We are interested in making materials that have a negative index of refraction. No naturally occurring material that we know of has this property, but it could be achieved in an metamaterial . An optical metamaterial is composed of elements that are smaller than the wavelength of light, but that can interact with light in interesting ways. We are developing ways to make optical metamaterials through self-assembly.
Metamaterials with a negative refractive index could be used in super-resolution imaging or cloaking, but they are very hard to make because the structural elements must be much smaller than the wavelength of light. For visible wavelengths, that means that the elements must be 100 nm or smaller. Most ways of making such structures require the same kind of "top-down" fabrication techniques that are used in making microchips, but these techniques aren't very good at making 3D materials.
One simple way to make a 3D optical metamaterial is to create a suspension of nanoscale electromagnetic resonators, each of which responds isotropically to incoming light. "Resonator" means that when light of a certain frequency range hits the element, it is strongly scattered, and "isotropic" means that the resonance doesn't depend on the orientation of the resonator or the direction of the incoming light. These isotropic resonators don't need to be arranged in an orderly way to yield a negative refractive index. A disordered arrangement of such resonators is called a "metafluid." This idea was first proposed by Urzhumov, Shvets, Fan, Capasso, Brandl, and Nordlander in Optics Express in 2007.
The challenge is figuring out how to make the resonators. They have to be smaller than the wavelength, and highly symmetric, so that their response is isotropic. Urzhumov and coworkers proposed that gold nanoparticles arranged in tetrahedral clusters with gaps of a few nanometers between the particles might work well. The resulting metafluid might look something like this:
In 2010, Jonathan Fan, working with Federico Capasso and collaborating with our group and others, was able to make electromagnetic resonators by assembling gold nanoshells in a drying colloidal droplet. Each resonator was a triangle of three gold nanoshells. Jon and colleagues measured the electromagnetic response of individual clusters and showed that they have both electric and magnetic dipole resonances (see Fan, Wu, Bao, Bao, Bardhan, Halas, Manoharan, Nordlander, Shvets, Capasso. Science, 2010). The frequencies of the two resonances can be tuned relative to one another by changing the separation gaps between the nanoshells.
Jon explained the resonance of the clusters by analogy to an LC circuit. Each particle has a plasmonic resonance, because incident light can excite a surface wave. When the particles are close enough to each other, the fields from neighboring particles can interact, producing a magnetic resonance. In the circuit analogy, the gaps between the nanoparticles act like capacitors, and the nanoparticles themselves like inductors. Below is an electron microscope image (left) of one of Jon's trimers, along with a diagram (right) showing the equivalent LC circuit.
Scale bar: 100 nm
The gaps between the particles are only a few nanometers, so small that you can't see them in the electron microscope image. If the gaps are too large, the coupling between the nanoparticles is too weak to give a strong magnetic response. If -they are too close together, the particles could touch and short the circuit. We were able to make such precise gaps by putting a self-assembled monolayer of polymer on each particle. This "bottom-up" method can control the gap thickness much more precisely than top-down methods such as lithography.
Making uniform nanoscale particles
The gold nanoshells that Jon used are uniform and smooth, but aren't so easy to make and aren't stable for long times. We realized that it would be easier to work with solid gold particles, but the usual synthesis methods yield polydisperse, nonspherical metal nanoparticles. If we were to assemble these particles into clusters, the gap spacing would be non-uniform, and there would be "hot spots" due to the crystalline facets. Monodisperse, smooth gold particles are needed to ensure that the separation gaps and resonances are uniform.
We worked with Gi-Ra Yi's group at Sungkyunkwan University (Korea) to make and characterize these particles. Prof. Yi's group developed a synthesis method that combines crystal growth and etching (Lee, Schade, Sun, Fan, Bae, Mariscal, Lee, Capasso, Sacanna, Manoharan, Yi. ACS Nano). They first make octahedral gold particles, then slowly etch them to transform them smooth, monodisperse nanospheres. These spherical particles can serve as seeds for the growth of larger octahedra which can in turn be etched again. The size of the gold nanospheres can therefore be adjusted as desired. Li Sun and Nick Schade found that these particles show much more reproducible optical properties than conventional gold particles, both when they are on a glass slide and when they are very close to a thin metal film, as shown below. This reproducibility is crucial for assembling uniform electromagnetic resonators.
Self-assembly of tetrahedral clusters
More recently we have been trying to make tetrahedral clusters rather than the triangular ones that Jon Fan made, which have anisotropic resonances. The tetrahedron is the simplest structure that supports isotropic electric and magnetic dipole resonances. But how do you get spherical gold nanoparticles to assemble into tetrahedral clusters?
Nick Schade showed that this problem can be solved through a nonequilibrium self-assembly method. As a proof of concept, he mixed polystyrene microspheres of two different sizes. The large spheres could stick irreversibly to — or "park" on — the smaller spheres. To make them stick, Nick used either oppositely charged particles or particles with complementary DNA strands on their surfaces, as shown below:
Surprisingly, this method yields lots of tetrahedra (Nick found about a 90% yield) when the ratio of the diameter of the large spheres to the small ones is 2.45. Our collaborators, Miranda Holmes-Cerfon and Beth Chen, used a "random parking model" to show that there is a critical size ratio, 1 + the square root of 2, or about 2.41, where every cluster becomes a tetrahedron. The critical size ratio arises not just from packing constraints but also because of a long-time lower bound or "minimum parking" number, which is a function of the size ratio. At the critical point, this lower bound and the upper bound set by packing constraints come together. The result is that all clusters contain exactly four large spheres: Tetrahedral_clusters.avi
Have a look at our paper in Physical Review Letters to learn more (Schade, Holmes-Cerfon, Chen, Aronzon, Collins, Fan, Capasso, Manoharan. Physical Review Letters, 2013).
Nick and Nabila Tanjeem are working on using this approach with our ultrasmooth, spherical gold particles. This technique might allow us to make nano-scale metal tetrahedra in bulk and in high yield, for use in a metafluid. Nabila is also exploring alternative routes to negative-index metamaterials, such as the self-assembly of chiral nanostructures.