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

TL;DR

This paper investigates the theoretical possibility of resonant amplification of electromagnetic modes due to nonlinear effects in Euler-Heisenberg electrodynamics, identifying specific conditions under which certain modes can be amplified in a cavity.

Contribution

It formulates resonant conditions for electromagnetic mode amplification in nonlinear electrodynamics and applies them to various cavity geometries, revealing which modes can be resonantly amplified.

Findings

Mode with frequency 2ω₁ - ω₂ can be resonantly amplified.

Third harmonics and combined frequency 2ω₁ + ω₂ are not amplified.

Resonant conditions depend on cavity geometry.

Abstract

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.