Using microfluidics for tunable metamaterials

Metamaterials—electromagnetic media structured on sub-wavelength scales—present new opportunities for the manipulation of light across the entire electromagnetic spectrum. Unusual optical properties can be accessed with the use of metamaterials that have pre-designed dispersion. For instance, ‘invisible’ metallic structures, perfect absorption, extraordinary transparency, and enhancement of nonlinear effects in conventional active materials can be achieved. These exciting physical prospects have stimulated a wide range of research in the development of new technologies for meta-devices that have tunable and switchable properties.¹

Researchers are now exploring planar metamaterials with spatially variable characteristics for wavefront shaping.² Metamolecules in a planar array, however, are difficult to individually tune using current techniques. Such techniques are based on the integration of lump active elements in the metamolecules (transistors or diodes), current injection, or suppression of superconductivity.¹ Furthermore, these methods depend on undesirable energy losses (limited by the material properties) for modulation and they require a network of wires. Inevitably, this causes interference and the electromagnetic resonant properties of the metamaterial to be ruined. Conversely, the ability to control resonant properties of every individual metamolecule in a planer metamaterial is desirable. This offers ultimate freedom in dynamically shaping wavefronts via reconfigurable spatial phase gradients. In our previous work, we achieved the tunability of metamaterials with the use of microelectromechanical systems.^3–5 With these systems, however, it is difficult to tune the individual metamolecules because of their control system design complexity.

Here we exploit a novel and radically different approach for dynamically casting the shapes of resonators in a metamaterial array, with the use of liquid metal (mercury). As such, we have produced the first proof-of-principle demonstration for a planar metamaterial in which the resonant properties of every individual metamolecule can be continuously controlled. Our new metamaterial—a random access reconfigurable metamaterial (RARM)⁶—therefore offers ultimate freedom for dynamically controlling wavefronts of electromagnetic radiation.

In our RARM methodology (see Figure 1), we use microfluidic technology to create an array of microcavities that can be filled (in a controlled manner) with liquid metal. Our microfluidic network control system—see Figure 1(e)—is a purposely designed ternary valve multiplexer, which we use to address each metamolecule in the array individually. This system therefore provides the mechanism for dynamically changing the filling factor of resonators, and thus their resonant electromagnetic properties (at will and with random access). The individually addressable metamolecules form a metamaterial array, in which the phase and amplitude modulation of incident light can be controlled at sub-wavelength levels.

Figure 1. Illustrations of a random access reconfigurable metamaterial (RARM) with a tunable flat lens function. (a) The randomly addressable metamaterial can be used as a flat lens, with a tunable focal distance, when the resonant properties of metamolecules in the array are altered (by changing the metal filling fraction). The tuning process for a single metamolecule is depicted in (b), (c), and (d). First, the liquid metal fills the ring-shaped microcavity. The gap of the metal ring is then controlled by changing the pressure of the air inlet. PDMS: Polydimethylsiloxane. (e) A ternary code microfluidic system is used to control the RARM flat lens.

Our metamaterial consists of a 2D square metamolecule array (metallic split ring) and two perpendicularly placed metal gratings: see Figure 1(a). The metal gratings are constructed from 1mm-wide copper wires, with a period spacing of 2.5mm, and are used to enhance the transmission efficiency of the metamaterial. We form the split ring metamolecules by filling the ring-shaped microcavities with liquid metal. We are then able to progressively tune the resonance of the metamolecules by changing the gap between them. We achieve this by simply substituting the liquid metal in the cavities with air plugs. Furthermore, we are able to create and individually control the gaps between the metamolecules, as they are connected—with microchannels—to a pneumatic valve array (which regulates air pressure in the channels). By changing the air inlet channel and pumping pressure, we can control the size and orientation of the gap, as shown in Figure 1(b–d). By altering the pressure balance between the air and liquid metal, we make this process continuous and fully reversible. Each row of metamolecules in the array is different (in the x-direction), which creates a 1D spatial phase distribution. The metamaterial itself is supported on a 1mm-thick poly(methyl methacrylate) substrate, whereas the microchannel and microcavity architecture is imbedded into a 2mm-thick polydimethylsiloxane (PDMS) layered structure. The ring cavities are located in the layer that is bonded with the poly substrate, which also hosts the metamolecule-filling channels (see Figure 2). The microfluidic control system is also fabricated within a PDMS layered structure (1mm thick).

Figure 2. Realization of the RARM. (a) Photograph of the microfluidic chip, a square array of metamolecules that are partially filled with liquid metal, a microchannel pneumatic array, and a ternary valve multiplexer (that can be used to address individual metamolecules in the array). (b) Photograph of a single molecule being tuned. Air pushes mercury away from the cavity void and forms a large air gap. (c) The gap in the metamolecule is restored to the initial state when the air pressure decreases.

Our electromagnetic wave RARM focusing experimental results are presented in Figure 3. In these experiments, we illuminated the metamaterial with a 16GHz plane wave that was propagating along the z-direction (i.e., normal to the plane of the metamolecule array) and polarized along the y-direction. We performed all of our measurements in a microwave anechoic chamber, in which we used a vector network analyzer with a horn antenna as the wave source and a monopole antenna mounted on an xy scanner as the probe. We scanned the receiving probe at different distances (in 5mm steps) from the sample to map the transmitted field. Our experimental results, as well as the corresponding simulation results for different phase gradient distributions, are shown in Figure 3. In our experiments, we measured a diffraction efficiency of about 10%. This efficiency can be increased further by maintaining the transmission coefficient during the gap tuning, i.e., by optimizing the metamolecules. The xz and xy cross sections (see Figure 3) show that the beam can be focused into a linear intensity hotspot, which has a full width at half-maximum of 2.1 wavelengths (λ) when the measured focal length is 5.1λ. We are able to continuously tune the focal length from 5.1 to 15.2λ by adjusting the spatial phase gradient.

Figure 3. Experimental and corresponding simulation results that indicate how the RARM lens hotspot changes with variable spatial phase distribution (φ). Results are shown for designed focal lengths of (a) 5 wavelengths (λ) and (b) 10λ. For these measurements, the light is propagating along the z-direction and is linearly polarized along the y-direction. The 3D full Maxwell numerical modeling of the electric field intensity distributions on the xz plane is shown in the first (left) column, and can be compared with the experimental results on the xz and xy planes in the second and third columns, respectively. The corresponding spatial phase distributions (obtained from the hyperbolic lens equation) are shown in the fourth column. a.u.: Arbitrary units.

We have developed the first proof-of-principle demonstration for a RARM with a tunable flat lens function. We form this metamaterial by casting liquid metal microwave resonators through microfluidic channels. Our RARM can be used as a densely integrated tunable lens array, and has several potential applications in high-resolution displays, as well as sensor and imaging systems. In the future, we plan to refine our RARM for a larger electromagnetic spectral range (up to optical frequencies). This will increase the number of its possible applications, e.g., 3D holographic displays for mobile phones, high-performance devices for space division multiplexing in the next generation of telecommunication networks, and adaptive wavefront correction devices.