MODAL ANALYSIS OF MULTILAYER CONICAL DIELECTRIC WAVEGUIDES FOR AZIMUTHAL INVARIANT MODES

By using fleld expansion in terms of the Legendre polynomials and Schelkunofi functions, Maxwell's equations in the spherical coordinate system are cast into a matrix form which lends itself to the analysis of a multilayer conical waveguide. The matrix formulation is then used to obtain an eigen-value problem whose eigen-values are the allowable wave-numbers for propagation in the radial direction. To verify the proposed numerical approach, it is used to evaluate the resonance frequency of a partially fllled spherical resonator. The computed resonance frequencies are then compared with those obtained using commercial software based on the flnite- element method. The computation time is enormously reduced using the semi-analytical method of this work. Although results are shown for lossless isotropic dielectrics, the method is also applicable to conical waveguides made of lossy dielectrics even with negative permittivity.