Unified Scattering Parameters formalism in terms of Coupled-Mode Theory for investigating hybrid single-mode/two-mode photonic interconnects

In terms of Linear Algebra, a directional coupler between a single-mode waveguide and a two-mode waveguide can be thought of as formally equivalent to a set of three mutually coupled single-mode waveguides. Its responses, easily derived in the frame of ternary Coupled-Mode Theory, are used to establish analytically the scattering parameters of a hybrid ring-based modal multiplexer.