Abstract
Metamaterials have extraordinary abilities, such as imaging beyond the diffraction limit and invisibility. Many metamaterials are based on splitring structures, however, like atomic orbital currents, it has long been believed that closed rings cannot produce negative refractive index. Here we report a lowloss and polarizationindependent negativeindex metamaterial made solely of closed metallic nanorings. Using symmetry breaking that negatively couples the discrete nanorings, we measured negative phase delay in our composite ‘chess metamaterial’. The formation of an ultrabroad Fanoresonanceinduced optical negativeindex band, spanning wavelengths from 1.3 to 2.3 μm, is experimentally observed in this structure. This discrete and monoparticle negativeindex approach opens exciting avenues towards symmetrycontrolled topological nanophotonics with ondemand linear and nonlinear responses.
Introduction
The theory of diamagnetism was established more than one and a half centuries ago by Weber^{1}. At the atomic level, an orbiting current around the nucleus produces microscopic magnetic fields resulting in the magnetism of materials. However, the magnetic relaxation time of orbiting electrons is much longer than the period of optical waves, diminishing the magnetism of natural materials at optical frequencies^{2}. Inspired by the atomic orbiting current, metallic closedring structures were considered for artificial magnetic responses arising from the induced circulating current. The weak diamagnetism of the closedring structures prevents them from having effective permeability below zero, and hence negative indices of refraction^{3}. By opening a small gap, the splitring resonator exhibits a negative permeability due to the significantly enhanced inductance–capacitance resonance. The combination of splitring resonator with the Drude response from an array of continuous metallic wire into a twoelement system led to the first negative index material (NIM) at microwave frequencies and the rapidly emerging field of metamaterials^{4,5,6,7,8,9,10,11}. However, the longstanding question of the possibility to obtain negative magnetic permeability and negative refractive index with an ensemble of singleelement closed rings has remained. Artificial materials, through the engineering of metaatoms of micro and nanostructures, have exhibited electromagnetic properties that are not accessible in naturally occurring materials, such as negative refraction^{4,5}, superlensing^{6,7,8}, electromagnetic cloaking^{9,10} and unique topological effects^{11}. Significant efforts have been devoted to scale NIMs down to the optical domain. The fishnet of metaldielectric multilayers is one of the most successful optical NIM structures^{12,13,14,15,16}. The magnetic responses of such structures result from the excitation of gap surface plasmons, and the electrical responses are governed by the cutoff frequency of the waveguide mode of the air holes, resulting in negativephase index^{15,16}. Another interesting NIM approach using coupled metal–insulator–metal waveguides has been demonstrated and theoretically extended for broadangle operation^{17,18}. Both approaches however rely on continuous metallic structures to form coupled waveguide modes.
Here, we experimentally demonstrate optical negative index in a metamaterial that is solely made of closed and discrete metallic nanorings. This is achieved by a subtle symmetry breaking of their arrangement in space. Using a Michelson interferometer, negativephase delay is directly observed in such a metamaterial, confirming the proposed singlecomponent strategy. The symmetry breaking allows the nanorings to negatively couple to each other and leads to a polarizationindependent optical negative index, with extremely broadband from 1.3 to 2.3 μm in the metamaterial. This discrete and monoparticle negativeindex approach opens exciting avenues towards isotropic negativeindex metamaterials, the key for practical applications.
Results
Theory and design of closed nanoring chess metamaterial
Discrete metallic nanorings have been studied in rather simple configurations as plasmonic resonators, but have not been able to produce negative permeability or negative indices^{2,3,19,20}. We instead consider two layers of coupled rings as schematically shown in Fig. 1a. The localized mode under consideration is the symmetric dipolar mode with charge distribution of the same sign at the inner and outer surface of the ring walls (Fig. 1b). Plasmon interactions can be comprehensively described using the analogy with the hybridization of wavefunctions in quantum systems^{21,22}. The coupling between plasmonic nanorings lifts the degeneracy of the singleparticle mode and gives the antisymmetric (ω_{−}) and symmetric (ω_{+}) modes with magnetic and electric dipole moments, respectively. Symmetric modes have their current flowing in phase in the two rings, whereas for the antisymmetric modes, the currents oscillate out of phase (Fig. 1b). The frequency split Δω=ω_{+}−ω_{−}=κω_{0} is proportional to the coupling coefficient κ. The coupling coefficient between longitudinally coupled electric dipoles is usually positive, and therefore ω_{+} corresponds to the higher energy antibonding mode and ω_{−} to the lower energy bonding mode. When the spatial symmetry of the coupled nanorings is broken as illustrated in Fig. 1a, that is, the rings are sufficiently shifted (by at least dx=dy>L/2, where L is the length of the dipole moment of the single ring), the mode dispersion undergoes a dramatic change due to the modification of the nearfield Coulomb interaction, leading to an inversion of the plasmon hybridization scheme. While maintaining charge distribution, an initially bonding mode with magnetic dipole moment when the rings are aligned now becomes antibonding, resulting from symmetry breaking (Fig. 1b). The ordering of the modes after symmetry breaking changes the sign of Δω and thus corresponds to negative coupling between the nanorings (Supplementary Fig. S1). We show that a threedimensional (3D) metamaterial built from such negatively coupled discrete rings leads to a negative index and we term it the ‘chess metamaterial’.
Fabrication and experiment
We fabricated two layers of shifted gold nanorings on quartz substrates with planarized SU8 photoresist as spacer. Multiple electron beam lithography processes were employed for the alignment between the layers^{22,23}. An oblique view of the aligned nanorings structure is shown in Fig. 2a. For shifted nanorings, an equal amount of lateral shift, that is dx=dy, in the transverse plane is used, and results in metamaterials completely insensitive to the incoming polarization at normal incidence, a property crucial for device applications. This was confirmed by polarizationresolved measurements, presented in Supplementary Figs S2–S5, and so the chess metamaterial properties can thus be probed with unpolarized light. We note that polarizationindependent fishnet metamaterials have also been reported^{24,25}.
To directly observe the induced negative index, we performed transmission phase measurements with a Michelson interferometer, shown in Fig. 2b. The idler of a femtosecond tunable optical parametric oscillator was used as light source. The pulse duration is 200 fs with a repetition rate of 80 MHz. Comparison of the time delay between the interferogram on the chess metamaterial and the interferogram on an unpatterned region of the substrate infers the additional phase, that is the refractive index of the metamaterial^{26} (Supplementary Fig. S6).
Measured interferograms at the excitation wavelengths of 1,900 and 2,000 nm, obtained from the chess metamaterial with shifts dx=dy=300 nm and a spacer thickness of s=50 nm, are presented in Fig. 2c. The temporal shift between the reference and the metamaterial interferograms in Fig. 2c shows a negative index of −0.93 observed at 1,900 nm at the experimentally observed antisymmetric resonance (Supplementary Fig. S7), whereas in Fig. 2d, an index of +0.65 is obtained at 2,000 nm. This is in very good agreement with the fullwave simulation where a negative index of −1 is obtained around ω^{−}_{s=50 nm, shifted}. The ambiguity between a phase lag and lead is overcome by comparison with simulations or by measuring continuously the delay from a point where the index is known (Supplementary Fig. S8). We have thus directly observed, for the first time, negative index in a metamaterial made of negatively coupled closedring structures. The assignment of an index to a thin film has been subject to debate and is justified by the possibility to explain the optical observables by the retrieved effective paramaters^{26,27}.
Symmetrydependent hybridization
The influence of spatial symmetry breaking and the properties of the chess metamaterials can be further understood by analysing the optical transmission spectra of the coupled nanorings. Figure 3a shows calculated spectra for the case of a thin interlayer (s=50 nm), with aligned (dx=dy=0 nm) nanorings. In this case, the hybridization of the nanorings is normal and the antisymmetric mode occurs at longer wavelength (lower frequencies) than the symmetric mode, ω^{−}_{s=50 nm, aligned}<ω^{+}_{s=50 nm, aligned}, indicating a positive coupling between the rings. When the shift is increased (Fig. 3b), the two modes converge towards each other and spectrally cross (Fig. 3c). Figure 3d shows a metamaterial with lateral shifts of dx=dy =L. We observe drastic change compared with the normal hybridization picture. In this regime, the antisymmetric mode instead occurs at a shorter wavelength (higher frequencies), ω^{−}_{s=50 nm, shifted}>ω^{+}_{s=50 nm, shifted}. The relative spectral position of the symmetric (ω^{+}_{s=50 nm, shifted}) and antisymmetric (ω^{−}_{s=50 nm, shifted}) modes in the case of a shift of L is thus inverted, showing a negative coupling between the two nanorings due to the symmetry breaking^{28}. The change in the sign of the coupling between the nanorings corresponds to a crossing of the real parts of the eigenfrequencies, and therefore leads to the spectral overlap between the antisymmetric and symmetric modes. The charge and electromagnetic fields distributions at each of the bonding and antibonding resonances are numerically analysed and presented in Supplementary Fig. S1. Figure 3e shows an always positive index for aligned rings, whereas a negativeindex region occurs in Fig. 3f for a full shift. The additional resonances in Fig. 3, correspond to the hybridization of higher order multipoles of the rings^{29}. Nearfield patterns at these resonances are presented in Supplementary Fig. S1.
The evolution of the index of refraction for two layers of nanorings with symmetry breaking revealed an always positive refractive index for the aligned nanorings (dx=dy=0), whereas a negativeindex region is obtained when there is sufficient shift between the strongly coupled nanorings (Fig. 3). The emergence of optical negative index in this metamaterial stems from the spectral overlap of symmetric and antisymmetric modes, corresponding to electric and magnetic dipole moments, respectively. In the negative coupling regime, the longlived resonance (antisymmetric mode) occurs at higher energy than the shortlived resonance (symmetric mode). The modes can thus naturally overlap because the second resonance (antisymmetric mode) occurs in the broad negative tail (strongly coupled to far field) of the first resonance (symmetric mode) leading to negative refractive index. In the case of aligned resonators (positive coupling), the modes are difficult to overlap, which leads to positive index or a single negative medium^{5,22}. Any attempt to build 3D metamaterials from those systems leads to a bandgap instead of a negativeindex passband (Supplementary Figs S9 and S10). We shall demonstrate that a medium built from such negatively coupled discrete plasmonic particles will support backward propagating waves.
Threedimensional chess metamaterials
A multilayer of the chess metamaterial, exclusively exploiting localized resonances, leads to the tight coupling and the Fanotype interferences between those multiple localized modes. This results in the formation of an ultrabroad negative index band. Figure 4 shows the fabricated 3D chess metamaterial consisting of tenlayer closed ring and spacer. The symmetry is laterally broken by shifting each layer with respect to the adjacent ones. The transmission spectra of the 3D chess metamaterials with different numbers of fabricated gold nanoring layers, from two to five, are calculated using finitedifference time domain numerical simulations (Fig. 5a). Measurement results are shown in Fig. 5b, and good agreement with calculations is found. By stacking the shifted nanorings, a passband builds up between the wavelengths of 1.3 and 2.3 μm. This extremely broad passband constitutes the negativeindex region originating from the negative coupling between the nanorings (Supplementary Fig. S11). The negative index can be interpreted as resulting from Fano resonances or the spectral overlap between resonant modes of opposite symmetry. These modes interact with the incident light continuum and contribute to the effective permittivity and the permeability. The strategy presented here, consisting of overlapping spectrally localized resonances can thus be regarded as a negative index originating from Fano resonances. Figure 5c shows the effective refractive index of the metamaterial made of 20 layers of metallic nanorings, which is unambiguously determined by replacing the metamaterial with a thin film model^{30,31}. The figure of merit (FOM) is an important parameter of negativeindex metamaterials and is simply defined as FOM=n′/n″ where n′ and n″ are the real and imaginary parts of the index. For a bulk metamaterial structure made of twenty ring layers presented in Fig. 5c, we found an FOM of ~10 at 2 μm (Supplementary Fig. S12). The broadband and lowloss operation can also be observed from the real and imaginary parts of the index of refraction. In thin metamaterials, the localized modes reradiate in free space and the radiation loss is high. In thicker samples, the loss is decreased because the radiation from different rings cancelled inside the structure when they are out of phase, leading to decreased radiation loss of the bulk metamaterial. Figure 5d shows the time evolution of the wave inside the metamaterial structure at the middle of the passband, demonstrating the backward waves in a bulk metamaterial made of a single type of discrete resonators. Movies of the time evolution of wavefronts in the metamaterial in negative and positiveindex regions are presented in Supplementary Movies 1–6. Moreover, phase measurements on the multilayer metamaterial, using a broadband Mach–Zehnder interferometer, confirm the broadband nature of our structure (Supplementary Fig. S8). We have however not fabricated the 20 layers of rings to observe the full bandwidth (~1 μm) of the system. We would like to note that the assignment of effective index to our structure is justified by the singlemode operation in the region of interest, but, the index presented here is only valid for near normal incidence, when the inplane wavevector is much smaller than the inplane reciprocal lattice vector of the metamaterial. The transition in the real part of the index is also observed in the fishnet structure^{32}, and alternative methods for retrieval have been discussed elsewhere^{33}. In our structure, it originates from a transition from a negativeindex mode to a positive index mode governing propagation in the system (Supplementary Figs S13 and S14). Interestingly, wavefronts are uniformly distributed in our metamaterial unlike the fishnet system, where light was mainly travelling through the air holes^{15}. Our strategy, as a fully discrete particle route, is thus a possible path toward 3D isotropic optical metamaterials^{34,35,36}. It is worth noting that symmetry breaking, despite being considered in the context of Fano resonances, has never been used to create a complex effective medium (see ref.37 and references therein), and particularly a negativeindex medium operating at optical frequency.
Discussion
We reported the first experimental demonstration of an ultrabroadbandnegative index in bulk optical metamaterials by controlling the symmetries of 3D localized plasmonic resonances using discrete closed metallic nanorings. A 3D, polarizationindependent, negativeindex metamaterial using one type of metaatom at optical frequencies in a ‘Fanoinduced negative index’ approach has been reported. We have broken the paradigm of negative index with closed nanorings. The ability to manipulate light with the spatial symmetry of 3D coupled metallic nanoparticles may enable a new era in the design of metamaterials, opening the way to the observation of complex topological effects. We have also overcome the problem of current optical negativeindex metamaterials (based on infinitely long metallic components) as plasmonic waveguiding systems (fishnet and coupled coaxial waveguides, for example) that are inherently 2D and thus insufficient to realize 3D isotropic metamaterials, but our structure is still angular dependant. The exclusive use of localized plasmonic modes should allow the design of angleindependent metamaterials and pave the way towards lowloss linear and nonlinear metamaterials (where symmetries have a fundamental role), novel designs of microwave, terahertz and optical metaplasmonic devices.
Methods
Sample fabrication
The samples were fabricated by stacked electron beam lithography. The 30nmthick firstring layer and the alignment marks are patterned on a 4nmthick indium tin oxide film coated on a glass substrate by EBL (electron beam lithography, CRESTEC CABL9,510CC). The lithography is followed by ebeam evaporation of gold (Solution, CHA Industries) and liftoff process. The 80nmthick interlayer made of SU8 2000.5 (Microchem Corp.) is diluted by a thinner solvent (Cyclopentanon), spun over the firstring layer, crosslinked by UV light exposure, and baked on a hot plate. The thickness of the interlayer can be controlled by changing the ratio between SU8 2000.5 and the solvent as well as the spinning speed. Because of the very low viscosity of the interlayer, the surface of the interlayer is automatically planarized and the distance between the ring layers is 50 nm after 95 °C baking on a hot plate. The fabrication is repeated using alignment marks of adjacent layers until the obtainment of the 3D chess metamaterial.
Optical measurements
The transmission spectra are measured using a Brucker instrument Fourier transform infrared spectrometer equipped with a Cassegrain objective. The nearinfrared illumination is focused on the 30 × 30 μm^{2} samples. The sample area is filtered using an aperture. The transmitted signal is collected by another microscope objective on to a liquid nitrogencooled mercurycadmiumtelluride detector.
In the measurement of Fig. 2, using the Michelson interferometer, the thickness of the metamaterial is d_{meta}=110 nm and the thickness of the reference SU8 just beside the structure is d_{ref}=80 nm (Supplementary Fig. S6). The time delay between the two interferograms on the sample and on the reference is given by: Δt=2d_{meta}n_{meta}/c_{0}−[2d_{ref}n_{ref}/c_{0}−2(d_{meta}−d_{ref})/c_{0}] and thus: n_{meta}=1+c_{0}Δt/2d_{meta}+(n_{ref}−1)d_{ref}/d_{meta}. Phase measurements of the multilayer metamaterial are performed using a broadband Mach–Zehnder interferometer coupled to a spectrometer, and capable of providing the broadband phase response in a single measurement (Supplementary Fig. S8).
Numerical simulations
Numerical simulations of the chess metamaterial are carried out using a FDTD (finitedifference time domain) package (CST Microwave Studio). The periodic systems are modelled using their unit cells with periodic boundary conditions. The theoretical effective parameters are calculated from numerical simulation results using an inversion algorithm.
Additional information
How to cite this article: Kanté, B. et al. Symmetry breaking and optical negative index of closed nanorings. Nat. Commun. 3:1180 doi: 10.1038/ncomms2161 (2012).
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Acknowledgements
The authors acknowledge funding support from the US Department of Energy, Office of Basic Energy Sciences under Contract No. DEAC0205CH11231 through Materials Sciences Division of Lawrence Berkeley National Laboratory (LBNL). The authors thank J. Rho for his help and discussion.
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Contributions
B.K. designed the chess metamaterials and performed the theoretical calculations. Y.S.P. fabricated the samples. B.K., K.O'B., D.S., and N.D.L.K. conducted optical measurements. X.Z. and X.B.Y. guided the research. B.K., Z.J.W., X.B.Y. and X.Z. prepared the manuscript. All authors contributed to data analysis and discussions.
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Supplementary information
Supplementary Figures
Supplementary Figures S1S14 (PDF 3711 kb)
Supplementary Movie 1
Time evolution of phase fronts in the metamaterial made of 20 layers of rings in the negative index region. The animation shows backward waves in the structure at 1.7 μm. In all Supplementary Movies, light is incident from air and is exiting in glass. (MOV 424 kb)
Supplementary Movie 2
Time evolution of phase fronts in the metamaterial made of 20 layers of rings in a positive index region. The animation shows forward waves in the structure at 3 μm. (MOV 428 kb)
Supplementary Movie 3
Time evolution of phase fronts in the metamaterial made of 20 layers of rings in the negative index region. The animation shows backward waves in the structure at 1.4 μm. (MOV 1027 kb)
Supplementary Movie 4
Time evolution of phase fronts in the metamaterial made of 20 layers of rings in the negative index region. The animation shows backward waves in the structure at 1.9 μm. (MOV 1028 kb)
Supplementary Movie 5
Time evolution of phase fronts in the metamaterial made of 20 layers of rings in a positive index region. The animation shows forward waves in the structure at 2.5 μm. (MOV 1031 kb)
Supplementary Movie 6
Time evolution of phase fronts in the metamaterial made of 20 layers of rings in a positive index region. The animation shows forward waves in the structure at 2.7 μm. (MOV 1029 kb)
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Kanté, B., Park, YS., O’Brien, K. et al. Symmetry breaking and optical negative index of closed nanorings. Nat Commun 3, 1180 (2012). https://doi.org/10.1038/ncomms2161
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