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Soviet Journal of Quantum Electronics

Influence of transverse inhomogeneity of the radiation field and of the active medium on the dynamics of superradiance from an extended system

V.D. Laptev, N. M. Reutova, I. V. Sokolov

Published Oct 31, 1983• 1 citation
Publisher

Abstract

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.

DOI
10.1070/qe1983v013n10abeh004893

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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 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.
The work based on a semiclassical description, presents the results of studying the processes of absorption and radiation of a field in the form of a standing wave in a waveguide filled with a two-level active medium. Under conditions of spatial inhomogeneity of the field intensity, interference of quasi-periodic oscillations of population inversion occurs in different local regions of the waveguide. A quasiperiodic change in population inversion is determined by the Rabi frequency, which is known to be associated with the probability of induced radiation with a positive population inversion, or induced absorption with its negative value. Since the population inversion change is accompanied by absorption or emission of field quanta, this leads to the exchange of energy between the field and the active medium located in the waveguide. It is shown that the attenuation of a large-amplitude field to a waveguide filled with an unexcited active medium is nonlinear. In the developed mode, this process has the character of energy exchange between the field and the active medium. In this case, the wave attenuation is replaced by its growth, just as it happens in the well-known case of Landau kinetic damping. Competition of the processes of radiation and absorption leads to the fact that the nature of the oscillations (nutations) of the population inversion at different points of the waveguide space is different. The interference of nonsynchronous spatially localized oscillations of the population inversion in the volume of the waveguide leads to changes in the field amplitude. The paper also discusses the process of field excitation in a waveguide with a pre-inverted two-level active medium, taking into account external mechanisms for the absorption of wave energy. Consideration of these problems is important for understanding the processes of generation of induced radiation, which, as noted by C. Towns, is to a large extent coherent radiation.
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.
Peculiarities of the implementation of a superradiant generation mode in a laser with a distributed feedback of the waves and an inhomogeneously broadened spectral line of the active medium are investigated. Based on a numerical solution of the semiclassical Maxwell-Bloch equations for the amplitudes of counterpropagating electromagnetic waves, polarization, and inversion of a two-level medium population, it is shown that a sequence of coherent high-power pulses is generated by the Bragg structure in a wide range of the laser parameters as a result of the selected mode and the cw pumping.
Using one-dimensional semiclassical Maxwell — Bloch equations with account for the coherent polarisation dynamics, we have studied spike generation regimes of a superradiant distributed feedback laser in the case of inhomogeneous broadening of the spectral line of an active medium. By analysing the dynamic spectra of inversion of the active medium and laser radiation, we have revealed the relationship of individual spikes of radiation and their modulation with specific parts in the spectral line of the active medium and mode beatings. It has been shown that the broadening and shift of the lasing spectrum with respect to the initial electromagnetic Bragg-cavity modes is accompanied by a strong spectral gradient of inversion that is typical of the superradiant regimes.
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.