Momentum in nonlinear optics

Abstract

Although it is well known that light carries momentum and exerts a pressure on objects, a conservation of momentum principle is apparently rarely used in optics. In nonlinear optics light waves interact and may exchange both energy and momentum. We demonstrate that a conservation of momentum principle holds in these cases and in fact its use is widespread but generally unrecognized in the standard mathematical methods. In both the cases of linear basis waves interacting nonlinearly, e.g. coupled-wave theory and frequency mixing, and fully nonlinear waves, we demonstrate that a governing Hamiltonian is related to momentum. Action principles are used to discuss the generality of these results.