Electromagnetic field expansion in a Wilson basis

A Wilson basis is an ingenious modification of a Gabor frame, with basis functions that have a notionally compact support in phase space. We shall give a short description of an algorithm for the construction of a Wilson basis. Through spatial scaling of the Wilson basis relative to a higher-order LP-mode, the basis may appear to vary from effectively local to effectively global. For mode-matching purposes local is advantageous. However, the field expansion requires fewer coefficients in the more global basis.