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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 8 — Aug. 1, 2007
  • pp: 2257–2267

The T-matrix revisited

P. C. Waterman  »View Author Affiliations

JOSA A, Vol. 24, Issue 8, pp. 2257-2267 (2007)

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We consider electromagnetic scattering from penetrable cylinders of general cross section. After summarizing the basic T-matrix equations the low-frequency case is examined, which leads for nonmagnetic materials to the exact result T = i R R 2 in the Rayleigh limit, satisfying both reciprocity and energy constraints. Here elements of R are given by integrals of regular wave functions over the cylinder surface. A “Rayleigh expansion” is then found that is convergent throughout the Rayleigh region and the lower end of the resonance region and requires no matrix inversion. For bodies of high aspect ratio, there is a problem with significance loss during numerical integration, due to large oscillatory terms. A class of surfaces has now been found for which these terms can be removed, however, enabling us to treat aspect ratios up to 1000:1. These methods are expected to apply also in three dimensions.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(080.3630) Geometric optics : Lenses
(290.3770) Scattering : Long-wave scattering
(290.4020) Scattering : Mie theory
(290.5870) Scattering : Scattering, Rayleigh

ToC Category:

Original Manuscript: March 22, 2007
Manuscript Accepted: April 5, 2007
Published: July 11, 2007

P. C. Waterman, "The T-matrix revisited," J. Opt. Soc. Am. A 24, 2257-2267 (2007)

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