Arbitrary Order Perturbation Expansion Applied to Steady-State Nonlinear Kerr Effect Relaxations in Coupled AC and DC Weak Fields

The steady state response of the nonlinear Kerr effect to a small ac field superimposed on a dc field is analysed using second-order perturbation theory. We justify the truncature effect entailed in solving the infinite set of differential equations that yield the electric polarization and birefringence, and hence draw inferences from the appearance of single and double harmonics as the fundamental frequencies of nonlinear Kerr effect. The addition of small inertial effects in the solution of this phenomenon results in the appearance of a contribution within the master matrix which is proportional to the square of the frequency corresponding to the order of perturbation. The study is based on the Smoluchowski equation of rotational Brownian motion.