Novel variational approach for analysis of photonic crystal slabs
We propose a new method, based on variational principle, for the analysis of photonic crystal (PC) slabs. Most of the methods used today treat PC slabs as three-dimensional (3D) crystal, and this makes these methods very time and/or memory consuming. In our proposed method, we use the Bloch theorem to expand the field on infinite plane waves, whose amplitudes depend on the component perpendicular to the slab surface. By approximating these amplitudes with appropriate functions, we can find modes of PC slabs almost as fast as we can find modes of two-dimensional crystals. In addition to this advantage, we can also calculate radiation modes with this method, which is not feasible with the 3D plane wave expansion method.