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Журнал технической физики

Перенос и пленение резонансного излучения в двухуровневой системе

В.А. Ямщиков, V. G. Rogachev, Евгений Александрович Кудряшов, Григорий Николаевич Качалин

Published Jan 1, 2020• 0 citations
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Abstract

A theoretical research of the population kinetics of a two-level system with allowance for the transfer of spontaneous emission under continuous optical pumping is presented. It is shown that in the case when the photon mean free path in a resonantly absorbing medium is less than or comparable with the characteristic size of this medium, spontaneous emission can be an additional pump source. Two approaches were used to consider the influence of the spontaneous photon contribution to the kinetics of levels. The first approach is to solve the radiation transfer equation in the diffusion approximation. The second approach is related to the solution of the Bieberman-Holstein equation.

DOI
10.21883/os.2020.08.49714.318-19

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A theoretical research of the population kinetics of a two-level system with allowance for the transfer of spontaneous emission under continuous optical pumping is presented. It is shown that in the case when the photon mean free path in a resonantly absorbing medium is less than or comparable with the characteristic size of this medium, spontaneous emission can be an additional pump source. Two approaches were used to consider the influence of the spontaneous photon contribution to the kinetics of levels. The first approach is to solve the radiation transfer equation in the diffusion approximation. The second approach is related to the solution of the Bieberman-Holstein equation.
Abstract The population kinetics of a two-level system has been theoretically investigated taking into account the transfer of spontaneous radiation under continuous optical pumping. It is shown that, when the photon mean free path in a resonantly absorbing medium is smaller than the characteristic size of this medium or comparable to it, the spontaneous radiation may become an additional pump source. The contribution of spontaneous photons to the kinetics of level has been considered within two approaches. The first approach consists of solution of the radiation transfer equation within the diffusion approximation. The second approach is related to solution of the Biberman–Holstein equation.
A theoretical study has been made of the transmission of a monochromatic, well-collimated beam of radiation normally incident on idealized material containing only two energy levels. The nonlinear partial differential equations governing the variation of population and photon density in space and time have been solved exactly for arbitrary initial conditions under the assumption that spontaneous emission and thermal relaxation from the excited state can be neglected. These conditions are satisfied in practice when the radiation is in the form of a pulse whose duration is short compared with the characteristic times of these relaxation processes. Two cases are considered in detail: (a) when all atoms are in the ground state and the material absorbs; and (b) when there is a population inversion and the material amplifies. In case (a), the radiation, with a characteristic velocity, ``bores'' its way through an optically dense substance emerging delayed in time and leaving the material in a perfectly transparent or saturated state. In case (b), an incoming pulse is amplified and sharpened—to a degree determined by the gain of the medium. In addition to these cases, the dependence of the apparent spontaneous emission lifetime on the size and population distribution of the material is mentioned.
In this work, a stationary problem analytical solution of the non-monochromatic directional radiation transfer through a medium filled with alkali metal atoms and a buffer gas is obtained. The three-level atom approximation was used to describe the level population kinetics. The processes of absorption and stimulated emission of photons, collisional mixing of the levels of the alkali metal atom fine structure, and spontaneous transitions were taken into account. The absorption of spontaneous radiation by the medium was not taken into account. Using the example of a medium consisting of potassium vapor and a helium buffer gas, the analytical and numerical solutions are compared.
A new method is developed for the description of transfer and scattering of a time-dependent laser pulse, which is based on a hierarchy of Bogoliubov-Born-Green-Kirkwood-Yvone (BBGKY) equations for reduced density matrices. The systems of equations are obtained for the atomic and photon density matrices and the correlation operator in the second-order Born approximation. The system of equations describes stimulated and spontaneous scattering of laser radiation in an optically thin medium, where reabsorption of spontaneous radiation can be neglected. The method proposed in the paper yields for the first time the correct expressions for nonstationary resonance fluorescence spectra, which do not give the negative values for fluorescence intensity. The expressions obtained for the resonance emission spectra coincide in limiting cases with those obtained within the framework of the quantum regression theorem.
The problem about fluorescence of organic molecules located in micropartical-cavity at two-photon absorption in the condition of laser pulse radiation influence taking into account stimulated transitions was theoretically investigated. The approach based on the metod of open-resonator theory with light fields expanded in series of quasinormal vibrational eigenmodes of a dielectric full sphere was used. For active molecules in microcavity the model of generalized two-level system noted with processes of two-photon absorption and emission, spontaneous and stimulated emissions on stokes frequencies was considered. The kinetic equations solution were obtained.
Spontaneous emission from a system of NNN identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state ∣z0〉|{z}_{0}〉∣z0​〉.