## Point-group symmetries in electromagnetic scattering

JOSA A, Vol. 16, Issue 4, pp. 853-865 (1999)

http://dx.doi.org/10.1364/JOSAA.16.000853

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### Abstract

A relation is developed between point-group symmetries of light-scattering particles and symmetry relations for the electromagnetic scattering solution in the *T*-matrix formulation. A systematic derivation of a representation of symmetry operations is presented in the vector space on which the *T* matrix operates. From this the set of symmetry relations of the *T* matrix is obtained for various point groups. As examples several symmetry groups relevant to modeling atmospheric particles are treated, such as the *K* group of spherical symmetry, the *C*_{∞v} group of axial symmetry, and the *D*_{∞h} group of dihedral axial symmetry. The *D*_{∞h} symmetry relations for the *T* matrix in spheroidal coordinates (denoted by script font) are also derived. Previously known symmetry relations of the *T* matrix can be verified, and new relations are found for *D*_{Nh} symmetry, i.e., for the important case of particles with dihedral symmetry and an *N*-fold axis of rotation.

© 1999 Optical Society of America

**OCIS Codes**

(290.1310) Scattering : Atmospheric scattering

(290.5850) Scattering : Scattering, particles

**Citation**

F. Michael Schulz, Knut Stamnes, and J. J. Stamnes, "Point-group symmetries in electromagnetic scattering," J. Opt. Soc. Am. A **16**, 853-865 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-4-853

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### References

- M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
- F. M. Schulz, K. Stamnes, and J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998).
- C.-R. Hu, G. W. Kattawar, M. E. Parkin, and P. Herb, “Symmetry theorems on the forward and backward scattering Mueller matrices for light scattering from a nonspherical dielectric scatterer,” Appl. Opt. 26, 4159–4173 (1987).
- H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
- P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1970).
- P. C. Waterman, “Matrix methods in potential theory and electromagnetic scattering,” J. Appl. Phys. 50, 4550–4566 (1979).
- P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
- P. Barber, “Differential scattering of electromagnetic waves by homogeneous isotropic dielectric bodies,” Ph.D. thesis (University of California, Los Angeles, Los Angeles, Calif., 1973).
- P. Barber and C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
- L. Tsang, J. A. Kong, and R. T. Shin, “Radiative transfer theory for active remote sensing of a layer of nonspherical particles,” Radio Sci. 19, 629–642 (1984).
- V. V. Varadan and V. K. Varadan, “Multiple scattering of electromagnetic waves by randomly distributed and oriented dielectric scatterers,” Phys. Rev. D 21, 388–394 (1980).
- N. G. Khlebtsov, “Orientational averaging of light-scattering observables in the T-matrix approach,” Appl. Opt. 31, 5359–5365 (1992).
- D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
- L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, New York, 1995).
- M. I. Mishchenko, “Light scattering by size–shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 4652–4665 (1993).
- M. I. Mishchenko and L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
- M. I. Mishchenko and L. D. Travis, “Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight,” J. Geophys. Res. 102, 16989–17013 (1997).
- M. I. Mishchenko, L. D. Travis, and A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
- S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975).
- S. Asano and M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
- V. G. Farafonov, “Scattering of electromagnetic waves by a perfectly conducting spheroid,” Radio Eng. Electron. Phys. 29, 39–45 (1984).
- N. V. Voshchinnikov and V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
- N. V. Voshchinnikov, “Electromagnetic scattering by homogeneous and coated spheroids: calculations using the separation of variable method,” J. Quant. Spectrosc. Radiat. Transf. 55, 627–636 (1996).
- P. N. Francis, “Some aircraft observation of the scattering properties of ice crystals,” J. Atmos. Sci. 52, 1142–1154 (1995).
- H. Laitinen and K. Lumme, “T-matrix method for general star-shaped particles: first results,” J. Quant. Spectrosc. Radiat. Transf. 60, 325–334 (1998).
- M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831–16847 (1997).
- F. M. Schulz, K. Stamnes, and J. J. Stamnes, “Shape-dependence of the optical properties in size–shape distributions of randomly oriented prolate spheroids, including highly elongated shapes,” J. Geophys. Res. (to be published).
- F. M. Schulz, K. Stamnes, and J. J. Stamnes, “Modeling of the radiative transfer properties of media containing particles of moderately and highly elongated shape,” Geophys. Res. Lett. 25, 4481–4484 (1998).
- C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).
- C. J. Bouwkamp, “On spheroidal wave functions of order zero,” J. Math. Phys. 26, 79–93 (1947).
- M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf. 55, 535–575 (1996).

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