Vector theory of four-wave mixing: polarization effects in fiber-optic parametric amplifiers

We present a vector theory of four-wave mixing and use it to study the polarization-dependent nature of four-wave mixing and the conditions under which the gain of a dual-pump fiber-optic parametric amplifier becomes polarization independent. We find that in the absence of self- and cross-phase modulations, any pair of orthogonally polarized pumps can provide polarization-independent gain, but this gain is minimum for linearly polarized pumps and becomes maximum when the two pumps are circularly polarized. Self-and cross-phase modulations induce nonlinear polarization rotation and change the orthogonality between the two pump polarizations. We discuss the general case of elliptically polarized cases and show that only linearly and circularly polarized pumps can maintain their orthogonality along the fiber. A stability analysis shows that the case of linearly polarized pumps is more stable than the circular one against small deviations from the ideal case but that the latter provides much more amplification. (C) 2004 Optical Society of America.