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Embedded channel waveguides formed on a z-cut erbium-doped lithium niobate (Er:LiNbO3) substrate by a high-energy ion implantation technique are first described. A detailed theoretical design of a waveguide laser for continuous wave operation is then discussed, taking into account realistic input parameters and measured data. To simulate waveguide modes and to predict laser outputs from our fabricated waveguide sample, a numerical tool is developed in FORTRAN based on the full vectorial finite element method. Using the developed tools, the waveguide dimension is optimized, ensuring single-mode operation at both pump (980 nm) and laser (1531 nm) wavelengths. Finally, laser outputs as a function of various waveguide parameters are analyzed. The proposed analysis allows the effective optimization of the ion-implanted waveguide laser in Er:LiNbO3.