Transmission of light through periodic arrays of square holes: From a metallic wire mesh to an array of tiny holes

A complete landscape is presented of the electromagnetic coupling between square holes forming a two-dimensional periodic array in a metallic film. By combining both experimental and theoretical results along with a first-principles Fano model, we study the crossover between the physics of metallic wire meshes (when holes occupy most of the unit cell) and the phenomenon of extraordinary optical transmission, which appears when the size of the holes is very small in comparison with the period of the array.

Figure 1

(Color online) (a) Measured zero-order transmittance spectra corresponding to the four samples. The spectra were obtained under normal incident radiation. (b) Calculated zero-order transmittance for an infinite periodic array of holes with the same geometrical parameters as in (a). Inset shows the transmittance as a function of wavelength and side of the holes $\left(a\right)$, which is varied continuously from $a=30$ to $70\mathrm{\mu }\mathrm{m}$. The dot-dash line displays the spectral location of the transmission peak for each value of $a$. (c) Calculated transmittance for a $21\times 21$ hole array.

Figure 2

(Color online) Plots of the three different terms contributing to the transmission through the hole array as written in Eq. (2) for $a=\left(\mathrm{a}\right)$ 38, (b) 48, (c) 58, and (d) $68\mathrm{\mu }\mathrm{m}$. The rest of the geometrical parameters are as in Fig. 1. The red (gray) dashed lines and solid black lines correspond to the resonant $(\mid \mathrm{\Delta }{E}_0{\mid }^2)$ and interference $\left[2\mathrm{Re}\right(\mathrm{\Delta }{E}_0\left)\right]$ terms, respectively. These magnitudes are normalized to the nonresonant contribution [dotted blue (dark gray) lines, constant value 1].

Figure 3

(Color online) Electric field patterns at resonance corresponding to $a=\left(\mathrm{a}\right)$ 38 and (b) $68\mathrm{\mu }\mathrm{m}$. The rest of the geometrical parameters are as in Figs. 1, 2. Both patterns were calculated just above the nonilluminated side of the samples and the amplitude is normalized to the incident one. Black square boxes in both panels correspond to the perimeters of the holes in the two cases.