Nonlinear Kerr effect relaxation including inertial effects in alternating fields

Abstract

The complex birefringence of a dielectric medium is found for the nonlinear stationary response arising from the application of a unidirectional field superposed on an alternating field. Effects arising from dipolar inertia are included. The starting point is the Fokker–Planck–Kramers equation which is solved by assuming that the molecules are polar and anisotropically polarizable and are compelled to rotate in two dimensional space (plane rotator). Kerr effect relaxation is characterized by the ensemble average 〈cos 2θ〉(t). Time evolution of this gives rise to harmonic components in ω and 2ω. They are given to second order in the driving field. Cole–Cole diagrams for each component are presented for various values of P, the ratio of the induced dipole moment to the permanent dipole moment, and τI/τ, the inertial parameter (τI and τ being the friction time and the Debye relaxation time, respectively). It is shown how these diagrams behave in the high-frequency region, and a method of extracting information about molecular parameters such as τI, τ, and P from them is proposed.