Fast Analysis of Photonic Crystal Structures With Mixed-Order Prism Macroelements

In this paper, a new concept of a mixed-order prism macroelement is introduced for the analysis of photonic crystal slabs and waveguiding structures. The mixed-order concept used here implies arbitrary orders of variation towards different directions and it differs essentially from the well-known mixed-order approximation that is an integral part of every Whitney element. The reduction of degrees of freedom, achieved by the employment of such elements, facilitates the solution of the resulting eigenvalue equation. Thus, an efficient 3-D finite-element analysis tool is developed to calculate the band structure of both symmetric and asymmetric photonic crystal slabs. Dispersion relation results for two different types of photonic crystal waveguides are also presented, to further verify the method.