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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 4 — Apr. 1, 2009
  • pp: 870–881

Linearization of the T-matrix solution for quasi-homogeneous scatterers

Constantine A. Valagiannopoulos and Nikolaos L. Tsitsas  »View Author Affiliations


JOSA A, Vol. 26, Issue 4, pp. 870-881 (2009)
http://dx.doi.org/10.1364/JOSAA.26.000870


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Abstract

Interesting applications arising in optical and chemical engineering, environmental science, and biology motivate the investigation of electromagnetic wave scattering problems by radially inhomogeneous obstacles. Our main purpose is the investigation of plane-wave scattering by quasi-homogeneous obstacles, that is, obstacles with wavenumbers not exhibiting large variations from a specific average value k ¯ . The analysis is presented separately for a slab (1D), a cylindrical (2D), and a spherical (3D) scatterer. First, we consider a step approximation of the wavenumber and express the field coefficients by applying a T-matrix method for the corresponding piecewise homogeneous scatterer. Then, by performing an appropriate Taylor expansion, we express the field coefficients as linear combinations of the distances of the wavenumber samples from k ¯ . The combinations’ weights are called layer-factors, because each one describes the contribution of a specific layer in the scattered field. Furthermore, it is shown that the far-field pattern of the quasi-homogeneous scatterer is decomposed into that of the respective homogeneous scatterer plus the perturbation far-field pattern, depending on the wavenumber’s deviations from k ¯ . Several numerical results are presented concerning the comparison of the far-field patterns computed by the proposed technique and the T-matrix method, as well as investigations of the perturbation far-field pattern and the layer-factors. Linear, sinusoidal, Lunenburg type, and triangular wavenumber profiles are analyzed.

© 2009 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(290.4020) Scattering : Mie theory
(290.5825) Scattering : Scattering theory
(160.2710) Materials : Inhomogeneous optical media

ToC Category:
Materials

History
Original Manuscript: December 2, 2008
Manuscript Accepted: January 28, 2009
Published: March 19, 2009

Citation
Constantine A. Valagiannopoulos and Nikolaos L. Tsitsas, "Linearization of the T-matrix solution for quasi-homogeneous scatterers," J. Opt. Soc. Am. A 26, 870-881 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-4-870

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