General matrix theory of self-imaging in multimode interference (MMI) couplers

We present a simple and very general matrix method for predicting the properties of integrated optical multimode interference (MMI) couplers with single-mode input and output guides. We derive a set of N/spl times/N matrices which (in the paraxial limit) can be used to predict the complex mode amplitudes in the output guides from the complex mode amplitudes in the input guides for any type of MMI coupler, splitter or recombiner. We compare this theory with experiment for an 11/spl times/11 nonuniform coupler.