We have applied a new simplified combination of numerical methods for studying the time and three-dimensional space dependence of quasi-three-level Yb3+:Yttrium Aluminum Garnet (YAG) end-pumped lasers passively Q-switched by a Cr4+:YAG saturable absorber. We base our 3-D model on iterative, efficient, time- and space-dependent numerical propagation of the optical field through the laser cavity. The complex-valued laser field is coupled to the Yb3+:YAG and Cr4+:YAG media via complex optical permittivities, which are subsequently altered by gain/loss intensity saturation. The calculation is simplified using the radial symmetry of the system, with the cavity round-trip time as the smallest increment for updating the permittivities. We also include the effects of field diffraction in an intra-cavity air gap. For specified CW spatial pump conditions, self-consistent repetitively pulsed solutions for the laser field in a flat-flat or flat-convex mirror cavity are found with no ad hoc laser mode size or shape assumptions; these solutions are not Gaussian modes. We concentrate on compact lasers with multi-Watt average output power, operating at modest pulse energy (~1.0 mJ), high repetition rate (~5 kHz) and short pulse duration (~1.5 ns). Typical room-temperature pump-to-laser slope power efficiencies exceeding 50% are predicted, depending on laser pump and cavity loss parameters. Model results agree well with recently published experimental data.

中文翻译：

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紧凑型 Yb³⁺:YAG 端泵浦被动调 Q 激光器的数值多维 (r, z, t) 分析方法

我们应用了一种新的简化数值方法组合来研究准三能级 Yb3+:钇铝石榴石 (YAG) 端泵浦激光器的时间和三维空间相关性，该激光器由 Cr4+:YAG 可饱和吸收体被动调Q。我们的 3-D 模型基于光场通过激光腔的迭代、高效、时间和空间相关的数值传播。复值激光场通过复光学介电常数耦合到 Yb3+:YAG 和 Cr4+:YAG 介质，随后通过增益/损耗强度饱和度进行改变。使用系统的径向对称性简化了计算，腔往返时间作为更新介电常数的最小增量。我们还包括了腔内气隙中场衍射的影响。对于指定的 CW 空间泵条件，在平平或平凸镜腔中找到激光场的自洽重复脉冲解，没有特别的激光模式尺寸或形状假设；这些解决方案不是高斯模式。我们专注于具有多瓦平均输出功率、以中等脉冲能量 (~1.0 mJ)、高重复率 (~5 kHz) 和短脉冲持续时间 (~1.5 ns) 运行的紧凑型激光器。典型的室温泵到激光器斜率功率效率预计超过 50%，这取决于激光泵和腔损耗参数。模型结果与最近公布的实验数据非常吻合。我们专注于具有多瓦平均输出功率、以中等脉冲能量 (~1.0 mJ)、高重复率 (~5 kHz) 和短脉冲持续时间 (~1.5 ns) 运行的紧凑型激光器。典型的室温泵到激光器斜率功率效率预计超过 50%，这取决于激光泵和腔损耗参数。模型结果与最近公布的实验数据非常吻合。我们专注于具有多瓦平均输出功率、以中等脉冲能量 (~1.0 mJ)、高重复率 (~5 kHz) 和短脉冲持续时间 (~1.5 ns) 运行的紧凑型激光器。典型的室温泵到激光器斜率功率效率预计超过 50%，这取决于激光泵和腔损耗参数。模型结果与最近公布的实验数据非常吻合。