Theory of variable-ratio power splitters using multimode interference couplers

In this letter, we analyze the integrated optical N x N generalized Mach-Ze hnder interferometer (GMZI) employing multimode interference (MMI) couplers . A transfer matrix is used to derive analytic expressions for the intensit y distribution at the output ports of the GMZI as a function of the phase s hifts applied to the arms. These expressions form a system of nonlinear equ ations which are numerically solved for the phase shifts, enabling a new in terpretation of the GMZI as a variable-ratio power splitter. The performanc e of the GMZI has been simulated, and it is found that the power splitting ratio is tolerant to both the accuracy of the applied phase shifts and to f luctuations in wavelength.