Transfer matrix for treating stratified media including birefringent crystals

TL;DR

This paper introduces a generalized transfer matrix method for efficiently calculating the polarization states of light interacting with layered isotropic and birefringent media, crucial for precise optical system design.

Contribution

It develops a comprehensive transfer matrix framework for arbitrarily oriented birefringent crystals, enabling accurate modeling of polarized light in complex multilayer optical systems.

Findings

Efficient calculation of polarization states in layered media.

Matrix reduction from birefringent to isotropic materials.

Application to optical systems like wave plates in CMB polarimetry.

Abstract

Birefringent crystals are extensively used to manipulate polarized light. The generalized transfer matrix developed allows efficient calculation of the full polarization state of light transmitted through and reflected by a stack of arbitrarily-many discrete layers of isotropic and birefringent materials at any frequency and angle of incidence. The matrix of a uniaxial birefringent crystal with arbitrary rotation is calculated, along with its reduction to the matrix of an isotropic medium. This method is of great practical importance where tight control of systematic effects is needed in optical systems employing birefringent crystals, one example being wave plates used by cosmic microwave background polarimetry with wide field-of-view telescopes.