On resonant generation of electromagnetic modes in nonlinear electrodynamics: Classical approach

The paper explores a theoretical possibility of resonant amplification of electromagnetic modes generated by a nonlinear effect in Euler-Heisenberg electrodynamics. Precisely, we examine the possibility of the amplification for the third harmonics induced by a single electromagnetic mode in radiofrequency cavity, as well as the generation of signal mode of combined frequencies induced by two pump modes ($ω_1$ and $ω_2$) in the cavity. Solving inhomogeneous wave equations for the signal mode, we formulate two resonant conditions for a cavity of arbitrary shape, and apply the obtained formalism to linear and rectangular cavities. We explicitly show that the third harmonics as well as the mode of combined frequency $2ω_1 + ω_2$ are not resonantly amplified while the signal mode with frequency $2ω_1 - ω_2$ is amplified for a certain cavity geometry.

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