Analysis of Generalized Mach–Zehnder Interferometers for Variable-Ratio Power Splitting and Optimized Switching

The nonideal integrated optical N x N generalized Mach–Zehnder interferometer (GMZI) employing multimode interference (MMI) couplers is analyzed using transfer matrix techniques. Deviations in the phase relations and the power splitting ratio of the MMI couplers are included in the theory, along with the effects of phase errors in the interferometer arms. The predictions of the theory are compared to the response of a 4 x 4 GMZI which has been fabricated. The device is operated as both a variable-ratio power splitter and a switch by compensating for the phase errors in the interferometer arms, but the performance is ultimately limited by the nonideal imaging in the MMI couplers. The practicality of these applications is investigated by performing a tolerance analysis for the operation of 1 x N power splitters and switches for N up to 10.