Influence of the longitudinal inhomogeneity of the refractive index of a nonlinear crystal on the parametric gain

A theoretical study is made of the influence of a longitudinal optical inhomogeneity of a nonlinear crystal on the value and spectral dependence of the gain, which is calculated numerically for arbitrary parameters of the inhomogeneity. An analytic dependence of the gain in the inhomogeneity parameters is obtained in the two most typical cases of a weak inhomogeneity (linear and step) in nonlinear LiNbO₃ crystals. A study is made of the influence of an inhomogeneity on the width and shape of the parametric gain profile. The results are used to formulate requirements in respect of the inhomogeneity parameters of nonlinear crystals suitable for optical parametric oscillators. A report is given of an experimental study of the dependence of the average power of a singly resonant parametric oscillator on the inhomogeneity parameter of an LiNbO₃ crystal. The experimental results confirm the theoretical predictions.