electromagnetic Plane Wave Field.- 2.4. The Lorentz Model of the Material Dispersion.- 2.4.1. The Classical Lorentz Model of Dielectric Resonance.- 2.4.2. The Velocity of Energy Flow of a Monochromatic Field in a Multiple-Resonance Lorentz Medium.- 3. The Angular Spectrum Representation of the Pulsed Radiation Field.- 3.1. Introduction and Mathematical Preliminaries.- 3.2. The Fourier-Laplace Representation of the Radiation Field.- 3.3. The Scalar and Vector Potentials of the Radiation Field.- 3.3.1. The Special Case of a Nonconducting, Nondispersive Medium.- 3.3.2. The Spectral Lorentz Condition for Dispersive, Conducting Media.- 3.4. The Angular Spectrum of Plane Waves Representation of the Radiation Field.- 3.5. Polar Coordinate Form of the Angular Spectrum Representation.- 3.5.1. Transformation to an Arbitrary Polar Axis.- 3.5.2. Weyl's Proof.- 3.5.3. Weyl's Integral Representation.- 3.5.4. Sommerfeld's Integral Representation.- 3.5.5. Ott's Integral Representation.- 4. The Angular Spectrum Representation of Pulsed Electromagnetic Beam Fields.- 4.1. The Angular Spectrum Representation of the Freely Propagating Electromagnetic Field.- 4.1.1. Geometric Form of the Angular Spectrum Representation.- 4.1.2. The Angular-Spectrum Representation and Huygen's Principle.- 4.2. Polarization Properties of the Freely Propagating Electromagnetic Field.- 4.2.1. The Polarization Ellipse for the Complex Field Vectors.- 4.2.2. The Relation Between the Electric and Magnetic Polarization Ellipses.- 4.2.3. The Uniformly Polarized Field.- 4.3. The Pulsed, Plane-Wave Electromagnetic Field.- 4.3.1. The Unit Step-Function Modulated Signal.- 4.3.2. The Rectangular-Pulse Modulated Signal.- 4.3.3. The Delta-Function Pulse and the Impulse Response of the Model Medium.- 4.3.4. The Hyperbolic-Tangent Modulated Signal.- 4.4. The Quasimonochromatic Approximation and the Heuristic Theory of Pulse Propagation.- 5. Advanced Saddle-Point Methods for the Asymptotic Evaluation of Single Contour Integrals.- 5.1. The Saddle-Point Method Due to Olver.- 5.1.1. Peak Value of the Integrand at the Endpoint of Integration.- 5.1.2. Peak Value of the Integrand at an Interior Point of the Path of Integration.- 5.1.3. The Application of Olver's Method.- 5.2. The Uniform Asymptotic Expansion for Two First-Order Saddle Points.- 5.2.1. The Uniform Asymptotic Expansion for Two Isolated First-Order Saddle Points 165 Contents.- 5.2.2. The Uniform Asymptotic Expansion for Two Neighboring First-Order Saddle Points.- 5.3. The Uniform Asymptotic Expansion for a First-Order Saddle Point and a Simple-Pole Singularity of the Integrand.- 5.4. The Uniform Asymptotic Expansion for Two First-Order Saddle Points at Infinity.- II: Asymptotic Theory of Plane Wave Pulse Propagation in a Single Resonance Lorentz Medium.- 6. Analysis of the Phase Function and Its Saddle Points.- 6.1. The Behavior of the Phase in the Complex ?-Plane.- 6.1.1. Brillouin's Analysis.- 6.1.2. Numerical Results.- 6.2. The Location of the Saddle Points and the Approximation of the Phase.- 6.2.1. The Region Removed from the Origin.- a) The First Approximation.- b) The Second Approximation.- 6.2.2. The Region Near the Origin.- a) The First Approximation.- b) The Second Approximation.- c) Behavior of the Second Approximation.- 6.3. Analytic Determination of the Dominant Saddle Point.- 6.4. Numerical Determination of the Saddle-Point Locations and the Associated Phase Behavior at the Saddle Points.- 6.5. Procedure for the Asymptotic Analysis of the Field A(z, t).- 7. Evolution of the Precursor Fields.- 7.1. The Field Behavior for ? < 1.- 7.2. The First Precursor Field (Sommerfeld's Precursor).- 7.2.1. The Nonuniform Approximation.- 7.2.2. The Uniform Approximation.- 7.2.3. The Instantaneous Angular Frequency.- 7.2.4. The Unit Step-Function Modulated Signal.- 7.2.5. The Rectangular-Pulse Modulated Signal.- 7.2.6. The Delta-Function Pulse.- 7.2.7. The Hyperbolic-Tangent Modulated Signal.- 7.3. The Second Precursor Field (Brillouin's Precursor).- 7.3.1 The Nonuniform Approximation.- 7.3.2. The Uniform Approximation.- 7.3.3. The Instantaneous Angular Frequency.- 7.3.4. The Unit Step-Function Modulated Signal.- 7.3.5. The Rectangular-Pulse Modulated Signal.- 7.3.6. The Delta-Function Pulse.- 7.3.7. The Hyperbolic-Tangent Modulated Signal.- 8. Evolution of the Main Signal.- 8.1. The Nonuniform Asymptotic Approximation.- 8.2. The Uniform Asymptotic Approximation.- 8.2.1. Frequencies ?p in the Range 0 ? ?p ? $$\sqrt {\omega _0^2 - {\delta ^2}} $$.- 8.2.2. Frequencies ?p in the Range ?p ? $$\sqrt {\omega _0^2 - {\delta ^2}} $$.- 8.2.3. Frequencies ?p in the Range $$\sqrt {\omega _0^2 - {\delta ^2}} $$ < ?p < $$\sqrt {\omega _0^2 - {\delta ^2}} $$.- 8.3. Special Pulses.- 8.3.1. The Unit Step-Function Modulated Signal.- 8.3.2. The Rectangular-Pulse Modulated Signal.- 8.3.3. The Delta-Function Pulse.- 8.3.4. The Hyperbolic-Tangent Modulated Signal.- 9. The Continuous Evolution of the Total Field.- 9.1. The Total Precursor Field.- 9.2. Resonance Peaks of the Precursors and the Main Signal.- 9.3. The Signal Arrival and the Signal Velocity.- 9.3.1. Transition from the Precursor Field to the Main Signal.- 9.3.2. The Signal Velocity.- 9.3.3. Comparison of the Signal Velocity with the Other Velocities of Light.- 9.4. Special Pulses.- 9.4.1. The Unit Step-Function Modulated Signal.- 9.4.2. The Rectangular-Pulse Modulated Signal.- 9.4.3. The Delta-Function Pulse.- 9.4.4. The Hyperbolic-Tangent Modulated Signal.- 10. Physical Interpretation of the Pulse Dynamics.- 10.1. Review of the Physical Problem and Its Asymptotic Description.- 10.2. Approximations Having Physical Interpretations.- 10.2.1. The Quasimonochromatic Contribution.- 10.2.2. The Non-Oscillatory Contribution.- 10.3. Physical Model of Pulse Dynamics.- 10.3.1. The Nonuniform Physical Model.- 10.3.2. The Uniform Physical Model.- 10.4. Summary and Conclusions.- References.