NONLINEAR ELECTROOPTICAL RESPONSE .1. STEADY-STATE KERR-EFFECT RELAXATION ARISING FROM A WEAK AC ELECTRIC-FIELD SUPERIMPOSED ON A STRONG DCBIAS FIELD

The dynamic Kerr effect (excluding inertial effects) of an assembly of both polar and anisotropically polarizable molecules acted on by a st rong external de electric field superimposed on a weak ac electric fie ld is evaluated by starting from the Smoluchowski equation valid in th e noninertial limit. The calculation proceeds by expanding the expecta tion value of the second Legendre polynomial which describes the Kerr effect relaxation, as a power series up to the second order in the sma ll ac field strength, so that frequency components in omega and 2 omeg a exist. This is accomplished using the matrix continued fraction meth od which allows one to express exactly the solution of the infinite hi erarchy of differential-recurrence relations for the first and second order ac responses of ensemble averages of the Legendre polynomials (r elaxation functions). In order to illustrate these results, diagrams s howing the behavior of the real and imaginary parts of the complex bir efringence functions are presented. In particular, the relaxation spec tra clearly indicate the differences between the first order response (equivalent to that obtained using linear response theory) and the sec ond order one. We present also the solutions for the particular cases where only either permanent or induced dipole moments are taken into a ccount. The calculation then radically simplifies as the matrix contin ued fractions now reduce to scalar ones. (C) 1997 American Institute o f Physics.