A time-sinusoidal circularly polarized plane standing wave solution is obtained for isotropic lossless dielectric media with arbitrary nonlinearity. The spatial variation of the standing wave depends on the nonlinearity and is found by solving a problem of centralforce motion in which the electric complementary energy density furnishes the potential and the spatial coordinate has the role of time. Two special nonlinear dielectric response laws-cubic and quintic-are treated, and explicit solutions for the spatial variation of the wave amplitude and phase are obtained in terms of elliptic functions and elliptic integrals, respectively. The standing-wave solution is applied to give steady state solutions of two reflection/transmission problems (a) reflection from, or resonance modes between, ideally conducting planes and (b) reflection and transmission at a plane interface between two nonlinear dielectric media.
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Carroll, M.M. Reflection and transmission of circularly polarized waves in nonlinear dielectrics. Appl. Phys. 19, 321–329 (1979). https://doi.org/10.1007/BF00900476