Polarization-dependence of optical second harmonic generation for chiral cylindrical structure and explanation for nonlinear optical imaging of cholesteric liquid crystals

We developed a comprehensive elliptic expression of the polarization dependence of SHG for chiral cylindrical structures in a vectorial form with the coefficients as functions of the molecular polarizability and orientational order parameters. The use of the vectorial form simplifies the analyses, and presents a clear picture of chiral effects. As an example, the theory has been used to explain the SHG imaging of cholesteric liquid crystals (CLC) of collagen solutions. We found that the chiral contributions indeed exist and the ratio between chiral and polar second order susceptibilities is evaluated as ∣α123/α333∣⩽0.2.