The linear combination of atomic orbitals method widely used to calculate the band structure of semiconductors has been applied [1] to 2-D photonic structures of very high core to background index contrast. In the present study the method has been extended to include realistic values of the index contrast. The Mie resonances of the isolated scatterer in the photonic crystal case are analogous to the atomic orbitals in the electronic case. The parameters appearing in the tight-binding (TB) like dispersion relation are obtained by fitting to band structure calculation results obtained by the plane wave expansion method. Dependence of the relevant parameters on the dielectric constant of the core and the filling ratio of the structure will be presented. The transferability of the TB matrix elements is tested by accurately reproducing the band structure of different lattices with or without defects. This TB scheme opens the possibility to formulate the propagation of EM waves in periodic and random systems in much simpler form.
[1] E. Lidorikis, M. Sigalas, E.N. Economou and C.M. Soukoulis, Phys. Rev. Lett. 81, 1405(1998)