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Advanced Solid-State Lasers

Spectroscopic Effects of Stimulated Emission Under Fast Pumping Conditions

Michael L. Kliewer, A. Suchocki, Richard C. Powell

Published Jan 1, 1987• 0 citations
Publisher

Abstract

Solutions of the rate equations for a two-level system describing spectral properties in the presence of stimulated emission under picosecond-pulse pumping conditions are examined. The materials of interest are broad band tunable, vibronic laser crystals whose lasing properties under normal pumping conditions have been related to spectral properties through the McCumber theory1. The population inversion at threshold can then be determined by three methods: lifetime shortening, band narrowing, and peak gain measurements.

DOI
10.1364/assl.1987.tud1

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Solutions of the rate equations for a two-level system describing spectral properties in the presence of stimulated emission under picosecond-pulse pumping conditions are examined. The materials of interest are broad band tunable, vibronic laser crystals whose lasing properties under normal pumping conditions have been related to spectral properties through the McCumber theory1. The population inversion at threshold can then be determined by three methods: lifetime shortening, band narrowing, and peak gain measurements.
In two recent works, the authors have investigated the spectro-temporal properties of the random laser emission from solid state dye-doped powders in picosecond pumping regime. Each emission pulse consists, both above and below threshold, in a collection of narrow peaks of a spectro-temporal width at the theoretical limit (ΔωΔt≅1). The distribution of path lengths traveled inside the diffusive active medium by photons that can be amplified by stimulated emission explains this behavior, as demonstrated by a simple theoretical model developed by the authors. The aim of the present work is, first, to develop an implemented model that does not depend on fitting parameters, and which is compatible with the energetic and spectro-temporal properties of the material; and second, to get knowledge about the spatial properties of the emission. The transverse coherence size of each emitted photon packet has been measured; and in addition, we have shown the existence of spatial fluctuations of the emission of these materials, as our model predicts.
The existence of multiple-quantum transitions in optically pumped lasers, along with splitting of the laser line due to the modulation of the wave function at an angular frequency determined by the rate of pumping, is demonstrated for a certain class of incoherent broad-band sources pumping large pump bands in crystals. The source consists of a large number of stationary elements emitting wave fields continuously at various arbitrary frequencies and arbitrary phases. The distribution of frequencies and phases among the various elements is random. The pump band belongs to the class found in laser crystals of the ionic type. The analysis shows that such sources pumping such bands act like narrow-line sources pumping narrow lines. The effective linewidth is directly related to the pump rate.
An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon.In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.
An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon. In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.
An analysis of a three-level system using time-dependent perturbation theory shows that two distinct photon-emission processes take place within such a system when stimulated optical emission occurs: one-and two-photon transitions. The two-photon transition consists of the emission of a stimulated photon followed by the absorption of a coherent pump photon. In three-level systems which possess a narrow pump level, two-photon transitions are dominant at high pump powers while the maser line is split into two lines due to the modulation of the wave function at an angular frequency determined by the rate of pumping. This might lead to the possibility of frequency-modulating the maser line. These results are extended qualitatively to include optical masers which possess broad pump-bands.
This paper describes a model and provides the mathematical formulation for describing the spike pulsing phenomenon observed in optically pumped three-level lasers. The model is based on the pumping of electrons from a ground state to an excited pump band from which they relax very rapidly to the excited laser level. With population inversion then achieved, laser action starts and repetitive pulses with decreasing amplitude are generated; the pulses then damp out and the laser output reaches a steady state as long as sufficient pump radiation energy is available. The equations describing the system in terms of the population inversion and photon density are nonlinear. However, approximations are made which permit the required relations between the transition rates to be established for such action to progress. The time variation of the population inversion and the photon density at the laser frequency are obtained for both the pumping time interval and the stimulated emission laser region.