Planar optical waveguides which have a higher refractive index than that of substrate were fabricated by proton exchange between $Li^+$ and $H^+$. Benzoic acid was used as proton source and process was carried out under the various reaction time and temperature. The depth of waveguide layer and the generated mode number were investigated by standard prism coupler. The cut-off depth for the fabrication of single mode optical waveguides was obtained by the function which was expressed on refractive index profile. Finally the experimental conditions for cut-of depth of single mode could be confirmed. Channel waveguides were manufactured from these confirmed conditions and the effective confinement of the induced light into waveguides was observed.