Influence of an optical inhomogeneity on the effective length of nonlinear crystals

A theoretical investigation is made of the influence of an optical inhomogeneity (a longitudinal linear variation of the birefringence) on the effective length of nonlinear crystals which, in the presence of this inhomogeneity, is shorter than their geometric length. The constant field approximation is used to find dependences of the effective length on the inhomogeneity and also to determine the optimal length of inhomogeneous crystals for second harmonic generation, parametric amplification, and parametric light generation.