Pulse propagation in spatially dispersive media

Abstract
The propagation of a Gaussian electromagnetic (optical) pulse with center frequency ω¯ (laser) through a spatially dispersive exciton-polariton medium is investigated by a combination of analytical and numerical methods. The analysis used extends previous work by Garrett and McCumber to the multiwave coupled exciton-polariton case. With the assumption of normal incidence on a semi-infinite medium, laser frequencies very close to exciton resonance and far from resonance are studied. Numerical results are obtained for power spectrum P(z,ω) and amplitude profile f(z,t) for parameters suitable to CdS 1S A exciton (a fairly typical semiconductor). For pulses with Γτ1 or Γτ1 the pulse remains essentially Gaussian, and its peak propagates with velocity close to the classical group velocity vgj=(dωjdkr), where j is the polariton branch index and kr is the real part of the propagation wave number. The power spectrum shows a crossover from lower to upper branch as the laser frequency is varied through resonance. Some comparison with experiments on CuCl, GaAs, CdSe, and CdS semiconductors is also given.