## Calculation of the *T* matrix and the scattering matrix for ensembles of spheres

JOSA A, Vol. 13, Issue 11, pp. 2266-2278 (1996)

http://dx.doi.org/10.1364/JOSAA.13.002266

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### Abstract

We present a method for determination of the random-orientation polarimetric scattering properties of an arbitrary, nonsymmetric cluster of spheres. The method is based on calculation of the cluster *T* matrix, from which the orientation-averaged scattering matrix and total cross sections can be analytically obtained. An efficient numerical method is developed for the *T*-matrix calculation, which is faster and requires less computer memory than the alternative approach based on matrix inversion. The method also allows calculation of the random orientation scattering properties of a cluster in a fraction of the time required for numerical quadrature. Numerical results for the random orientation scattering matrix are presented for sphere ensembles in the form of densely packed clusters and linear chains.

© 1996 Optical Society of America

**History**

Original Manuscript: February 26, 1996

Revised Manuscript: May 21, 1996

Manuscript Accepted: April 18, 1996

Published: November 1, 1996

**Citation**

Daniel W. Mackowski and Michael I. Mishchenko, "Calculation of the T matrix and the scattering matrix for ensembles of spheres," J. Opt. Soc. Am. A **13**, 2266-2278 (1996)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-13-11-2266

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### References

- J. H. Brunning, Y. T. Lo, “Multiple scattering of EM waves by spheres. Part I. Multiple expansion and ray-optical solutions,” IEEE Trans. Antennas Propag. AP-19, 378–390 (1971). [CrossRef]
- F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Multiple electromagnetic scattering from a cluster of spheres. I. Theory,” Aerosol Sci. Technol. 3, 227–235 (1984). [CrossRef]
- D. W. Mackowski, “Analysis of radiative scattering for multiple sphere configurations,” Proc.R. Soc. London Ser. A 433, 599–614 (1991). [CrossRef]
- K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. I. Theory for external aggregation,” J. Opt. Soc. Am. A 11, 3251–3260 (1994). [CrossRef]
- K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. III. Spheres containing arbitrarily located spherical inhomogeneities,” J. Opt. Soc. Am. A 12, 893–904 (1995). [CrossRef]
- Y.-L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34, 4573–4588 (1995). [CrossRef] [PubMed]
- K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 33, 4716–4731 (1991). [CrossRef]
- P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the Block–Toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990). [CrossRef]
- S. B. Singham, G. C. Salzman, “Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation,” J. Chem. Phys. 84, 2658–2667 (1986). [CrossRef]
- M. I. Mishchenko, D. W. Mackowski, L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589–4599 (1995). [CrossRef] [PubMed]
- D. W. Mackowski, “Calculation of total cross sections of multiple sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994). [CrossRef]
- P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971). [CrossRef]
- P. W. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrary shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975). [CrossRef] [PubMed]
- M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991). [CrossRef]
- N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (1992). [CrossRef] [PubMed]
- C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chaps. 3 and 4.
- H. Domke, “The expansion of scattering matrices for an isotropic medium in generalized spherical functions,” Astrophys. Space Sci. 29, 379–386 (1974). [CrossRef]
- A. R. Edmunds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1957), Chap. 4.
- K. A. Fuller, G. W. Kattawar, “Consummate solution to the problem of classical electromagnetic scattering by an ensemble of spheres. I. Linear chains,” Opt. Lett. 13, 90–92 (1988). [CrossRef] [PubMed]
- F. Borghese, P. Denti, R. Saija, G. Toscano, O. I. Sindoni, “Use of group theory for the description of electromagnetic scattering from molecular systems,” J. Opt. Soc. Am. A 1, 183–191 (1984). [CrossRef]
- D. W. Mackowski, “Electrostatics analysis of radiative absorption by sphere clusters in the Rayleigh limit: application to soot particles,” Appl. Opt. 34, 3535–3545 (1995). [CrossRef] [PubMed]
- S. B. Singham, C. F. Bohren, “Light scattering by an arbitrary particle: the scattering-order formulation of the coupled dipole method,” J. Opt. Soc. Am. A 11, 1867–1872 (1988). [CrossRef]
- B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]
- M. I. Mishchenko, J. W. Hovenier, “Depolarization of light backscattered by randomly oriented nonspherical particles,” Opt. Lett. 20, 1356–1358 (1995). [CrossRef] [PubMed]
- M. K. Singham, S. B. Singham, G. C. Salzman, “The scattering matrix for randomly oriented particles,” J. Chem. Phys. 85, 3807–3815 (1986). [CrossRef]
- W. M. McClain, W. A. Ghoul, “Elastic light scattering by randomly oriented macromolecules: computation of the complete set of observables,” J. Chem. Phys. 84, 6609–6622 (1986). [CrossRef]
- F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Reliability of the theoretical description of electromagnetic scattering from nonspherical particles,” J. Aerosol Sci. 20, 1079–1081 (1989). [CrossRef]

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