Anomalous Electromagnetic Tunneling in Bianisotropic $ϵ\text{−}\mu$-Zero Media

Quantum tunneling, one of the most celebrated effects arising from the wave nature of matter, describes the partial penetration of an incident propagating wave through a potential barrier in the form of an evanescent field that exponentially decays from the incident interface. A similar tunneling effect has also been observed in classical systems, such as the frustrated total internal reflection. Here we reveal an unexplored form of tunneling for electromagnetic waves which features opposite behaviors for the electric and magnetic fields, with one turning into a growing field, and the other a decaying field, in a medium that exhibits both $ϵ\text{−}\mu$-zero and bianisotropy. Our Letter provides a new mechanism for manipulating electromagnetic waves for novel device applications.

Figure 1

Field profiles in BEMZ slabs with $|\kappa |=0.5$, $d=2/3\lambda$. Solid line: Amplitudes of electric fields. Dashed line: Amplitudes of magnetic fields. (a) The BEMZ slab is sandwiched between two dielectrics of impedance $Z_1$ for $z<0$ and impedance $Z_2$ for $z>d$. (b) Two BEMZ slabs with opposite $\kappa$ are joined together and placed between dielectrics of the same impedance $Z_1$.

Figure 2

The BEMZ unit cell. (a) Schematic representation. The split ring resonators (SRRs) on the top layer respond magnetically, and the metallic wires on the bottom layer responds electrically. The wires are biased from the center towards the $z$ direction to provide bianisotropy. (b) The retrieved real parts of the effective permittivity, permeability, and magnetoelectric parameters. The gray region marks the location of the band gap. The two split rings have the same gap width $g=0.7\mathrm{mm}$ and line width $w=0.4\mathrm{mm}$. Other geometric parameters are $a_1=4.6\mathrm{mm}$, $a_2=2.7\mathrm{mm}$, $b=1.6\mathrm{mm}$, and $w^{\prime }=0.3\mathrm{mm}$. The substrate has a thickness of 0.508 mm, a dielectric constant of 2.2, and loss tangent of 0.0009. The dimensions of the BEMZ unit cell are $5.5\times 6\times 5.5{\mathrm{mm}}^3$.

Figure 3

The composite BEMZ metamaterials. (a) Sample 1: $\kappa >0$ & $\kappa <0$ set and (b) sample 2: $\kappa <0$ & $\kappa >0$ set, together with the simulated real parts of electric and magnetic fields along the $yoz$ plane. (c) The simulated and measured transmissions of the two samples. The stars and circles indicate the frequencies when the transmission phases are zero. (d) The averages of simulated electric and magnetic fields over the unit-cell surfaces that are perpendicular to $z$.

Figure 4

(a) Experimental setup for the evanescent wave measurement. The simulated and measured (b) transverse and (c) longitudinal electric fields within the two samples.