Title

REFLECTION OF VARIOUS TYPES OF WAVES BY LAYERED MEDIA

Authors

Authors

S. Mokhov;B. Y. Zeldovich

Comments

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Abbreviated Journal Title

Commun. Appl. Math. Comput. Sci.

Keywords

reflection; electromagnetic waves; acoustic waves; continuous spectrum; Schrodinger equation; volume Bragg grating; reflectionless potential; Mathematics, Applied; Physics, Mathematical

Abstract

The one-dimensional wave equation describing propagation and reflection of waves in a layered medium is transformed into an exact first-order system for the amplitudes of coupled counter-propagating waves. Any choice of such amplitudes, out of continuous multitude of them, allows one to get an accurate numerical solution of the reflection problem. We discuss relative advantages of particular choices of amplitude. We also introduce the notion of reflection strength S of a plane wave by a nonabsorbing layer, which is related to the reflection intensity R by R = tanh(2) S. We show that the total reflection strength by a sequence of elements is bounded above by the sum of the constituent strengths, and bounded below by their difference. Reflection strength is discussed for propagating acoustic waves and quantum mechanical waves. We show that the standard Fresnel reflection may be understood in terms of the variable S as a sum or difference of two contributions, one due to a discontinuity in impedance and the other due to a speed discontinuity.

Journal Title

Communications in Applied Mathematics and Computational Science

Volume

3

Issue/Number

1

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

61

Last Page

75

WOS Identifier

WOS:000207655600003

ISSN

1559-3940

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