Application of novel high order time domain vector finite element method to photonic band-gap waveguides

We apply the novel high order time domain vector finite element methods (Rieben, R. et al., IEEE Trans. Antennas and Propag., 2004) to the particular case of photonic band-gap structures. We demonstrate some key advantages to such methods when applied to these structures; namely, the ability to use single element thick PML regions and the benefits of high order energy conserving time integration methods. In addition to these benefits, high order vector finite element methods excel at modeling geometries defined by non-orthogonal, unstructured grids and at reducing the effects of numerical dispersion when compared to traditional second order accurate FDTD and FE methods.