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.