A theoretical analysis upon the four-dimensional (4D) spatio-temporal temperature\ndependent dynamics of 888 nm pumped Nd:YVO4 dual-rod laser is established, which is valid in\nboth continuous-wave (CW) and acousto-optic (AO) Q-switched pulse lasers conditions. Our model\ncan accurately solve the 4D thermal generation and temperature evolution not only in the steady\nQ-switched state, but also in the first few unstable giant or dwarf pulses region. Factors including\nground state depletion (GSD), energy transfer upconversion (ETU), fluorescence branching ratios,\ntemperature-dependent cross sections and nonradiative relaxations processes are comprehensively\nconsidered for precisely estimating thermal effects, valid in both the steady pulse region and the\nunstable region at the beginning. Moreover, temporal and spatial temperature profiles and their\ncoupling effect on output properties at different repetition-rates are discussed. Experiments of\nhigh-power high-repetition-rate 888 nm end-pumped Nd:YVO4 dual-rod CW and AO Q-switched\nlasers are also firstly presented and the experimental results enjoy good consistency with our theory.
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