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Electromagnetic eigenfrequencies in a spheroidal cavity (calculation by spheroidal eigenvectors). (English) Zbl 0990.78009

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), (h1), 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 nsm (2) and g nsm (4) in the resulting relation

f nsm (h)=f ns (0)[1+h 2 g nsm (2) +h 4 g nsm (4) +O(h 6 )]·

Analogous expressions are obtained with the use of the parameter v=1-a 2 /b 2 (for |v|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:
78A40Waves and radiation (optics)
78M25Numerical methods in optics