ANALYTICAL SOLUTIONS FOR THE DYNAMIC KERR-EFFECT - LINEAR-RESPONSE OFPOLAR AND POLARIZABLE MOLECULES TO A WEAK AC ELECTRIC-FIELD SUPERIMPOSED ON A STRONG DC BIAS FIELD

The infinite hierarchy of differential-recurrence relations for ensemb le averages of the spherical harmonics pertaining to the noninertial r otational Brownian motion of an ensemble of polar and anisotropically polarizable molecules in a strong external de electric field is derive d by averaging the underlying Langevin equation. This procedure avoids recourse to the Fokker-Planck equation, the solution of which involve s complicated mathematical manipulations. By calculating the Laplace t ransforms of the relaxation functions for the dynamic Kerr effect of, symmetric top molecules, two equilibrium correlation functions are est ablished, thus allowing one to express the corresponding birefringence ac responses by using linear response theory. Exact analytic solution s for the spectra of these correlation functions and relaxation times are first calculated for two limiting cases, namely, pure induced dipo le moments and pure permanent moments, using the continued fraction me thod. The general case where both types of moments are taken into acco unt, is then considered using matrix continued fractions. Furthermore, exact analytical expressions for the Kerr effect relaxation time are also derived in terms of integrals (which are evaluated exactly) and c ompared with the matrix continued fraction result. Plots of the relaxa tion time are presented for various values of the parameters xi and si gma characterizing the permanent and the induced dipole moments. Featu res of the relaxation behavior are emphasized in figures showing the r eal and imaginary parts of the spectra of the birefringence function. Moreover, Cole-Cole diagrams are presented for various values of xi an d sigma in order to see how they deviate from the Debye-like spectra. (C) 1997 American Institute of Physics.