Waveguide Arrays as Plasmonic Metamaterials: Transmission below Cutoff

Since the work of Ebbesen et al. [Nature (London) 391, 667 (1998)], there has been immense interest in the optical properties of subwavelength holes in metal layers. While the enhanced transmission observed is generally associated with surface plasmon polaritons (SPPs), theoretical predictions suggest a similar response with perfectly conducting materials. However, Pendry et al. [Science 305, 847 (2004)] proposed that, if textured on a subwavelength scale, even perfect conductors support surface modes. Here, using microwave radiation incident upon an array of metal waveguides, we observe peaks in the transmissivity below cutoff and confirm the crucial role of these SPP-like modes in the mechanism responsible.

Figure 1

Photograph of part of the sample used in the present study ($d=9.53\mathrm{mm}$, $a=6.96\mathrm{mm}$). The coordinate system is also shown.

Figure 2

(a) Intensity of the nondiffracted transmitted beam (gray scale plotted on a linear scale: black $T=0.0$, white $T=1.0$) as a function of frequency $\nu$ and in-plane wave vector $k_x=2\pi \nu \sin \theta /c$. The shaded region in the bottom right-hand corner corresponds to momentum space within which modes may not be directly coupled to as they are beyond the light line (solid black line). The white dotted line represents the first-order diffracted light line associated with the periodicity of the array. Data are recorded only for angles of incidence up to 50°. As a guide to the eye, the solid gray lines provide a trace of the position of the transmission peaks associated with each mode. The dotted segments provide an estimation of the band structure in the region where the transmission peaks are not a good indication of the mode position. (b) Nondiffracted transmission spectra recorded from the sample at angles of $\theta =5°$, 21°, and 26° [illustrated by gray dotted-dashed lines in (a)], together with the predictions from the numerical model. In order to reduce the complexity of the problem, model solutions are requested only at frequencies below the onset of diffraction (at 29.0, 23.2, and 21.9 GHz for $\theta =5°$, 21°, and 26°, respectively). The electric field distributions associated with the resonances labeled ① and ② are shown in Fig. 3.

Figure 3

Predictions of the time-averaged electric field enhancements of the resonances labeled ① ($\theta =5°$, 22.8 GHz) and ② ($\theta =26°$, 21.4 GHz). In the gray scale plots, the lightest shading corresponds to field enhancements of six times and greater. TM-polarized radiation is incident in the $xz$ plane from above. The line graph illustrates the same quantities plotted along a line in the $z$ direction through the center of a tube. The shaded area corresponds to the region inside the cavity.