Analyzing the Intracavity Frequency Doubling of the Simultaneous Q-Switched Mode-Locked Diode-Pumped Pulsed Nd3+ Laser with Cr4+:YAG as a Polarized Saturable Absorber

The intracavity frequency doubling of a simultaneous passively Q-switched mode-locked diode-pumped Nd3+ laser is studied with a polarized isotropic Cr4+:YAG saturable absorber. A general recurrence formula for the mode-locked pulses under the Q-switched envelope at a fundamental wavelength has been reconstructed in order to analyze the temporal shape behaviour of a single Q-switched envelope with mode-locking pulse trains. This formula has been derived taking into account the impact of the intracavity frequency doubling and polarized Cr4+:YAG saturable absorber (the Fresnel losses). The presented mathematical model essentially describes the self-induced anisotropy appearing in the polarized Cr4+:YAG in the nonlinear stage of the giant pulse formation. For the anisotropic Nd3+:YVO4 active medium, the generated polarized waves are fixed through the lasing cycle. Second harmonic peak power, pulse width, pulse duration, shift pulse position of central mode and rotational angle as a function of the absorber initial transmission are estimated. The calculated numerical results are in good qualitative and quantitative agreement with the available experimental data reported in references.