Wave Propagation and Group Velocity

Wave Propagation and Group Velocity

1st Edition - January 1, 1960

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  • Author: Léon Brillouin
  • eBook ISBN: 9781483276014

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Wave Propagation and Group Velocity contains papers on group velocity which were published during the First World War and are missing in many libraries. It introduces three different definitions of velocities: the group velocity of Lord Rayleigh, the signal velocity of Sommerfeld, and the velocity of energy transfer, which yields the rate of energy flow through a continuous wave and is strongly related to the characteristic impedance. These three velocities are identical for nonabsorbing media, but they differ considerably in an absorption band. Some examples are discussed in the last chapter dealing with guided waves, and many other cases of application of these definitions are quoted. These problems have come again into the foreground, in connection with the propagation of radio signals and radar. Reflection in the Heaviside layers requires a real knowledge of all these different definitions. Group velocity also plays a very important role in wave mechanics and corresponds to the speed of a particle. The present book should be very useful to physicists and radio engineers and should give them a good basis for new discussions and applications.

Table of Contents

  • Foreword


    Chapter I. Introduction

    1. Phase Velocity and Group Velocity

    2. Examples and Discussion: Dispersive Media

    3. Groups and Signals

    4. Signal Velocity, First Attempts

    5. Actual Measurements of the Velocity of Light

    6. Havelock's Pamphlet

    7. General Remarks

    Chapter II. About the Propagation of Light in Dispersive Media

    1. Introduction and Results

    2. The Incident Signal

    3. General Solution of the Problem

    4. Discussion of the Obtained Solution

    5. Uniqueness of the Solution and Boundary Conditions

    6. The Forerunners

    Chapter III. About the Propagation of Light in Dispersive Media

    1. How to Use the Saddle-Point Method of Integration

    2. Examination of the Complex n-Plane

    3. Location of the Saddle Points

    A. The Region about the Origin

    B. Saddle Points Far from the Origin

    4. Successive Motion of the Saddle Points as a Function of Time. Choice of the Path of Integration

    5. The Forerunners

    A. Saddle Points near the Origin

    B. Saddle Points at a Great Distance

    6. Signal Velocity

    7. Summary of Results

    8. The Method of the Stationary Phase Compared to the Saddle Point Method

    Chapter IV. Propagation of Electromagnetic Waves in Material Media

    1. Definitions: Role of a Dielectric Coefficient Depending on Density and Temperature

    2. Dependence of the Dielectric Coefficient on Frequency; Evaluation of the Electrical Energy

    3. Waves; Phase Velocity; Energy Density of a Plane Wave

    4. The Group Velocity U

    5. Velocity of Energy Transport U1

    6. Signal Velocity, S

    7. The Forerunners

    8. Summary of the Most Important Results; Generalization to Other Types of Waves

    Chapter V. Wave Propagation in a Dispersive Dielectric

    1. Formula of Lorentz-Lorenz

    2. Material Medium of Low Density, Consisting of Harmonic Oscillators

    3. Propagation of the Waves in the Medium

    4. The Velocities U, U1, and S in the Medium

    5. The Forerunners

    6. A Real Transparent Medium, Having Several Absorption Bands

    7. Quantized Atomic States, Kramers' Dispersion Formula

    8. The Relation between the Problem Treated and the Analogous Technical Problems

    Chapter VI. Waves in Wave Guides and Other Examples

    1. Guided Waves

    2. Acoustic Waves

    3. Rectangular Tube

    4. Physical Significance of Guided Waves

    5. Electromagnetic Guided Waves

    6. Some Other Typical Examples

    Author Index

    Books Published by L. Brillouin

Product details

  • No. of pages: 166
  • Language: English
  • Copyright: © Academic Press 1960
  • Published: January 1, 1960
  • Imprint: Academic Press
  • eBook ISBN: 9781483276014

About the Author

Léon Brillouin

About the Editor

H. S. W. Massey

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