## 1 Introduction  
Optical waveguides are the basic building blocks of integrated photonics and enable the miniaturization and integration of passive and active optical devices. Various techniques can be used to produce waveguides, among them being femtosecond (fs) laser inscription [1], UV light illumination [2], high-energy ion implantation [3, 4, 5, 6], metal ion in-diffusion [7], and proton exchange [8]. Ion implantation is a unique and relatively universal technique for producing optical waveguides by changing the refractive index (RI) in the surface region of a material. Implanted high-energy ions, both light ions such as protons (H\({}^{+}\)) and helium (He\({}^{+}\)) and swift-heavy ions such as silicon (e.g., Si\({}^{++}\)) and carbon (e.g., C\({}^{3+}\)), interact with electrons and/or nuclei in the near-surface region of a material. This can lead to the formation of planar waveguide structures through local RI changes. This technique has been used to create well-defined guiding structures in a variety of crystalline and amorphous materials [4].  
Due to their optical transitions in the visible region, crystals doped with rare-earth (RE) ions, e.g., praseodymium, samarium, or europium, have been used as active media for solid-state lasers operating in that spectral region [9, 10]. Among these ions, trivalent praseodymium (Pr\({}^{3+}\)) is of particular interest due to its high absorption cross-section of more than \(10^{-19}\) cm\({}^{2}\) for blue pump light that can be provided by readily available InGaNlaser diodes and because its emission spectrum includes several strong lines in the visible region [9, 11, 12]. First compact Pr\({}^{3+}\) waveguide lasers in different host crystals have been successfully demonstrated using fs laser inscription, for example, in SrAl\({}_{12}\)O\({}_{19}\)[13], YLiF\({}_{4}\) (YLF) [14, 15, 16], or LiLuF\({}_{4}\)[17]. Furthermore, planar Pr\({}^{3+}\) waveguide lasers have been realized by the epitaxial growth of Gd and Lu co-doped YLF layers on YLF substrates [18]. Although these waveguide lasers enabled optical powers in the watt range, there are limitations concerning the photonic integration of fs-laser-written and planar epitaxially grown waveguides. Due to the small RI change, which is typically in the range of 10\({}^{-4}\)[19], the minimum bending radius of fs laser-inscribed waveguides is rather limited to centimeters [20], which is much larger than the desired sub-millimeter range. Smaller bending radii could be achieved in ridge waveguides with crystal-to-air interfaces, but such structures cannot be fabricated by diamond blade dicing since this fabrication technique is limited to straight structures. However, they could be fabricated using other methods like chemical mechanical polishing [21], fs laser ablation [22], or (ion beam) etching [23], which is yet to be developed for YLF.  
In this work, we report on the fabrication of diamond blade diced ridge waveguides in swift-heavy carbon ion (C\({}^{3+}\))-implanted Pr:YLF crystals. The RI changes in the near-surface region were quantitatively investigated for different ion implantation doses. The waveguide propagation losses were characterized for both TE and TM polarized light. Fluorescence spectra and fluorescence lifetime characteristics in the ridge waveguides were investigated and compared to those of a bulk Pr:YLF crystal. Small-signal optical gain at the orange and red fluorescence lines was achieved under pumping waveguides with a frequency-doubled laser at a 444 nm wavelength.