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Soviet Journal of Quantum Electronics

Maximum achievable population inversion in finite volumes

G. N. Vinokurov

Published Sep 30, 1977• 1 citation
Publisher

Abstract

A calculation is made of the steady-state population inversion distribution in homogeneously pumped active media of spherical or cylindrical form. It is assumed that reflections from the boundaries of the active medium have been completely eliminated and it is shown that the inversion decrease, caused by the amplification of spontaneously emitted radiation, is mainly a function of the overall volume of the active medium. For active media of equal volume, the stored inversion is minimal for a sphere.

DOI
10.1070/qe1977v007n09abeh012810

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A calculation is made of the steady-state population inversion distribution in homogeneously pumped active media of spherical or cylindrical form. It is assumed that reflections from the boundaries of the active medium have been completely eliminated and it is shown that the inversion decrease, caused by the amplification of spontaneously emitted radiation, is mainly a function of the overall volume of the active medium. For active media of equal volume, the stored inversion is minimal for a sphere.
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We discuss a possibility for obtaining the self-amplified spontaneous emission of gamma radiation in an active medium with hidden population inversion of nuclear states. Hidden inversion appears in cooled nuclear ensembles due to assistance of the nuclear recoil in emission and absorption of gamma quanta. Establishing a hidden inversion allows an amplification of gamma radiation to occur in a particular frequency range without excess of the number of excited nuclei over the number of unexcited nuclei. We formulate a set of requirements to the pumping radiation and to the amplifying nuclear medium crucial to the development of gamma-ray lasing.
The widely used technique for determining optical gain and absorption from single-pass, amplified spontaneous emission (ASE) is analyzed with particular attention given to active-volume saturation and three-dimensional effects. The results for homogeneously broadened media show that the population inversion and hence the gain in the active region is diminished by high levels of spontaneous and ASE. The externally measured gain is further reduced for large output collection apertures that admit incompletely amplified off-axis rays. Criteria are given for the excitation and detection geometries required to ensure accurate (∼10-percent) gain measurement. The simultaneous measurement of the equilibrium absorption coefficient can be made under less restrictive conditions.
Amplified spontaneous emission of laser media having a spherical or disk shape is numerically analyzed. Some properties are discussed and a comparison with linear systems is made. Analytical approximations, for the case of high pumping rates and high efficiency, are obtained. Energy level schemes of dye systems are used in the analysis and in the numerical calculations. A coupled set of radiative transfer and rate equations is solved under quasi-steady-state conditions. The model takes into account the fluorescence spectrum and gain saturation effects with radially symmetric distributions of the active dye molecular densities. As a comparison, the numerical examples also include an H2O system which is relevant in astrophysics.