Hybrid planewave/finite-difference transfer method for solving photonic crystals in finite thickness slabs

We present a novel method to solve Maxwell´s equations for corrugated slabs sandwiched between two dielectric semispaces, as models for photonic crystal applications. Within the slab region (0<z<h) the permittivity function ε(x, y, z) may vary arbitrarily in all three coordinates (x, y, z). The only restriction imposed on the dielectric constitution of the structure is that the permittivity function ε(x,y) in the lower (z<0) and upper (z>h) semispaces, does not depend on z. Focusing on the essentials we will assume in the following that the dielectrics are isotropic. From the discussion in the paper it is obvious that the inclusion of the anisotropic behavior is a routine procedure. We present dispersion diagrams for typical corrugated structures, and compare our results with those obtained by the widely-used planewave method. Using the planewave method we necessarily have to periodize the structure in;all directions in the space. This artificial periodization results in nonphysical guided bands which exist even outside the lightline. Our numerical results show that this shortcoming can be avoided quite elegantly