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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Switching effect in dense media

Valerică Ninulescu, Iuliana Sterian, Andreea-Rodica P. Sterian

Published Aug 9, 2002• 3 citations
Publisher

Abstract

Maxwell-Bloch equations generalized for a dense medium of two- level atoms are used to describe the dynamics of the system under the action of an ultrafast optical pulse. Starting with an uninverted system, the final population is one of the two extreme cases, depending on the ratio of the Rabi frequency and the parameter describing the near dipole-dipole interactions. Based on numerical investigations for typical pulse shapes, the mechanism of switching is explained.

DOI
10.1117/12.478641

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Maxwell-Bloch equations generalized for a dense medium of two- level atoms are used to describe the dynamics of the system under the action of an ultrafast optical pulse. Starting with an uninverted system, the final population is one of the two extreme cases, depending on the ratio of the Rabi frequency and the parameter describing the near dipole-dipole interactions. Based on numerical investigations for typical pulse shapes, the mechanism of switching is explained.
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 Ω 0 ε , 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, Ω 0 ε ≈ 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.
We performed a numerical investigation of the dynamics of the Bloch equations, extended for dense media (media having many atoms within a cubic resonance wavelength), for optical pulses whose duration is much less than an induced-dipole dephasing time. We find a signature of near dipole-dipole interaction which may provide a useful method for validating the first-principles model, for measuring the strength of the interaction, and for coherent pumping. Further, we demonstrate a new and unique optical switching mechanism which may lead to the development of important devices.
We performed a numerical investigation of the dynamics of the optical Bloch equations, extended for near dipole-dipole (NDD) interactions in dense collections of two-level systems. As a function of peak field strength, the inversion that remains in the medium following excitation by an ultrashort optical pulse has step-like transitions between the ground state and the excited state. The medium is left fully inverted if the peak Rabi frequency (peak field strength written in units of frequency) is equal to the NDD interaction strength. Remarkably, this result is independent of pulse area. About this point is a region of peak field strength for which the dense medium is left fully, or nearly fully, inverted. On the weak side of this region, the dense medium is left in the ground state. On the strong side of this region, the medium alternates between absorbing (ground state) and amplifying (inverted) as a function of peak field strength. This response can be used to measure the strength of the NDD interaction, for coherent optical pumping, and also constitutes a new and unique intrinsic optical switch, which, unlike optical bistability, does not have hysteresis and is independent of dissipation from incoherent effects.
We investigate ultrashort pulse propagation in a dense medium of two-level atoms. We numerically solve the coupled nonlinear Maxwell-Bloch equations by assuming that the fields are slowly varying in time only. We find that while intrinsic optical switching of the atomic inversion persists in extended media, self-phase-modulation effects, coherent energy transfer, and reflections can be large even for films that are only a small fraction of a wavelength thick. If the propagation distance is sufficiently large, a physical boundary that separates fully excited atoms from atoms in the ground state can be created within the medium. In turn, this leads to a rapid spatial modulation of the nonlinear polarization, and a deterioration of the intrinsic optical switching mechanism. We then show that, although the slowly varying envelope approximation in space may be preempted by the fast longitudinal variation of the field and atomic variables, the mean-field approximation remains valid in the regime of ultrafast optical switching, provided the film thickness is sufficiently small such that the medium is nearly uniformly excited. These results are generated by utilization of our calculational method that fully accounts for the longitudinal dynamics of the fields, including reflections.
The dynamics of pulses with durations comparable to the inverse transition frequency that propagate in an optical medium is studied in terms of two integrable systems of Maxwell-Bloch equations. The first model describes the field interaction with a nondegenerate medium with a permanent dipole moment and permanent external pumping. A general formula is derived for the N -soliton solution. Particular solutions are used as examples to investigate the effect of permanent dipole moment and pumping on the soliton dynamics. The second model describes the interaction between two-component electric-field pulses and a two-level degenerate medium with permanent upper-level pumping. For different initial magnetic-sublevel populations, soliton solutions are used as examples to show that pumping causes a change in polarization dynamics. A two-soliton solution is used to analyze the interaction of solitons in a two-level medium with external pumping.