Brewster Effect Research Articles

Low frequency coupling in the planar rectangular lattice

The solution for the three−dimensional problem of multiple scattering by a doubly periodic planar array of bounded obstacles is specialized to consider low frequency coupling effects for spheres. For all of the usual boundary conditions, we derive closed form approximations for the transmission and reflection amplitudes explicitly in terms of the physical parameters of the isolated scatterers, lattice spacings, and direction of incidence. The results are compared with those obtained earlier for the grating of parallel cylinders and for the periodic line (and planar random distribution) of spheres. We show, for example, that the pseudo−Brewster effects are anisotropic for the rectangular lattice cell and that the leading effects of close packing for a square array of rigid spheres may be approximated by single scattering by an equivalent spheroid representing elongation in the plane of the array and contraction along the normal. For dense packing at very low frequencies, we obtain explicit closed form approximations including up to octupole−octupole coupling effects.