We present a design approach for compact reconfigurable light routers with N access waveguides (WGs) based on multimode interference (MMI) couplers. The proposed devices comprise two MMI couplers, which are employed as power splitters and combiners, respectively, linked by an array of N single-mode WGs. When the effective refractive index of the WGs is modulated with the proper relative optical phase difference, the light can switch paths between the preset output channel and the remaining output WGs. Taking advantage of the transfer phases between the access ports of the MMI couplers, we derive very simple phase relations between the modulated WGs that enable the reconfiguration of the output channel distribution when the appropriate coupling lengths of the MMI couplers are chosen. In this way, very compact expressions for calculating the channel assignment of the devices as a function of the applied phase shift are derived for the general case of N access WGs. Moreover, the situation where the applied phase shift varies sinusoidally, as in acoustically driven devices, is discussed. A transfer matrix formalism is employed to calculate the transmission properties of the routers. In particular, devices with six and seven access WGs are thoroughly described.
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