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High-quality epitaxial layers of heavily doped Yb:KLu( WO4)2 grown on KLu(WO4)2 substrates by liquid phase epitaxy were characterized in terms of lattice mismatch and refractive indexes of the layer and the substrate. The effective refractive indexes of the guided modes that these structures can support were modeled and measured experimentally for the transverse electric (TE) and transverse magnetic (TM) mode excitation by dark m-lines spectroscopy. The upper limit for optical losses in these waveguides corresponding only to scattering processes was estimated to be ~1.5 dB/cm at λ=632.8 nm. These results show that, apart for highly efficient thin-disk laser applications, these epilayers can be used as waveguide devices at wavelengths different from those used to excite Yb3+.