Low-Loss Multilayered Metamaterial Exhibiting a Negative Index of Refraction at Visible Wavelengths

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We experimentally demonstrate a low-loss multilayered metamaterial exhibiting a double-negative refractive index in the visible spectral range. To this end, we exploit a second-order magnetic resonance of the so-called fishnet structure. The low-loss
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  Low-Loss Multilayered Metamaterial Exhibiting a Negative Indexof Refraction at Visible Wavelengths Carlos Garcı´a-Meca,* Juan Hurtado, Javier Martı´, and Alejandro Martı´nez  Nanophotonics Technology Center (NTC), Universidad Polite´ cnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain Wayne Dickson and Anatoly V. Zayats  Nano-optics and Near-field Spectroscopy Laboratory, Department of Physics, King’s College London,Strand, London WC2R 2LS, United Kingdom (Received 22 October 2010; revised manuscript received 7 January 2011; published 11 February 2011)We experimentally demonstrate a low-loss multilayered metamaterial exhibiting a double-negativerefractive index in the visible spectral range. To this end, we exploit a second-order magnetic resonance of the so-called fishnet structure. The low-loss nature of the employed magnetic resonance, together with theeffect of the interacting adjacent layers, results in a figure of merit as high as 3.34. Awide spectral range of negative index is achieved, covering the wavelength region between 620 and 806 nm with only twodifferent designs. DOI: 10.1103/PhysRevLett.106.067402 PACS numbers: 78.20.Ci, 42.25.Bs Optical media with a negative index of refraction aretheoretically allowed by Maxwell’s laws of electromagne-tism [1]. Although not found in natural materials, a nega-tive refraction index has been successfully achieved usingartificial nanostructured materials termed metamaterials[2]. The interest in negative index media (NIM) lies inthe importance of their exceptional properties, such as thepossibility of superlensing or light storing [3,4]. Metamaterials exhibiting a negative index of refractionhave been experimentally demonstrated in several rangesof the electromagnetic spectrum [2,5]. However, it is in the visible regime where we can take full advantage of NIMproperties. For instance, the superior imaging ability of NIMs would be essential for visible microscopy, withapplications in microelectronics, bio- and nanotechnology.The desired features for a NIM are low loss and isotropy.This last property includes by itself some other featuressuch as polarization independence and negative-index be-havior in the three spatial directions. The strict condition toobtain a negative real part of the refractive index  n ¼ n 0 þ in 00 is  " 00  0 þ  00 " 0 <  0  [6], where the permittivity andpermeability are  " ¼ " 0 þ i" 00 and   ¼  0 þ i 00 , respec-tively. Therefore, a NIM having negative  " 0 and   0 , calleddouble-negative NIM, is required if low losses are de-manded. Up to now, only in a few experiments havenegative index metamaterials been demonstrated inthe visible spectrum, and none of the above features havebeen attained [7–9]. Although a large part of the visible spectrum has been covered by the nanofabricated NIMs(wavelengths from 580 to 780 nm), the current challenge isto improve the above-mentioned aspect in order to makethese metamaterials suitable for practical applications.In this work, we have fabricated multilayer NIMs thatexhibit double-negative behavior at visible wavelengthswhile presenting low-loss and polarization independentoptical properties at normal incidence. This has beenachieved by exploiting the properties of a second-ordermagnetic resonance of the so-called fishnet structure, incontrast to previous works that used first-order magneticresonances, both related to gap surface plasmon polariton(SPP)Bloch modes.Moreover, the fabricated metamaterialis the first experimental NIM in thevisible regime made upof several unit cells along the propagation direction, animportant step towards bulk NIMs in this band.The recent experimental demonstrations of NIMs in thevisible range are based on different variations of theso-called fishnet metamaterial [7–9] (see Fig. 1), which consists of   2 N  þ 1  alternating metal ( m ) and dielectric ( d ) a hts(a)(b)(d)(c) k  E ,H  P1P2  E ,H  P2P1 FIG. 1 (color online). (a) Schematic of a fishnet metamaterialmade up of three unit cells in the propagation direction. Theoverall number of layers is 7 (4 metal layers and 3 dielectriclayers). (b) Top-view SEM image of the fabricated 3-unit-cellfishnet structure 3 (see Table I). (c) Detail of image in (b).(d) Detail of the fabricated 3-unit-cell fishnet structure 4. PRL  106,  067402 (2011) PHYSICAL REVIEW LETTERS  week ending11 FEBRUARY 2011 0031-9007 = 11 = 106(6) = 067402(4) 067402-1   2011 American Physical Society  stackedholearraysresultingin N   metamaterialunitcellsinthe propagation direction ( N  ¼ 1  corresponds to  m - d - m , N  ¼ 2  to  m - d - m - d - m; ... ). This structure can be describedby an effective permittivity governed by the cutoff fre-quency of the waveguide mode supported by the holesdespite wavelength-scale nanostructuring [10,11]. The negativeindexof thisstructurearises fromthecombinationof this effective negative permittivity with the permeabilityresonance resulting from the excitation of a gap SPP in themetal-dielectric-metal multilayer [10–12]. Since the multi- layered structure is periodically patterned and forms aplasmonic crystal, its SPP Bloch modes can be excited atcertain frequencies when diffraction of light on the peri-odic structure contributes towards matching the wave vec-tors of SPP and photons [13–15]. In all recent experimental realizations, the fishnet nega-tive index is a consequence of the excitation of the first-order SPP Bloch mode along the   -  X   direction of theBrillouin zone of the square lattice crystal. The main draw-back of this approach is the high loss due to the weak nature of this resonance in the employed configurations.For instance, in experiments [7–9], the maximum figure of  merit (FOM), which is a standard loss measure defined as FOM ¼j n 0 =n 00 j , is 0.5, 0.7, and 0.3, respectively, implyinglarge absorption losses. Theoretical analysis reveals thatthe use of SPP Bloch modes in the   - M   direction of theBrillouin zone (the so-called second order magnetic reso-nance) makes attainable a strong permeability resonancewith an associated negative permeability within the nega-tive permittivity region [16]. In the overlapping band, thestructure exhibits a double-negative refractive index withlow loss. One of the fundamental advantages of this struc-ture is that the square lattice structure leads to polarizationinsensitive optical properties at normal incidence.Although there are ways to improve the loss aspect infishnet structures based on the first-order SPP resonance[17], it has been shown that, for a polarization independentconfiguration, the FOM associated with the second-orderresonance is noticeably higher than that of the first-orderone. Thus, the use of the second-order resonance is moreadequate if our goal is to achieve low-loss and polarizationindependence simultaneously. It is worth mentioning thatpolarization independence has not been attained in pre-vious experiments, either due to the geometry of the em-ployed structures (based on nonsquare holes or lattices) orto fabrication limitations.Another issue is the transition from two-dimensional tobulk metamaterial behavior in this geometry. It is knownthat the constitutive parameters of the fishnet metamaterialchange with an increasing number of functional layers,until they stabilize for a certain  N   [16,18]. Moreover, the addition of more layers in this metamaterial also enhancesthe FOM [16,18,19]. Thus, the fabrication of a multiple- functional-layer fishnet metamaterial is highly desirable.Given the previous considerations, we designed severalseven-layer ( N  ¼ 3 ) fishnet structures with the secondorder magnetic resonance in the visible spectral range.Structures with a single functional layer were investigatedfor comparison (see Table I). It is worth stressing that onlysingle-layer fishnet structures with negative index in thevisible spectrum had been fabricated until now.The designed structures with several sets of parameters(Table I) were fabricated as follows. Soda lime glass(refractive index of 1.51) was used as a bulk substrate.Silver layers of thickness  t  were deposited by  e -beamevaporation at  2 : 5 A  s  1 . Spin-on resist FOX-12 (pro-vided by Dow Corning) based on hydrogen silsesquioxane(HSQ) was used as the interlayer dielectric. The resist wasdiluted in methyl isobutyl ketone in a ratio of   1:6  andspinned at 6000 rpm with an acceleration of   3000 rpm  s  1 . It was annealed after deposition to remove solventsand densify the film. The resulting refractive index of thedielectric layers (thickness  s ) in the considered spectralrange was 1.41. An additional HSQ layer of the samethickness was deposited on top of the outer silver layer toavoid environmental effects. Thus, the one- and three-unit-cell structures were made up of four and eight layers,respectively. To create the periodic pattern of square holes,focused ion-beam milling was used due to its ability toachieve high aspect ratio geometries. Geometrical patternswere designed on a pixel-by-pixel basis, with each pointrepresented by its spatial coordinate (specifying ion-beamposition) and an associated dwell time controlling themilling duration. Initially, depth calibration was performedusing atomic force microscope characterization of struc-tures fabricated with a range of milling times. Lateraldimensions were adjusted using scanning electron micro-scope (SEM) data to ensure ion-beam tail effects wereincorporated in the final designs. The ion current used forall fabrication was maintained at a maximum of 10 pA,ensuring the smallest focused spot size, at an acceleratingvoltage of 30 kV. Top-view SEM images of some of thefabricated structures are shown in Fig. 1.Experimental and simulated spectra of the fabricatedmetamaterials are presented in Fig. 2. Numerical modelingwas performed with CST Microwave Studio. In the simu-lations, silver was characterized by a Drude-Lorentz modelincluding a term accounting for interband transitions [20].Theadjustableparameters  (chosensuchthatthecollisionfrequency   c ¼ 8 : 5  10 13 s  1 ) and    were set to matchexperimental data. Note that, due to the interbandtransitions term, the losses ascribed to Ag are somewhat TABLE I. Geometrical parameters of the fabricated structures.Structure  N   Ag layers HSQ layers  t  (nm)  s  (nm)  h  (nm)  a  (nm)1 1 2 2 35 30 250 4002 1 2 2 35 30 220 3653 3 4 4 35 15 250 4004 3 4 4 35 15 220 350 PRL  106,  067402 (2011) PHYSICAL REVIEW LETTERS  week ending11 FEBRUARY 2011 067402-2  higher than in previous works. The optical transmissionspectra were measured using a fiber-coupled spectrometerwith a liquid-nitrogen-cooled CCD and  W  -halogen white-light source. The normal incidence transmission spectraare the same (within fabrication tolerances) for the twoorthogonal polarizations of the incident light along themain axes of the crystal lattice, which confirms the polar-ization independence at normal incidence. A good agree-ment between the simulations and the measurements isobserved, verifying the reliability of the numerical results,from which the effective metamaterial parameters can beextracted. Discrepancies at short wavelengths belowWood’s anomaly (dips around 600 nm) are due to thefact that only zero-order transmission is captured inthe measurements, while total transmission is calculatedin the simulations, including high-order diffraction beams.A generalized version of the retrieval algorithm describedin [21] was used to account for the bianisotropy introducedby the substrate and top HSQ layer. The retrieved parame-ters of the fabricated structures with  N  ¼ 3  are shown inFig. 3, where we also depict the retrieved parameters forthe free-standing case to allow for comparison withprevious works where bianisotropy was not considered(note that the fabricated structures were optimized for thefree-standing case). Results are very similar in both cases.The main features of all the fabricated metamaterials aresummarized in Table II together with the data for the otherexperimentally made metamaterials for the free-standingcase. As can be seen, a high FOM with a maximum valueof 1.9 is observed in the 1-functional-layer structures. Thespectral ranges covered by the NIM region in these meta-materials span 656–712 nm (structure 1) and 620–672 nm(structure 2). A further improvement of the figure of meritis achieved with the 3-functional-layer structure, reachingvalues as high as 3.34. In this case, the NIM spectral rangesare 693–806 (structure 3) and 620–713 nm (structure 4). Aminimum negative index of   1 : 3  is achieved (structure 3),with a  FOM ¼ 2 : 73  at the wavelength at which  n ¼ 1 . Itis worth mentioning that the ratio of the free space wave-length to the size of the unit cell along the propagationdirection goes from 12.4 to 15.6. It has been shown that thezeroth-order Bloch mode dominates propagation inside afishnet structure so that it can be considered as homoge-neous[22].An indicator of this propertyis the convergenceof the refractive index with increasing  N  , which has beenverified for the fishnet configuration used here at  N   8 [16]. Nevertheless, the optical properties of the fabricated 640 660 680 700 720 740-2.0-1.00.01.02.03.0710 730 750 770 790 810 830-2.0-1.00.01.02.03.0600 620 640 660 680 700 720 740-2.0-1.00.01.02.03.0660 690 720 750 780 810 840-2.0-1.00.01.02.03.0 Wavelength (nm) n  FOM (b)(a) (c)(d)Wavelength (nm)   FOMFOMFOM ε  n  ε  n  ε  n  ε  FIG. 3 (color online). FOM and real (solid) and imaginary(dashed) parts of the fabricated structures effective parameterswith [(a) structure 3 and (b) structure 4] and without[(c) structure 3 and (d) structure 4] the substrate and top HSQlayer.   ¼  0 þ i 00 is the bianisotropy parameter.TABLE II. Main features of fabricated metamaterials in comparison with previous experiments. The numbers in parenthesis incolumn 1 refer to the corresponding structure in Table I. The polarization independence column refers only to the case of normalincidence.Reference N min ( n 0 ) max (FOM)  n<  0  bands Polarization independent Double negative[7] 1   0 : 6  (780 nm) 0.5 (780 nm)   750 – 800 nm  No No[8] 1   1  (776 nm) 0.7 (772 nm) 753–810 nm No No[9] 1   0 : 25  (580 nm) 0.3 (580 nm) 567–602 nm No NoThis work (1) 1   0 : 68  (690 nm) 1.9 (678 nm) 656–712 nm Yes YesThis work (2) 1   0 : 66  (650 nm) 1.75 (642 nm) 620–672 nm Yes YesThis work (3) 3   1 : 3  (752 nm) 3.34 (734 nm) 694–806 nm Yes YesThis work (4) 3   1 : 13  (670 nm) 3.19 (655 nm) 620–713 nm Yes Yes 500 550 600 650 700 750 800 8500.00.20.40.60.81.0500 550 600 650 700 750 800 8500.00.20.40.60.81.0500 550 600 650 700 750 8008500.00.20.4Simulation    T  r  a  n  s  m   i  s  s   i  o  n   (  a .  u .   )   T  r  a  n  s  m   i  s  s   i  o  n   (  a .  u .   ) (b)(a) (c) 500 550 600 650 700 750 8008500.00.20.40.60.81.0 Wavelength (nm)(d) Experiment P1Experiment P2 Wavelength (nm) 0.81.00.6 FIG. 2 (color online). Normal incidence zero-order measuredand simulated transmission spectra of different fabricated meta-materials: (a) structure 1 (see Table I), (b) structure 2,(c) structure 3, and (d) structure 4. Polarization of the incidentlight with respect to the crystal lattice is shown in Fig. 1. PRL  106,  067402 (2011) PHYSICAL REVIEW LETTERS  week ending11 FEBRUARY 2011 067402-3  structures have been optimized for their specific number of unit cells.The angular dependence of the optical properties of thefabricated metamaterials has also been studied. The trans-mission dispersion measurements were performed in theangular range of   0  – 30  , showing a very good agreementbetween simulations and experiment (Fig. 4). The mainphysical phenomena involved in the creation of the double-negative band can be observed in the dispersion plot. Onone side, the wide transmission band around 1.86 eV(667 nm) can be identified with the localized resonanceoccurring at the cutoff frequency of the waveguide modesupportedby the holes (see also Fig.2). This modecontrolsthe effective permittivity of the metamaterial [11]. On theother side, the forbidden band observed approximately at1.75 eV (708 nm), corresponds to the SPP in the   - M  direction of the Brillouin zone, which is responsible forthe permeability resonance. Remarkably, the SPP Blochmodes corresponding to this resonance exhibit weak dis-persion, in contrast to the highly dispersive SPP modessupported by unstructured metal-dielectric-metal multi-layers or previous typical fishnet configurations. Thismay be ascribed to the large size of the apertures comparedto the unit cell size and the hybridization of the SPP modewith the above-mentioned localized resonance [10]. Theflatness of the SPP band responsible for the magneticresonance suggests the possibility to achieve nearlyangle-independent NIM properties in a considerable angu-lar range.It is worth mentioning that by using an active opticalmedium as the dielectric layer and under optical pumpingconditions it becomes feasible to overcome losses and evenachieve gain in a fishnet metamaterial [23]. In this sense,our metamaterial is merely passive and its performancecouldbemuchimprovedbymakinguse ofanactive opticalmedium in the wavelength region at which the negative-index behavior is obtained.In conclusion, we have experimentally characterizedmultilayer fishnet metamaterials with simultaneouslynegative permittivity and permeability in the visible re-gime. This entails an important step towards homogeneousNIMs in this spectral range. The metamaterial exhibits lowlosses and polarization independence at normal incidence.In addition, it has been found that the gap-SPP Blochmodes determining the permeability resonance displayweak dispersion. Further refinement of the fabricationprocess is expected to extend the negative-index bandtowards shorter wavelengths.Financial support by the Spanish MICINN (ContractsNo. CSD2008-00066 and No. TEC2008-06871-C02) andby the Valencian government (Contract No. PROMETEO-2010-087) is acknowledged. C.G.-M. acknowledges finan-cial support from Grant FPU of MICINN. W.D. and A.Z.acknowledge financial support from EPSRC (U.K.). *To whom correspondence should be addressed.cargarm2@ntc.upv.es[1] V.G. Veselago, Sov. Phys. Usp.  10 , 509 (1968).[2] R.A. Shelby, D.R. Smith, and S. Schultz, Science  292 , 77(2001).[3] J.B. Pendry, Phys. Rev. Lett.  85 , 3966 (2000).[4] K.L. Tsakmakidis, A.D. Boardman, and O. Hess, Nature(London)  450 , 397 (2007).[5] C.M. Soukoulis, S. Linden, and M. 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Drachev  et al. , Opt. Express  16 , 1186 (2008).[21] C.E. Kriegler  et al. , IEEE J. Sel. Top. Quantum Electron. 16 , 367 (2010).[22] C. Rockstuhl  et al. , Phys. Rev. B  77 , 035126 (2008).[23] S. Xiao  et al. , Nature (London)  466 , 735 (2010). 2.42.22.01.81.61.4 H E H  0 2000 4000 6000 80002.42.22.01.81.61.4 H     E  n  e  r  g  y   (  e   V   ) 0.00.20.40.60.00.20.40.60.8 Simulated Measured  (1,1) magnetic resonanceLocalized waveguide mode k (cm ) x  -1 10 3    E  n  e  r  g  y   (  e   V   ) FIG. 4 (color online). Simulated and measured transmission of structure 1 as a function of transverse wave vector and photonenergy. The incident light is p  polarized with respect the plane of incidence. The response is similar for  s  polarized light (notshown). PRL  106,  067402 (2011) PHYSICAL REVIEW LETTERS  week ending11 FEBRUARY 2011 067402-4
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