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Strictly speaking the concept of band is a peculiarity of structures with a translational symmetry. However, it is erroneously and commonly used also for quasicrystals where the translational modulation of the refractive index is absent. In this paper we will refer to band gap only for structures showing translational symmetry.
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In our simulations the RCWA method results to be more suitable than the FDTD approach. The reason is doublefold: necessity of lower memory and exact normalization of the signal. For FDTD, the simulation required about four times more memory than the RCWA counterpart. Indeed, because the simulation is two dimensional, we had to make use of four detectors measuring the Poynting vector in order to normalize the transmission. Moreover, it was the complication in the FDTD simulations to precisely define these detectors which convinced us of the advantage of the RCWA method. Indeed, for some of our structures, it was not possible with FDTD to discern completely the transmitted from the reflected signal, giving rise to not completely correct results (we never observed any discrepancy in zero-transmission regions compared to the RCWA method. The only difference was in the intensity of the transmission).
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In our simulations the RCWA method results to be more suitable than the FDTD approach. The reason is doublefold: necessity of lower memory and exact normalization of the signal. For FDTD, the simulation required about four times more memory than the RCWA counterpart. Indeed, because the simulation is two dimensional, we had to make use of four detectors measuring the Poynting vector in order to normalize the transmission. Moreover, it was the complication in the FDTD simulations to precisely define these detectors which convinced us of the advantage of the RCWA method. Indeed, for some of our structures, it was not possible with FDTD to discern completely the transmitted from the reflected signal, giving rise to not completely correct results (we never observed any discrepancy in zero-transmission regions compared to the RCWA method. The only difference was in the intensity of the transmission).
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