Accurate mesh representation of non-cartesian boundaries of high Q optical resonators in Cartesian meshes

This paper presents a new discretisation of Cartesian meshes based on spatial anti-aliased filtering of geometry boundaries in TLM. The method is compared against some other techniques presently used to alleviate stair casing error when representing circular boundaries. The antialiasing method provides the best convergence to actual resonances for E-waves amongst the techniques studied. For H-waves, the new method produces uniform convergence, but an anisotropic sub-pixel smoothing produces smaller error for finer meshes.