N×N Multimode interference(MMI) couplers are investigated. The mode field transmitting matrix based on the phase relations in MMI couplers is introduced to analyze the MMI couplers. Field transmitting equations of MMI couplers, phase shifter and Mach-Zehnder interferometer (MZI) optical switches are derived. The driving conditions of MZI switches for different switching situations are obtained by solving the field transmitting equations. The design of 4×4 switch is completed for a promising silicon-on-insulator waveguide structure.