Abstract
Starting from the time-harmonic Maxwell's equations in cylindrical coordinates,
we derive and solve the finite-difference (FD) eigenvalue equations for determining
vector modes of axially symmetric resonator structures such as disks, rings, spheres and
toroids. Contrary to the most existing implementations, our FD scheme is readily adapted
for both eigenmode and eigenfrequency calculations. An excellent match of the FD
solutions with the analytically calculated mode indices of a microsphere resonator
provides a numerical confirmation of the mode-solver accuracy. The comparison of the
presented FD technique with the finite-element method highlights the relative strengths
of both techniques and advances the FD mode-solver as an important tool for cylindrical
resonator design.
© 2010 IEEE
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