# Continuous-Wave and Mode-Locked Operation of an In-Band Pumped Tm,Ho,LuCaGdAlO4 Laser
## 3 Continuous-Wave (CW) Laser Results  
The CW laser performance of the Tm,Ho,Lu:CALGO crystal was studied with the four mirror laser cavity shown in Figure 2. The pump waist radius in the position of the crystal was measured to be \(w_{\rm P}\) = 18 \(\upmu\)m in both planes. The values for the laser beam radius calculated by the ABCD formalism were \(w_{\rm L}\) = 33 and 36 \(\upmu\)m in the sagittal and tangential planes, respectively. The single pass pump absorption was estimated under lasing conditions by measuring the residual power behind M\({}_{2}\). It depended only weakly on the OC transmission \(T_{\rm OC}\) and varied from 66.2% to 85.9%, as a function of the incident power (due to the recycling effect), as shown in Figure 3a. Five different OCs were used to evaluate the laser performance in the CW regime, as shown in Table 1 and Figure 3b. The lowest threshold for CW operation was 124 mW with respect to the absorbed pump power using the lowest \(T_{\rm OC}\) = 0.2%. A maximum output  
Figure 3: (**a**) Single pass pump absorption under lasing conditions vs. OC transmission, \(T_{\rm OC}\); (**b**) input-output characteristics of the CW Tm,Ho,Lu:CALGO laser for different OCs. The laser is naturally \(\pi\)-polarized (vertical). Figure 2: Experimental set up of the CW Tm,Ho,Lu:CALGO laser. Pump laser: Raman-shifted Er Fiber Laser (FL); L\({}_{1}\): AR coated plano-convex lens (\(f\) = 75 mm); M\({}_{1}\)-M\({}_{2}\): concave dichroic mirrors (Radius of Curvature, RoC = \(-\)100 mm); M\({}_{3}\): flat rear total reflector; OC: wedged output coupler. PBS: polarization beam splitters. HWP: half-wave plate. power of 524 mW was obtained with the highest 5% OC at an absorbed pump power of \(\sim\)2.04 W, corresponding to a slope efficiency of \(\eta=27.9\%\). The laser output spectra shown in Figure 4a were measured with a resolution better than 1 nm. The laser central wavelength in the CW regime varied with the transmission of the OC from 2079 to 2087 nm. This wavelength shift is expected for the three-level laser systems of Tm\({}^{3+}\) and Ho\({}^{3+}\), where reabsorption increases at lower inversion rates when using lower OC transmission, and it is also in line with the gain spectra for \(\pi\)-polarization. All CW laser results for the different OCs are summarized in Table 1.  
The total round-trip resonator losses \(\delta\) (reabsorption losses excluded), as well as the intrinsic slope efficiency \(\eta_{0}\) (accounting for the mode matching and quantum efficiencies), were estimated with the Caird analysis [25] by fitting the measured slope efficiency as a function of the OC reflectivity \(R_{\text{OC}}\). The fitting results and the best fit curve are shown in Figure 4b, giving the values of \(\eta_{0}=38.1\%\) and \(\delta=1.3\%\). The above CW laser wavelengths are above the limit of \(\sim\)2075 nm established in previous experiments with 800 nm pumping [23], below which the naturally selected polarization switches from \(\pi\) to \(\sigma\) due to the rather close combined gain cross sections for the two principal polarizations [22]. Indeed, we established that in all cases the output polarization of the CW Tm,Ho,Lu:CALGO laser was parallel to the crystal \(c\) axis. The wavelength tuning performance of the Tm,Ho,Lu:CALGO laser in the CW regime was studied by inserting a Lyot filter (3 mm thick quartz plate with a diameter of 20 mm and the optical axis at 60\({}^{\circ}\) to the surface) in the arm containing the OC, at an incident pump power of 2.5 W (pump \(\pi\)-polarization). The Brewster angle of the Lyot filter was in the horizontal plane so that it enforced laser oscillation in \(\sigma\)-polarization. The recorded tuning curves are shown in Figure 5a,b for two different OCs. They are rather smooth and without any gaps. A maximum wavelength tuning range of 160 nm at the zero level, from 1984 to 2144 nm, was obtained with the 0.2% OC. A slightly narrower wavelength tuning range of 158 nm, from 1985 nm to 2143 nm, was obtained with the 0.5% OC, which provided higher output power.