Anomalous Band Formation in Arrays of Terahertz Nanoresonators

We investigate band formation in one-dimensional periodic arrays of rectangular holes which have a nanoscale width but a length of $100\mu \mathrm{m}$. These holes are tailored to work as resonators in the terahertz frequency regime. We study the evolution of the electromagnetic response with the period of the array, showing that this dependence is not monotonic due to both the oscillating behavior of the coupling between holes and its long-range character.

Figure 1

(a) Schematic of a periodic array of rectangular holes. The structure is illuminated by normally incident $p$-polarized light. (b) Scanning electronic microscope images of two different periods, $d=100\mu \mathrm{m}$ and $d=2\mu \mathrm{m}$. (c) Normalized transmitted amplitudes with varying the periods from $d=200\mu \mathrm{m}$ to $d=2\mu \mathrm{m}$. (d) Corresponding normalized-to-area transmitted amplitudes.

Figure 2

Normalized-to-area amplitude (a) and normalized-to-area transmission (b) computed for the six cases of finite array of rectangular holes with $l=100\mu \mathrm{m}$ and $w=200\mathrm{nm}$ considered in Fig. 1. Triangles in (b) render the results obtained from a minimal model (see details in the main text).

Figure 3

(a) Imaginary and real parts (shown as blue lines and red lines, respectively) of the EM coupling between two holes, $G_{01}$ (see main text for details on this magnitude). Panels (b) and (c) render the computed real and imaginary parts, respectively, of $S$ versus the number of holes $N$. All the magnitudes shown in this figure are evaluated at the resonance frequency of a single hole, $f_R=1.43\mathrm{THz}$ (${\lambda }_R=209\mu \mathrm{m}$). (d) Maximum normalized-to-area transmission $T_{\max }$ versus the number of apertures computed for the different values of $d$ considered in (b) and (c). Inset displays the case corresponding to $d=202\mu \mathrm{m}$. Dashed gray line in main figure corresponds to the value of $T_{\max }$ for a single isolated hole.