A simple stochastic formulation of the multiple scattering representation solution of the classical linear incoherent trapping problem is presented for a broad audience. A clear connection with the alternative Holstein's solution ansatz is emphasized by the (re)interpretation of the fundamental mode as the one associated with a relaxed nonchanging spatial distribution of excitation. Expressions for overall relaxation parameters (ensemble emission yield and lifetime) as well as time-resolved (decay and spatial distribution) and steady-state quantities (spectra and spatial distribution) are given with the fundamental mode contribution singled out. The multiple scattering representation is advocated for final undergraduate and beginning graduate physics instruction based on physical insight and computation feasibility. This will be illustrated in the following instalment of this contribution.
A simple stochastic formulation of the multiple scattering representation solution of the classical linear incoherent trapping problem is presented for a broad audience. A clear connection with the alternative Holstein's solution ansatz is emphasized by the (re)interpretation of the fundamental mode as the one associated with a relaxed nonchanging spatial distribution of excitation. Expressions for overall relaxation parameters (ensemble emission yield and lifetime) as well as time-resolved (decay and spatial distribution) and steady-state quantities (spectra and spatial distribution) are given with the fundamental mode contribution singled out. The multiple scattering representation is advocated for final undergraduate and beginning graduate physics instruction based on physical insight and computation feasibility. This will be illustrated in the following instalment of this contribution.
A computational model study for complete frequency redistribution linear incoherent two-level atomic radiation trapping in optically dense media using the multiple scattering representation is presented. This model study discuss at length the influence of the spectral distributions, overall opacity and emission quantum yield to trapping distorted ensemble quantities stressing physical insight and with a non-specialist audience in mind. Macroscopic reemission yield, lifetime, steady state spectra and spatial distributions are calculated as a function of intrinsic emission yield, opacity and external excitation mode for Doppler, Lorentz and Voigt lineshapes. The work could constitute the basis for a final undergraduate or beginning graduate project in computational physics instruction and implements the analytical developments of the previous instalment of this contribution.
Abstract There are three principal mathematical approaches to describing trapping: the Holstein equation, the method of combining the equation of radiative transfer with the rate equation for the excited state atoms, and the multiple-scattering representation. Ultimately, these three descriptions are equivalent-as they should be, since they describe the same physical process. Their different formulations stem from different views of the trapping problem. Each method has its specific advantages and disadvantages for the evaluation, hence it is very helpful to fully understand all three formulations.
Theoretical treatment of resonance radiation trapping under steady-state conditions, particularly of quenching experiments, is presented. Applying operator manipulations, Holstein's equation of radiation trapping [Phys. Rev. 72, 1212 (1947)] is solved by a perturbation expansion, which can be physically interpreted in terms of multiple scatterings. The resulting expression shows that in a steady-state quenching experiment radiation trapping invalidates the relation of the Stern-Volmer type except when the amount of the buffer gas is small. In the limit of low buffer-gas pressure, a simple expression is given for the effective lifetime in the Stern-Volmer relation: the average time of the detected resonant photons remaining within the enclosure. While it is true that this suggested approach is perturbative in nature, the asymptotic behavior of the high-order expansion coefficients, however, enables us to reduce the summation over infinitely many alternatives to some leading terms. Such a reduction procedure helps curtail the computation time and improve the precision. Finally, some numerical illustrations of our suggested ideas are presented, which shows this approach is a good tool to treat the steady-state trapping effect.
Time dependent description of resonance Raman scattering is performed for a general system, by a density matrix reformulation of damping theory originally used for resonance fluorescence of atom. Radiative damping in the intermediate states can be described in terms of "damping operator" in realistic situations. In large ergodic systems, the scattering reduces to luminescence if the relaxation time within the excited states is much shorter than the radiative lifetime. In a typical case, time resolved emission spectra consist of various stages (i) scattering complex where absorption and emission are inseparable, (ii) dynamical and then (iii) kinetic relaxations giving rise to the hot luminescence, which finally converges to (iv) the ordinary luminescence from relaxed excited states. Hot luminescence does not appear within a motionally narrowed line. The interpretation of spectra depends also on the method of observation.
The purpose of this paper is to propose a theoretical treatment of radiation trapping in a multiple lines coupled system in which coupling includes collisional energy transfer and cross absorption between the excited states. First, to describe the coupled system, the Holstein equation of radiation trapping is extended to an integral differential master equation group in which the vector and matrix form is adopted. Then by use of operator manipulations, the asymptotic solution in the form of a series expansion in terms of operators is presented. Finally, the asymptotic solution is reduced, leading to a result which can not only give the system a complete description, but also has far more advantages than the simple cut off solution. A numeral illustration of a two excited states system is also presented.
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.