Light scattering by rectangular solids in the discrete-dipole approximation: A new algorithm exploiting the block-toeplitz structure

Piotr J. Flatau, Graeme L. Stephens, Bruce T. Draine

Research output: Contribution to journalArticle

72 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)593-600
Number of pages8
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume7
Issue number4
DOIs
StatePublished - Apr 1990

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition

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