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Zbl 0990.78009
Kokkorakis, G.C.; Roumeliotis, J.A.
Electromagnetic eigenfrequencies in a spheroidal cavity (calculation by spheroidal eigenvectors). (English)
[J] J. Electromagn. Waves Appl. 12, No.12, 1601-1624 (1998). ISSN 0920-5071; ISSN 1569-3937/e

Summary: The electromagnetic eigenfrequencies $f_{nsm}$ in a perfectly conducting spheroidal cavity are determined analytically. The analytical determination is possible in the case of small values of $h= d/(2a)$, $(h\ll 1)$, where $d$ is the interfocal distance of the spheroidal cavity and $2a$ the length of its rotation axis. In this case exact, closed-form expressions are obtained for the expansion coefficients $g^{(2)}_{nsm}$ and $g^{(4)}_{nsm}$ in the resulting relation $$f_{nsm}(h)= f_{ns}(0)[1+ h^2 g^{(2)}_{nsm}+ h^4 g^{(4)}_{nsm}+ O(h^6)].$$ Analogous expressions are obtained with the use of the parameter $v= 1- a^2/b^2$ (for $|v|\ll 1$), where $2b$ is the length of the other axis of the spheroidal cavity. The electromagnetic field is expressed in terms of spheroidal eigenvectors. Numerical results are given for the lower-order modes.

MSC 2000:: *78A40 Waves and radiation
78M25 Numerical methods in optics

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