Behavior of the nonlinear refractive indices and birefringence in the neighborhood of first- and second-order phase transitions in lyotropic liquid crystals

Abstract

We investigated the behavior of the nonlinear refractive indices ${(n}_{2})$ and birefringence $(\ensuremath{\Delta}{n}_{2})$ in the vicinity of the nematic-to-isotropic $(N\ensuremath{-}I)$ and nematic uniaxial-to-nematic biaxial $(N\ensuremath{-}N)$ phase transitions in a lyotropic liquid crystal. The single-beam Z-scan technique is used to measure ${n}_{2}$ in different relative configurations of the electric field of the laser beam and the symmetry axes of the phases. In the $N\ensuremath{-}I$ transition, the nonlinear optical birefringence shows a discontinuity at the transition temperature ${(T}_{c}),$ as observed in the linear birefringence. On the other hand, in the $N\ensuremath{-}N$ transition, $\ensuremath{\Delta}{n}_{2}$ was shown to be proportional to $|T\ensuremath{-}{T}_{c}{|}^{\ensuremath{-}\ensuremath{\beta}},$ with $\ensuremath{\beta}\ensuremath{\sim}0.5,$ in both uniaxial and biaxial nematic domains. No discontinuity was observed on $\ensuremath{\Delta}{n}_{2}$ in the $N\ensuremath{-}N$ transition. The symmetric invariants of the order parameter were shown to be linear functions of the temperature in the uniaxial nematic domain, in good agreement with the mean-field prediction.