A waveguide is fabricated by first preparing two waveguide precursor pieces. Each waveguide precursor piece includes a single-crystal substrate, and an epitaxial coating layer of an oxide coating material on the substrate. The oxide substrate material preferably comprises yttrium as a substrate-material cation, and the oxide coating material preferably comprises a coating-material cation selected from the group consisting of ytterbium, thulium, erbium, and holmium. The two substrates are placed together with the coating layers in contact to form a precursor structure. The precursor structure is heated to an elevated diffusion temperature so that the coating layers bond together and the coating materials and the respective substrate materials interdiffuse to form the waveguide having an interdiffused region. A laser beam may be directed through the interdiffused region, while the interdiffused region is optionally optically pumped through one or both of the substrates.