Light tunneling anomaly in interlaced metallic wire meshes

For long wavelengths, three-dimensional connected metallic wire meshes are impenetrable by light and have an electromagnetic response similar to that of an electron gas below the plasma frequency. Surprisingly, here it is shown that when two opaque metallic meshes are spatially interlaced, the combined structure enables an anomalous light tunneling in the long wavelength regime. The effect is due to the destructive interference of the waves scattered by the two wire meshes, which leads to a Fano-type resonance. The Fano resonance occurs when the longitudinal (plasmon) mode satisfies the Fabry-Pérot condition.

Figure 1

(a) Geometry of the interlaced wire meshes. The wires of each network are spaced by a distance $a$ along the coordinate axes. The distance between the two nonconnected networks is $a/2$. (b) Band diagram of the electromagnetic modes along the direction $\mathrm{\Gamma }X$. Solid lines: analytical model; discrete symbols: full wave simulations. The inset shows the cubic unit cell of the structure. The wires are PEC and are embedded in a dielectric with permittivity ${\varepsilon }_h=1$; the radii of the wires are $r_{w,\mathrm{A}}=0.001a$ and $r_{w,\mathrm{B}}=0.05a$. (c) Electric field profile for ($i$) Low-frequency longitudinal mode at $\omega a/c=0.20$, (ii) high-frequency longitudinal mode at $\omega a/c=2.30$, (iii) one of the degenerate TEM modes at $\omega a/c=2.32$. The modes are marked with green stars in (b).

Figure 2

(a) Amplitude of the transmission coefficient as function of the incidence angle for the normalized frequency $\omega a/c=1.32$ and normalized thickness $L/a\approx 6$. The remaining structural parameters are as in Fig. 1. The inset shows the geometry of the problem. (b) Amplitude of the transmission coefficient as a function of the normalized thickness for the fixed frequency $\omega a/c=1.32$ and incidence angle 80°. The solid lines represent the analytical results, and the discrete symbols represent the full wave simulations results.

Figure 3

(a), (b) Similar to Fig. 2 considering that the wires in mesh B have a finite conductivity and $a=1\mathrm{mm}$. (c) Similar to (a) considering that the wires in both meshes are made of copper and $a=1\mathrm{cm}$. In all the panels, the solid lines represent the analytical results, and the discrete symbols represent the full wave simulations results.

Figure 4

(a) Density plot of the transmission coefficient amplitude as a function of the normalized thickness $L/a$ and of the incidence angle ${\theta }^{\mathrm{inc}}$ at the fixed frequency of $\omega a/c=1.32$. (b) Incidence angle ${\theta }^{\mathrm{inc}}$ as a function of $L/a$ for the $n\mathrm{th}$ ($n=1,2,...$) Fabry-Pérot resonance of the propagating longitudinal mode at $\omega a/c=1.32$.

Figure 5

(a) Density plot of the transmission coefficient amplitude as a function of the normalized frequency $\omega a/c$ and of the incidence angle ${\theta }^{\mathrm{inc}}$ for the fixed slab thickness $L/a\approx 6$. (b) Incidence angle ${\theta }^{\mathrm{inc}}$ as a function of the normalized frequency $\omega a/c$ for the $n\mathrm{th}$ ($n=1,2,...$) Fabry-Pérot resonance of the propagating longitudinal mode and $L/a\approx 6$.

Figure 6

($\mathrm{a}i$), ($\mathrm{b}i$) Phase difference (black dashed lines) and normalized amplitude (blue and green lines) of the $z$ component of the macroscopic polarizations $P_{z,\mathrm{A}}$ and $P_{z,\mathrm{B}}$ [Eq. (6)] associated with the wire meshes A and B for ($\mathrm{a}i$) the first FP resonance ($L/a\approx 2$) and ($\mathrm{b}i$) the second FP resonance ($L/a\approx 4$). The solid blue (dot-dashed green) line represents the contribution from the wire mesh A (wire mesh B). The normalized frequency is $\omega a/c=1.32$, and the incidence angle is 80°. The remaining simulation parameters are as in Fig. 2. (aii), (bii) Full wave simulation results of the microscopic current density for the scenarios ($\mathrm{a}i$) (first FP resonance) and ($\mathrm{b}i$) (second FP resonance), respectively.

Figure 7

Band diagram of the electromagnetic modes along the $\mathrm{\Gamma }X$ direction for each individual wire mesh. Solid lines: analytical model; discrete symbols: full wave simulations [16]. The wires are PEC and are embedded in air. The lattice period is $a$. Blue color: wire mesh A with $r_{w,\mathrm{A}}=0.001a$. Green color: wire mesh B with $r_{w,\mathrm{B}}=0.05a$.

Figure 8

Amplitude of the transmission coefficient as function of the normalized thickness for the fixed frequency $\omega a/c=1.32$ and incidence angle ${80}^{\circ }$. Blue color: wire mesh A with $r_{w,\mathrm{A}}=0.001a$. Green color: wire mesh B with $r_{w,\mathrm{B}}=0.05a$. Solid lines: analytical model [12]; discrete symbols: full wave simulations [16]. The inset shows the geometry of the problem.