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 ($\omega_1$ and $\omega_2$) 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 $2\omega_1 + \omega_2$ are not resonantly amplified while the signal mode with frequency $2\omega_1 - \omega_2$ is amplified for a certain cavity geometry.