$\epsilon_{def}=30$ is shown.[]{data-label="fig:pointDefect"}](defect-all){width="0.95\columnwidth"}

In this section the quality of IM optimized Wannier functions is demonstrated by using them as a basis set for photonic crystal defect structure analysis. In figure \[fig:reprBS\] the reconstructed tight-binding band structure of a square lattice of dielectric rods in air (TM polarization) is shown. The number of lattice sites taken into account in the nearest neighbor approximations were increased successively. The deviation of the reconstructed band structure from the original band structure decreases by increasing the number of next neighbors taken into account. By restricting to lattice sites separated by up to four lattice constants the band structure is reproduced well except for small deviation at higher bands and symmetry points. The slight mismatch for higher bands is due to the fact that the higher band Wannier functions are not as well localized as the lower ones.

We further calculated the modes and frequencies of a point defect structures which consist of a single rod with deviating permittivity $\epsilon_{def}$ at ${\mathbf{R}}_{def}$ in the Sq-D structure. The light propagation inside the band gap between the first and the second band is forbidden and the formation of a localized defect mode is possible. We split up the 