Metamaterials with periodically arrayed structures possess unique properties including, in certain instances, negative refractive indices. Possible applications of these artificial materials include high-gain antennas, superlenses, and cloaking devices. Normally, the electromagnetic properties of metamaterials depend on their structural parameters, which are fixed at the time of formation. New applications are possible if their electromagnetic properties can be modulated dynamically in real time.

Researchers have recently tried to create metamaterials whose resonance frequency can be tuned by adding extra parts, such as varactor diodes,^{1} ferro-electric materials,^{2} and liquid crystals.^{3} We have designed a metamaterial that can be tuned by introducing mechanical movement during its operation. The unit cell comprises two layers of substrates—see Figure 1(a)—with two etched copper rings opposite each other on the substrate surfaces. The thicknesses of the substrate and the metallic rings are 0.25 and 0.017mm, respectively. The two substrates can be driven to move relative to one another either along or perpendicular to gaps in the rings. When the structure is illuminated by a plane wave *k* along direction *x* with its electric field pointing along the gap's direction, current flows along the rings, induced by the wave's electric and magnetic fields.

Mutual capacitance occurs as the result of the coupling of the two metallic rings and can be changed when the two substrates are moved relative to one another. The resonance frequency decided by the effective capacitance can then be modulated, i.e., when working near the resonance frequency, the material's resonance and other parameters can be tuned. This tuning method can also be illustrated by an equivalent circuit—see Figure 1(b)—in which *C*_{1} to *C*_{4} are the gap's capacitances and *C*_{5} to *C*_{7} are the mutual capacitances between the two rings. *L*_{1}, *L*_{2}, *R*_{1}, and *R*_{2} are the equivalent inductances and resistors. When moving one of the substrates, the gap capacitances remain constant while the mutual coupling capacitances change. Therefore, the resonance frequency can be tuned. Because there are no extra parts involved, this tunable metamaterial can keep its original, simple construction.

**Figure 1. **(a) Geometric structure of the unit cell. The cell lengths (l) and ring length (a) are 5 and 4mm, and the widths of the gap (g) and ring (w) are 0.5 and 0.2mm, respectively. E, H, and k are the directions of the electric and magnetic fields, and the wave vector, respectively. S_{x}and S_{y} are the slip distances along their respective axes. (b) Equivalent circuit of the unit cell employing capacitors (C_{x}), resistors (R_{x}), and inductors (L_{x}).

Figure 2(a) shows a larger sample of the metamaterial formed with the unit cell arranged periodically. The two substrates can be moved relative to one another by an external force producing slip distances in the *y* direction, shown as *S*_{y}. We expect that the resonance frequency will shift with different slips corresponding to the dynamic tuning of the electromagnetic parameters. Negative-material parameters can exist near the resonance-frequency range for metamaterials. Therefore, we expect that this negative region can be tuned.

**Figure 2. **(a) Metamaterial formed by reproducing the unit cell periodically. The two substrate layers can be moved by a force (F) producing slip S_{y}. (b) Transmission under slip S_{y}. (c) Retrieved permittivity under slip S_{y}. (d) Resonance frequency with slip S_{y}.

Figure 2(b) shows calculated transmission spectra for different slip distances. It is clear that there are a series of resonance dips, which shift gradually from 9.6 to 7.7GHz when *S*_{y}varies from 0 to 0.8mm. The two rings can be regarded as capacitors, and the capacitance decreases with increasing slip distance. Therefore, the resonance frequency will change downward. The retrieved permittivity—see Figure 2(c)—displays peaks corresponding to the resonance frequency. But the peaks shift to lower frequency gradually with *S*_{y} increasing from 0 to 0.8mm. Also note that the negative permittivity indeed exists. As expected, the negative region also shifts with slip distance.

Finally, Figure 2(d) shows the resonance frequency for slip *S*_{y}. The data shows that the resonance frequency drops from 8.2 to 6.2GHz by changing *S*_{y} from 0 to 0.8mm. For simplicity, we only show the results for displacements in the *y* direction. We obtain similar data when we move the substrates along the *x* direction.

In summary, we have demonstrated a frequency-tunable electromagnetic metamaterial based on mechanical movement. The method can be used effectively to tune the resonance frequency, as well as a material parameter (permittivity), without adding any extra parts. In our next steps, we will focus on designing reconfigurable antennas and tunable devices such as tunable filters and phase shifters at microwave frequencies.

Yifu Wang, Chunlei Du, Xiaochun Dong

Institute of Optics and Electronics Chinese Academy of Sciences

Chengdu, China

Yifu Wang is a PhD student. His major research interests include subwavelength optics, metamaterials, and electromagnetic-bandgap materials and their applications in microwave devices.

Chunlei Du is currently a professor. She leads a research group in micro/nano-optics that is engaged in theoretical methods, components/systems design, and micro/nanofabrication. Since the early 1990s, the group has produced 150 publications and 50 patents in these fields.

Xiaochun Dong is an associate professor. His current research interests are subwavelength optics, plasmonics, microfabrication, and micro/nano-optics.

References:

1. D. Wang, L. Ran, H. Chen, M. Mu, J. Kong, B. Wu, Active left-handed material collaborated with microwave varactors, *Appl. Phys. Lett*. 91, pp. 164101, 2007.

2. T. Hand, S. Cummer, Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings, *J. Appl. Phys*. 103, pp. 066105, 2008.

3. Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, Electrically tunable negative permeability metamaterials based on nematic liquid crystals, *Appl. Phys. Lett*. 90, pp. 011112, 2007.