Anisotropic elliptical dichroism and influence of imperfection of circular polarization upon anisotropic circular dichroism.

Abstract

In spite of the importance of anisotropic circular dichroism, in practice, it is difficult to get rid of the artifacts that arise from the imperfection of the circular polarization. Undesirable linear dichroism, interference of two orthogonal polarization states, and linear birefringence prevent us from making accurate measurements. We propose a theoretical method for evaluating the contributions of the first two, which are thought to be the main artifacts when specimens are not thick enough. Using the time-dependent perturbation theory and taking into account the direction of light propagation toward an orientationally fixed molecule, we formulated the transition probability of systems perturbed by arbitrarily polarized light and the absorption difference associated with two kinds of polarized light. We also formulated, as an extension of the dissymmetry factor of circular dichroism, a newly defined dissymmetry factor associated with two arbitrary polarization states. Furthermore, we considered a mixed-state of photon ensemble in which polarization states distribute at a certain width around a certain average. Although the purity of polarization and ellipticity does not correspond immediately, by considering the mixed state it is possible to treat them consistently. We used quantum statistical mechanics to describe the absorption difference for two kinds of photon ensembles and applied the consequent formula to examine the reported experimental results of single-molecule chiroptical responses under discussion in the recent past. The artifacts are theoretically suggested to be sensitive to the incident direction of elliptically polarized light and to the oriented systems, the ellipticity, and the orientation of ellipse. The mixed state has little, if any, effect when the polarization state distribution is narrow.