Study on self-imaging properties for line-tapered multimode interference couplers

The line-tapered multimode interference (MMI) couplers have advantage of compact dimension compared with conventional straight MMI couplers and then are more suitable for integrated optical components. In this paper, the self-imaging properties including general self-image and overlapping-image properties for the line-tapered MMI couplers are discussed thoroughly. Based on the width equation we defined, compact equations for the positions, amplitudes, phases of general images and overlapping images are deduced. Three disciplines for general self-imaging and four disciplines for overlapping-imaging are summarized and discussed. In addition, the overlapping-image properties are further studied by matrix analytic method and an inductive reasoning method of constructing phase and intensity matrix is developed based on it. Finally, all the theoretical results are compared with simulations results obtained by the finite-difference beam propagation method (FD-BPM). Both theoretical and simulation results are shown in this paper and demonstrated to be coincided with each other to a great extent.