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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Pump quantum efficiency in the three-micron laser emission in concentrated Er systems

Voicu Lupei, Serban Paul Georgescu

Published Aug 16, 1994• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.184628

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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 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.
A detailed analysis of the non-exponential behaviour of the kinetics of the initial laser level for three-micron generation 4I11/2, in ErAG (Erbium Aluminium Garnet) crystals (laser transition 4I11/2 →4I13/2), excited in the 4H11/2 level with short laser pulses of variable intensity, is performed. The observed non-exponentiality of the 4I11/2 decay and its dependence on the energy of the exciting pulse cannot be satisfactorily described with a rate equation modelling which includes only two-ion energy transfer processes among Er3+ ions as up-conversion from the terminal laser level (4I13/2), up-conversion from the initial one. and cross-relaxation from 4I9/2 and 4S3/2 (thermalised, at room temperature, with 2H11/2) Our analysis has shown that the inclusion of three-ion up-conversion processes from both initial and terminal three-micron laser levels leads to an excellent agreement between experimental and theoretical non-exponentiality of the 4I11/2 decay for various pumping intensities and allows the estimation of the three-ion up-conversion rates The best agreement with the experimental non-exponentialities was obtained ω111 = ω222 = 2 x 10-34 cm6s-1 and q2 = 0.9, where ω111 and ω222 represent the rates of three-ion upconversion from 4I13/2 and 4I11/2, respectively, and q2 is the ratio o two-ion up-conversio rates.
In our work, we develop a numerical model for studding the variation of phenomenological and optical parameters in an Er+3 system of 6 excited levels that is subject to a lasing condition. The model is using a four order Runge- Kutta method to solve a system of eight time-dependent variables. The simulations, based on the change of pumping wavelength, prove that the highest efficiency is reached for a 970 nm pump wavelength, concordant with the existing literature results. Different processes, including: three ion-ion up-conversion processes, two pumping processes and the inherent spontaneous transition, are considered.
The possibilities to obtain efficient 3-?m lasing in erbium systems on the self-saturated transition 4/ 11/2?4/13/2 are analyzed. In the frame of the mathematical model based on analytical expressions for population inversion, photon flux density, and quantum efficiency, obtained in the stationary regime, and which explains the main characteristics of 3-?m generation, the influence of various interaction mechanisms such as cross-relaxations, transfer to impurities, excited-state absorption (ESA) and so on is analyzed. It is shown that, although ESA from the terminal laser level could improve the generation characteristics, the driving mechanism for 3-?m erbium lasers is the cooperative upconversion from the terminal laser level.