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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. 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)

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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:

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

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)

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  1. M. Kerker, L. H. Kauffman, and W. A. Farone, “Scattering of electromagnetic waves from two concentric spheres when the outer shell has a variable refractive index. numerical results,” J. Opt. Soc. Am. 56, 1053-1056 (1966). [CrossRef]
  2. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).
  3. L. Shafai, “Scattering by spherically symmetrical objects,” Can. J. Phys. 50, 749-753 (1972). [CrossRef]
  4. Y. Nomura and K. Takaku, “On the propagation of the electromagnetic waves in an inhomogeneous atmosphere,” Res. Inst. Electron. Commun. Tohoku Univ. 7B, 107-114 (1955).
  5. K. S. Shifrin, Physical Optics of Ocean Water (American Institute of Physics, 1988).
  6. Z.-F. Sang and Z.-Y. Li, “Partial resonant response of composites containing coated particles with graded shells,” Phys. Lett. A 332, 376-381 (2004). [CrossRef]
  7. S. Saengkaew, T. Charinpanitkul, H. Vanisri, W. Tanthapanichakoon, Y. Biscos, N. Garcia, G. Lavergne,L. Mees, G. Gousebet, and G. Grehan, “Rainbow refractrometry on particles with radial refractive index gradients,” Exp. Fluids 43, 595-601 (2007). [CrossRef]
  8. F. Onofri, D. Blondel, G. Gréhan, and G. Gouesbet, “On the optical diagnosis and sizing of spherical coated and multilayered particles with phase-Doppler anemometry,” Part. Part. Syst. Charact. 13, 104-111 (1996). [CrossRef]
  9. V. N. Lopatin, N. V. Shepelevich, and I. V. Prostakova, “Modelling optical properties of organicmineral complexes in water ecosystems,” J. Phys. D 38, 2556-2563 (2005). [CrossRef]
  10. L. Kai and P. Massoli, “Scattering of electromagnetic-plane waves by radially inhomogeneous spheres: a finely stratified sphere model,” Appl. Opt. 33, 501-511 (1994). [CrossRef] [PubMed]
  11. I. Gurwich, N. Shiloah, and M. Kleiman, “The recursive algorithm for electromagnetic scattering by tilted infinite circular multilayered cylinder,” J. Quant. Spectrosc. Radiat. Transf. 63, 217-229 (1999). [CrossRef]
  12. A. Y. Perelman, “Scattering by particles with radially variable refractive indices,” Appl. Opt. 35, 5452-5460 (1996). [CrossRef] [PubMed]
  13. W. Yang, “Improved recursive algorithm for light scattering by a multilayered sphere,” Appl. Opt. 42, 1710-1720 (2003). [CrossRef] [PubMed]
  14. B. R. Johnson, “Light scattering by a multilayer sphere,” Appl. Opt. 35, 3286-3296 (1996). [CrossRef] [PubMed]
  15. N. L. Tsitsas and C. Athanasiadis, “On the scattering of spherical electromagnetic waves by a layered sphere,” Q. J. Mech. Appl. Math. 59, 55-74 (2006). [CrossRef]
  16. T. D. Visser, D. G. Fischer, and E. Wolf, “Scattering of light from quasi-homogeneous sources by quasi-homogeneous media,” J. Opt. Soc. Am. A 23, 1631-1638 (2006). [CrossRef]
  17. E. Baleine and A. Dogariu, “Variable-coherence tomography for inverse scattering problems,” J. Opt. Soc. Am. A 21, 1917-1923 (2004). [CrossRef]
  18. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
  19. P. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw Hill, 1953).
  20. C. T. Tai, Dyadic Green Functions in Electromagnetic Theory (IEEE Press, 1994).

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