The application of the Rayleigh-Fourier and Rayleigh least-squares methods to reflection and transmission of electromagnetic waves at periodic rough interfaces between general homogeneous media is considered. For the calculation of the reflected and transmitted amplitudes, it is shown that the Rayleigh-Fourier method converges when the Waterman-Fourier method does and is therefore not limited by the validity of the Rayleigh hypothesis. It is also shown that the Rayleigh least-squares method applied to boundary-value problems is numerically convergent if the solution exists uniquely. A numerical application of both methods to the case of a sinusoidal interface between a perfectly conducting medium and a bi-isotropic medium corroborates these results. We indicate very general conditions under which the Rayleigh-Fourier and Rayleigh least-squares methods have the properties indicated above; they include anisotropic elastic solid media in particular.

• Received 22 February 1995

DOI:https://doi.org/10.1103/PhysRevE.54.6802