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Physics - Optics & Lasers | Electromagnetic Pulse Propagation in Casual Dielectrics

Electromagnetic Pulse Propagation in Casual Dielectrics

Oughstun, Kurt, Sherman, G.C.

Softcover reprint of the original 1st ed. 1994, XII, 465 pp. 121 figs.

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  • About this book

Electromagnetic Pulse Propagation in Causal Dielectrics presents a systematic treatment of the theory of the propagation of transient electromagnetic fields (such as ultrashort, ultrawide-band pulses) through homogeneous, isotopic, locally linear media which exhibit both dispersion and absorption. The subject of the book is twofold. Part I presents a detailed rigorous treatment of the fundamental theory of electromagnetic pulse propagation in causally dispersive media that is applicable to dielectric, conducting, or semiconducting media. Part II provides a detailed asymptotic description of plane-wave pulse propagation in a Lorentz model dielectric and provides a rigorous account ot the signal velocity of a pulse in that dispersive medium.

Content Level » Research

Keywords » Electromagnetic fields and waves - Optics - Propagation and transmission - mathematical methods in physics

Related subjects » Optics & Lasers

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.

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