On the mathematical description of combined PMD PDL effects in optical communications and how their induced impairments can be minimized

TL;DR

This paper introduces a novel mathematical framework using the extended Lorentz Group's spinor representation to describe combined PMD and PDL effects in optical fibers, enabling new methods to minimize impairments.

Contribution

It establishes a new theoretical approach based on Lorentz Group representations for modeling combined PMD-PDL effects and proposes a practical technique to reduce impairments via optical phase conjugation.

Findings

Mathematical description of combined PMD-PDL effects using spinor representation.

Identification of optical phase conjugation as a transformation between polarization states.

A practical method to cancel PDL effects in optical fibers.

Abstract

In this paper it is shown that the correct mathematical framework of combined polarization mode dispersion and polarization dependent losses (combined PMD-PDL effects or impairments) in optical fibers is the irreducible spinor representation of the extended Lorentz Group. Combined PMD-PDL effects are shown to be formally identical to Lorentz Transformations acting on spin 1/2 zero mass particles. Since there are two different irreducible spinor representations of the restricted Lorentz Group, there must also exist two kinds of states of polarizations (SOPs) that are relevant in the description of PMD-PDL effects. The optical process that allows to convert one kind into the other is identified as optical phase conjugation. Optical phase conjugation plays the same role as the time inversion operator in the Lorentz Group representation theory. A practical and extremely important example of utility of these ideas, a technique that significantly reduces the PMD-PDL induced impairments, is presented. This technique allows to cancel the PDL part of the combined PMD-PDL impairments in a very simple and straightforward way.