Brillouin L. Wave propagation and group velocity

New York and London: Academic Press, 1960.– xii, 164 p.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.Foreword
PrefacePhase Velocity and Group Velocity
Examples and Discussion: Dispersive Media
Groups and Signals
Signal Velocity, First Attempts
Actual Measurements of the Velocity of Light
Havelock's Pamphlet
General Remarks
About the Propagation of Light in Dispersive Media, by A. Sommerfeld
Introduction and Results
The Incident Signal
General Solution of the Problem
Discussion of the Obtained Solution
Uniqueness of the Solution and Boundary Conditions
The Forerunners
About the Propagation of Light in Dispersive Media, by L. Brillouin
How to Use the Saddle-Point Method of Integration
Examination of the Complex n-Plane
Location of the Saddle Points
A. The Region about the Origin
B. Saddle Points Far from the Origin
Successive Motion of the Saddle Points as a Function of Time. Choice of the Path of Integration
The Forerunners
A. Saddle Points near the Origin
B. Saddle Points at a Great Distance
Signal Velocity
Summary of Results
The Method of the Stationary Phase Compared to the Saddle Point Method
Propagation of Electromagnetic Waves in Material Media
Definitions: Role of a Dielectric Coefficient Depending on Density and Temperature
Dependence of the Dielectric Coefficient on Frequency; Evaluation of the Electrical Energy
Waves; Phase Velocity; Energy Density of a Plane Wave
The Group Velocity U
Velocity of Energy Transport U1
Signal Velocity, S
The Forerunners
Summary of the Most Important Results; Generalization to Other Types of Waves
Wave Propagation in a Dispersive Dielectric
Formula of Lorentz-Lorenz
Material Medium of Low Density, Consisting of Harmonic Oscillators
Propagation of the Waves in the Medium
The Velocities U, U1, and S in the Medium
The Forerunners
A Real Transparent Medium, Having Several Absorption Bands
Quantized Atomic States, Kramers' Dispersion Formula
The Relation between the Problem Treated and the Analogous Technical Problems
Waves in Wave Guides and Other Examples
Guided Waves
Acoustic Waves
Rectangular Tube
Physical Significance of Guided Waves
Electromagnetic Guided Waves
Some Other Typical Examples