Addendum to complete electromagnetic multipole expansion including toroidal moments Rev. Mex. Fis E 52 (2006) 188-197

E. Ley Koo, A. Góngora T., H. Torres Bustamante


This Addendum reports exact and complete solutions for the electromagnetic field of poloidal currents uniformly distributed on spherical toroidal surfaces, which has been a pending task of Section 3 in [1]. This result is important by
itself, and also because it allows the identification of new and alternative solutions and the reasons behind them.


Electromagnetic radiation; multipole expansion; electric, magnetic, toroidal moments

Full Text:



A. Góngora T. and E. Ley-Koo, Rev. Mex. Fis. E52 188-197 (2006)

T. Kaelberer, V.A. Fedotov, N. Papasimakis, D.P. Tsai and N. Zheludev. Toroidal dipolar response in a metamaterial. Science, 330(6010):1510-1512 (2012) 2

N. Papasimakis, V.A. Fedotov, V. Savinov, T. A. Raybould and N. Zheludev. Electromagnetic toroidal excitaciones

in matter and free space. Nature Materials DOI: 10.1038/NMAT4563 263-271 (2016)

N. Talebi, S. Guo and P. van Aken. Theory and application of toroidal moments in electrodynamics: their emergence,

characteristics, and technological relevance. Nanophotonics 7(1) pp. 93-110 (2018)

E. Ley-Koo, Recent Progress in Conned Atoms and Molecules: Superintegrability and Symmetry Breaking, Rev.

Mex. Fis. Vol. 64 (4) pp. 326-366 (2018).

E. Ley-Koo, Ch. Esparza-Lopez, H. Torres-Bustamante. Exact solutions for electromagnetic elds inside and outside

a spherical surface with magnetic/electric dipole distributed sources. Rev. Mex. Fis. E. Vol. 64 (2) pp. 139-148 (2018)



  • There are currently no refbacks.

Revista Mexicana de Física E

ISSN: 2683-2216 (on line), 1870-3542 (print)

Semiannual publication of Sociedad Mexicana de Física, A.C.
Departamento de Física, 2o. Piso, Facultad de Ciencias, UNAM.
Circuito Exterior s/n, Ciudad Universitaria. C. P. 04510 Ciudad de México.
Apartado Postal 70-348, Coyoacán, 04511 Ciudad de México.
Tel/Fax: (52) 55-5622-4946, (52) 55-5622-4840.