Abstract

In this work the authors will present analytical results that explain the numerical simulations of M. E. Crenshaw et al.¹ on the extended optical Bloch equations that include near dipole–dipole interactions. These simulations have shown the possibility of an ultrafast switch, caused by an incident unaltered pulse in a thin dense medium of two-level atoms. The switching parameter, defined as $\frac{{\Omega }_0}{\epsilon }$, is a ratio of the Rabi frequency to the strength of the near dipole–dipole interaction Our analysis will show an exact solution for the first switching condition, $\frac{{\Omega }_0}{\epsilon }\approx 1$. Furthermore, an asymptotic analysis will show that to leading order in the asymptotic expansion, only three possible final states of the medium occur. These states, if characterized by the population inversion w, are total inversion (w_f= 1), no inversion (w_f= -1), or half inversion (w_f= 0). For the case w_f= 0, a reduced system in a phase plane is derived. This reduced system will help us understand this self-transparent behavior. We will conclude by presenting the results on the stability analysis in parameter space.

© 1992 Optical Society of America