Optical metamaterials

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.

Some background

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:

The metafluid: a disordered collection of isotropic electromagnetic resonators.

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.

A trimer composed of metal nanoparticles is analogous to a split-ring resonator.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.

Reproducibility of single particle scattering spectra for spherical crystals compared with conventional gold nanoparticles

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:

Clusters self-assemble in bidisperse mixtures of polystyrene microspheres

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.

Publications

Schade, N. B. Self-Assembly of Plasmonic Nanoclusters for Optical Metafluids, 2015. Publisher's VersionAbstract

I discuss experimental progress towards developing a material with an isotropic, negative index of refraction at optical frequencies. The simplest way to make such a material is to create a metafluid, or a disordered collection of subwavelength, isotropic electromagnetic resonators. Small clusters of metal particles, such as tetrahedra, serve as these constituents. What is needed are methods for manufacturing these structures with high precision and in sufficient yield that their resonances are identical.

Jonathan Fan et al. [Science, 328 (5982), 1135-1138, 2010] demonstrated that colloidal self-assembly is a means of preparing electromagnetic resonators from metal nanoparticles. However, the resonances are sensitive to the separation gaps between particles. Standard synthesis routes for metal nanoparticles yield crystals or nanoshells that are inadequate for metafluids due to polydispersity, faceting, and thermal instabilities. To ensure that the separation gaps and resonances are uniform, more monodisperse spherical particles are needed. An additional challenge is the self-assembly of tetrahedral clusters in high yield from these particles. In self-assembly approaches that others have examined previously, the yield of any particular type of cluster is low.

In this dissertation I present solutions to several of these problems, developed in collaboration with my research group and others. We demonstrate that slow chemical etching can transform octahedral gold crystals into ultrasmooth, monodisperse nanospheres. The particles can serve as seeds for the growth of larger octahedra which can in turn be etched. The size of the gold nanospheres can therefore be adjusted as desired. We further show that in colloidal mixtures of two sphere species that strongly bind to one another, the sphere size ratio determines the size distribution of self-assembled clusters. At a critical size ratio, tetrahedral clusters assemble in high yield. We explain the experimentally observed 90% yield with a nonequilibrium “random parking” model based on irreversible binding. Simulations based on this model reveal that 100% yield of tetrahedra is possible in principle. Finally, we combine these results and present methods for the self-assembly and purification of tetrahedral plasmonic nanoclusters, the simplest building blocks for isotropic metafluids.

Lee, Y. - J. ; Schade, N. B. ; Sun, L. ; Fan, J. A. ; Bae, D. R. ; Mariscal, M. M. ; Lee, G. ; Capasso, F. ; Sacanna, S. ; Manoharan, V. N. ; et al. Ultrasmooth, Highly Spherical Monocrystalline Gold Particles for Precision Plasmonics . ACS Nano 2013, 7 11064-11070. Publisher's VersionAbstract

Ultrasmooth, highly spherical monocrystalline gold particles were prepared by a cyclic process of slow growth followed by slow chemical etching, which selectively removes edges and vertices. The etching process effectively makes the surface tension isotropic, so that spheres are favored under quasi-static conditions. It is scalable up to particle sizes of 200 nm or more. The resulting spherical crystals display uniform scattering spectra and consistent optical coupling at small separations, even showing Fano-like resonances in small clusters. The high monodispersity of the particles we demonstrate should facilitate the self-assembly of nanoparticle clusters with uniform optical resonances, which could in turn be used to fabricate optical metafluids. Narrow size distributions are required to control not only the spectral features but also the morphology and yield of clusters in certain assembly schemes.

Fan, J. A. ; Bao, K. ; Sun, L. ; Bao, J. ; Manoharan, V. N. ; Nordlander, P. ; Capasso, F. Plasmonic Mode Engineering with Templated Self-Assembled Nanoclusters . Nano Letters 2012, 12, 5318-5324. Publisher's VersionAbstract

Plasmonic nanoparticle assemblies are a materials platform in which optical modes, resonant frequencies, and near-field intensities can be specified by the number and position of nanoparticles in a cluster. A current challenge is to achieve clusters with higher yields and new types of shapes. In this Letter, we show that a broad range of plasmonic nanoshell nanoclusters can be assembled onto a lithographically defined elastomeric substrate with relatively high yields using templated assembly. We assemble and measure the optical properties of three cluster types: Fano-resonant heptamers, linear chains, and rings of nanoparticles. The yield of heptamer clusters is measured to be over 30%. The assembly of plasmonic nanoclusters on an elastomer paves the way for new classes of plasmonic nanocircuits and colloidal metamaterials that can be transfer-printed onto various substrate media.

Fan, J. A. ; He, Y. ; Bao, K. ; Wu, C. ; Bao, J. ; Schade, N. B. ; Manoharan, V. N. ; Shvets, G. ; Nordlander, P. ; Liu, D. R. ; et al. DNA-Enabled Self-Assembly of Plasmonic Nanoclusters. Nano Letters 2011, 11, 4859-4864. Publisher's VersionAbstract

DNA nanotechnology provides a versatile foundation for the chemical assembly of nanostructures. Plasmonic nanoparticle assemblies are of particular interest because they can be tailored to exhibit a broad range of electromagnetic phenomena. In this Letter, we report the assembly of DNA-functionalized nanoparticles into heteropentamer clusters, which consist of a smaller gold sphere surrounded by a ring of four larger spheres. Magnetic and Fano-like resonances are observed in individual clusters. The DNA plays a dual role: it selectively assembles the clusters in solution and functions as an insulating spacer between the conductive nanoparticles. These particle assemblies can be generalized to a new class of DNA-enabled plasmonic heterostructures that comprise various active and passive materials and other forms of DNA scaffolding.

Fan, J. A. ; Bao, K. ; Wu, C. ; Bao, J. ; Bardhan, R. ; Halas, N. J. ; Manoharan, V. N. ; Shvets, G. ; Nordlander, P. ; Capasso, F. Fano-like Interference in Self-Assembled Plasmonic Quadrumer Clusters . Nano Letters 2010, 10, 4680-4685. Publisher's VersionAbstract

Assemblies of strongly interacting metallic nanoparticles are the basis for plasmonic nanostructure engineering. We demonstrate that clusters of four identical spherical particles self-assembled into a close-packed asymmetric quadrumer support strong Fano-like interference. This feature is highly sensitive to the polarization of the incident electric field due to orientation-dependent coupling between particles in the cluster. This structure demonstrates how careful design of self-assembled colloidal systems can lead to the creation of new plasmonic modes and the enabling of interference effects in plasmonic systems.

Fan, J. A. ; Wu, C. ; Bao, K. ; Bao, J. ; Bardhan, R. ; Halas, N. J. ; Manoharan, V. N. ; Nordlander, P. ; Shvets, G. ; Capasso, F. Self-Assembled Plasmonic Nanoparticle Clusters. Science 2010, 328, 1135-1138. Publisher's VersionAbstract

The self-assembly of colloids is an alternative to top-down processing that enables the fabrication of nanostructures. We show that self-assembled clusters of metal-dielectric spheres are the basis for nanophotonic structures. By tailoring the number and position of spheres in close-packed clusters, plasmon modes exhibiting strong magnetic and Fano-like resonances emerge. The use of identical spheres simplifies cluster assembly and facilitates the fabrication of highly symmetric structures. Dielectric spacers are used to tailor the interparticle spacing in these clusters to be approximately 2 nanometers. These types of chemically synthesized nanoparticle clusters can be generalized to other two- and three-dimensional structures and can serve as building blocks for new metamaterials.