Correction of phase errors in multimode interference couplers using rectangular surface-relief grating

Performance of multimode interference couplers is constrained by the phase errors caused by the deviations of the modes propagation constants from the required quadratic dependence upon mode number. In this work, we show that by creating a rectangular grating on the top surface of the coupler with a spatial frequency matching the intensity distribution of the i-th order mode, it is possible to control the phase errors of all spatial modes up to the i-th order. The effect of the grating on the propagation constants of higher-order modes is studied using perturbation-based and strict vector calculus. The efficacy of the method was demonstrated using numerical examples of an MMI-based two-mode (TE0 and TE1) coupler in the 1.31 mu m wavelength region and the singlemode (TE0) 1.31/1.55 mu m wavelength splitter, both made of medium index contrast material (TiO2:SiO2).