Photonic band structures in 2-D periodic media

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The existence of photonic band gaps in periodic dielectric structures has been the subject of many recent investigations.1,2 The band structure in any periodic media can be computed from an exact solution of Maxwell’s equations. In this paper, we investigate the band structure in 2-D periodic media. Several periodic structures are considered in order to find one for which propagation would be forbidden in the plane of the modulation. We consider arrays of rods with square cross-sections and 2-D grids. We predict band gaps for TE and TM modes. The width of the bands is a function of the index contrast and the occupation fraction of each material in the structure. In arrays of rods (grids), the minimum index contrast required to produce a TE band gap is larger (smaller) than the one required to produce a TM band gap. In all the structures that we investigated, the minimum index contrast required to produce a TM gap was not very sensitive to the filling fraction. Furthermore, there was no overlap of TE and TM bands in any of the structures, hence there were no complete band gaps. Other periodic structures with a more circle like Brillouin zone will be considered, taking into consideration that the symmetry of the atom in the lattice may induce band degeneracy.