Theory of variable-ratio power splitters using multimode interference couplers

In this letter, we analyze the integrated optical N/spl times/N generalized Mach-Zehnder interferometer (GMZI) employing multimode interference (MMI) couplers. A transfer matrix is used to derive analytic expressions for the intensity distribution at the output ports of the GMZI as a function of the phase shifts applied to the arms. These expressions form a system of nonlinear equations which are numerically solved for the phase shifts, enabling a new interpretation of the GMZI as a variable-ratio power splitter. The performance 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 fluctuations in wavelength.