Abstract

Real-time correlation of 2-D optical patterns has previously been demonstrated using degenerate four-wave mixing in nonlinear optical materials.¹ The approach is shown schematically in Fig. 1. Previous analysis² has assumed a very thin nonlinear material in which case the correlation is accurate-in this paper, a closed form solution for the output is presented which includes an arbitrary material thickness Z₀ and shows that the error in correlation can be significant in some typical cases and that a limitation on the scannable field exists. The error stems from the k vector mismatch for k vectors at an angle to the beam optic axis and, for the non- collinear case, from the relative transverse movement of the two beams in the nonlinear material.

© 1983 Optical Society of America