Three-photon Stokes-Mueller polarimetry

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 $4\ifmmode\times\else\texttimes\fi{}16$ 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 $\ensuremath{\gamma}$ matrices that are analogs 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.