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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Dynamics of superradiant medium in resonator

Ashat M. Basharov, G. G. Grigoryan, Yu. V. Orlov, A. Yu. Shashkov, T. G. Yukina, Nikolay V Znamenskiy

Published Apr 6, 2007• 0 citations
Publisher

Abstract

Experimental data and theoretical model concerning superradiant emission from the LaF3 medium doped with impurity praseodymium ions are presented in cases of free medium and when the medium is placed into resonator. The spiky structure of superradiance is registered and studied. When the medium is placed inside a cavity, a new channel of energy removal by superradiance related to the cavity mode appears; the old noncavity channels are preserved. The duration of superradiance in each channel is decreased and the modulation arises. These peculiarities of superradiance induced by the presence of resonator are explained on the basis of the developed mean-field theory.

DOI
10.1117/12.740174

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Experimental data and theoretical model concerning superradiant emission from the LaF3 medium doped with impurity praseodymium ions are presented in cases of free medium and when the medium is placed into resonator. The spiky structure of superradiance is registered and studied. When the medium is placed inside a cavity, a new channel of energy removal by superradiance related to the cavity mode appears; the old noncavity channels are preserved. The duration of superradiance in each channel is decreased and the modulation arises. These peculiarities of superradiance induced by the presence of resonator are explained on the basis of the developed mean-field theory.
Experimental data concerning superradiant emission from the LaF 3 medium doped with impurity praseodymium ions are presented in the cases of a free medium and when the medium is placed into an optical resonator. The spike structure of superradiance is registered and studied. When the medium is placed inside a cavity, a new channel of energy removal by superradiance related to the cavity mode appears; the old noncavity channels are preserved. The duration of superradiance in the cavity channel is decreased, and regular modulation arises. These peculiarities of superradiance induced by the presence of an optical resonator are explained.
Experimental data and theoretical model describing stochastic pulsations within oscillatory mode of superradiant emission from the LaF3 medium doped with impurity praseodymium ions are presented. The model deals with three-level system with close upper levels and reflects our experimental data on fluorescence of praseodymium ions. The mean-field approximation is used to develop the superradiance theory. In determined case basic equations of the developed model are reduced to well known Lorenz equations of deterministic chaotic dynamics.
Experimental results and a theoretical model describing superradiance of praseodymium ions in the trifluoro lanthanum matrix at the 3 P 0 — 3 H 6 transition upon coherent excitation of the adjacent 3 H 4 — 3 P 0 transition are presented. It is found that when a superradiant medium is placed into a resonator, whose eigenfrequency is close to the superradiant transition ( 3 P 0 — 3 H 6 ) frequency, the superradiant pulse duration decreases and its modulation appears, which is independent of the resonator length. It is shown that these properties are qualitatively described within the framework of the mean-field model of coherent radiation of superradiant media in a resonator.
Based on the analysis of the experimental data on the observation of the fluorescence and superradiance of praseodymium ions in a matrix of lanthanum trifluoride, a model of superradiance of three-level radiators with two close upper levels is developed in the mean-field approximation and studied. The uppermost level is coherently pumped by an ultrashort pulse of electromagnetic field, after which the excitation is transferred to the close energy level, from which the superradiance transition occurs to the lower level. In limiting cases, the considered model is reduced to the known models of superradiance and describes the ordinary regimes of monopulse and multipulse (oscillatory) superradiance. However, in a certain region of parameters, the model under discussion describes such a multipulse superradiance signal in which electromagnetic field spikes composing it follow in time with random intervals and amplitudes, so that the regime of regular chaotic dynamics is demonstrated in a single superradiance signal. In a certain time interval, the proposed model can be described by the Lorenz equations with the parameters corresponding to the chaotic dynamics of spikes composing the superradiance signal. The presented results of the numerical simulation of the model equations qualitatively correspond to the picture of stochastic pulsations observed experimentally.
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.
A new effect has been observed in the superradiance of praseodymium ions in a lanthanum trifluoride matrix: the effect of selecting transverse pumping structures upon the oblique-incidence pumping of superradiant media. A simple explanation for this effect is given. The possible reasons for the stochastization of the oscillatory regime of superradiance, a phenomenon observed upon both the normal and oblique incidence of pumping radiation on a crystal and when the crystal is placed in a resonator with an eigenfrequency close to the frequency of the superradiant transition, are analyzed.