Three-Dimensional Nonlinear Stokes - Mueller Polarimetry

TL;DR

This paper develops a comprehensive formalism for three-dimensional nonlinear Stokes-Mueller polarimetry, enabling advanced material and biological structure analysis through high-resolution nonlinear microscopy.

Contribution

It introduces a novel 3D nonlinear Stokes-Mueller formalism, including the derivation of generalized vectors, matrices, and the $X$-matrix for susceptibility characterization.

Findings

Derived expressions for 3D nonlinear Stokes vectors and Mueller matrix.

Introduced the $X$-matrix for susceptibility analysis and depolarization.

Applicable to high-resolution nonlinear microscopy and material studies.

Abstract

The formalism is developed for a tree-dimensional ($3D$) nonlinear Stokes-Mueller polarimetry. The expressions are derived for the generalized $3D$ linear and nonlinear Stokes vectors, and the corresponding nonlinear Mueller matrix. The coherency-like Hermitian square matrix $X$ of susceptibilities is introduced, which is derived from the nonlinear Mueller matrix. The $X$-matrix is characterized by the index of depolarization. Several decompositions of the $X$-matrix are introduced. The $3D$ nonlinear Stokes-Mueller polarimetry formalism can be applied for three and higher wave mixing processes. The $3D$ polarimetric measurements can be used for structural investigations of materials, including heterogeneous biological structures. The $3D$ polarimetry is applicable for nonlinear microscopy with high numerical aperture objectives.