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Оптика и спектроскопия

Аналитическое решение задачи о переносе немонохроматического направленного излучения в резонансно поглощающей среде

В.М. Ямщиков

Published Jan 1, 2023• 1 citation
Publisher

Abstract

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.

DOI
10.21883/os.2023.05.55724.4104-22

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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.
The study solves the problem of the luminescent photons propagation in a resonantly absorbing medium consisting of atoms of the studied substance and a buffer inert gas. The Monte Carlo method was used in numerical experiments carried out to simulate real processes that occur in a chamber designed to determine the lifetime of an individual atom in an excited state by the method of measuring the luminescence intensity decay time. Findings of the research show that when luminescent photons are repeatedly scattered (scattering means the process of absorption and re-emission of a photon by an atom) in a medium, the luminescence decay time noticeably increases, reaching a value greater than the average lifetime of an individual atom in an excited state. The reflection of photons from the walls that make up the chamber can lead to errors in measuring the lifetime. The process of luminescence decay is studied theoretically for various detunings of the laser frequency from the resonant transition frequency. A three-level model of the atom and a model of complete frequency redistribution were applied. The study describes an algorithm based on the Monte Carlo method, which is used to model the three-level population kinetics, laser radiation transfer, radiation trapping, and frequency redistribution
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.
The resonance fluorescence of a degenerate V -type three-level atom in the field of an intense monochromatic wave with arbitrary polarization composition is investigated. The equations of motion, the general form of the radiation relaxation operator, and the analytical expressions for the angular distribution of the intensity of the spontaneous radiation from atoms, and the total intensity of the resonance fluorescence for such systems are obtained. The angular distribution of the spontaneous radiation from atoms for the D line of alkali-metal vapors is investigated. It is predicted theoretically that the intensity of the resonance fluorescence will decrease as the intensity of the pump wave increases in observations in a direction of the electric field vector of the laser wave.
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.
Potassium (K) and rubidium (Rb) are two kinds of typical alkali atoms, which have the similar energy-level structures. In a mixture of potassium and rubidium, energy transfer among atoms is different from that in a simple sample of potassium or rubidium vapor. When potassium and rubidium mixed vapor is irradiated simultaneously by a potassium resonance doublet and a rubidium resonance doublet, energy transfer will be induced by inelastic collisions between the excited potassium atoms and the unexcited potassium atoms, the excited rubidium atoms and the unexcited rubidium atoms, the excited potassium atoms and the unexcited rubidium atoms, the unexcited potassium atoms and the excited rubidium atoms, the excited potassium atoms and the excited rubidium atoms, and etc. Two processes of energy transfer between two upper-state levels of atomic potassium or rubidium such as 42P3/2 → 42P1/2 and 52P3/2 → 52P1/2, are known as direct-relaxation. Four processes of energy transfer such as 42P1/2 → 52P1/2, 42P1/2 → 52P3/2, 42P3/2 → 52P1/2, and 42P3/2→ 52P3/2, are called as cross-relaxation. In this study, we evaluate quantitatively the effect of cross-relaxation on the population distribution of atomic potassium and rubidium as well as the output power of the complex potassium-rubidium lasing system. The results demonstrate four cross-relaxation rates are much smaller than two direct-relaxation rates so that the influence can be negligible under the given temperature conditions. The conclusion might be helpful to better understand the kinetic principle of collisional energy transfer of a complex lasing system with mixed alkali metal media.
An investigation was made of the mechanisms of quenching of excited states and of excitation of atomic levels as a result of absorption of laser radiation by alkali metal (Na, K, Cs) vapors. It was found that several processes participated in the excitation of atomic levels: collisional mechanism of excitation energy transfer from molecules to atoms, photodissociation, predissociation, and nonresonant excitation of atomic levels (radiative collisions). The partial contribution of each of these processes (dependent on the vapor density, intensity of laser radiation, and its frequency) should be allowed for in the balance of the filling and deactivation of molecular and atomic states. Qualitative characteristics were obtained for these processes and an analysis was made of their likely role in the emission of radiation from diatomic molecules in alkali metal vapors.