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Applied Optics

Steady-state atomic fluorescence radiance expressions for continuum excitation

G. D. Boutilier, M. B. Blackburn, Jean Michel Mermet, Stephan Weeks, Hiroki Haraguchi, James D. Winefordner, Nicolo’ Omenetto

Published Aug 1, 1978• 30 citations
Publisher

Abstract

Several general expressions for the atomic fluorescence radiance excited by a laser source are presented for both two-level and three-level systems. The laser has been approximated to a spectral continuum since its bandwidth is assumed to be much larger than the absorption profile. Two types of three-level systems are considered: (1) systems where two excited states are close together, both coupled radiatively with the ground state (Na, K, Cs, etc.); and (2) systems where one level is close to the ground state, both being radiatively connected with a third excited state (T1, In, Ga, etc.). Expressions are given for both linear and saturating conditions, and the use of such expressions for absolute species measurement is discussed. In our treatment, we have made the assumption that the rate equations approach is valid.

DOI
10.1364/ao.17.002291

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Several general expressions for the atomic fluorescence radiance excited by a laser source are presented for both two-level and three-level systems. The laser has been approximated to a spectral continuum since its bandwidth is assumed to be much larger than the absorption profile. Two types of three-level systems are considered: (1) systems where two excited states are close together, both coupled radiatively with the ground state (Na, K, Cs, etc.); and (2) systems where one level is close to the ground state, both being radiatively connected with a third excited state (T1, In, Ga, etc.). Expressions are given for both linear and saturating conditions, and the use of such expressions for absolute species measurement is discussed. In our treatment, we have made the assumption that the rate equations approach is valid.
Several calculations have been carried out using the transition operator technique. The radiative decay in a two-level quantum system with excited state coupled by an external perturbation has been investigated and an expression obtained for P(t), the probability of finding the atom in its excited state at time t. This is seen to possess a steady value for yt >> 1 and a third term which decays at nearly half the rate of its second. Next radiative decay of an atom with two close-lying excited states is considered and |bq| 2 , the spectral density for spontaneous emission from the uppermost level, calculated. This shows that the proximity of the upper two levels makes the line-shape non-Lorentxian. Heisenberg equations of motion were then derived for the transitions operators of an ℓ-level atom undergoing radiative decay, the possibility of overlapping pairs of levels being ignored. These master equations were then used to obtain the spectral profiles of certain atomic lines, employing the so-far avoided Markoff approximation. First the spectral density of the scattered radiation was found for transitions between levels 5P3/2 and 4S (ground state), and 6S and 5P 3/2, in the potassium atom when driving fields of arbitrary strength coupled levels 6S and 4P3/2, and 4P 3/2 and 4S. Triple-peaked profiles were obtained. Spectral profiles for emission were then derived for transitions between levels 3P and (ground state), and 3P and in the hydrogen atom when a driving field of arbitrary strength coupled levels The former profile was double the latter quadruple-peaked. Lastly master equations were derived for an atom, with two excited levels undergoing radiative decay, when allowance was made for thepossibility of their overlapping. A driving field of arbitrary magnitude coupled the uppermost and ground states. The spectrum for the scattered light resulting from transitions between the uppermost and ground state was found and graphs computed for various field strengths and separations of the excited states.
The dependence of steady-state fluorescence of a diatomic system on the frequency of a laser field is investigated. The steady-state fluorescence intensity can be presented in special geometry as the sum of two parts. The first part is described using an independent two-level system. The second is related to the two-photon excitation process and is described using a three-level system. The respective analytical expressions are obtained for the line profiles, their width, and intensity at the maxima.
A complete and detailed treatment of a three-level atom interacting with two near-resonant monochromatic fields is presented. It is assumed that the only damping mechanism is radiative damping, and that the atoms all have the same resonance frequencies, as is the case in an atomic beam. Detailed analytic solutions as well as numerical examples are determined from quantum-electrodynamic equations of motion. In addition, approximation techniques are presented which allow one to get accurate quantitative predictions for strong applied fields from simple rate-equation-like arguments. Absorption and emission spectra are determined, as are the transient and steady-state response of the atom. Two of the more interesting predictions are an emission spectrum containing up to seven components and a prediction of steady-state populations larger than 0.5 in the second excited state.
A two-state atom in a perturber gas is irradiated by intense light with an arbitrary spectral profile. The authors derive a general expression for the fluorescence spectrum in terms of the conventional low-intensity absorption profile and the spectral density of the incident light. This result, which contains previous results as special limiting cases, describes the transition from the three-line fluorescence spectrum excited by intense monochromatic light and the power-broadened Lorentzian spectrum produced by broad-band excitation.
This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states which are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As recently shown, the quasi-energies of the laser-dressed states receive radiative corrections which are nontrivially different from the results which one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for the analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P and 2S states.
We describe the resonance fluorescence spectrum of an atomic three-level system where two of the states are coupled by a single monochromatic laser field. The influence of the third energy level, which interacts with the two laser-coupled states only via radiative decays, is studied in detail. For a suitable choice of parameters, this system gives rise to a very narrow structure at the laser frequency in the fluorescence spectrum which is not present in the spectrum of a two-level atom. We find those parameter ranges by a numerical analysis and use the results to derive analytical expressions for the additional narrow peak. We also derive an exact expression for the peak intensity under the assumption that a random telegraph model is applicable to the system. This model and a simple spring model are then used to describe the physical origins of the additional peak. Using these results, we explain the connection between our system, a three-level system in the V configuration where both transitions are laser driven, and a related experiment that was recently reported.