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## Über dieses Buch

The propagation of acoustic and electromagnetic waves in stratified media is a subject that has profound implications in many areas of applied physics and in engineering, just to mention a few, in ocean acoustics, integrated optics, and wave guides. See for example Tolstoy and Clay 1966, Marcuse 1974, and Brekhovskikh 1980. As is well known, stratified media, that is to say media whose physical properties depend on a single coordinate, can produce guided waves that propagate in directions orthogonal to that of stratification, in addition to the free waves that propagate as in homogeneous media. When the stratified media are perturbed, that is to say when locally the physical properties of the media depend upon all of the coordinates, the free and guided waves are no longer solutions to the appropriate wave equations, and this leads to a rich pattern of wave propagation that involves the scattering of the free and guided waves among each other, and with the perturbation. These phenomena have many implications in applied physics and engineering, such as in the transmission and reflexion of guided waves by the perturbation, interference between guided waves, and energy losses in open wave guides due to radiation. The subject matter of this monograph is the study of these phenomena.

## Inhaltsverzeichnis

### 1. Introduction

Abstract
The propagation of acoustic and electromagnetic waves in stratified media is a subject that has profound implications in many areas of applied physics and in engineering, just to mention a few, in ocean acoustics, integrated optics, and wave guides. See for example Tolstoy and Clay 1966, Marcuse 1974, and Brekhovskikh 1980.
Ricardo Weder

### 2. Propagation of Acoustic Waves

Abstract
The propagation of acoustic waves in a n + 1 dimensional stratified fluid is described by the following wave equation
$$\frac{{{{\partial }^{2}}}}{{\partial _{t}^{2}}}u\left( {x,y,t} \right) - c_{0}^{2}\left( y \right)\Delta u\left( {x,y,t} \right) = 0,$$
(1.1)
where Δ denotes the n+1 dimensional Laplacian
$$\Delta = \sum\limits_{i = 1}^n {\frac{{{\partial ^2}}}{{\partial x_i^2}}} + \frac{{{\partial ^2}}}{{\partial _y^2}},$$
(1.2)
where the derivatives are in distribution sense x=(x1,x2,…xR n , yR, tR.
Ricardo Weder

### 3. Propagation of Electromagnetic Waves

Abstract
The propagation of electromagnetic waves in three dimensional dielectric wave guides is described by the Maxwell system of equations
$$\nabla \times \bar{E} = - {{\mu }_{0}}\left( z \right)\frac{{\partial \bar{H}}}{{\partial t}},$$
(1.1)
,
$$\nabla \times \bar H = - { \in _0}\left( z \right)\frac{{\partial \bar E}}{{\partial t}},$$
(1.2)
,
$$\nabla \cdot \left( {{ \in _0}\left( z \right)\overline E } \right) = 0,\nabla \cdot \left( {{\mu _0}\left( z \right)\overline H } \right) = 0,$$
(1.3)
where
$$x = \left( {{x_1},{x_2}} \right) \in {R^2},z \in R,and\overline E \left( {x,z,t} \right) = \left( {{E_1}\left( {x,z,t} \right),{E_2}\left( {x,z,t} \right),{E_3}\left( {x,z,t} \right)} \right),\overline H \left( {x,z,t} \right) = \left( {{H_1}\left( {x,z,t} \right),{H_3}\left( {x,z,t} \right)} \right)$$
, are the functions from R4 into R3 that correspond respectively to the electric and magnetic fields.
Ricardo Weder

### Backmatter

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