Expansion of the orientational distribution function f(θ, t) of molecular dipoles in terms of Legendre polynomials with spherical modified Bessel functions in(μE/kT) as coefficients yields an analytic relation between the steady-state birefringence Δnz(ω) and the electro-optic coefficient for a poled nonlinear optical system. A rotational diffusion equation, with the diffusion constant D, for the distribution function describing the onset and the decay of the induced optical and electro-optic properties is solved, with the help of the recurrence relation for spherical modified Bessel functions. It is found that the onset of birefringence involves at least two time constants, with rise times of 1/2D and 1/6D, while the onset of the electro-optic effect is dominated by the rise time of 1/2D. After removal of the dc poling field, the birefringence and the electro-optic effect are found to relax in time with different decay time constants, 1/6D and 1/2D, respectively. This is due to the difference in the tensor rank describing the birefringence and the electro-optic effect.
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