Degenerate-four-wave mixing as a Sturm–Liouville problem

The problem of steady-state degenerate holographic four-wave mixing in transmission geometry in nonlinear dynamic media is reduced to a Sturm-Liouville or a one-dimensional quantum-mechanical scattering problem, which is treated exactly. Linear absorption in the medium is accounted for, and pump depletion is allowed. No restrictions are placed on the spatial phase mismatch between light-interference fringes and refractive-index gratings. Energy and phase transfer are considered simultaneously.