Theory of Polarization Attraction in Parametric Amplifiers Based on Telecommunication Fibers

TL;DR

This paper develops a theoretical model for polarization-sensitive parametric amplification in optical fibers, predicting how the signal's polarization state is attracted to the pump's SOP and analyzing the impact of PMD on amplifier efficiency.

Contribution

It provides an analytical solution for the coupled wave equations in fiber-based parametric amplifiers, including effects of PMD and polarization attraction.

Findings

Output SOP is determined by pump SOP regardless of initial signal SOP.

The theory predicts the rate of efficiency degradation due to PMD.

Analytical solutions are valid beyond zero PMD limit.

Abstract

We develop from first principles the coupled wave equations that describe polarization-sensitive parametric amplification based on four-wave mixing in standard (randomly birefringent) optical fibers. We show that in the small-signal case these equations can be solved analytically, and permit us to predict the gain experienced by the signal beam as well as its state of polarization (SOP) at the fiber output. We find that, independently of its initial value, the output SOP of a signal within the parametric gain bandwidth is solely determined by the pump SOP. We call this effect of pulling the polarization of the signal towards a reference SOP as polarization attraction, and such parametric amplifier as the FWM-polarizer. Our theory is valid beyond the zero polarization mode dispersion (PMD) limit, and it takes into account moderate deviations of the PMD from zero. In particular, our theory is capable of analytically predicting the rate of degradation of the efficiency of the parametric amplifier which is caused by the detrimental PMD effect.