Non-linear Resonant Transient and Steady-state Response in a Classical Model

The Doppler-broadened steady state and transient response of a thermal ensemble of anharmonic oscillators to incident laser radiation is investigated. Non-linear polarization of this classical system is obtained by analytically solving the dynamical equations up to third order in the electric field. Except for the sign of the third-order transient polarization, the results are in striking contrast to those obtained in semi-classical theory. In particular, the classical response at resonance is unsaturated up to this order. The Doppler-integrated third-order free induction decay (FID) signal vanishes in the usual approximation of the homogeneous width being smaller than the Doppler width. The physical conclusion of the paper is negative: resonant non-linear and coherent effects such as saturation and nutation typical of the quantum mechanical two-level atoms do not arise for classical anharmonic oscillators.