Abstract
Axisymmetric modes of cylindrical and coaxial cavity resonators filled with a nonlinear nondispersive medium are considered. It is assumed that the dependence of the electric displacement on the electric field aligned with the resonator axis can be approximated by an exponential function. Based on a rigorous approach, exact implicit expressions for the electromagnetic fields in these modes are derived. It is rigorously proved that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in this work, exactly coincides with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to take place only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.
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