General framework for treating generation, propagation, and polarization of luminescence in anisotropic media

Complete polarimeters deliver the full polarization transfer matrix of a medium that relates input polarization states to output polarization states. In order to interpret the Mueller matrix of a luminescent medium at the emission frequency, accountings are required for polarization transformations of the medium at the excitation frequency, the light scattering event, and the polarization transformations at the emission frequency. A general framework for this kind of analysis is presented herein. The fluorescence Mueller matrix is expressed as a product of Mueller matrices of the medium at the excitation and emission frequencies and a scattering matrix, integrated over path length. The Stokes vector for the incident light, evolving according to the Mueller matrix of the medium at the excitation frequency, is multiplied by the scattering matrix to give a Stokes vector of the emitted light along the propagation direction. The scattering matrix is derived from an incoherent orientation ensemble average over a phenomenological scattering tensor that embodies intrinsic molecular scattering proprieties, and dynamical processes that occur during the excited state. The general framework is evaluated for three anisotropic materials carrying luminescent dye molecules including the following: a chiral fluid, a stretched polymer film, and a chiral, biaxial crystal. In the latter case, the most complex, the Mueller matrix was collected in conoscopic illumination and the fluorescence Mueller matrix, mapped in k-space, was fully simulated by the strategy outlined above. Luminescence spectroscopy has typically stood apart from the developments in polarimetry of the past two generations. This need not be indefinite.