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Physical Review A

Coherent reflection as superradiation from the boundary of a resonant medium

M. G. Benedict, Evgenii Dmitrievich Trifonov

Published Sep 1, 1988• 81 citations
Publisher

Abstract

The reflection of short optical pulses from the boundary of a resonant medium is investigated theoretically by the coupled system of the Maxwell and optical Bloch equations. In order to describe the reflected wave, the slowly-varying-envelope approximation in space is not exploited. The coherent reflection is shown to be in connection with Dicke superradiance. It takes place if the relaxation time of the polarization is longer than the superradiation time of the atoms in an optically thin boundary layer of the medium. That is why much of the relevant information can be obtained already in the thin-medium limit, which is considered separately. The conditions of strong reflection from an extended medium are similar to the ones found for a thin sample. The transition into the incoherent and stationary regime is discussed.

DOI
10.1103/physreva.38.2854

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The reflection of short optical pulses from the boundary of a resonant medium is investigated theoretically by the coupled system of the Maxwell and optical Bloch equations. In order to describe the reflected wave, the slowly-varying-envelope approximation in space is not exploited. The coherent reflection is shown to be in connection with Dicke superradiance. It takes place if the relaxation time of the polarization is longer than the superradiation time of the atoms in an optically thin boundary layer of the medium. That is why much of the relevant information can be obtained already in the thin-medium limit, which is considered separately. The conditions of strong reflection from an extended medium are similar to the ones found for a thin sample. The transition into the incoherent and stationary regime is discussed.
The superradiance (SR) of initially inverted two-level active medium in a cavity is considered. We discuss the results specific for the rigorous simulation of the SR pulse (obtained on the basis of 1D Maxwell-Bloch equations solution without slowly varying envelope approximation (SVEA) in the spatial variable): the strong dependencies of the counter-propagating waves correlation and pulse development acceleration not only on the module of the cavity mirrors reflection coefficient, but on the integer- factor of the ratio of the sample length and half of the resonant wavelength. The simple modification of the SVEA model approximately describing the above features is considered.
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.
A theoretical model for the propagation of coherent light pulses in resonant media where a large number of atoms cooperate in spontaneous emission (superradiance) is discussed. The medium is supposedly free of inhomogeneous broadening, and no lossy relaxation mechanisms are taken into account. The conditions for the emission of all spontaneous radiation in the direction of pulse propagation are described. A semi-classical model is used and, at each point in the medium, the propagation field and the spontaneous damping field are considered separately. The equation governing the evolution of a superradiant system in the presence of an applied pulse is derived. A mechanism of energy transfer from the traveling pulse to the medium is described which includes superradiant spontaneous emission effects. As a result of the neglect of all lossy relaxation processes, all energy stored in the medium is eventually returned to the pulse by coherent spontaneous emission. Therefore, in this theory, all pulses travel through the medium without energy loss. Numerical results for square input pulses are discussed which show two possible types of propagation behavior: (a) Low input intensities produce a negative tail to the input (positive) pulse and sharpening of the tail with the advance in the medium; (b) higher input intensities produce, after sufficient penetration, a steady-state pulse envelope somewhat similar to the $2\ensuremath{\pi}$ pulses of self-induced transparency. The steady-state solutions of the equations of motion are found numerically and the pulse shapes are computed for different degrees of superradiance. In the limit of strong superradiance, very asymmetric pulse envelopes of large area are found. For negligible superradiance, approximately $2\ensuremath{\pi}$ hyperbolic-secant pulses are obtained. The effects of inhomogeneous broadening are briefly considered, and the consequences of important superradiant damping in photon-echo experiments are qualitatively discussed.
We investigate the problem of resonant reflection and transmission of an ultrashort light pulse passing through a thin layer consisting of two-level atoms. The local-field correction that leads to an inversion-dependent resonance frequency generates a new mechanism of nonlinear transparency. When the excitation frequency is somewhat larger than the original resonant frequency, then the transmission of the layer exhibits a transient bistable behavior on the time scale of superradiation, which can be much shorter than the relaxation times. This type of bistability is essentially different from the ordinary stationary intrinsic bistability investigated earlier by other authors.
We consider the propagation of extremely short pulses through a dielectric thin film containing resonant atoms (two-level atoms) with permanent dipole. Assuming that the film width is less than the field wavelength, we can solve the wave equation and reduce the problem to a system of generalized Bloch equations describing the resonant atoms. We compute the stationary solutions for a constant irradiation of the film. Superimposing a small amplitude linear wave we calculate the reflection and transmission coefficients. From these, one can then deduce the different parameters of the model. We believe that this technique could be used in experiments to obtain the medium atomic and relaxation parameters.
We consider the propagation of extremely short pulses through a dielectric thin film containing resonant atoms (two level atoms) with permanent dipole. Assuming that the film width is less than the field wave length, we can solve the wave equation and reduce the problem to a system of generalized Bloch equations describing the resonant atoms. We compute the stationary solutions for a constant irradiation of the film. Superimposing a small amplitude linear wave we compute the reflection and transmission coefficients. From these, one can then deduce the different parameters of the model. We believe this technique could be used in experiments to obtain the medium atomic and relaxation parameters.