Conservation law for multiple four-wave-mixing processes in a nonlinear optical medium

When two optical waves at frequencies ${\mathrm{\omega }}_1$ and ${\mathrm{\omega }}_2$ interact in a medium with cubic nonlinearity, multiple four-wave-mixing processes can generate pairs of sidebands. A conservation law that connects the amplitudes of the pump waves and sidebands is shown to arise from the Manley-Rowe relations and from the infinite set of conservation relations of the nonlinear Schrödinger equation. The conservation relation is examined theoretically and verified experimentally for a variety of input pump power levels and asymmetries. It can be used as a diagnostic measure to determine if nonlinearities of higher order than cubic are present.