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2004-06-22
Symmetry Relations of the Translation Coefficients of the Spherical Scalar and Vector Multipole Fields
By
, Vol. 48, 45-66, 2004
Abstract
We offer symmetry relations of the translation coefficients of the spherical scalar and vector multi-pole fields. These relations reduce the computational cost of evaluating and storing the translation coefficients and can be used to check the accuracy of their computed values. The symmetry relations investigated herein include not only those considered earlier for real wavenumbers by Peterson and Ström [9], but also the respective symmetries that arise when the translation vector is reflected about the xy-, yz-, and zx-planes. In addition, the symmetry relations presented in this paper are valid for complex wavenumbers and are given in a form suitable for exploitation in numerical applications.
Citation
Kristopher Kim , "Symmetry Relations of the Translation Coefficients of the Spherical Scalar and Vector Multipole Fields," , Vol. 48, 45-66, 2004.
doi:10.2528/PIER04040601
http://www.jpier.org/PIER/pier.php?paper=0404061
References

1. Stratton, J. A., Electromagnetic Theory, McGraw-Hill Book Company, 1966.

2. Stein, S., "Addition theorem for spherical wave functions," Quart. Appl. Math., Vol. 19, No. 1, 15-24, 1961.

3. Cruzan, O. R., "Translational addition theorems for spherical vector wave functions," Quart. Appl. Math., Vol. 20, No. 1, 33-40, 1962.

4. Danos, M. and L. C. Maximon, "Multipole matrix elements of the translation operator," J. of Math. Phys., Vol. 6, 766-778, 1965.
doi:10.1063/1.1704333

5. Chew, W. C., "A derivation of the vector addition theorem," Micro. Opt. Tech. Lett., Vol. 37, No. 7, 256-260, 1990.

6. Witmann, R. C., "Spherical wave operators and the translation formulas," IEEE Trans. Antennas Propagat., Vol. 36, No. 8, 1078-1087, 1988.
doi:10.1109/8.7220

7. Kim, K. T., "The translation formula for vector multipole fields and the recurrence relations of the translation coefficients of scalar and vector multipole fields," IEEE Trans. Antennas Propagat., Vol. 44, No. 11, 1482-1487, 1996.
doi:10.1109/8.542073

8. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New Jersey, 1995.

9. Peterson, B. and S. Ström, "T matrix for electromagnetic scattering from an arbitrary number of scatterers and representation of E(3)," Physical Review D, Vol. 8, No. 10, 3661-3678, 1973.
doi:10.1103/PhysRevD.8.3661

10. Bruning, J. H. and Y. T. Lo, "Multiple scattering of EM waves by spheres, Part I — multipole expansion and ray optical solutions," IEEE Trans. Antennas Propagat., Vol. 19, No. 3, 378-390, 1971.
doi:10.1109/TAP.1971.1139944

11. Hamid, A.-K., I. R. Ciric, and M. Hamid, "Multiple scattering by an arbitrary configuration of dielectric spheres," Can. J. Phys., Vol. 68, 1419-1428, 1992.

12. Hansen, J. E. (Ed.), Spherical Near-FieldA ntenna Measurements, Peter Peregrinus Ltd., U.K., 1988.

13. Tsang, L. J. and J. A. Kong, "Effective propagation constant for coherent electromagnetic waves in media embedded with dielectric scatterers," J. Appl. Phys., Vol. 11, 7162-7173, 1982.
doi:10.1063/1.331611

14. Chew, W. C., "Recurrence relations for three-dimensional scalar addition theorem," J. Electromagnetic Waves Appl., Vol. 6, No. 2, 133-142, 1992.

15. Chew, W. C. and Y. M. Yang, "Efficient ways to compute the vector addition theorem," J. Electromagnetic Waves Appl., Vol. 7, No. 5, 651-665, 1993.

16. Chew, W. C., J. H. Lin, and X. G. Yang, "An FFT T-matrix method for 3D microwave scattering solutions from random discrete scatterers," Microwave. Opt. Technol. Lett., Vol. 9, No. 4, 194-196, 1995.

17. Chan, C. H. and L. Tsang, "A sparse-matrix canonical-grid method for scattering by many scatterers," Microwave Opt. Technol. Lett., Vol. 8, No. 2, 114-118, 1995.

18. Waterman, P. C., Matrix formulation of electromagnetic scattering, Proceedings of IEEE, Vol. 53, 805-811, 1965.

19. Kim, K. T., "A storage-reduction scheme for the FFT T-matrix method," IIEEE Antennas andWir eless Propagation Letters.

20. Edmonds, A. R., Angular Momentum in Quantum Mechanics, Princeton University Press, 1974.

21. Rose, M. E., Multipole Fields, Wiely, 1955.

22. Brink, D. M. and G. R. Satchler, Angular Momentum, Oxford University Press, 1979.

23. Newton, R. G., Scattering Theory of Waves andParticles, McGraw-Hill Book Company, 1966.