Abstract
An approximate solution of the boundary value problem for an inhomogeneous medium is shown by using the phase function method and the spectral representation of the Rayleigh diffraction formula under the condition that the spatial and temporal variation of the permittivity of medium is sufficiently smooth and small compared with that of the incident monochromatic electromagnetic waves. The formula obtained holds only in the neighborhood of the boundary plane. In the special case that the incident electromagnetic wave is plane and the variation of permittivity is induced by a monochromatic plane ultrasonic wave, the formula coincides with the Raman-Nath diffraction. Moreover, partially coherent wave propagation in an inhomogeneous medium is analyzed. The expression of van Citter-Zernike's theorem for an inhomogeneous medium is shown.
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