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Optics Letters

Analysis of switching phenomena in a dense medium of two-level atoms

Carlos Lizárraga C., Alejandro B. Aceves

Published May 1, 1993• 1 citation
Publisher

Abstract

The switching characteristics of a dense medium of two-level atoms is studied analytically. Switching depends on the ratio of the Rabi frequency to the strength of the near-dipole-dipole interaction. When this ratio is nearly one, an exact solution is obtained. Other values of the parameter are studied by the use of asymptotic analysis, and the conditions for switching are determined from an analytic expression.

DOI
10.1364/ol.18.000687

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 20, 2004•1 citation
The switching characteristics of a dense medium of two-level atoms is studied analytically. Switching depends on the ratio of the Rabi frequency to the strength of the near-dipole-dipole interaction. When this ratio is nearly one, an exact solution is obtained. Other values of the parameter are studied by the use of asymptotic analysis, and the conditions for switching are determined from an analytic expression.
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 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 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.
In condensed matter of densities such that there are many atoms within a cubic atomic resonance wavelength, induced near dipole-dipole interactions (NDD) effects can cause dynamic frequency chirp in near resonant electromagnetic field-matter interactions.1 Using semiclassical theory for two-level atomic systems and a Green's function solution to the wave equation, we derive a self-consistent set of renormalized Bloch–Maxwell equations, useful for discussion of nonlinear optical processes in condensed matter systems, and discuss some of their implications. The strength of the induced near dipole-dipole coupling is found to be ε = (4π/3) u2n, and it causes inversion-dependent frequency chirp in the system. Here, u is the matrix element of the transition dipole moment and n is the density of atoms.
The effect that may be exerted by an interatomic near dipole-dipole interaction upon optical transient processes in dense resonance media is analyzed. The behavior of the macroscopic polarization after a one-pulse excitation of a dense ensemble of two-level atoms is considered. It is shown that the free polarization signal is of oscillatory nature, with the oscillation frequency varying in time and being dependent on the dipole-dipole interaction constant, the intensity and duration of the exciting pulse, and the detuning of its carrier frequency from the resonance. The free polarization signal decay, which depends on the magnitude and sign of the sum of the detuning of the exciting pulse carrier frequency from the resonance and the Lorentz frequency, may obey either a power or an exponential law. The signal decay rate is determined not only by the inhomogeneous broadening, but also by the ratio of the above parameters. The peculiarities of echo-responses under one- or two-pulse excitation conditions are studied.