Double Stokes Mueller polarimetry of second-harmonic generation in ordered molecular structures

Second-harmonic generation (SHG) is highly sensitive to the structure of ordered aggregates, and therefore, the polarization measurement of SHG can help to elucidate the organization of molecules in crystalline structures. The double Stokes Mueller formalism is developed for the SHG polarimetry and convenient expressions are derived for the double Mueller matrix in terms of the nonlinear susceptibilities. The polarization analysis is presented for cylindrically symmetric structures, providing the method to calculate the characteristic susceptibility component ratios and orientations of molecules in the ordered aggregates. This information, for example, can be used to investigate collagen or myosin structure in biological tissues.