Small-frequency-shift stimulated-four-photon mixing in optical fibers: optimum phase-matching conditions

When the frequency shift of amplified Stokes and anti-Stokes waves in stimulated four-photon mixing processes is small, the equations governing the interaction can be simplified, and the general case of depleted pump power can be solved analytically. This yields expressions for the phase mismatch as a function of pump power required for maximum amplification of the generated frequencies.