Stationary state and dynamics of birefringence and nonlinear optical properties induced by electric field poling in polymeric films

Abstract

AbstractWe present a theoretical study concerning the effect of the electric field poling process on the molecular angular distribution of polar nonlinear‐optical molecules in a polymeric environment. This is required for investigating the contribution of the molecular order to the anisotropy and nonlinear‐optical processes (second‐harmonic generation (SHG), electro‐optic Pockels (EOPE) and Kerr (EOKE) effects). We demonstrate mathematically that the order parameters at thermodynamical equilibrium are defined exactly by the spherical modified Bessel functions (An(μE/kT) = in(μE/kT)/io(μE/kT)). They can be related to Langevin functions but with complicated relations for high orders of n. Their evolution with μE/kT confirms that the second order nonlinear‐optical processes (SHG and EOPE) are more sensitive to the strength of the poling field than are the linear (birefringence) and third‐order nonlinear‐optical effects (EOKE). We show that it is possible to measure the molecular anisotropy of nonlinear‐optical molecules by quadratic electro‐optic experiments. The transients of the poling are studied with the rotational diffusion equation, characterized by a rotational diffusion constant D. This is solved using important recurrence relations of Legendre polynomials. An almost exact analytical solution is found for the physical and practical case where μE/kT is close to 1, and the nonvanishing order parameters are almost equal to the rigourous expressions given by the spherical modified Bessel functions. It is shown that the onset of birefringence and nonlinear‐optical processes (SHG, EOPE and EOKE) involves two time constants τ1,2 = [2D(2 ± √1–(μE/kT)2/5)]−1 which depend on D and μE/kT. After the removal of the poling field, the relaxation of the linear and nonlinear‐optical properties is also discussed.