Optical implementation of second-order nonlinear Volterra operators with use of triple correlation

Following the Volterra theorem, every nonlinear operator can be implemented with a sum of integrals applied over the input. The second-order Volterra operator that describes many useful systems can be related to a single inte gral that is a projection of an operation called the triple correlation. Th is operation may be easily implemented optically and thus be incorporated i nto fast real-time nonlinear control systems. We present a theoretical inve stigation of the relation existing between the Volterra operators and the t riple correlation as well as an experimental demonstration that validates t he theory. (C) 2001 Optical Society of America.