非线性电动力学中电磁模的共振产生：经典方法
On resonant generation of electromagnetic modes in nonlinear electrodynamics: Classical approach
摘要：
本文探讨了欧拉-海森堡电动力学中非线性效应产生的电磁模共振放大的理论可能性。准确地说，我们研究了射频腔中单个电磁模式引起的三次谐波放大的可能性，以及腔中两种泵浦模式（$ω_1$和$ω_2$）引起的组合频率的信号模式的产生。求解信号模式的非齐次波动方程，我们制定了两个谐振腔的任意形状的条件，并适用于线性和矩形腔的形式。我们明确地表明，三次谐波以及模式的组合频率$2ω_1 + ω_2$不共振放大，而信号模式的频率$2ω_1 - ω_2$放大一定的腔的几何形状。
英文摘要：
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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