METHOD OF PROJECTION OPERATORS FOR PHOTONIC BAND STRUCTURES WITH PERFECTLY CONDUCTING ELEMENTS

We introduce the method of projection operators based on plane-wave ex pansion to compute photonic band structures in periodic media containi ng perfectly conducting elements. Eigenfunctions of a unit configurati on potential generate suitable projection operators in the form of a s et of eigenvectors in the Fourier domain. By simply applying a project ion operator onto a proper subspace, a quadratic or cubic eigensystem for finitely conducting media can be transformed into an ordinary symm etric 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 per fect conductors. The methodology developed here, in fact, can be viewe d as a generalization of the conventional metal waveguide or cavity th eory. 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 metallodielectri c cylinder structures.