Three-dimensional nonlinear Stokes-Mueller polarimetry

The formalism is developed for a three-dimensional (3D) nonlinear Stokes-Mueller polarimetry that describes a method of acquiring a complete complex valued 3D nonlinear susceptibility tensor of a material. The expressions are derived for 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 that provide a possibility to obtain nonlinear susceptibility tensors of constituting materials in the heterogeneous media. 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. (C) 2019 Optical Society of America