Nonlinear Stokes Mueller Polarimetry

TL;DR

This paper extends Stokes Mueller polarimetry to nonlinear optical processes, providing a comprehensive algebraic framework for analyzing second- and third-harmonic generation and other nonlinear interactions.

Contribution

It introduces a generalized nonlinear Stokes Mueller formalism, including explicit relations between nonlinear susceptibilities and measured Mueller matrices.

Findings

Unified algebraic framework for nonlinear polarimetry

Explicit expressions for nonlinear Stokes vectors and Mueller matrices

Discussion on combining linear and nonlinear optical elements

Abstract

The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarimetry.