polarization, 5th band (bottom). The dashed green line shows the locality of the best-localized Wannier function in each generation. Every 100 generations these Wannier functions served as a starting point for the subsequent CG optimization step (red crosses). On the right-hand side, the modulus square of the SM-optimized Wannier functions is shown for an early (20000th) and a later (60000) generation, respectively.[]{data-label="fig:ga_im"}](all-g-te-im "fig:"){width="0.95\columnwidth"}

To support this hypothesis, we applied the GA method to solve the optimization problem. For all considered structures no significant variation of the locality has been observed for different GA generations. Representative examples are shown in figure \[fig:ga\_im\]. One can clearly see, that over many thousands of generations the locality of the Wannier functions optimized with respect to IM criterion stays constant. This proves numerically that the considered optimization problem possesses a single extremum, making the procedure independent on the choice of the initial set of Bloch phases. As a consequence, the use of the IM as a locality criterion together with the CG as an optimization method represents a fast as well as reliable method for the construction of maximally localized Wannier functions. Figures \[fig:MLWF\_dielRods\_tm\] and \[fig:MLWF\_airRods\_te\] show the maximally localized Wannier functions for the first 