LIGHT-SCATTERING BY RECTANGULAR SOLIDS IN THE DISCRETE-DIPOLE APPROXIMATION - A NEW ALGORITHM EXPLOITING THE BLOCK-TOEPLITZ STRUCTURE

The discrete-dipole approximation is used to study the problem of light scattering by homogeneous rectangular particles. The structure of the discrete-dipole approximation is investigated, and the matrix formed by this approximation is identified to be a symmetric, block-Toeplitz matrix. Special properties of block-Toeplitz arrays are explored, and an efficient algorithm to solve the dipole scattering problem is provided. Timings for conjugate gradient, Linpack, and block-Toeplitz solvers are given; the results indicate the advantages of the block-Toeplitz algorithm. A practical test of the algorithm was performed on a system of 1400 dipoles, which corresponds to direct inversion of an 8400 X 8400 real matrix. A short discussion of the limitations of the discrete-dipole approximation is provided, and some results for cubes and parallelepipeds are given. We briefly consider how the algorithm may be improved further. © 1990 Optical Society of America.