Method of projection operators for photonic band structures with perfectly conducting elements

We introduce the method of projection operators based on plane-wave expansion to compute photonic band structures in periodic media containing perfectly conducting elements. Eigenfunctions of a unit configuration potential generate suitable projection operators in the form of a set of eigenvectors in the Fourier domain. By simply applying a projection operator onto a proper subspace, a quadratic or cubic eigensystem for finitely conducting media can be transformed into an ordinary symmetric eigensystem in the limit of perfect conductors. The procedure is equivalent to finding solutions of wave equations under the condition that the electromagnetic fields are entirely zero inside periodic perfect conductors. The methodology developed here, in fact, can be viewed as a generalization of the conventional metal waveguide or cavity theory. The method is numerically handy, fast, and readily extendible to general metallodielectric photonic crystals. As examples, we present photonic band structures in two-dimensional metal and metallodielectric cylinder structures.