structure (TM polarization). For the 1st, 2nd and 4th bands Bloch functions fulfill Bloch criterion conditions at least approximately, and an analytical set of Bloch phases leads to well localized Wannier functions. Even in the case when the Bloch functions do not maximize the Bloch criterion Eq. (\[eq:blochCrit\]) exactly, the Wannier functions optimized with respect to exhibit a tendency to localize around its Wannier center. The same tendency has been obtained for all four test structures in both fundamental polarizations. This suggests to use the analytical set of Bloch phases as an initial set of phases for the numerical optimization, using either second moment or integrated modulus methods. This should help avoiding the local minima trapping problem and can reduce the computation time considerably.

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![Frequencies of the modes in a point defect consisting of a single rod with differing permittivity $\epsilon_{def}$ in a a square lattice of dielectric rods in air (TM polarization). The dots indicate the results of the Wannier function approach by taking the first eight bands into account. They are in complete agreement with plane wave calculations (red line) [@mpb-art]. At the bottom the real part of two defect modes with $\epsilon_{def}=1$ and 