The dependence of the eigenvalues of the TM1 n and TE1 n electromagnetic triplet modes on the shape of a triaxial ellipsoid cavity resonator is investigated. For an ellipsoid with semi-axes proportional to 1 : (1 + 1 ) : (1 + 2 ) the fractional perturbations of the triplet components are found to second order in 1 and 2 . The formulae are derived from the results of Kokkorakis and Roumeliotis (1997 J. Electromagn. Waves Appl. 11 279–92) for prolate and oblate spheroids. Finite-element calculations were carried out to confirm the accuracy of the formulae and to determine the next correction terms.
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James B. Mehl (2009) studied this question.
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