Wilson basis expansion of electromagnetic fields and source distributions - Wave decomposition and propagation tools for optical fibre scattering

The spatial and spectral confinement properties of Wilson basis functions allow for an efficient expansion of electromagnetic fields. A planar, transverse electromagnetic source distribution can be decomposed into one-way field generating distributions associated with longitudinally progressive and regressive waves with the aid of a Poincaré-Steklov operator, which is readily evaluated in a planar Wilson basis owing to the spectral confinement. The construction of a Wilson-basis propagator for an elementary propagation step is equally straightforward.A cascaded application of one-way Wilson-basis propagation steps may be performed efficiently with negligible loss of accuracy. This multi-step approach provides a computationally expedient tool for optical-fibre interconnect problems.