  We report the fabrication and characterization of a
Ti$^{4+}$:Tm$^{3+}$:LiNbO$_3$ optical waveguide in view of photon-echo quantum
memory applications. In particular, we investigated room- and
cryogenic-temperature properties via absorption, spectral hole burning, photon
echo, and Stark spectroscopy. We found radiative lifetimes of 82 $\mu$s and 2.4
ms for the $^3$H$_4$ and $^3$F$_4$ levels, respectively, and a 44% branching
ratio from the $^3$H$_{4}$ to the $^3$F$_4$ level. We also measured an optical
coherence time of 1.6 $\mu$s for the $^3$H$_6\leftrightarrow{}^3$H$_4$, 795 nm
wavelength transition, and investigated the limitation of spectral diffusion to
spectral hole burning. Upon application of magnetic fields of a few hundred
Gauss, we observed persistent spectral holes with lifetimes up to seconds.
Furthermore, we measured a linear Stark shift of 25 kHz$\cdot$cm/V. Our results
are promising for integrated, electro-optical, waveguide quantum memory for
photons.
