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Journal of Physics B Atomic Molecular and Optical Physics

Radiation trapping in atomic vapours in finite-cylinder vapour cells excited by a laser beam

Andreas F. Molisch, Bernhard P Oehry, Walter Schupita, Gottfried Magerl

Published Apr 28, 1997• 20 citations
Publisher

Abstract

We compute radiation trapping in a two-level atomic vapour excited by a laser beam, taking into account saturation effects and using a realistic vapour-cell geometry, the finite cylinder. By using an approximation for the angular distribution of the fluorescence radiation, CPU-time requirements are kept low. We then analyse various practical cases and present useful practical rules of thumb when certain simplifications are valid. When we consider the decay of an initial excitation, the decay at late times can be computed by using an equivalent one-dimensional geometry. For early times, it is usually important to include the three dimensionality of the problem. Finally, we present calculations how the `burn-through' effect of a strong laser affects the approximation of the geometry.

DOI
10.1088/0953-4075/30/8/007

Related papers

Nonlinear radiation trapping in an atomic vapor excited by a strong laser pulse

Nikolai N. Bezuglov, Andrey N. Klyucharev, A. F. Molisch +3 more

We investigate radiation trapping in an atomic vapor which has been excited by a strong short laser pulse. Since the saturation of the vapor by the pulse leads to a decrease in the effective absorption coefficient, the radiation trapping becomes nonlinear. We derive approximate analytical expressions for the excited-state density in the directly excited region, the fluorescence-excited region, and the density averaged over the whole cell. Starting out from fairly simple approximate expressions based on a prescribed distribution of excited atoms, we then develop physically motivated correction factors that drastically improve the accuracy. All these expressions are given for three important cell geometries: the plane-parallel slab, the infinite cylinder, and the sphere. We compare our results to accurate numerical solutions, and find agreement within 5--10%. We then derive the decay time of the emergent radiation, and find that it can be smaller than the natural lifetime of the excited atoms, in agreement with recent experimental results obtained for sodium vapors.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 1, 1997•17 citations

Radiation Trapping in Atomic Vapours

Andreas F. Molisch, Bernhard P Oehry

Abstract Radiation from spectral lines can be absorbed and re- emitted many times in atomic vapours before it reaches the boundaries of the container encasing the vapour. This effect is known as radiation trapping. It plays an important role practically everywhere where atomic vapours occur, e.g. in spectroscopy, in gas lasers, in atomic line filters, in the determination of atomic lifetimes, in measurements of atomic interaction potentials, and in electric discharge lamps. This book for the first time assembles all the information necessary for a treatment of practical problems, emphasizing both physical insights and mathematical methods. After an introduction that reviews resonance radiation and collisional processes in atomic vapours, physical effects and mathematical methods for various types of problems (e.g. with or without saturation, particle diffusion, reflecting cell walls, etc.) are explained in detail. The last part of the book describes the applications of these methods to a variety of practical problems like cross-section measurements or the design of discharge lamps.Atoms can both absorb and emit electromagnetic radiation like visible light In an assembly of many atoms, e.g., in a vapour or in a gas, radiation emitted by one atom may be reabsorbed by one of its neighbours, just to be reemitted a little later. The game can go on for quite some time—until the photon manages somehow to escape from this prison. At first glance, quite easy to understand. On the other hand, there must be some reason for this voluminous book full of sums, integrals and matrices. Our interest in this subject originally stemmed from investigations on atomic line filters we did for the European Space Agency, ESA. We believed that radiation trapping would have some influence on the performance of these filters and were looking for a simple means to take it into account We started out the same way as probably anyone new to the field would have done when faced with the problem of trapping. We read the classical paper of Holstein, and thought that was all there was to it. We soon had to realize, however, that the assumptions made by Holstein were not fulfilled in our problem, and decided to give the whole matter a closer look. That ‘closer look’ obtained a momentum of its own, and trapping became the centre of our own research in the following years. As our overview of the subject increased. we found that trapping plays a role in a staggering variety of situations. Trapping appears to be important in most experimental setups and in most engineering applications where atomic vapours are involved.

•Nov 26, 1998•191 citations

Solution of the Holstein equation of radiation trapping by the geometric quantization technique. II. Two- and three-dimensional geometries

Nikolai N. Bezuglov, Andreas F. Molisch, Andrey N. Klyucharev +2 more

We solve the Holstein equation describing radiation trapping in an atomic vapor by the geometric quantization technique. The treatment is based on studying the integral trapping equation as a wave equation for an associated quasiparticle with a complicated form of its dispersion law. The latter is determined by the spectral properties of the vapor medium. Extending our previous work, which dealt with one-dimensional (1D) geometries, we consider here more realistic two- and three-dimensional (2D and 3D) vapor cell geometries. For this, an explicit representation of the phase factors is derived when the quasiparticle is reflected under arbitrary angles from the surface of the cell confining the vapor. We give closed-form equations to obtain analytically the complete 3D spectrum of escape factors in finite cylinder, sphere, parallelepiped, and finite prismlike geometries for all practically occurring line shapes and opacities. In addition, the relevant semiclassical variational method is applied to develop a perturbation theory for the evaluation of escape factors in more complicated geometries that are sometimes adopted in experiments, including infinite (or finite) elliptical cylinders, prolate and oblate ellipsoids. Comparisons with numerical calculations show that results are accurate within $5%$ for the ground modes and even better for higher-order modes.

Physical Review A•Jun 1, 1999•18 citations

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Radiation trapping in plane-parallel slab geometry — experiment and theory

Piotr P. Wiewior, J. Chora̧ży, T. Kotowski +1 more

The Holstein‐Biberman equation describing the evolution of the excited atoms population in a dense sodium vapour optically saturated by a short resonant light pulse was solved numerically. It was found that in a strongly excited medium the decay of the Na(3P) atoms is faster than in the case of the weak excitation. A subnatural decay of the resonance fluorescence signal for some experimental gemetries was predicted. The experimental data confirming the theoretical results are also presented.

AIP conference proceedings•Jan 1, 1995•0 citations

Investigation of Radiation Trapping in Atomic Vapour Excited by Weak Resonant Laser Pulses

J. Chora̧ży, T. Stacewicz

We present results of our investigations on radiation trapping in sodium vapour excited to 3.P level by weak laser pulses.The evolution of the fluorescence signal as well as the evolution of excited atoms distribution were studied using the Monte Carlo method.Some predictions of these investigations were checked experimentally.

Acta Physica Polonica A•Sep 1, 1999•0 citations
We compute radiation trapping in a two-level atomic vapour excited by a laser beam, taking into account saturation effects and using a realistic vapour-cell geometry, the finite cylinder. By using an approximation for the angular distribution of the fluorescence radiation, CPU-time requirements are kept low. We then analyse various practical cases and present useful practical rules of thumb when certain simplifications are valid. When we consider the decay of an initial excitation, the decay at late times can be computed by using an equivalent one-dimensional geometry. For early times, it is usually important to include the three dimensionality of the problem. Finally, we present calculations how the `burn-through' effect of a strong laser affects the approximation of the geometry.
We investigate radiation trapping in an atomic vapor which has been excited by a strong short laser pulse. Since the saturation of the vapor by the pulse leads to a decrease in the effective absorption coefficient, the radiation trapping becomes nonlinear. We derive approximate analytical expressions for the excited-state density in the directly excited region, the fluorescence-excited region, and the density averaged over the whole cell. Starting out from fairly simple approximate expressions based on a prescribed distribution of excited atoms, we then develop physically motivated correction factors that drastically improve the accuracy. All these expressions are given for three important cell geometries: the plane-parallel slab, the infinite cylinder, and the sphere. We compare our results to accurate numerical solutions, and find agreement within 5--10%. We then derive the decay time of the emergent radiation, and find that it can be smaller than the natural lifetime of the excited atoms, in agreement with recent experimental results obtained for sodium vapors.
Abstract Radiation from spectral lines can be absorbed and re- emitted many times in atomic vapours before it reaches the boundaries of the container encasing the vapour. This effect is known as radiation trapping. It plays an important role practically everywhere where atomic vapours occur, e.g. in spectroscopy, in gas lasers, in atomic line filters, in the determination of atomic lifetimes, in measurements of atomic interaction potentials, and in electric discharge lamps. This book for the first time assembles all the information necessary for a treatment of practical problems, emphasizing both physical insights and mathematical methods. After an introduction that reviews resonance radiation and collisional processes in atomic vapours, physical effects and mathematical methods for various types of problems (e.g. with or without saturation, particle diffusion, reflecting cell walls, etc.) are explained in detail. The last part of the book describes the applications of these methods to a variety of practical problems like cross-section measurements or the design of discharge lamps.Atoms can both absorb and emit electromagnetic radiation like visible light In an assembly of many atoms, e.g., in a vapour or in a gas, radiation emitted by one atom may be reabsorbed by one of its neighbours, just to be reemitted a little later. The game can go on for quite some time—until the photon manages somehow to escape from this prison. At first glance, quite easy to understand. On the other hand, there must be some reason for this voluminous book full of sums, integrals and matrices. Our interest in this subject originally stemmed from investigations on atomic line filters we did for the European Space Agency, ESA. We believed that radiation trapping would have some influence on the performance of these filters and were looking for a simple means to take it into account We started out the same way as probably anyone new to the field would have done when faced with the problem of trapping. We read the classical paper of Holstein, and thought that was all there was to it. We soon had to realize, however, that the assumptions made by Holstein were not fulfilled in our problem, and decided to give the whole matter a closer look. That ‘closer look’ obtained a momentum of its own, and trapping became the centre of our own research in the following years. As our overview of the subject increased. we found that trapping plays a role in a staggering variety of situations. Trapping appears to be important in most experimental setups and in most engineering applications where atomic vapours are involved.
We solve the Holstein equation describing radiation trapping in an atomic vapor by the geometric quantization technique. The treatment is based on studying the integral trapping equation as a wave equation for an associated quasiparticle with a complicated form of its dispersion law. The latter is determined by the spectral properties of the vapor medium. Extending our previous work, which dealt with one-dimensional (1D) geometries, we consider here more realistic two- and three-dimensional (2D and 3D) vapor cell geometries. For this, an explicit representation of the phase factors is derived when the quasiparticle is reflected under arbitrary angles from the surface of the cell confining the vapor. We give closed-form equations to obtain analytically the complete 3D spectrum of escape factors in finite cylinder, sphere, parallelepiped, and finite prismlike geometries for all practically occurring line shapes and opacities. In addition, the relevant semiclassical variational method is applied to develop a perturbation theory for the evaluation of escape factors in more complicated geometries that are sometimes adopted in experiments, including infinite (or finite) elliptical cylinders, prolate and oblate ellipsoids. Comparisons with numerical calculations show that results are accurate within 55%5 for the ground modes and even better for higher-order modes.
In three-level atoms where one level is the ground state and one is a metastable state, even low-intensity resonance radiation can lead to bleaching. This effect causes the radiation trapping to become nonlinear and thus greatly complicates the simulation of such a system. We set up equations to model an optically excited three-level atomic vapor in a two- or three-dimensional cylindrical cell; the model includes the effects of radiation trapping, particle diffusion, and quenching. We then develop a fast and efficient approximate method for the solution of these equations. Results are compared to Monte Carlo simulations; agreement within 15% is achieved.