Letter pubs.acs.org/NanoLett
A Metafluid Exhibiting Strong Optical Magnetism Sassan N. Sheikholeslami,*,† Hadiseh Alaeian,‡ Ai Leen Koh,§ and Jennifer A. Dionne† †
Department of Materials Science and Engineering, ‡Department of Electrical Engineering, and §Stanford Nanocharacterization Laboratory, Stanford University, Stanford, California 94305, United States S Supporting Information *
ABSTRACT: Advances in the field of metamaterials have enabled unprecedented control of light-matter interactions. Metamaterial constituents support high-frequency electric and magnetic dipoles, which can be used as building blocks for new materials capable of negative refraction, electromagnetic cloaking, strong visible-frequency circular dichroism, and enhancing magnetic or chiral transitions in ions and molecules. While all metamaterials to date have existed in the solid-state, considerable interest has emerged in designing a colloidal metamaterial or “metafluid”. Such metafluids would combine the advantages of solution-based processing with facile integration into conventional optical components. Here we demonstrate the colloidal synthesis of an isotropic metafluid that exhibits a strong magnetic response at visible frequencies. Protein-antibody interactions are used to direct the solution-phase selfassembly of discrete metamolecules comprised of silver nanoparticles tightly packed around a single dielectric core. The electric and magnetic response of individual metamolecules and the bulk metamaterial solution are directly probed with optical scattering and spectroscopy. Effective medium calculations indicate that the bulk metamaterial exhibits a negative effective permeability and a negative refractive index at modest fill factors. This metafluid can be synthesized in large-quantity and high-quality and may accelerate development of advanced nanophotonic and metamaterial devices. KEYWORDS: nanophotonics, plasmonics, optical magnetism, nanoparticle assembly
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response.17 The metamolecule was composed of three closely spaced, nonmagnetic metal nanoparticles. The plasmon resonance of each nanoparticle provided a strong electric dipole, which when coupled to adjacent particles gave rise to a strong optical-frequency circulating displacement current and hence a magnetic dipole. However, due to the planar nature of the structure the magnetic mode was only active for a particular illumination polarization and direction. Achieving an optical magnetic response for unpolarized light and a broad range of illumination angles requires three-dimensional structures with a high degree of symmetry and strong interparticle coupling. Further, the creation of a metafluid requires a high yield of assembled metamolecules. While synthetic progress has been made toward this goal,18 no reports to date have directly demonstrated emergent optical magnetism in a liquid metamaterial. In this paper, we experimentally demonstrate a metafluid exhibiting strong optical-frequency magnetism. The constituent metamolecules exhibit an isotropic magnetic dipole, and this magnetic-dipole scattering can be directly observed from the bulk metafluid. The metamolecule’s strong magnetic polarizability forms the basis for bulk media exhibiting a negative permeability and negative index at modest fill factors, as
lmost all familiar optical properties of materials, such as their color, luster, and refractive index, arise from the interaction of the electric field of light with matter. However, as demonstrated by the field of metamaterials, controlling the interaction of light’s magnetic field with matter can yield unprecedented optical properties.1,2 Indeed, metamaterials exhibiting an optical-frequency magnetic response have enabled applications ranging from electromagnetic cloaking3,4 and subdiffraction-limited optical imaging5,6 to strong visiblefrequency optical activity.1,2,7 While metamaterials are conventionally patterned using either electron beam lithography (EBL) or focused ion beam (FIB) milling, nanoparticle self-assembly has emerged as a powerful technique to generate complex nanostructures.1,8−13 Unlike EBL or FIB, nanoparticle self-assembly has the potential to produce three-dimensional geometries with high throughput and relatively low capital investment. Nanoparticle selfassembly is also compatible with colloidal processing, providing a platform for synthesis of a liquid metamaterial or “metafluid”. In contrast to solid-state metamaterials, a metafluid could be directly applied to devices via spincasting or spray-coating for gradient refractive index applications. Alternatively, a metafluid could enable enhanced solution-phase spectroscopy of natural electric, magnetic, or chiral transitions.14−16 En route to a liquid metamaterial, a self-assembled nanoparticle cluster (i.e., a “metamolecule”) was recently shown to exhibit a strong optical-frequency magnetic © XXXX American Chemical Society
Received: May 6, 2013 Revised: July 30, 2013
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approximately 1010 metamolecules/mL. Details concerning the sample synthesis and purification can be found in the Supporting Information. Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) are used to characterize the structures of the assembled metamolecules, shown in Figure 2.
indicated by effective medium calculations. Our approach is based on protein-directed assembly of colloidal metallic nanoparticles, which allows us to synthesize metamolecules with nanoscale precision and on gram-scales. Figure 1 outlines the general strategy for self-assembly of the metamolecules forming our metafluid. The figure also includes
Figure 2. Electron microscopy images of self-assembled metamolecules. The top row shows two examples of high-resolution transmission electron microscopy images. The bottom rows show examples of low voltage scanning electron microscopy images, indicating the three-dimensional structure. All scale bars are 100 nm.
Figure 1. Protein directed assembly of an isotropic metafluid. (a) Silver nanoparticles (i) are functionalized with biotin terminated ligands and mixed in a high ionic strength buffer with streptavidin coated polystyrene nanoparticles (ii) to form core−satellite metamolecules (iii). (b) Photograph of the starting aqueous solutions of silver and polystyrene nanoparticles (i and ii, respectively) and the assembled metafluid (iii).
The samples are prepared by dropcasting the liquid metamaterial onto a copper grid and postembedding the droplet in a methyl cellulose polymer to help maintain the three-dimensional structure as the solvent dries on the membrane.19 The metamolecules are made in high-yield with good monodispersity. The three-dimensional structure of the metamolecules is partially evident from the individual SEMs. A tomographic tilt series confirms their highly symmetric structures, as visualized in three dimensions at high resolution using TEM (Supporting Information video). Using the geometry from the electron microscopy images as a starting point, we simulate the near- and far-field response of the synthesized metamolecules via Generalized Multiparticle Mie (GMM) theory, a semianalytical solution to Maxwell’s equations.20 An individual metamolecule is modeled as 32 silver nanoparticles of 36 nm diameter surrounding the surface of a 90 nm diameter polystyrene sphere, with an average interparticle spacing of 3.8 nm.
photographs of the colloidal starting materials and the bulk metafluid. First, citrate-capped silver nanoparticles of approximate diameter d1 = 36 nm are synthesized according to standard literature procedures and subsequently functionalized with a small number of biotin-terminated polyethylene glycol (PEG) ligands. The biotin-functionalized silver nanoparticles are then added to a solution of streptavidin coated polystyrene nanoparticles of approximate diameter d2 = 90 nm in a high ionic strength buffer. The highly specific chemical recognition of the protein streptavidin to the biotin antibody allows the silver nanoparticles to closely and symmetrically pack around the polystyrene nanoparticle with an average interparticle separation of a ∼ 4 nm. The resultant metamolecules are dispersed in aqueous media with a concentration of B
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Figure 3. Simulated optical properties and experimental darkfield microscopy of individual metamolecules. Light is assumed to be propagating in z with the electric field polarized along x. (a) The near-field properties of the metamolecule at the magnetic dipole resonance frequency (668 nm). The cross-sectional colormap (x−z plane) shows the near-field magnetic enhancement, while the overlaid arrows display the displacement current between the silver nanoparticles. The strong magnetic field enhancement across the middle of the metamolecule and the circulating displacement currents are a signature of the magnetic dipole mode. The scale bar is 25 nm. (b) Calculated far-field scattering properties of the metamolecule, assuming a surrounding media index of n = 1.42 (average of water and glass). Optical scattering along the x-axis, where the electric dipolar modes do not radiate, reveals the magnetic dipole mode in the structure. (c) Experimental dark-field scattering spectrum of an individual metamolecule, considering both unpolarized and cross-polarized configurations. The cross-polarized configuration filters out the scattering from the electric dipolar mode, confirming that the longer-wavelength shoulder in the unpolarized spectrum arises from magnetic dipole scattering.
We first consider linearly polarized optical excitation with the electric field E oriented along the x-axis. The total far-field scattering intensity of the metamolecule is shown in Figure 3b. We also calculate the directional scattering along the x-axis to remove the contribution of the dominant electric dipolar modes and reveal the magnetic dipolar mode and higher-order modes. We assign the lowest energy mode as the magnetic plasmon mode, in agreement with previous studies.21,22 The magnetic character of this mode is confirmed through near-field maps, plotted in Figure 3a at the peak of the magnetic resonance (668 nm). As seen, a cross-section through the middle of the metamolecule reveals a strong local magnetic field enhancement. The plot also includes the calculated displacement currents, superimposed as arrows, revealing the circulating currents characteristic of a magnetic plasmon mode. An additional cross-section taken near the side of the metamolecule shows that the displacement currents are driven through every ring in the metamolecule (see Supporting Information). For reference, a movie of the near-field dynamics over two optical cycles is also included in the Supporting Information. The symmetrical geometry of the assembled core−satellite structures suggests a highly isotropic optical response. Indeed, calculations with different angles of incidence and polarization show negligible differences in the scattering spectrum. Additionally, recent theoretical studies have demonstrated that the magnetic mode of these core satellite metamolecules is robust with respect to defects and irregularities in the packing density.24 However, in agreement with previous studies of planar particle assemblies22,23 we find that the magnetic plasmon mode is sensitive to the interparticle spacing and dielectric environment. We include a larger set of calculations in the Supporting Information showing how variations in the metamolecule geometry result in spectral shifts of the magnetic plasmon resonance. For average interparticle spacings between approximately 2.5 and 5 nm (a range achievable with proteindirected assembly), the magnetic plasmon mode will shift its peak between wavelengths of ∼600 to over 700 nm. Optical characterization of the magnetic plasmon mode in individual metamolecules was performed using a scattering dark-field microscope. A dilute solution of the metamolecules
was introduced into a thin liquid cell atop an inverted microscope, allowing the particles to remain in their fluidphase. The light scattered from individual metamolecules was collected and analyzed in a spectrometer for unpolarized excitation. The scattering spectrum for one metamolecule is included in Figure 3c. For unpolarized excitation, the scattering contains contributions from all allowed modes with a shoulder on the low energy side centered at 700 nm, indicative of the magnetic mode. To confirm the magnetic nature of this peak in the unpolarized spectrum we excite the metamolecule using polarized light and filter the scattering through a crossedpolarizer.17,25 This setup eliminates most of the contribution from the dominant electric dipolar mode, revealing the magnetic mode near 700 nm and higher order electric plasmon modes around 520 nm. The experimental dark-field measurements are in good agreement with the GMM calculations for a dielectric embedding medium of 1.42, an average of the water and glass media constituting the liquid cell. Experimental details and additional single metamolecule darkfield measurements are included in the Supporting Information. The optical magnetism of the bulk liquid metamaterial was probed using a home-built angle and polarization-resolved light scattering setup, illustrated in Figure 4.26 A polarized laser is sent down a test tube filled with a solution of the metamolecules, and the polarization-filtered light is collected by a photodetector as a function of angle in 5° increments. The light scattered by magnetic dipoles will have a cosine-squared dependence, polarized axially with respect to the incident beam. In contrast, the light scattered by electric dipoles will have a sine-squared dependence that is transversely polarized with respect to the incident beam. This measurement can therefore directly quantify the magnetic dipole of the colloidal metamaterial. Since the metamolecules are suspended in water (n = 1.33), the magnetic resonance is predicted to blue shift from 668 nm (as calculated in Figure 3b) to 631 nm (calculations included in the Supporting Information). Accordingly, we probe the magnetic dipole of the ensemble metafluid using a polarized HeNe source at 633 nm. Note that scattering from electric quadrupoles is minimal at this wavelength (see Supporting C
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Figure 4. Optical characterization of the bulk metafluid. The top panel shows the experimental setup for measuring the electric dipolar (ED) and magnetic dipolar (MD) modes of the sample by polarization- and angle-resolved light scattering. The modes are distinguished by scattering with orthogonal polarizations and angular dependence. The bottom panel shows experimental data collected at 5° angular increments. The strong scattering of the magnetic dipole mode in the assembled metafluid is more than 12% of the strength of the electric mode and an order of magnitude greater than the control, unassembled particle solution.
Figure 5. Calculated effective medium properties of the colloidally assembled metamaterial. (a) The effective permeability (μeff) plotted as a function of fill factor and wavelength. The permeability becomes negative at fill factors greater than 0.25 for wavelengths near the magnetic dipole resonance. (b) The effective refractive index (neff) plotted as a function of fill factor and wavelength. The effective index becomes negative at fill factors greater than 0.45. (c) The real and imaginary components of the effective permeability at two different fill factors (solid line fill factor = 0.5, dashed line fill factor = 0.1). (d) The real and imaginary components of the effective refractive index at two different fill factors (solid line fill factor = 0.5, dashed line fill factor = 0.1).
Information). The bottom panel of Figure 4 plots the normalized scattering intensity from the self-assembled colloidal metamaterial and from a control sample consisting of the same number and concentration of unassembled silver and dielectric particles. Note that the very small magnetic dipole scattering from the control (unassembled) sample originates from the first order magnetic Mie type mode of the dielectric particle.27 The substantial magnetic dipole scattering from the assembled metamaterial is approximately 12% of the strength of the electric dipole scattering and more than an order of magnitude greater than the control sample. To our knowledge, this measurement is the first direct evidence of magnetic dipole scattering in a bulk colloidal metamaterial liquid. Having developed a synthesis for the gram-scale production of metamolecules, we can predict the effective optical properties of bulk media composed of these resonators. First, we extract the electric and magnetic dipole polarizabilities28 using a multimodal decomposition of the electromagnetic fields scattered by a metamolecule. Then, the relative effective permittivity, permeability, and refractive index can be calculated using the Maxwell-Garnett formula23,29,30 (note that this approach does not account for interparticle coupling). Figure 5 plots the effective permeability and refractive index of our metamolecules dispersed in water as a function of wavelength and fill factor; the effective permittivity is included in the Supporting Information. As seen, the optical properties of the metamaterial are highly tunable with fill factor. At low fill factors of ∼0.1 or less, the permeability is close to unity across all wavelengths, while the index is near 1.33, the index of water. However, as the fill factor is increased, the permeability and refractive index become negative. For relatively low fill factors
of 0.25, the permeability drops below zero at the magnetic dipole resonance. For fill factors of 0.5, refractive indices of the bulk media are negative for wavelengths between 645 and 681 nm. Although our colloidal metafluid cannot be concentrated to such high densities in solution, fill factors of 0.5 can be achieved through spray coating or spin-casting the colloidal metamaterial solution onto a substrate. These calculations indicate the potential that bulk media assembled from our metamolecules can achieve negative magnetic permeabilities and negative refractive indices. Colloidal approaches to metamaterial synthesis produce three-dimensional structures with nanoscale precision, free from the constraints of conventional, top-down lithographic methods. By leveraging protein-directed assembly, we have demonstrated the large-scale synthesis of an isotropic metafluid. The metafluid exhibits a strong magnetic response at visible frequencies, originating from the subwavelength structure of strongly coupled nonmagnetic nanoparticles. By using angle and polarization-resolved scattering and spectroscopy, we have presented the first direct measurements of optical magnetism in a colloidal metamaterial liquid. This liquid metamaterial could form the basis for new tunable or gradient-index media, applied either as a gel-coating onto solid-state devices or integrated into microfluidic cells. The metamaterial could also create new opportunities for enhanced solution-phase spectroscopy of electric, magnetic, or chiral transitions. Further, based on their facile large-scale synthesis, these fluid materials might accelerate D
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(23) Alu, A.; Salandrino, A. Opt. Express 2006, 14, 1557−1567. (24) Vallecchi, A.; Albani, M.; Capolino, F. Opt. Express 2013, 21, 7667. (25) Enkrich, C.; Wegener, M.; Linden, S.; Burger, S.; Zschiedrich, L.; Schmidt, F.; Zhou, J. F.; Koschny, T.; Soukoulis, C. M. Phys. Rev. Lett. 2005, 95, 203901. (26) Sharma, N. L. Phys. Rev. Lett. 2007, 98, 217402. (27) Garcia-Etxarri, A.; Gomez-Medina, R.; Froufe-Perez, L. S.; Lopez, C.; Chantada, L.; Scheffold, F.; Aizpurua, J.; Nieto-Vesperinas, M.; Saenz, J. J. Opt. Express 2011, 19, 4815−4826. (28) Jackson, J. D. Classical Electrodynamics; Wiley: New York, 1998. (29) Vallecchi, A.; Albani, M.; Capolino, F. Opt. Express 2011, 19, 2754−2772. (30) Simovski, C. R.; Tretyakov, S. A. Phys. Rev. B 2009, 79, 045111.
the evolution of metamaterials from an academic pursuit to an industrial technology.
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ASSOCIATED CONTENT
S Supporting Information *
Additional information, figures, references, and movies. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS We thank Natthi Sharma, Aitzol Garcia-Etxarri, and Andrea Baldi for insightful discussions and John Perrino from the Stanford Cell Sciences Imaging Facility for help with TEM sample preparation. S.N.S. acknowledges funding by the NSFACC Postdoctoral Fellowship under award number 1137024. J.A.D. acknowledges funding from an Air Force Office of Scientific Research Young Investigator Grant (FA9550-11-10024) and a National Science Foundation Career Award (DMR-1151231).
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