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Physica C Superconductivity

A theory of cooperative effects in stimulated Cerenkov radiation

H. Dekker

Published Jan 1, 1976• 0 citations
OpenAlex

Abstract

In this paper the possibility of cooperative effects in Cerenkov radiation will be discussed theoretically. A crude sketch is given of a possible capture of photons from a part of the rather broadband Cerenkov spectrum in a high quality resonator. We then introduce a classical Markoffian master equation for the system, accounting for Cerenkov emission as well as reabsorption. Both elementary quantum theory and classical electrodynamics provide us with the same formula for the transition rate of the stimulated Cerenkov process. At present we restrict ourselves to the macroscopic evolutions. The stationary electron distribution is calculated explicitly, as well as the equation governing the photon numbers. A non-equilibrium second order phase transition will be seen to occur for a critical value of the electronic input current density. Rough estimates are presented for threshold parameters. © 1977.

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Physical Review A•Sep 1, 1973•20 citations
In this paper the possibility of cooperative effects in Cerenkov radiation will be discussed theoretically. A crude sketch is given of a possible capture of photons from a part of the rather broadband Cerenkov spectrum in a high quality resonator. We then introduce a classical Markoffian master equation for the system, accounting for Cerenkov emission as well as reabsorption. Both elementary quantum theory and classical electrodynamics provide us with the same formula for the transition rate of the stimulated Cerenkov process. At present we restrict ourselves to the macroscopic evolutions. The stationary electron distribution is calculated explicitly, as well as the equation governing the photon numbers. A non-equilibrium second order phase transition will be seen to occur for a critical value of the electronic input current density. Rough estimates are presented for threshold parameters. © 1977.
The Dicke theory of coherent spontaneous emission is generalized by means of group-theoretical methods. Effects of superradiation and the structure of coherent responses of an equilibrium medium to pulsed excitation are considered. A method of calculating cooperative effects in second-order perturbation theory is developed. The role of collective properties of a system of radiators in experiments with high power exciting radiation is discussed. Some "anomalous" features of stimulated Raman scattering are accounted for.
In this paper we discuss the quantum features of cooperative radiation processes in a two-level system taking into account non-Markovian effects. If the initial condition is spatially uniform, the many-mode atom-field master equation which has been derived and semiclassically discussed in a previous paper, reduces to the well-known single-mode model laser master equation. Hence, using a suitable projection operator, we derive a generalized non-Markovian master equation which turns out to be correct already in the first Born approximation. This master equation incorporates the effects both of stimulated emission and absorption and of spontaneous emission. When stimulated processes can be neglected, it reduces to a previously known Markovian superradiance master equation, whereas in general it describes non-Markovian oscillations of the radiated intensity. Finally we derive a linear system of equations for the probability of occupation of the Dicke states which generalizes a previously discussed system, taking into account the contribution of stimulated processes.
We treat the interaction between an electromagnetic radiation bath and a material system in the semi-classical picture: the radiation is treated according to the Maxwell equations, but the process of emission/absorption is described through the concept of a photon; on the other hand, the material system is modelled according to quantum mechanics, assuming a discrete two-level energy spectrum. This very simple model allows one to elaborate the elementary theory of the absorption/emission coefficients, both for the spontaneous and for the stimulated processes which will be described within the electric dipole approximation. Selection rules for allowed transitions are eventually obtained and the nature of high-order transition is briefly outlined. Finally, a qualitative description of the light amplification by stimulated emission of radiation is presented.
A quantum-mechanical model of multi-photon lasers is proposed for arbitrary degeneracy of the multi-photon processes of photon emission and absorption governing the interaction between the active medium and the radiation field. Equations of motion are derived for the mean values of the intensive, slowly varying operators essential to the description of the dynamics. Stationary solutions are found and their stability is studied proving the existence of a non-equilibrium first-order phase transition. The critical value of the inversion parameter required for laser action is shown to vary by a jump depending on the degree of degeneracy of the multi-photon processes of emission and absorption considered.
A systematic method is proposed for calculating the density matrix of subsystems interacting with their environment under conditions of thermodynamic equilibrium. The density matrix of photons resonantly interacting with a surrounding gas is calculated. It is shown that use of the Gibbs distribution allows one to completely eliminate inelastic processes from the calculations. A correct account of photon-photon correlators indicates the presence of new cooperative effects. A new branch of the polariton spectrum is predicted, which is due to the presence of excited atoms in the medium. With the help of the density matrix the mean filling numbers of the photon modes are calculated. In terms of wavelengths, we have obtained a generalization of the Planck formula which accounts for photon cooperative phenomena. The manifestation of these effects in kinetic processes is discussed.
In this paper we attempt to unify the theoretical treatment of a variety of cooperative interaction phenomena occurring in resonantly interacting radiation-matter systems. The system consists of a multimode optical field interacting with NNN resonant atoms in a region of large spatial extent. The field and atoms may or may not be coupled to reservoirs. We derive a set of coupled master equations for the reduced matter and radiation density operators of the composite system in the first Born approximation, using a method due to Bogoliubov. These equations describe within a single framework phenomena involving superradiant emission and coherent propagation. In the first place, our theory generalizes existing formulations of the superradiance problem by treating the radiation field as part of the dynamical system rather than as a reservoir. Hence, our equations describe stimulated interaction effects, which are entirely absent in the usual superradiance master equations. Moreover, our equations contain terms describing the self-consistent interaction of an average field with a set of polarizable atoms, as in the coupled Bloch and Maxwell equations of the theory of coherent pulse propagation, and enable us to describe fluctuations, arising from incoherent emission, about the average behavior described by the Bloch-Maxwell theory. We solve formally the dynamical equation for the radiation density operator and obtain a displaced multivariate Gaussian distribution centered on the solution of the Maxwell wave equation, which has as parameters the first and second moments of the matter density operator. Then we derive and discuss the field and atomic-moment equations, both in the wave-number and position representations. The moment equations enable us to show the relationship between descriptions of superradiant damping based on the Bloch equations and those based on the existence of correlated atomic states, including both as special cases. We introduce reduced matter moments, which allow us to separate incoherent- and coherent-emission effects and enable us to discuss the question of the closure of the moment equations. Then we consider cases where the behavior of the atomic system is dominated by a strong coherent pump wave or where the atoms are in a symmetric correlated state and show how the slowly-varying-envelope approximation simplifies the radiation-moment equations in these two cases. In the former case, we obtain an approximate theory which consists, in lowest order, of the Bloch-Maxwell equations with radiative-damping terms, plus an equation describing the time development of the correlation function for field fluctuations. Returning to our general formalism, we relate the usual parameters of the theory of radiative decay and of resonant interactions to the more general quantities appearing in our spatial analysis. Finally, we discuss the importance of the stimulated-emission terms appearing in our theory and describe several extensions, including the introduction of inhomogeneous broadening.