Numeric Multi-Dimensional (r, z, t) Analysis Method for Compact Yb³⁺:YAG End-Pumped, Passively Q-Switched Lasers

We have applied a new simplified combination of numerical methods for studying the time and three-dimensional space dependence of quasi-three-level Yb
³⁺
:Yttrium Aluminum Garnet (YAG) end-pumped lasers passively Q-switched by a Cr
⁴⁺
: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 Yb
³⁺
:YAG and Cr
⁴⁺
: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.