Nanorods in an electric field create liquid crystals for transformation optics

Advances in optical engineering are often associated with the development of new materials. One example is liquid crystals, organic fluids formed by rodlike molecules that align parallel to each other. Tailoring the temperature range of their existence, refractive indices, surface alignment, and dielectric and elastic properties made possible a multibillion-dollar liquid-crystal display industry. A newly emerging field is that of optical metamaterials for ‘transformation’ optics.¹ In these materials, the index of refraction varies from point to point in a broad range, including negative and zero values. It would be ideal if we could fabricate these materials with 3D reconfigurable architecture, as that would allow us to control light propagation with a finesse previously unknown, making possible applications such as sub-wavelength imaging, invisibility cloaking, and light concentrators.

The challenge is that to direct the waves of light into desired trajectories, the local dielectric and magnetic properties of a metamaterial should vary so widely in space that no single natural substance can fit the bill. The metamaterials need to be constructed artificially, by selecting proper metallic and dielectric elements and then arranging them in space into predesigned architectures. The building units must be smaller than the wavelength of light to avoid scattering. Some metastructures can be fabricated by lithography, but this technique is of limited applicability for complex 3D and reconfigurable architectures. We propose an alternative approach,^2,3 using a dispersion of metal nanoparticles in a fluid and controlling their concentration and orientation by a nonuniform electric field.

Metal nanorods (NRs) can be dispersed in a dielectric fluid such as water or toluene. The electric field polarizes the NRs and aligns them along the field lines. If the field is nonuniform, it also creates a force moving the NRs, usually toward the region of stronger field. The particle does not need to be charged: the two ends of the rod with the two polarization charges of the same absolute value but opposite signs find themselves in slightly different fields. The effect is called dielectrophoresis. Previously, it was used to manipulate supramicron particles.⁴ In optical metamaterials, however, one prefers to work with much smaller (nanometer-scale) particles, to avoid light scattering. Since the dielectrophoretic force is proportional to the particle' volume, it was not clear whether it would be strong enough to manipulate the nanoparticles. Our work shows that the dielectrophoretic effect is in fact a very potent way to control the spatial location and orientation of nanoparticles and thus the optical performance of the metamaterial.

We use a dispersion of gold (Au) NRs in toluene. Their diameter is 10–20nm and length 40–80nm. The volume fraction is low, 0.01–0.1%, and thus the dispersion is spatially uniform and isotropic, i.e., the NRs are distributed homogeneously in space far apart from each other and adopt arbitrary orientations. A nonuniform field transforms this fluid into a liquid crystal, as illustrated in Figure 1 in an experiment with two mutually perpendicular metal wires (2) and (3) in a glass cell (1). The dielectrophoretic force attracts the NRs to the electrode (2), where they align parallel to the electric field lines and condense into a cloud. The concentration of NRs is high near the electrode and low at the periphery of the cell. Consequently, the refractive index of the medium changes from a high value at the periphery (equal to the refractive index of pure toluene) to a smaller value near the electrode (2). The effect is most pronounced for light polarized perpendicularly to the electrode (2) and less so for light polarized parallel to it. This optical anisotropy is caused by the aligned assembly of the NRs, which resembles a liquid crystal formed by orientationally ordered rodlike molecules. The density variation represents a major difference compared with the normal liquid crystal, since all material properties, such as the refractive index, also change from point to point with the NR concentration.

Figure 1.Field-induced birefringent cloud of gold nanorods (Au NRs) concentrated and aligned in a high-electric-field region. A, P: Axes of the analyzer and polarizer. U, f: Amplitude and frequency of the applied voltage.

The most interesting effect is produced when the sample represents a circular glass capillary: see (1) in Figure 2. One electrode is a metal wire (2) running along the axis. The second electrode is a transparent indium tin oxide layer (3) at the outer surface of the capillary. The field-induced radial pattern of NRs with the concentration that decreases from the electrode to the periphery (4) resembles the theoretical optical cloak proposed by Vladimir Shalaev's group.⁵ By applying the electric field, we reduce the visibility of the central wire in light polarized normally to the cylinder: see Figure 2 and video.⁶

Figure 2.(a) Field-induced radial gradient structure of an Au NR dispersion. The visibility of the central wire (b) is reduced when the field is on (c).

The refractive index of toluene with the condensed cloud of NRs decreases when one moves from the NR-depleted periphery of the cylinder to the NR-rich region near the central electrode (2). The radial variation of the refractive index in the cloud (4) causes the light rays to bend around the wire (2), so its shadow is mitigated, representing an imperfect version of the cloaking effect. Theoretically, the refractive index at the inner surface of a cloaking shell should be 0. Our experiments^2,3 have not yet reached this limit, as the estimated field-induced change in the refractive index is ∼0.1. The task is to increase it further, by a factor of 10.

To make a 3D reconfigurable metamaterial, we need to learn how to reversibly intertwine the metal and dielectric elements at the scale of nanometers. Our approach based on the dielectrophoretic effect is only the first step forward. It shows that the architecture of metal and dielectric nanoscale elements can be controlled by the nonuniform electric field. The next steps would be to increase the concentration of NRs, to explore whether and how the dielectrophoretic forces can be supplemented by other forces such as electrophoretic and induced-charge electrophoretic ones, for a better control of the 3D architecture. The issues of light scattering and losses in the metal-dielectric composites also need to be addressed. We plan to apply the dielectrophoretic technique to NRs that are preassembled into chainlike and raftlike clusters⁷ to increase the initial concentration of NRs and to assemble clouds with differently oriented NRs in them. These tasks are formidable, but the rewards hold a major promise for optical engineering of the future.

This work was supported by Air Force Office of Scientific Research grant FA9550-10-1-0527, Department of Defense Multidisciplinary University Research Initiative grant FA9550-06-1-0337, and Department of Energy DE-FG02-06ER46331. We thank N. A. Kotov and P. Palffy-Muhoray for providing us with Au NR dispersions, and A. Agarwal, J. Fontana, P. Luchette, H.-S. Park, L. Tortora, B. Senyuk, H. Wonderly, and L. Qiu for help in sample preparation. We thank V. M. Shalaev, P. Palffy-Muhoray, C. Y. Lee, A. V. Kildishev, S. V. Shiyanovskii, and V. P. Drachev for fruitful discussions.