Four-wave mixing in fibers with random birefringence

Parametric amplification is made possible by four-wave mixing. In low-birefringence fibers the polarization axes and birefringence strength vary randomly with distance. Light-wave propagation in such fibers is governed by the Manakov equation. In this report the Manakov equation is used to study degenerate and nondegenerate four-wave mixing. 

The effects of linear and nonlinear wavenumber mismatches, and nonlinear polarization rotation, are included in the analysis. Formulas are derived for the initial quadratic growth of the idler power, and the subsequent exponential growth of the signal and idler powers (which continues until pump depletion occurs). These formulas are valid for arbitrary pump polarizations.