Reflection and Transmission Spectra of Multimode Interference Devices With Bragg Gratings

We numerically investigate the reflection and transmission spectra of multimode interference (MMI) devices incorporating uniform and sampled Bragg gratings with emphasis on their applications to an add-drop multiplexer (ADM). In numerical analysis, a rectangular index modulation is assumed as the grating and a 2×2 MMI device is treated to operate as a nearly two-mode interference (TMI) device, which is frequently used as an alternative to conventional directional couplers that have a disadvantage of large size. Although the first two guided modes are used in the TMI device, it is especially important to overlap their reflection bands. Therefore, a design method for attaining a sufficient overlap and some considerations are given. The spectral response of the TMI device with a uniform Bragg grating is analyzed by a combination of the mode-propagation method and the transfer-matrix method and discussed on the basis of the state of overlap. In the case of a sampled Bragg grating, it is found that although many modes are excited in the MMI section, multiple reflection bands (multi-channel) are created as expected. The treated device can be applied to single- and multi-channel ADMs.