Ergodic Theorem in the Solution of the Scalar Wave Equation with Statistical Boundary Conditions*
- 1 November 1961
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America
- Vol. 51 (11), 1246-1251
- https://doi.org/10.1364/josa.51.001246
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/Δv, where c is the free-space speed of light and Δv is the frequency spread of the time-varying boundary conditions. That is, if the boundary conditions are ergodic, the solutions are ergodic.Keywords
This publication has 2 references indexed in Scilit:
- On the Propagation of Mutual CoherenceJournal of the Optical Society of America, 1959
- Determination of the Intensity Distribution Resulting from the Random Illumination of a Plane Finite SurfaceOptica Acta: International Journal of Optics, 1958