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The approach for handling transient electrodynamics problems based on their description by an integral Volterra equation is presented. The expression for a resolvent of this three‐dimensional space‐time vector equation for the case of a time‐varying dielectric restricted by a plane boundary is derived. Using this approach it is demonstrated that an oblique incidence of a plane monochromatic wave on a boundary of a dielectric whose permittivity changes abruptly in time leads to a formation of a continuous wave spectrum. In the case of a point source of electromagnetic radiation, the presence of a plane boundary leads to a replacement of a convergence point of secondary spherical waves to the mirror symmetrical point. The field in this point has a bounded value, as differentiated from the case of an unbounded medium.

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This paper considers the switching effects on whispering gallery modes in circular dielectric resonators when their material is subject to abrupt time changes in permittivity. Both the transient response and the new steady-state regime are described in detail by means of an analytical approach.