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Journal of China Institute of Metrology

Theoretic estimation of lasing threshold of a three-level systsm containing cross relaxation

Li Huang

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

A Theoretical estimation of the threshold of end-pumped laser in three-level system containing the cross relaxation is deduced from the transition rate-equations and the transmission equations of the laser- and pump-light for active ions. The lasing performance of the crystal can be presupposed, and parameters, such as optimum length of the laser rod, optimum concentration of active ions and optimum reflectivity of reflectors in the resonant cavity et al., can be estimated by the use of deduced formula that will help to design the laser.

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A Theoretical estimation of the threshold of end-pumped laser in three-level system containing the cross relaxation is deduced from the transition rate-equations and the transmission equations of the laser- and pump-light for active ions. The lasing performance of the crystal can be presupposed, and parameters, such as optimum length of the laser rod, optimum concentration of active ions and optimum reflectivity of reflectors in the resonant cavity et al., can be estimated by the use of deduced formula that will help to design the laser.
The paper discuses the influence of cross-relaxation parameter on the characteristics of the sensitized photon avalanche. A system Pr3+ as activator ion and Yb3+ as sensitizer ion were considered for the avalanche process. By numerical modelling of a system of rate equations, time dependencies and pump rate dependencies of populations of energy levels were calculated for three different values of cross-relaxation rate. Correlation between cross-relaxation rate and threshold value of pump intensity was established.
The paper discusses the factors affecting the pump quantum efficiency for three-micron stationary emission in concentrated Er systems, driven by the up-conversion processes from the terminal laser level. It is shown that in the stationary regime analytical formulae for the quantum efficiency could be obtained as a function of pump conditions and global efficiency of the cross-relaxation processes. These formulae enable a selection of the active medium and pump conditions in order to obtain high pump efficiency.
A theoretical study is made of the influence of changes in the relaxation of a three-level system in a resonance field on the dispersion, absorption, and difference between the populations of levels activated by noncoherent pumping. This change in the relaxation is due to a tendency of a thermal reservoir to create an additional difference between the populations of quasienergy states that appear under the influence of the resonance field. It is shown that as a consequence there is a considerable change in the nature of the interaction with the radiation field in laser crystals with three-level active centers when the pump power is close to the threshold. The lasing conditions are found subject to such changes. It is shown that the threshold pump power can be reduced in this case to a value at which the difference between the populations of the active levels vanishes and lasing appears because of an inversion of the populations in a system of quasienergy levels. Under transient conditions the lasing frequency near the threshold should then depend on the pump
A rigorous density-matrix-based theory of lasing based on optically induced or autoionization-induced coherence between the levels is developed. The balance equations are obtained, and the conditions for lasing threshold are derived as a function of pumping strength and relaxation rates. Connection between the lasing without inversion and Raman and parametric processes is established. The main conclusion is that true CW lasing without inversion can indeed be obtained but only in a system where pumping and relaxation rates are favorable for attaining conventional lasing with population inversion. Practical implications of it, especially for the intersubband lasers, are discussed.
We analyze a laser system consisting of N closed three-level atoms confined in a single-mode cavity and derive the conditions for the onset of lasing without inversion or with inversion. We calculate the steady-state gain and lasing in the system and show that far above the lasing threshold, depending on the pumping and decay rates, the inversionless laser may operate in three different regimes, where the intensity of the laser depends linearly on N, is proportional to \ensuremath{\surd}N , or independent of N.