Hamiltonian formulation of cross mode modulation

We investigated the cross mode modulation (XMM) effect of a strong pump light on a weak probe light. The eigenmodes and the corresponding eigenvalues of the nonlinear system can be obtained by using the Hamiltonian approach, i.e., a theoretical framework using a linear coupled mode theory. The evolution of the probe light can be obtained based on eigenmodes and eigenvectors, which agrees with the numerical simulations of the coupled nonlinear Schrödinger equations.