## 3 Results and Discussion  
### Planar Waveguide Characterization--Induced Refractive Index Changes  
The penetration depth of the ions into the crystal during implantation can be calculated using the 'Stopping and Range of Ions in Matter' (SRIM) code [24]. For our implantation parameters, it was found to be approximately 6.5 \(\upmu\)m. Implanted ions lead to structural changes, i.e., to electronic defects (in the entire implanted area) and to crystal amorphization due to collisions with nuclei (in a narrow area around 6.5 \(\upmu\)m depth), resulting in RI changes that lead to the formation of planar waveguides.  
Samples Pr:YLF-1, Pr:YLF-2, and Pr:YLF-3 had similar prism coupler mode spectra, indicating that the measured RI changes for both polarizations already occurred at the lowest implantation dose of 2 \(\times\) 1014 ions/cm\({}^{2}\) and was quickly saturated for higher doses. The surface of Pr:YLF-4, however, was damaged, presumably due to the high implantation dose, so no guided modes could be excited with the prism coupler in this sample.  
The measured mode spectra for TM and TE polarizations for the Pr:YLF-3 sample are shown in Figures 3a and 3c, respectively, as examples. As can be seen, the first four lower-order TM-polarized modes have effective refractive indices \(n_{\text{eff}}\) higher than the respective bulk index \(n_{\text{o}}\), which is marked with a vertical red dashed line in Figure 3a. The corresponding mode dips are deep and narrow so that good confinement and low waveguide losses are expected. The effective indices of all TE-polarized modes are lower than the bulk index \(n_{\text{e}}\); thus, they are guided only due to the formation of a lower-index barrier located at the stopping range [4; 5] of implanted C\({}^{3+}\) ions. In Figure 3c, the TE mode dips are shallower and broader than those for TM polarization, indicating that the TE-polarized modes are relatively weakly guided and lossy.  
Since the built-in inverse Wentzel-Kramers-Brillouin (iWKB) solver of the prism coupler could not accurately reconstruct the complex RI profiles containing an optical barrier, a Matlab mode-solver code [25] was used. The RI profiles for TE and TM polarizations with the best match of the calculated mode indices with the measured ones for the first eight modes were found by varying the RI and width of the guiding layer in the simulation as well as the depth and width of the optical barrier (under its Gaussian shape assumption) (see Figure 3b,d). The near-surface RI of the guiding layer was found to be 1.469 for both polarizations, which is 0.012 higher than the \(n_{\text{o}}\) and 0.010 lower than the \(n_{\text{e}}\) bulk indices [26]. The optical barrier minimum is located at a 6.2 \(\upmu\)m depth, which is in good agreement with the SRIM calculation, and its width is slightly larger for TE-polarized light. Also, the barrier RI minima depth increases with the ion dose.  
Upon annealing, no significant changes in the waveguiding properties were observed for temperatures of up to 200 \({}^{\circ}\)C. After annealing at 250 \({}^{\circ}\)C, the mode spectra changed for both polarizations for the Pr:YLF-1 sample with the lowest ion dose, which was the first sample annealed at this temperature. These changes indicate that, although the optical barrier at the ions' stopping range is still preserved, the crystal structure in the guiding layer starts to return to its original birefringent state. To preserve the waveguiding properties  
Figure 2: A schematic of the experimental setup for small-signal gain measurements. BS: beam splitter; \(\lambda/2\): half-wave plate; DM: dichroic mirror; M: mirror; L\({}_{1}\), L\({}_{2}\): lenses; F: long-pass filter; P: polarizer; PM: power meter.  
of the Pr:YLF-2 and Pr:YLF-3 samples implanted with higher ion doses, annealing was stopped after the 200 \({}^{\circ}\)C step.