Modeling the Dynamic Emission of a Polarized $Cr^{4+}:YAG$ Crystal Investigated by Double-Pulse Pumping Generated by a Nd-Laser

A mathematical model describing the dynamic emission of intracavity polarized isotropic $Cr^{4+}:YAG$ solid-state saturable absorber was developed. This model considers double pumping laser pulses to simulate the actions of $Cr^{4+}:YAG$ as a dual Q-switched crystal (1.06 μm) and lasing medium (1.4 μm). The model describes the time evolution of interaction between the pumping laser pulse, partial polarizer and the polarized saturable absorber. The analysis of the polarization process is based on the assumption that at each moment of lasing evolution, the state of polarization represented by an eigenstate corresponds to the lowest radiation losses state. The model offers a simple mechanism for studying the kinetics of the pulsed lasers and the influence of the variations of the pumping laser power and nonlinear anisotropy parameter on the characteristics of the output laser pulses 1.06 μm and 1.4 μm. The angular rotation of the passive switch $Cr^{4+}:YAG$ reveals that the transmission of the polarized 1.06 μm laser radiation is strongly anisotropic in the saturation regime. The suggested model estimates the transmission of pumping laser density of the polarized light 1.06 μm radiation as a function of nonlinear anisotropy parameter, temporal behavior of the relative population inversion of Nd-laser, population inversion of the different polarized levels of $Cr^{4+}:YAG$ pulsed laser and the output laser pulse densities under impact of different values of the nonlinear anisotropy which is due to the self-induced anisotropy of its saturated absorption.