Theory of birefringence correction for polarization-controlled CARS

Polarization-controlled coherent Raman spectroscopy is used as a high-throughput method to characterize the anisotropic nature of a molecular system, such as the molecular orientation distribution. However, optical birefringence originating from the molecular anisotropy can cause the observed Raman spectrum to be significantly distorted, making it extremely challenging to obtain quantitative information from polarization Raman measurements. Here, the birefringence effect on the signal intensity and the spectral shape of a polarization-controlled coherent anti-Stokes Raman scattering (CARS) is theoretically described using a uniaxially symmetrical model system. Due to the complexity, the effect of phase delay in the incident lights is not considered but only that of the generated CARS signal is considered. A new analytical method is presented to eliminate the birefringence contribution from polarization-controlled CARS data by analyzing polarization intensity profiles and retrieving the resonant Raman susceptibility spectra. This method is tested with two sets of polarization-controlled CARS data simulated with various combinations of symmetries of multiple underlying Raman modes. The analysis result clearly demonstrates that the effect of birefringence can be corrected for polarization-controlled CARS data and the symmetry tensor elements of all underlying Raman modes can be quantitatively characterized.