THEORY OF THE FARADAY-EFFECT WITH WEAK LASER-PULSES

The propagation of a weak optical pulse along the direction of an appl ied magnetic field in an atomic or molecular gas is investigated theor etically. When the Zeeman splitting is much smaller that the inhomogen eous linewidth sigma, the Faraday rotation of the polarization plane d epends linearly on optical depth and is independent of time for long p ulses with t(p) >> sigma-1 (as in the conventional Faraday effect) but depends linearly on time and is independent of optical depth for shor t pulses with t(p) << sigma-1; t(p) is the pulse duration. In the inte rmediate-pulse-width regime, frequency pushing causes the polarization plane to rotate at greater average speeds as the pulse propagates.