Three-Photon Stokes Mueller Polarimetry

TL;DR

This paper develops a third-order optical polarimetry framework using Stokes Mueller polarimetry for third-harmonic generation, enabling detailed structural analysis of crystalline and biological materials.

Contribution

It introduces a comprehensive third-order polarimetry theory with new mathematical formulations for THG, including triple Mueller matrices and their relation to susceptibilities.

Findings

Derived expressions for THG Stokes vector and Mueller matrix.

Presented formulas for cylindrically symmetric and isotropic structures.

Established links between susceptibilities and measured Mueller matrices.

Abstract

The generalized theory of Stokes Mueller polarimetry is employed to develop the third-order optical polarimetry framework for third-harmonic generation (THG). The outgoing and incoming radiations are represented by 4-element and 16-element column vectors, respectively, and the intervening medium is represented by a $4\times 16$ triple Mueller matrix. Expressions for the THG Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, and expanded by four-dimensional $\gamma$ matrices that are analogues of Pauli matrices. Useful expressions of triple Mueller matrices are presented for cylindrically symmetric and isotropic structures. In addition, the relation between third-order susceptibilities and the measured triple Mueller matrix is provided. This theoretical framework can be applied for structural investigations of crystalline materials, including biological structures.