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

Abstract

We have applied a new simplified combination of numerical methods for studying the time and threedimensional 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.

Experimental and Modeled Output Characteristics of a Compact, Passively Q-Switched Tm:YLF Laser

“…The methods we use to model the Tm:YLF PQSL are based on those described in [17] for a Yb:YAG PQSL with smaller and simpler cavity configuration. A finite-difference version of the Helmholtz equation is used to calculate how a singlewavelength laser field propagates with diffraction in the optical cavity of Fig.…”

“…Each incremental longitudinal propagation step of the laser field in the cavity uses an efficient numerical solution of a finite-difference tri-diagonal matrix equation, which includes the local complex optical permittivity. The details of this finitedifference method are more fully described in [17]. After the field propagates a full round trip in the laser cavity, the permittivities are updated using the material rate equations and local optical intensities.…”

“…For calculation purposes, we assume wide, radial, super-Gaussian apodizations of the VBG and output-coupler reflectance. These help suppress edge build-up of numeric laser field artifacts from the slightly imperfect transparent boundary conditions of the wider mode [17].…”