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Three-waveguide optical switches are analyzed by means of the coupled mode theory. Assuming that three approximate waveguides of an optical switch are identical and equally spaced, we examine the switching behavior for cases where an incident beam is launched into (1) an outer waveguide and into (2) a center waveguide. For each beam-launching case, switching voltage is applied so that the overall index profile is detuned (1) symmetrically or (2) antisymmetrically. It is concluded that only three types of optical switches out of these four configurations can perform the switching operation. We derive the switching conditions for each of three possible types and draw the corresponding switching diagrams.