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arXiv:0711.0454 · Physical Review Letters

Driving Light Pulses with Light in Two-Level Media

Рамаз Хомерики, Jérôme J.-P. Leon

Published Oct 30, 2007• 10 citations
arXivHTMLPDF

Abstract

A two-level medium, described by the Maxwell-Bloch system, is engraved by establishing a standing cavity wave with a linearly polarized electromagnetic field that drives the medium on both ends. A light pulse, polarized along the other direction, then scatters the medium and couples to the cavity standing wave by means of the population inversion density variations. We demonstrate that control of the applied amplitudes of the grating field allows one to stop the light pulse and to make it move backward (eventually to drive it freely). A simplified limit model of the Maxwell-Bloch system with variable boundary driving is obtained as a discrete nonlinear Schrödinger equation with tunable external potential. It reproduces qualitatively the dynamics of the driven light pulse.

DOI
10.1103/physrevlett.99.183601

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A two-level medium, described by the Maxwell-Bloch system, is engraved by establishing a standing cavity wave with a linearly polarized electromagnetic field that drives the medium on both ends. A light pulse, polarized along the other direction, then scatters the medium and couples to the cavity standing wave by means of the population inversion density variations. We demonstrate that control of the applied amplitudes of the grating field allows one to stop the light pulse and to make it move backward (eventually to drive it freely). A simplified limit model of the Maxwell-Bloch system with variable boundary driving is obtained as a discrete nonlinear Schrödinger equation with tunable external potential. It reproduces qualitatively the dynamics of the driven light pulse.
The Maxwell–Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the two-level medium) as e.g. slow-light gap solitons that result from the nonlinear instability of the evanescent wave at the boundary. As nonlinearity couples the different polarizations of the electromagnetic field, the slow-light gap soliton is shown to experience effective scattering with charges in the medium, allowing it for instance to be trapped or reflected. This scattering process is understood qualitatively as being governed by a nonlinear Schrödinger model in an external potential related to the charges (the electrostatic permanent background component of the field).
Coupling a two-level medium, described by the Maxwell-Bloch (MB) equations, to an external cavity mode results in a prescribed boundary value for the electric field that can be tuned to the forbidden band gap of the medium. It is shown that there exists a threshold of energy density flux above which a solitonlike light pulse is generated and propagates in the medium at a fraction of the light velocity. When the driving frequency becomes close to the band gap edge, where the group velocity vanishes, the MB equations tend to the nonlinear Schr\"odinger equation which furnishes the theoretical ground to understand soliton generation by evanescent fields as a manifestation of nonlinear supratransmission, produced by an instability of the evanescent wave. Moreover, the propagation at a fraction of light velocity is shown to result from a continuous periodic exchange between polarization (electromagnetic energy) and population (density of atoms in the excited level). The process is demonstrated to occur at twice the internal frequency of the generated gap soliton. Last, when the medium spatial extension is of the order of the soliton dimension, an optical bistability is shown to occur at the supratransmission threshold allowing for different output intensities corresponding to a given input value.
We consider the problem of the propagation of short-duration light pulses in a two-level medium in the regime of strong interaction, near the resonance, with no restriction on the strength of the coupling between field and medium. We prove that the local variations of the population difference created by the electric field actually induce a nonlinear effect by coupling the fundamental of the field Fourier component to its harmonics. As a result, the multiscale averaging limit of the Maxwell-Bloch system is a new system of coupled nonlinear Schrodinger equations for the slowly varying envelope of the electric field. This system has one integrable limit when the electric field is circularly polarized: it is the scalar nonlinear Schrodinger equation. Moreover, it possesses three constants of the motion and a Hamiltonian formulation. Then we prove that our system is nonintegrable as it does not pass the Painleve test. Finally, a stability analysis shows that it is modulationally unstable and thus it propagates steady pulses of coherent light.
The temporal and spatial dynamics of one weak probe laser pulse, propagating through a A-type atomic medium with two-folded levels under the resonant excitation of one microwave driving field and one strong control field, is investigated in this paper. By numerically solving coupled Bloch-Maxwell equations, it is found that, in the absence of the microwave driving field, the atomic medium is transparent to the probe pulse at line center, which propagates over sufficiently long distances. By contrast, when the microwave driving field is applied, the probe pulse at line center can be rapidly absorbed on propagation. This substantial reduction of probe transmittance caused by the microwave driving field may lead to potential applications in designing a new kind of optical switching.
An effective two-level Maxwell-Bloch formalism is developed to describe various time-dependent phenomena in a three-level V-type system. The Maxwell-Bloch equations govern the temporal evolution of a probe field while a strong driving field is applied on the adjacent transition. The main assumption adopted throughout the paper is that the spontaneous decay rate on the coherently driven transition exceeds the decay rate on the probe transition as well as inverse time variations of both pulses. It is shown that the probe pulse interacts with such a medium in a manner similar to that in a self-induced transparency. An amplification without inversion of a relatively short probe pulse while propagating through an optically thick atomic medium is analyzed.
With the coherent interaction of a sequence of extremely short light pulses with a resonant medium (when the duration of the pulses and the delays between them are shorter than the relaxation times of the population difference T1 and polarization T2 of the medium), it is possible to create spatial electromagnetically induced gratings (EMIG) of polarization and population difference in the medium, as well as their ultrafast control. The dynamics of such gratings is of interest in connection with the possibility of ultrafast control over the properties of a medium at times of the order of the pulse duration and their influence on the stability of generation of extremely short pulses in a laser with a short linear cavity. In this paper, based on the numerical solution of the system of Maxwell-Bloch equations, an unusual and interesting possibility of the appearance of narrow and alternating sections in the medium is shown and studied in detail, in which harmonic polarization waves of the medium are formed, propagating in opposite directions relative to neighboring sections. This situation occurs when two extremely short attosecond pulses collide in a two-level resonant medium.