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Soviet Journal of Quantum Electronics

Dynamics of superradiance in a thin dielectric waveguide

V.D. Laptev, I. V. Sokolov

Published Sep 30, 1984• 1 citation
Publisher

Abstract

A semiclassical method is used to study cooperative spontaneous radiation (superradiance) emitted from an excited medium in a thin dielectric waveguide subject to an allowance for the highest-Q normal wave in the waveguide (constant profile fields). A radiation pulse is described by a nonlinear equation which represents weakening of the interaction between matter and a field of constant profile in the case of a large-area pulse. This results in partial utilization of the stored energy, reduces the steepness of the edges of a pulse and its maximum intensity, and suppresses oscillation replicas.

DOI
10.1070/qe1984v014n09abeh006211

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A semiclassical method is used to study cooperative spontaneous radiation (superradiance) emitted from an excited medium in a thin dielectric waveguide subject to an allowance for the highest-Q normal wave in the waveguide (constant profile fields). A radiation pulse is described by a nonlinear equation which represents weakening of the interaction between matter and a field of constant profile in the case of a large-area pulse. This results in partial utilization of the stored energy, reduces the steepness of the edges of a pulse and its maximum intensity, and suppresses oscillation replicas.
A study is made of the dynamics of a superradiance pulse in a transversely inhomogeneous active medium inside a tubular waveguide with dielectric walls. The problem is solved numerically in the approximation of a given field profile by expanding the radiation field in terms of the normal modes of the waveguide and the polarization and inversion of the medium in terms of basis functions dependent on the transverse coordinates. It is shown that an inhomogeneous transverse distribution of the field and of the initial inversion can suppress the appearance of oscillatory replicas (superradiant "ringing") of the main superradiance field and also can result in incomplete utilization of the energy stored in the active medium because of coherent dephasing of the polarization of the medium in different parts of a transverse cross section of the waveguide.
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.
This paper presents a semiclassical treatment of the evolution of an initially inverted system into a superradiant state in an extended, optically thick medium. In this process spontaneous emission and background thermal radiation initiate the collective radiative decay and produce a superradiant output pulse of intensity proportional to the square of the number of radiators. The treatment is based on the coupled Maxwell-Schr\"odinger equations, modified to include a fluctuating polarization source properly constructed to account for the effects of spontaneous emission. Computer results show that for a high-gain system only two parameters significantly influence the evolution process: TR{T}_{R}TR​, the characteristic radiation damping time of the collective system; and ${\ensuremath{\theta}}_{0}$, a function of the conditions which initiate the superradiant process. In this limit one obtains a normalized emission curve and simple analytical expressions for the time delay, pulse width, and peak intensity of the output radiation. These results are in good agreement with experiments. A comparison of our model with previous treatments of superradiance is given.
Abstract The possibility of generating extremely short pulses of terahertz (THz) radiation due to superradiance—collective spontaneous emission of a thin layer of a three-level resonant medium excited by a pair of attosecond (or femtosecond) pulses—is studied theoretically. The source of a terahertz pulse is a pulse of stopped nonlinear polarization of the medium, which arises in the interval between its excitation and deexcitation. The case of a three-level medium with equidistant energy levels (as in a quantum harmonic oscillator) the transition frequency of which lies in the THz range is considered. The influence of the populations of the excited levels of the medium on the shape of a terahertz superradiance pulse is discussed.