## 3 Results and Discussion
### Ridge Waveguide Characterization  
A scanning electron microscope (SEM) image of the ridge waveguides in sample Pr:YLF-3 is shown in Figure 4. The ridges are smooth without chipping and a shape close to a rectangle. However, the polishing cut of the facet, shown in the left inset of Figure 4, reveals a striped pattern, i.e., the end facets as well as the ridge side walls are not as smooth as, e.g., those of the diced LN ridge waveguides [8]. Better surface quality is expected in the future via optimized dicing parameters for YLF. The striped pattern is attributed to blade roughening during cutting. Thus, the choice of a different blade or sandwiching the Pr:YLF sample between two sacrificial LN substrates along the cut direction for dressing and guiding the blade might yield better results.  
Figure 4: A three-dimensional scanning electron microscope (SEM) image of two ridge waveguides in Pr:YLF-3. Left inset: details of the end facet of a 22 μm wide waveguide. Right inset: the output mode intensity profile of this ridge waveguide at a 632.8 μm wavelength.  
Figure 3: (**a**,**c**) Mode spectrum (intensity vs. refractive index) of waveguide Pr:YLF-3 for TM (\(n_{\mathrm{o}}\)) and TE (\(n_{\mathrm{e}}\)) polarization, measured at 532 μm wavelength. Respective bulk indices are indicated by red dashed lines. (**b**,**d**) Reconstructed refractive indices of planar waveguides (blue) and intensities of fundamental modes at 532 μm wavelength (red). Effective indices of first six modes for each polarization are shown with black horizontal lines.  
Waveguiding with good confinement of the guided modes was observed in sample Pr:YLF-3. The waveguides of sample Pr:YLF-2 had higher losses, possibly caused by weaker confinement because of the shallower optical barrier. Thus, only sample Pr:YLF-3 was analyzed with respect to waveguide losses and optical gain. To determine the in-coupled power, the measured incident power was corrected for the Fresnel loss of 0.15 dB at each waveguide facet, and for the coupling efficiency, it was estimated to be between 30% and 40% depending on the ridge width, with higher values for narrower waveguides. Through a comparison with the setup transmission without the sample, the propagation losses were estimated. The inset on the right side of Figure 4 shows a mode guided in a 22 um wide ridge waveguide. The guided mode is very broad as the waveguide is in multimode in the lateral direction because of the chosen ridge width.  
In this way, propagation losses of 0.4-2.9 dB/cm and 6.2-9.5 dB/cm were calculated in Pr:YLF-3 for TM and TE polarizations, respectively. Narrower waveguides had higher loss values for both polarizations, which can be explained by the stronger influence of the side wall roughness on propagation loss for such waveguides. The higher losses for TE-polarized light can be explained by the different guiding mechanisms. As observed during the prism coupler measurements, here, a barrier waveguide is formed. Modes of barrier waveguides naturally leak into the substrate. For TM polarization, the lowest propagation loss of 0.4 dB/cm was found for a 22 um wide ridge waveguide. Compared to ion-implanted waveguides in other materials, this value is among the lowest reported losses and is comparable to those achieved in titanium-diffused diamond blade diced ridge waveguides or in fs laser-inscribed waveguides [8; 19].