TABLES OF NORMALIZED CUTOFF WAVE-NUMBERS OF ELLIPTIC CROSS-SECTION RESONATORS

Current methods to evaluate the mode resonance of elliptic cross section resonators are cumbersome for design purposes. In this paper, tables for the cutoff wavenumbers of TE(nm) and TM(nm) modes for both even and odd modes are tabulated in a new way, that reveals a simple relation to the equivalent circular cross section resonator and makes interpolation results accurate. These tables range for n = 0, ..., 3 for even modes and n = 1, ..., 4 for odd modes, with m = 1, ..., 5 for both. The tables cover 80 different modes for eccentricity in the range 0 less-than-or-equal-to e less-than-or-equal-to 0.99. Asymptotic formulae are given for higher modes and approximate formulae are given for small eccentricity 0 less-than-or-equal-to e less-than-or-equal-to 0.2. The accuracy of interpolation, approximate formulae and asymptotic formulae are compared with published results.