Stress sensitivity of electromagnetic resonances in circular dielectric disks

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Abstract
A formula for predicting the stress effect on the electromagnetic resonances of dielectric resonators is obtained by applying a perturbation method to the three-dimensional Maxwell’s equations in which the dielectric permittivity tensor is perturbed by the applied stress (or strain) field through the piezo-optic effect. The dielectric resonator, which is surrounded by infinite free space, can be isotropic or anisotropic and of arbitrary shape. By using previously obtained two-dimensional closed-form solutions as the approximate unperturbed solutions, stress effect on the electromagnetic resonances in a dielectric circular disk is studied. Frequency changes of both the transverse electric and transverse magnetic modes are computed for disks of gallium arsenide and under three cases of loading: (1) a pair of diametral forces, (2) steady vertical acceleration, and (3) steady horizontal acceleration. In the latter two cases, the bottom face of the disk is supported by a rigid base.