Coupled surface-plasmon-like modes between metamaterial

Perfectly conducting metals may be structured with holes to make metamaterials that support surface-plasmon-like modes at microwave frequencies. Results are presented for Fabry-Pérot-like standing wave resonances formed from coupled surface-plasmon-like modes supported by two such perforated metal substrates placed in close proximity.

Figure 1

Schematic illustration of the sample and experimental geometry. The plane and parallel faces of two aluminum substrates of thickness $t=30\mathrm{mm}$ are placed a distance $w=1\mathrm{mm}$ apart. A square array of equally spaced $\left({\lambda }_g\right)$, cylindrical holes (radius $r=1.57\mathrm{mm}$ and depth $d=20\mathrm{mm}$) are machined into each aluminum substrate. Each hole is filled with dielectric $ϵ$. $p$-polarized (TM) radiation of wavelength ${\lambda }_0=2\pi ∕k_0$ is incident in the $xy$ plane at an angle $\theta$ from the surface normal. The main diagram is drawn on an $xz$ plane that passes through the central axis of the cylindrical holes; the inset is a top view of one of the two substrates.

Figure 2

Experimental transmission data recorded as a function of frequency $\left(\nu \right)$ and $k_y=k_0\sin \theta$ from the unfilled-holes sample $(ϵ=1)$. The black solid line and the gray shaded region correspond to photons at $\theta =90°$ and angles beyond the capabilities of the experimental apparatus $(\theta >60°)$, respectively, and the band gap at $\theta =0$ is also marked. Left inset: Dispersion of $\theta =0$ modes with mode number (representative of $k_x$) Right inset: Comparison of experimental (circles) and modeled (line) data with radiation incident at $\theta =0$.

Figure 3

FEM model predictions of time-averaged electric field magnitudes on resonance of the second, seventh, and eighth Fabry-Pérot harmonics of the air-filled hole sample. The plots represent field enhancements, using a logarithmic gray scale between 0.01 and 4, normalized to the strength of the incident field. The microwave beam is incident in the positive $x$ direction, and the fields are plotted on an $xz$ plane of area approximately $37\times 18{\mathrm{mm}}^2$ passing through the central axes of the cylindrical holes. The metal regions are shaded white, and the outline of the structure is highlighted with a black line. For the seventh harmonic, the magnitude of the fields decrease exponentially into the holes with a decay length of $\sim 1.2\mathrm{mm}$.

Figure 4

Experimental transmission data recorded as a function of frequency $\left(\nu \right)$ and $k_y=k_0\sin \theta$ from the sample with filled holes $(ϵ=4.7)$. The cutoff frequency of the holes [Eq. (2)] is also shown. The black solid line and the gray shaded region correspond to photons at $\theta =90°$ and angles beyond the capabilities of the experimental apparatus $(\theta >60°)$, respectively. Left inset: Dispersion of $\theta =0$ modes with mode number (representative of $k_x$). Right inset: Comparison of experimental (circles) and modeled (line) data with radiation incident at $\theta =0$.

Figure 5

FEM model predictions of time-averaged electric field magnitudes on resonance of the seventh Fabry-Pérot harmonic of the elastomer-filled hole sample. The plots represent field enhancements, using a logarithmic gray scale between 0.01 and 4, normalized to the strength of the incident field. The microwave beam is incident in the positive $x$ direction, and the fields are plotted on an $xz$ plane of area approximately $37\times 18{\mathrm{mm}}^2$ passing through the central axes of the cylindrical holes. The metal regions are shaded white, and the outline of the structure is highlighted with a black line. The magnitude of the fields decreases exponentially into the holes with a decay length of $\sim 2.8\mathrm{mm}$.