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Journal of Mathematical Physics / Volume 21 / Issue 1

J. Math. Phys. 21, 60 (1980); http://dx.doi.org/10.1063/1.524333 (11 pages)

On electromagnetic multipole fields in a finite, spherically symmetric region

Arno D. Steiger

Lawrence Livermore Laboratory, University of California, Livermore, California 94550

The electromagnetic eigenfields for the region bounded by two concentric spheres are discussed and compared with the corresponding eigenfields of a spherical cavity. These characteristic fields are the solenoidal and irrotational multipole solutions of the vector Helmholtz equation that satisfy the source‐free boundary conditions. They constitute a complete set for the expansion of an arbitrary, square‐integrable electromagnetic field, which may be generated by surface and volume sources. The frequencies of the solenoidal and irrotational eigenfields for the annular region are analyzed as functions of the radius ratio, α=r1/r2 (r1<r2 =constant), of the two concentric spheres. The results are illustrated by graphs and tables. Two relations obtained by applying the implicit function theorem to the transcendental eigenfrequency equations are also derived by calculating the work performed against the radiation pressure as the electromagnetic field is compressed adiabatically. The multipole fields are expressed in terms of vector spherical harmonics and vector spherical multipoles. Two formulas for the reduction of vector products of multipole fields to sums of vector spherical harmonics are derived.

KEYWORDS and PACS

Keywords

MULTIPOLES, ELECTROMAGNETIC FIELDS, EIGENVECTORS, BOUNDARY−VALUE PROBLEMS, VECTOR FIELDS, SPHERES, BOUNDARY CONDITIONS

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.524333

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

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