Abstract

By assuming the random, time-varying boundary conditions for the scalar wave equation to be ergodic, we can associate with the time-varying boundary conditions an ensemble of strictly monochromatic boundary conditions. Formally solving and comparing the solutions for each type of boundary condition, we conclude that the time-averaged and ensemble-averaged powers (squares of the field) are the same at all points where the path difference to any two points on the boundary is small compared to c/Δν, where c is the free-space speed of light and Δν is the frequency spread of the time-varying boundary conditions. That is, if the boundary conditions are ergodic, the solutions are ergodic.

© 1961 Optical Society of America

Equivalence of the Ewald-Oseen extinction theorem as a nonlocal boundary-value problem with Maxwell’s equations and boundary conditions*

D. Dialetis
J. Opt. Soc. Am. 68(5) 602-610 (1978)

Some Properties of Coherent Light*

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Concept of Cross-Spectral Purity in Coherence Theory

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Fiber Optics. IX. Waveguide Effects*†

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