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Differential equations are derived for the propagation of two counterpropagating plane waves of arbitrary polarization in an optical medium having a cubic nonlinearity in dielectric susceptibility. It is shown that a simple analytic solution exists when both waves are circularly polarized. For waves polarized linearly, but with an angle θ between the polarizations at incidence, numerical solutions are found leading to elliptically polarized waves. Numerical solutions are also plotted for the reflection coefficient in the case when the pump waves are of equal amplitude and of the same polarization and an object wave of arbitrary amplitude (up to 30% of the pump amplitude) is incident with the orthogonal polarization.
© 1982 Optical Society of America
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