title: Spatial convolution and correlation of optical fields via degenerate four-wave mixing.
abstract: A nonlinear optical technique is described that performs, essentially instantaneously, the functions of spatial correlation and convolution of spatially encoded waves. These real-time operations are accomplished by mixing spatially dependent optical fields in the Fourier-transform plane of a lens system. The use of a degenerate four-wave mixing scheme eliminates (in the Fresnel approximation) phase-matching restrictions and (optical) frequency-scaling factors. Spatial bandwidth-gain considerations and numerical examples, as well as applications to nonlinear microscopy, are presented.
authors.forename: D M
authors.initials: DM
authors.lastname: Pepper
authors.forename: J
authors.initials: J
authors.lastname: Auyeung
authors.forename: D
authors.initials: D
authors.lastname: Fekete
authors.forename: A
authors.initials: A
authors.lastname: Yariv