PIER B
 
Progress In Electromagnetics Research B
ISSN: 1937-6472
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 36 > pp. 89-111

CARTESIAN MULTIPOLE EXPANSIONS AND TENSORIAL IDENTITIES

By E. Radescu, Jr. and G. Vaman

Full Article PDF (237 KB)

Abstract:
We establish the exact formulas of multipole expansion in Cartesian coordinates for the most general distribution of charges and currents (including toroidal sources).

Citation:
E. Radescu, Jr. and G. Vaman, "Cartesian multipole expansions and tensorial identities," Progress In Electromagnetics Research B, Vol. 36, 89-111, 2012.
doi:10.2528/PIERB11090702
http://www.jpier.org/pierb/pier.php?paper=11090702

References:
1. Dubovik, , V. M. , A. A. Tcheshkov, and , "Multipolnoe razlojenie v classichescoi i v kvantovoi torii polia i izluchenie," Fiz. Elem Chastits At. Yadra,/ Sov. J. Part. Nucl.,, Vol. 5, , 791/318-837, 1974.

2. Dubovik, , V. M. , V. V. Tugushev, and , "Toroid moments in electrodynamics and solid-state physics," Phys. Rep.,, Vol. 187, 145-202, , 1990.
doi:10.1016/0370-1573(90)90042-Z

3. Kaelberer, , T., V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, , "Toroidal dipolar response in a metamaterial,"," Science,, Vol. 330, 1510-1512, 2010..
doi:10.1126/science.1197172

4. Petschulat, J., , "Understanding the electric and magnetic response of isolated metaatoms by means of a multipolar field decomposition," Optics Express, , Vol. 18, , 14455-14466, 2010.

5. Kuo, C. Y., , R. L. Chern, and C. C. Chang, , "Multipole expansion of electromagnetic scattering wave by a small cylindrical pore on a perfect conducting semi-infinite half space," Progress In Electromagnetics Research B, , Vol. 26, 179-212, 2010.
doi:10.2528/PIERB10063008

6. Andrews, D. L. and W. A. Ghoul, "Irreducible fourth-rank Cartesian tensors," Phys. Rev. A,, Vol. 25, , 2647-2657, 1982.
doi:10.1103/PhysRevA.25.2647

7. Radescu, , E. E. , G. Vaman, and , "Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic and toroid," multipoles," Phys. Rev. E, , Vol. 65, , 046609-1-7, 2002.

8. Rowe, , "Spherical delta functions and multipole expansions," J. Math. Phys., Vol. 19, , 1962-1968, 1978.
doi:10.1063/1.523927

9. Weniger, , E. J., , "Addition Theorems as three-dimensional Taylor expansions," Int. J. Quant. Chem.,, Vol. 76, , 280-295, 2000..
doi:10.1002/(SICI)1097-461X(2000)76:2<280::AID-QUA16>3.0.CO;2-C

10. Edmonds, A., , Deformations of Atomic Nuclei, Publishing House for Foreign Literature, , Moscow, (in Russian), 1958 .

11. Applequist, J., , "Traceless cartesian tensor forms for spherical harmonic functions: New theorems and applications to electrostatics of dielectric media," J. Phys. A,, Vol. 22, , 4303-4330, 1989.
doi:10.1088/0305-4470/22/20/011

12. Landau, L. D. and E. M. Lifschitz, , Course of Theoretical Physics, Pergamon Press, , New York, , 1993.

13. Jackson, J. D., , Classical Electrodynamics,, Wiley, , New York, , 1999..

14. Hobson, , E. W., , The Theory of Spherical and Ellipsoidal Harmonics, , Cambridge University Press, Cambridge, , 1931.

15. Prudnikov, , A. P., Y. A. Brychkov, and O. I. Marichev, "Integrals and Series, ,", 1986.


© Copyright 2010 EMW Publishing. All Rights Reserved