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The three nonlinear coupled differential equations for a three-frequency backward-traveling-wave parametric interaction in a lossless dielectric are solved for the power density in the three fields as a function of position in the crystal. When the theory is applied to a single-pass oscillator, it predicts the existence and magnitude of a threshold pump power even for lossless media. The theoretical curves showing the power outputs in the signal and idler waves for the single-pass oscillator as a function of pump power and crystal parameters are given.
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John G. Meadors (1969) studied this question.
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