gradient method. Because this result presumably originates from the local nature of the integrated modulus measure, it should hold generally, not only for two-dimensional systems, but also in three dimensions for photonic as well as electronic lattices.

We also presented and tested an analytical formula for the set of Bloch phases to be used as a starting point of the optimization process. This initial set of Bloch phases is suggested because, albeit it does not solve the optimization problem in general, it does generate maximally localized Wannier functions in special cases where the optimization problem can be solved analytically. We expect that these two main results may significantly increase the efficiency of the Wannier function approach for the description of defect structures in photonic lattices.

This work was supported in part by the Deutsche Forschungsgemeinschaft (FOR 557).

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