EM modelling of arbitrary shaped dispersive chiral dielectric objects using a 3D leapfrog scheme on unstructured meshes

The standard Yee FDTD algorithm is widely used in computational electromagnetics because of its simplicity and divergence free nature. A generalization of this classical scheme to 3D unstructured co-volume meshes is adopted, based on the use of a Delaunay primal mesh and its high quality Voronoi dual. This circumvents the problem of accuracy losses, which are normally associated with the use of a staircased representation of curved material interfaces in the standard Yee scheme. The procedure has been successfully employed for modelling problems involving both isotropic and anisotropic lossy materials. Here, we consider the novel extension of this approach to allow for the challenging modelling of chiral materials, where the material parameters are frequency dependent. To adequately model the dispersive behaviour, the Z -transform is employed, using second order Padé approximations to maintain the accuracy of the basic scheme. To validate the implementation, the numerical results produced are compared with available analytical solutions. The stability of the chiral algorithm is also studied.