Phase matching for parametric amplification in a single-mode birefringent fiber: Influence of the non-phase-matched waves

In a single-mode birefringent fiber, phase matching in four-photon parametric amplification implies linear terms, which are due to dispersion and birefringence, and nonlinear terms, which are due to self- and cross-phase modulations. In the normal-dispersion regime combinations of these terms lead to three phase-matched regimes. When the pump is equally divided between the two polarizations one must take the nonphase-matched waves into account to obtain accurate values of the phase-matched wavelengths and of the gain. To calculate these parameters we analytically develop corrected models of both the four-wave mixing formalism and of the modulation instability formalism and show the correspondence between these two approaches. Then we experimentally show that the parametric gain increases with the value of the birefringence. (C) 1997 Optical Society of America.