Abstract
We have applied a new simplified combination of numerical methods for studying the time and three-dimensional space dependence of quasi-three-level Yb <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> :Yttrium Aluminum Garnet (YAG) end-pumped lasers passively Q-switched by a Cr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+</sup> :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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> :YAG and Cr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4+</sup> :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.
Highlights
A CTIVELY Q-switched Yb3+:Yttrium Aluminum Garnet (YAG) lasers [1] have evolved into so-called micro-lasers or microchip lasers of Yb3+:YAG passively Q-switched by Cr4+:YAG saturable absorbers [2]–[4]
The results presented below for non-uniformly pumped, passively Q-switched lasers show a much closer qualitative resemblance to such gain guided Bessel modes than to Gaussian modes (Fan [11] refers to such generic modes in Yb3+:YAG as “aperture guided”; we prefer the historical precedent of “gain guided”, originally applied to modes in oxide-stripe semiconductor lasers [12])
We summarize our simple procedure, which combines the results of finite-difference beam propagation method (FD-BPM) with a round-trip time-step for media alteration: (1) the laser fields are propagated for one cavity round-trip(here using radial FD-BPM, rather than diffraction integrals), (2) the laser’s media are perturbed by the resulting local field intensities and heating, and (3) the altered media affect the iteration of round-trip field propagation
Summary
A CTIVELY Q-switched Yb3+:YAG lasers [1] have evolved into so-called micro-lasers or microchip lasers of Yb3+:YAG (or their ceramic variants) passively Q-switched by Cr4+:YAG saturable absorbers [2]–[4]. In the present work we incorporate both the effects of gain and thermal mode confinement in a simultaneous unified approach using a finite-difference beam propagation method (FD-BPM) We contrast this method with “dynamic multimode analysis”[21]–[23] in which a commercial modeling package provides tools for multi-transverse-mode Gaussian expansion of the laser field to investigate laser dynamics. These modal expansion analyses did not include our regime of CW-pumping with passively-Q-switched self-pulsing operation. We present a similar, but simplified, version of a numerical, iterative FD-BPM solution and include the Q-switched pulse dynamics, without the previous concerns [26] for finding the resonant frequencies of the modes, which adds computational burden. These characteristics required a greatly revised calculation mesh configuration, and the development of the improved algorithm and time-step iteration strategy
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