Determination of 3D molecular orientation by concurrent polarization analysis of multiple Raman modes in broadband CARS spectroscopy

Abstract

A theoretical description is presented about a new analysis method to determine three-dimensional (3D) molecular orientation by concurrently analyzing multiple Raman polarization profiles. Conventional approaches to polarization Raman spectroscopy are based on single peaks, and their 2D-projected polarization profiles are limited in providing 3D orientational information. Our new method analyzes multiple Raman profiles acquired by a single polarization scanning measurement of broadband coherent anti-Stokes Raman scattering (BCARS). Because the analysis uses only dimensionless quantities, such as intensity ratios and phase difference between multiple profiles, the results are not affected by sample concentration and the system response function. We describe how to determine the 3D molecular orientation with the dimensionless observables by using two simplified model cases. In addition, we discuss the effect of orientational broadening on the polarization profiles in the two model cases. We find that in the presence of broadening we can still determine the mean 3D orientation angles and, furthermore, the degree of orientational broadening.

Coherent anti‐Stokes Raman scattering microscopy for polymers

“…A CARS susceptibility is a fourth‐rank tensor that determines the polarization state of CARS emission with respect to the polarization states of incident lights. A CARS susceptibility tensor, χ (3) , is a macroscopic value expressed by a sum of molecular hyperpolarizability tensors, α (3) , where R is a rotation matrix in the three‐dimensional Euler space for the transformation between the molecular frame to the laboratory frame 39 . The polarization dependence of a CARS signal is determined by the symmetry of the molecular hyperpolarizability and the orientational distribution of the molecules 40,41 .…”

“…where R is a rotation matrix in the three-dimensional Euler space for the transformation between the molecular frame to the laboratory frame. 39 The polarization dependence of a CARS signal is determined by the symmetry of the molecular hyperpolarizability and the orientational distribution of the molecules. 40,41 When the symmetry of molecular hyperpolarizability is known, the dependence on the orientational distribution of molecules can be used for the characterization of the orientational distribution of the molecules.…”

Concurrent polarization IR analysis to determine the 3D angles and the order parameter for molecular orientation imaging

“…It should be noted that this analytical model function is used simply for data simulation, not used for data analysis. A von Mises-Fisher distribution function, ρ vMF ( β ), shown in Fig.3a, is widely used to represent a cylindrical ODF [24]. A von Mises-Fisher distribution function monotonically decreases from the maximum at β = 0, and its orientation broadening is represented by a parameter, called the concentration parameter, k .…”

“…In the previous paper [24], a new spectral analysis method was proposed to determine the 3D angles of molecular orientation, analyzing coherent anti-Stokes Raman scattering (CARS) susceptibilities of two non-parallel Raman modes observed by a single polarization scan. In the paper, the spectral analysis method determines the 3D orientation angles of molecular systems with different symmetries and orientational broadening.…”

“…This concurrent polarization IR analysis method can also calculate those output values by a single step without iterative computation. Similar to the approach developed for polarization CARS [24], this new IR analysis method takes advantage of dimensionless parameters observed from two polarization IR absorption profiles. The concurrent polarization IR analysis method can be easily implemented to conventional IR microscopy by a simple addition of polarization rotating optics in the beam path.…”