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Acta Physica Polonica A

Modeling the Dynamic Emission of a Polarized Cr4+:YAG Crystal Investigated by Double-Pulse Pumping Generated by a Nd-Laser

Basem Abdul Ghani, M. Hammadi

Published May 1, 2009• 2 citations

Abstract

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.

DOI: 10.12693/aphyspola.115.873

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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.

A model of degenerate four-wave mixing (DFWM) in Cr4+:YAG saturable absorbers is given in the transient regime. Because of the presence of absorbing dipoles oriented along specific directions, the DFWM process exhibits an anisotropic behavior. The effects of pump beam fluences, relative polarization of the beams, crystal orientation, absorbance, excited-state absorption, and nonresonant losses are analyzed. The theoretical results are supported by DFWM experiments in Cr4+:YAG performed at 1.06 µm with nanosecond pulses.

We studied both experimentally and theoretically the transmission and polarization characteristics of a Cr4+ : YAG saturable absorber crystal as a function of the intensity and polarization state of an incident laser beam. We found that a birefringent absorption behaviour is induced and we show that the experimental results are well described by a full numerical model which includes excited-state absorption as well as a ground-state cross-absorption term. By using pump-probe measurements we show that a finite cross-saturation of the absorption is achieved along the crystal axes orthogonal to the polarization of the optical radiation. No induced refractive index birefringence is observed.

Polarization dependence of saturable absorption in Cr4+:YAG was investigated. We theoretically proposed its general analytical formula expressed in terms of the intensity and the polarization angle of the pump beam. We also derive transmission formulas for specific incident surfaces of (100)-, (110)-, and (111)-planes. In order to prove our model, we examined the polarization dependence in the transmittance of (110)-cut Cr4+:YAG. With the consideration of pump depletion in Cr4+:YAG, we succeeded to explain the polarization dependence that is consistent with past spectroscopic parameters of Cr4+:YAG.

We describe a systematic, rigorous procedure for the determination of the optical absorption saturation parameters for Cr4+:YAG and Cr4+:forsterite crystals at 1064 nm. A rate-equation approach was used to analyze the cw and pulsed transmission data of several crystals by accounting for the transverse as well as longitudinal variation of the beam intensity, saturation effects, and excited-state absorption. Use of an iterative procedure whereby the cw and pulsed data were simultaneously analyzed led to a considerable reduction in the error for the determination of cross sections. The average value of the absorption cross section sigmaa and the normalized excited-state absorption cross section fp=sigmaesa/sigmaa were determined to be 6.13×10−19 cm2 and 0.45, respectively, for Cr4+:forsterite and 19.6×10−19 cm2 and 0.06, respectively, for Cr4+:YAG. Detailed comparison was also made with previous saturation measurements in the literature. Our results further show that lumped models based on the thin-length approximation should be used with caution in the determination of cross sections, especially when the pump beam is tightly focused inside the absorber.

An investigation was made of changes in the profile and state of polarisation of a short (25 ns) resonant light pulse (λ ~ 1.06 μm) during its propagation in a YAG : Cr4+ crystal. The experimental results were in good agreement with a theory in which the absorption of light by the Cr4+ impurity centres in a YAG crystal is described phenomenologically as a consequence of the interaction of light with three orthogonal groups of resonant linear dipoles. The result demonstrated the fleasibility of controlling the profile of a light pulse propagating through polariser — YAG : Cr4+ crystal — polariser system. The application of a single-frequency pulse to this system generated output pulses with two or three intensity maxima. This was a direct result of a self-induced change in the state of the polarisation of the light in the YAG : Cr4+ crystal at the saturation absorption stage.