In this thesis, passive and active 3-branch Ti:LiNbO$ sb3$ waveguide devices were investigated. A multimode field-matching technique was employed to predict the power division in a passive 3-branch waveguide power divider. The limitation and range of validity of this method were pointed out. An alternative method was also employed to predict the power division when coupling between two neighbouring branches is not negligible, as is the case when the branching angle becomes small. The multimode field-matching method was also employed to predict the power division in an active 3-branch waveguide switch, where switching is achieved through the electrooptic effect of LiNbO$ sb3$. The edge effect of the electrodes on the beam steering was also considered. A linear mode-confinement modulator was then proposed and investigated as a derivative of the 3-branch waveguide switch.