Abstract
The space–time correlation of a wave field in a deterministic dispersive medium generated by space–time fluctuations of a scalar disturbance, over the infinite source plane, governed by the Helmholtz equation is investigated. The method of analysis is the spectral representation theorem coupled with Cauchy’s solution of the Helmholtz equation by Fourier transforms. Two cases are studied in detail: lateral correlation and longitudinal correlation. It is shown that the lateral correlation is propagated unchanged even for a dispersive medium, thereby generalizing a previous result of Parrent [ J. Opt. Soc. Am.49, 787 ( 1959)], who dealt with nondispersive media. The longitudinal correlation function varies depending on the interaction of space and time spectra on the source plane. Numerical results are presented for the modulus of the longitudinal wave-field correlation function for both dispersive and nondispersive media. The corresponding intensity correlations are also evaluated for the case in which the space and time fluctuations on the source plane are jointly Gaussian random functions propagating into a dispersive medium as well as the case in which they are non-Gaussian.
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