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.