Generalized Stokes vector for three photon process

Abstract

Stokes Mueller formalism is used to measure the optical properties of materials by probing the sensitive changes in the polarization state of light after scattering from the medium. The formalism can be extended to nonlinear scattering processes involving two and three photon processes also. In this paper, we derive the Stokes vector, viz. triple Stokes vector analytically from quantum theory of light for a three photon process. The state of polarization of light, with three simultaneous photons, incident on a material is described by triple Stokes vector, and has 16 components involving cubes of intensities dependence. The response of a material for the scattered light in a three photon process is described by 4 × 16 Mueller matrix. Polarization in Polarization out (PIPO) experiments can be carried out to determine the elements of Mueller matrix. We identify 16 independent points on Poincare sphere and construct triple Stokes vector for each point. Four measurements are done to determine the linear Stokes vector of scattered light, where the 16 polarization states are represented by triple Stokes vector and this determines the Mueller matrix of the sample.