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

Temporal structure of superradiance of praseodymium ions in the LaF 3 matrix: theory and experiment

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

Published Jun 15, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.752098

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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.
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.
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 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.
The spiky structure of the spontaneous emission from praseodymium ions in the LaF 3 lattice on the 3 P 0 - 3 H 6 transition under coherent pulsed excitation of the adjacent 3 H 4 - 3 P 0 transition has been studied experimentally and theoretically. The experimental results are in good agreement with the theoretical conclusions based on analysis of the emission dynamics of an excited ensemble of three-level systems in the mean field approximation. The generation of a spiky structure is interpreted as the emission of a cnoidal wave pulse. The recorded random pattern of time intervals between the spikes reflects the sensitivity of the cnoidal wave period to fluctuations in the system. The developed theory has been found to be related to models of deterministic chaotic dynamics.
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.