LAUSR

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 $2\times 2$ 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.