A theoretical analysis of mode-mixing in optical waveguides with nearest-neighbour mode coupling

Properties of the solutions of the coupled equations describing the flow of average mode power in optical waveguides are investigated. All of the important properties and their theoretical foundations are first reviewed for systems with arbitrary coupling and loss coefficients. It is then shown that, for the special class of systems with nearest-neighbour coupling, the solutions are expressible in terms of orthogonal polynomials. In particular, for systems obeying a quasi-uniform loss model and having coupling coefficients with simple dependence on mode number (uniform or linear), the solutions are associated with the classical polynomials. As illustrations of this analysis, the characteristics of optical power flow in three such systems are studied in detail. These include a slab-waveguide with uniform coupling, the corresponding cylindrical waveguide with uniform coupling, and a parabolic-index fibre with linear coupling dependence.