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Soviet Journal of Quantum Electronics

Selective absorption and spontaneous emission in a resonator

W. Brunner, Henryk Paul

Published Oct 31, 1975• 0 citations
Publisher

Abstract

A theoretical analysis is made of the influence of spontaneous radiation on the sensitivity of the method of continuous detection of an absorption line in which an absorption cell is placed inside a laser resonator. It is shown that this influence is negligible if the laser modes are coupled not only to the common reservoir of atoms or molecules but each mode additionally acquires energy from its own reservoir. If the contribution of the individual reservoirs to the total energy balance is small compared with the contribution of the common reservoir, the probability of spontaneous emission determines the maximum possible sensitivity of this absorption measurement method.

DOI
10.1070/qe1975v005n10abeh012065

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A theoretical analysis is made of the influence of spontaneous radiation on the sensitivity of the method of continuous detection of an absorption line in which an absorption cell is placed inside a laser resonator. It is shown that this influence is negligible if the laser modes are coupled not only to the common reservoir of atoms or molecules but each mode additionally acquires energy from its own reservoir. If the contribution of the individual reservoirs to the total energy balance is small compared with the contribution of the common reservoir, the probability of spontaneous emission determines the maximum possible sensitivity of this absorption measurement method.
We review the physics underlying the process of spontaneous emission, with a special focus on spontaneous emission into a resonator mode. We define the mode volume, verify the fundamental modal dimensions, present the spectral mode profile, the coherence time, the Q-factor, the Füchtbauer-Ladenburg equation, and the Purcell factor, and discuss their influence on different types of lasers. We obtain the relation between peak emission cross section, radiative lifetime, and emission linewidth. By interpreting spontaneous emission as stimulated emission driven by vacuum fluctuations, we derive the spontaneous-emission rate into a resonator mode and establish physical expressions for the fractions of spontaneous emission and total decay from the upper laser level into this mode. Furthermore, we discuss coupling of the atomic system with the coherent field inside a lasing resonator mode, resulting in the formation of a Mollow triplet, and demonstrate that it leads to a reduction of the spontaneous-emission rate by a factor of 2.
The nonlinear absorption and fluorescence spectra of 133 Cs vapours confined to the extremely thin cell are computed in the framework of perturbation theory regarding to the intensity of the laser light illumination. The amplitude as well as the sign of the longitudinal alignment of the ground state is shown to be defined by the spontaneous decay of the upper level. The sign and the magnitude of the nonlinear absorption resonance on the closed optical transition are shown to be defined by this process as well.
A theoretical analysis is made of the spontaneous emission from an excited atom or a molecule in a one-dimensional periodic structure formed by a screened two-conductor line filled with periodically distributed dielectric disks. It is shown that when the transition frequency lies within or close to the forbidden band of the periodic structure, the decay of an excited state of an atom or a molecule produces a characteristic long-lived dynamic state. This dynamic state is a superposition of the excited and ground states with an admixture of a photon "cloud," which surrounds the atom or molecule. A study is made of the distribution of the electromagnetic energy of the dynamic state. The energy and the decay law of the excited state are obtained and the spectrum of the emission which accompanies this decay is obtained. It is shown that the spontaneous emission can be suppressed strongly in volumes much greater than the wavelength. The possibility of the suppression of spontaneous emission from lasers is discussed.
Recently, we observed enhancement and inhibition of visible spontaneous emission by atoms in a confocal resonator.1 In these experiments, the partial emission rate of the atom into the resonator modes is modified by a factor of 1/(1 − R), where R is the mirror reflectivity. The change in the total spontaneous emission rate is proportional to the solid angle ΔΩ subtended by the mirrors; the change was small (+1.6%, −0.5%) because ΔΩ ≈ 0.04 sr was small. Currently we are conducting experiments in which atoms are placed in a concentric resonator of large solid angle ΔΩ ≈ 3.6 sr and finesse of ~10. We estimate that a 30% decrease and 300% increase should be observable in the total spontaneous emission rate, when the resonator is tuned off or on-resonance, respectively. Results of this new experiment are presented. In addition to studying spontaneous processes, one can also consider the stimulated emission which occurs when a cavity field builds up which contains more than one photon. We have formulated a model which describes both the spontaneous and stimulated emission by the atom into the cavity and clarifies the relationship between enhanced spontaneous emission and stimulated emission.
This chapter presents a tutorial review of spontaneous emission in optical resonators. Approximating correlation functions as delta functions means that the reservoir is assumed to lose its memory in a short time, compared to the time scale over which the dynamics of the small system occurs, the Markov approximation. In a generic cavity quantum electrodynamics experiment, an atom is coupled to one, or possibly a few, cavity mode(s). These modes are in turn coupled to the external world via mirror losses and diffraction. In addition, the atom might also be coupled to a continuum of vacuum modes, in the case where the cavity is open-sided. A simple physical interpretation of the spontaneous emission spectrum can be obtained if one adopts the point of view that the atom-cavity mode small system represents a single quantum system, and by analyzing its eigenenergy spectrum.