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International Conference on Mathematical Methods in Electromagnetic Theory

Kinetics of Pulsed Electromagnetic Generators Based on Superfluorescence with Taking Into Account Medium and Cavity

Sergiy F. Lyagushyn, Yu.M. Salyuk, Alexander I. Sokolovsky

Published Sep 22, 2006• 0 citations
Publisher

Abstract

Basic kinetic equation and kinetic equation for the total quasispin of an emitter subsystem have been obtained for the Dicke Hamiltonian modified with terms describing the motion of emitters in the framework of the reduced description method. A way to estimation of loss influence is outlined
DOI
10.1109/mmet.2006.1689855

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Superradiance, both optical and acoustic, is one of the most important methods of generating the coherent pulses and obtaining the information about emitters via resonant phenomena. The process of ordering in a system of excited emitters, which results in a powerful short radiation pulse, is described with correlation functions of emitter and field parameters. Their behavior is problem of interest, especially in a spatial system. The known theoretical approaches to such questions are based on using some ways of correlator decoupling, at the same time the validity and exactness of applied operations remain without evaluation. The authors propose a way to solve this problem in the framework of the Bogolyubov reduced description method in the Peletminskii–Yatsenko formulation. Additionally to the usual small parameter of the method (the interaction constant), a new small parameter (the difference between correlation functions in the theory using it as an independent reduced description parameter and the process picture with one less parameter) is introduced. The method is developed for a concentrated Dicke model. The conventional application of quasispin operators for two-level objects allows to describe the system of emitters as a spin system and use the perfect methods of calculating the averages of spin operator combinations, which were developed in the ferromagnetism theory.
The process of self-organization in a system of excited emitters studied by Dicke can be the basis of coherent emission generation without stimulated emission phenomena. Conventional analytic investigations in this field were concentrated on emitter subsystem behavior for obtaining the parameters of electromagnetic pulse. We propose the research into field characteristics in the process of pulse formation on the basis of the Bogolyubov method of reduced description by including into its parameters electromagnetic field strengths and binary correlation functions. We mean the macroscopic picture in a finite quantity of points, which provide the possibility of numerical modeling. Now we discuss the structure of numerical equations and the availability of physical parameters for such simulations.
The reduced description method proceeds from Bogolyubov’s idea that at large times the non-equilibrium system evolution can be described with the limited number of parameters and principle of correlation weakening. The way to the right choice of such parameters and constructing the time evolution equations for them was opened by the works of Kharkiv school in statistical physics. A quarter of a century ago at Dnipropetrovsk National University the developed method was first applied to the Dicke system of two-level emitters interacting via electromagnetic field. The paper presents a short review of the results obtained. They include the analysis of Dicke Hamiltonian structure, the choice of reduced description parameters satisfying the Peletminskii – Yatsenko scheme conditions, the realization of this scheme for concentrated and prolonged Dicke systems resulting in the temporal equation for emitter subsystemstatistical operator. The reduced description method possibilities are illustrated with using the effective Hamiltonian concept, in particular taking into account emitter motion and higher correlations. Reformulating the theory in terms of electromagnetic field allowed to construct the electrodynamics of medium formed by two-level emitters with considering binary correlations of field variables and to put forward the problem of correlation development picture. A new method of investigating correlations in quasispin subsystem with using ferromagnetism theory approach was also proposed.