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Fractal Fourier spectra of electromagnetic oscillations in a driven nonlinear resonator

We consider a cylindrical cavity resonator filled with a nonlinear nondispersive medium and driven by an alternating voltage. It is assumed that the medium lacks a center of inversion and the dependence of the electric displacement on the electric field can be approximated by an exponential function. We show that the Maxwell equations are integrated exactly in this case and the field components in the cavity are represented in terms of implicit functions of special form. We demonstrate that Fourier spectra of the driven electromagnetic oscillations in the cavity contain singular continuous components.