The spectral amplitudes of the scattered and transmitted fields for plane-wave incidence on an arbitrary rough interface in one dimension are derived exactly and simply by using Green’s theorem. Results are stated in terms of integrals on values of the field and its normal derivative on the interface. The energy constraint is derived, and individual energy contributions in each region are also related to the surface-field values. The latter contributions can be calculated from coupled linear equations that are also derived using Green’s theorem. The interface separates media of different but constant densities and sound speeds (acoustics) or different dielectrics (electromagnetics).
© 1985 Optical Society of America
Original Manuscript: April 29, 1985
Manuscript Accepted: July 16, 1985
Published: December 1, 1985
John A. DeSanto, "Exact spectral formalism for rough-surface scattering," J. Opt. Soc. Am. A 2, 2202-2207 (1985)