Influence of inhomogeneities in a nonlinear crystal on the conversion of an image by sum-frequency generation

A theoretical analysis is given of the influence of random longitudinal inhomogeneities in a nonlinear crystal on the resolving power and the phase-matching angle. It is shown that the longitudinal resolution is the same as for a homogeneous crystal, but the transverse resolution deteriorates by a factor (l/d)^1/2, and the spread of the phase-matching angle increases by the same factor; here, l is the length of the crystal, d is the correlation radius of the function exp(–is), and s is the phase shift due to inhomogeneitles.