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 integral that is a projection of an operation called the triple correlation. This operation may be easily implemented optically and thus be incorporated into fast real-time nonlinear control systems. We present a theoretical investigation of the relation existing between the Volterra operators and the triple correlation as well as an experimental demonstration that validates the theory.