Study Of Passively Q-switched Rate Equation Theory Based On Tm-doped Laser Crystal

Laser-diode (LD) pumped passively Q-switched all-solid-state laser has attractive features, such as all solid-state, compact structure, high repetition rate, and short pulse width. The output pulse with high repetition rate and short pulse width is of great interest in the fields of remote ranging, 3-dimensional imaging, and environmental monitoring. LD pumped 2μm lasers with high repetition rate and high average power have extensive applications for eye-safe remote sensing, laser ranging, coherent Doppler radar and medicine.In this paper, Cr²⁺:ZnSe saturable absorber is employed as a Q-switched crystal in the passively Q-switched laser. The operating performances of the passively Q-switched laser based on Tm³⁺-doped laser crystal are investigated theoretically. Taking into account the excited-state absorption of the saturable absorber, the system of rate equations of the Cr²⁺:ZnSe passive Q-switched Tm³⁺-doped laser is established. In the case of plane-wave approximation for the intracavity field distribution, the system of rate quations is solved analytically. The analytical fomulas of the pulse energy, the peak power and the pulse width are obtained, which clearly show the dependence of the pulse operating performance on the system parameters. The corresponding numerical calculations are carried out in detail. In order to analyze the characteristics of the laser output more accurately, the system of rate equations are made nessesary modifications by considering the spatial distribution of intracavity photon density, population inversion of gain medium and the population density of ground-state and excited-state in Cr²⁺:ZnSe Q-switched crystal. Through numerically solving the modified rate equations, the influences of the parameters involving the gain medium, the Q-switched crystal, and the resonator, as well asω_Plω_L, on the output lase pulse are studied.According to the pumping and Q-switched mechanisms of Cr²⁺:ZnSe passively Q-switched Tm³⁺,Ho³⁺ codoped all-solid-state lasers, the simplified rate equations are estabilished. For the different pump extations, the output pulse shape and the tempral dynamics of pulse operation are numerically simulated. The saturable behavior of Tm³⁺,Ho³⁺ codoped laser crystal is also studied. The evolutions of population at Ho³⁺ up-level with the pump intensity are simulated with and without the Tm³⁺-Ho³⁺ upconversion effects. Cosequently, the saturable threshold of pump intensity is obtained and the influence of Tm³⁺-Ho³⁺ upconversion on 2μm laser is discussed. The influences of the relavant parameters, involving the reflectivity of output mirror R, the lengths of the gain medium l and the Q-switched crystal l_s, on the characteristics of output pulse are analyzed in detail. The obtained results are very helpful to further comprehend the effects of the system parameters on the performances of the passively Q-switched laser, and provide nessesary guidance for the oprimization of laser design parameters.