Fig. 1. (a), (b) Schematic and corresponding photo of the dual-confocal Yb:KGW ring cavity. M1 and M2 have a radius of curvature (ROC) of 50 mm. M2 also acts as the OC with transmittance of 1% and 2% in two configurations. M3 and M4 have an ROC of 30 mm and provide the total GDD of –1200 and –1100 fs² in two different experiments. (c) Laser beam radius throughout the whole ring cavity, in which the green area marks the position of the gain crystal. (d) Detail of the beam radius inside the gain crystal.

Fig. 2. Flowchart of the simulation. The cavity mode is calculated by using q parameters, and the q parameters at different intracavity peak power K are calculated iteratively in steps of ΔK. In this way, we can obtain the cavity mode at any K according to Equation (7). In this process, the introduced nonlinear Kerr effect and the resonant cavity form the nonlinear ABCD matrix, where the calculation of the Kerr effect in the crystal is not equated to a thin lens. The laser crystal is split into a series of slices with a thickness of ΔL that is much less than the Rayleigh range, and the laser beam size in the crystal is calculated in an iterative manner, which avoids the coupling of the laser intensity and laser mode in the crystal.

Fig. 3. (a)–(d) The stability maps are simulated at various normalized intracavity peak powers of K = 0, 1, 1.5 and 2. Here, z is the distance between the concave mirrors on both sides of the crystal, and x is the displacement between the laser waist and the center position of the crystal (see Figure 1(a)). The absolute value of δ_K increases gradually when it is closer to the edge of the inner stability at K = 0. However, at K = 1, 1.5 and 2, δ_K always maintains a large value within a certain regime, which offers us a direction in our quest for the KLM regime. (e), (f) Variation of the δ_K parameter and the mode matching ratio η with the intracavity peak power K for some fixed configurations, indicating that the best intracavity peak power varies with z; the various configurations have different optimal values of δ_K and η, leading to a different K.

Fig. 4. Mode-locking characterization of the 1.64-GHz dual-confocal ring Yb:KGW oscillator with a 1% OC. (a) Optical spectrum of the mode-locked pulses centered at 1049 nm, with a full-width at half-maximum (FWHM) bandwidth of 5 nm. (b) Intensity autocorrelation trace with sech²-fitting of 269 fs indicated by the red curve and measured data with blue dots. Inset, autocorrelation trace measured in a 50 ps delay span. (c) Radio frequency spectrum of the fundamental repetition at 1.64 GHz and the harmonics within a 10 GHz span at 10 kHz RBW.

Fig. 5. Simulations of the 1.64-GHz dual-confocal ring Yb:KGW oscillator with a 1% OC. (a) The variation with the intracavity peak power K of the pump waist, laser waist and the mode matching ratio η at the position of Kerr-lens mode locking. (b) The variation of η and the |δ_K| parameter with the intracavity peak power K at the position of Kerr-lens mode locking.

Fig. 6. Simulations of the 1.68-GHz dual-confocal ring Yb:KGW oscillator with a 2% OC. (a) The parameters η and δ_K as a function of the intracavity peak power K for four fixed configurations. (b) The variation of η and the δ_K parameter with the intracavity peak power K at the position of Kerr-lens mode locking.

Fig. 7. Mode-locking characterization of the 1.68-GHz dual-confocal ring Yb:KGW oscillator with a 2% OC. (a) The optical spectrum of bidirectional and unidirectional Kerr-lens mode locking, where the inset is the near-field beam profile of unidirectional KLM operation. (b) Intensity autocorrelation trace with sech²-fitting of bidirectional and unidirectional KLM operation. (c) Radio frequency spectrum of the fundamental repetition at 1.68 GHz and the harmonics within a 10 GHz span at 10 kHz RBW.