Dolling, G.

Linden, S.

Wegener, M.

KITopen

March 1, 2007 / Vol. 32, No. 5 / OPTICS LETTERS 551First published in:Realization of a three-functional-layernegative-index photonic metamaterialG. Dolling and M. WegenerInstitut für Angewandte Physik and DFG-Center for Functional Nanostructures (CFN), Universität Karlsruhe (TH),D-76131 Karlsruhe, GermanyS. LindenInstitut für Nanotechnologie, Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft,D-76021 Karlsruhe, GermanyReceived November 8, 2006; revised December 5, 2006; accepted December 5, 2006;posted December 8, 2006 (Doc. ID 76875); published February 2, 2007We modify a recently theoretically suggested multilayer negative-index photonic metamaterial design andfabricate corresponding structures with up to three functional layers (seven actual layers) for the first timeto our knowledge. Measured transmittance and reflectance spectra agree well with theory. © 2007 OpticalSociety of AmericaOCIS codes: 160.4760, 260.5740.Metamaterials are man-made composite materialsconstructed from subwavelength building blocks thatare densely packed into an effective material.Throughout the past few years, photonic metamate-rials exhibiting artificial magnetism1–3 and a nega-tive refractive index4–8 n have become available atoptical frequencies. All of these studies, however, in-vestigated single functional layers only (five func-tional magnetic layers at 6 THz frequency are dis-cussed in Ref. 9). It is well known, e.g., fromelectronic crystals, that the crystal surface or amonolayer can exhibit properties that are rather dif-ferent from the bulk. Thus it is relevant to investi-gate whether the optical constants of a single layer ofa negative-index metamaterial really correspond tothose of many layers (bulk).In this Letter we report the successful fabricationof one-, two-, and three-functional-layer negative-index photonic metamaterials for the first time to ourknowledge. Our optical experiments agree well withnumerical calculations. This comparison shows thatthe key features do not change with the number offunctional layers.A single functional layer is shown in Fig. 1(a). Asdiscussed in detail previously,6–8,10 the incident lightfield can excite an antisymmetric current oscillationin the two metal layers of the broad stripes, leadingto part of a ring current and hence to a local magneticdipole moment and to negative magnetic permeabil-ity above the magnetic resonance frequency. The elec-tron oscillations along the thin wires lead to a dilutedDrude-metal response with negative electric permit-tivity below the effective plasma frequency. The com-bination of these two aspects results in a negative in-dex of refraction. The obvious first approach toextend this structure into the third dimension is tostack this building-block metal–dielectric–metal(mdm) with an additional spacer layer between (i.e.,mdm–spacer–mdm–spacer–) several or many11times. A simplified design results from altogether0146-9592/07/050551-3/$15.00 © EVA-STAR (Elektronisches Volltextarchhttp://digbib.ubka.uni-karlsruhe.de/vollteliminating the additional spacer between the build-ing blocks and then merging the adjacent pairs ofmetal layers into one, leading to the simple layer se-quence mdmdmdmdm.. .. Note that the lattice con-stant along the stacking direction, az, becomes muchsmaller than the wavelength of light. This meansthat the effective-medium approximation is very welljustified. Indeed, the design used in the experimentsbelow uses 31 nm silver and 21 nm MgF2; hence az=52 nm, which is 27 times smaller than the opera-tional wavelength of 1410 nm. Numerical calcula-tions show that the magnetic-dipole moments of thethree different functional layers add up to a finitemacroscopic magnetic field. The corresponding Hfield is illustrated in Fig. 1(c). It results mainly fromthe displacement current, i.e., from −iD=−i0Ein the frequency domain. To illustrate this aspect,Fig. 1(d) shows a snapshot of the E field phaseshifted by 90° with respect to Fig. 1(c).The silver-based samples are fabricated by stan-dard electron-beam lithography and a lift-off proce-dure. For details, see our Refs. 3 and 6–8. This fabri-cation procedure results in nonrectangular sidewalls, typically with an angle  of 8° with respect tothe substrate normal on all sides. Obviously, this ef-fect becomes particularly influential for thicksamples like the multilayer structures of interesthere. The electron micrographs shown in Fig. 2 re-veal good sample quality.Our calculations are based on a commercial finite-difference time-domain program package (CST MicroWave Studio). All geometrical parameters are indi-cated in Fig. 1; optical material parameters taken areMgF2 refractive index nMgF2=1.38, glass substrate re-fractive index nsubstrate=2.2, and the Drude modelfor silver with plasma frequency pl=1.371016 s−1and damping (or collision) frequency col=8.51013 s−1. This metal damping strongly influenceswhether a negative refractive index results from the2007 Optical Society of Americaiv – Scientific Articles Repository) exte/1000010989552 OPTICS LETTERS / Vol. 32, No. 5 / March 1, 2007parameter retrieval to be discussed below. The cho-sen damping value is identical to that recently ob-tained from the comparison with detailed interfero-metric experiments.7 Thus this value can beconsidered very trustworthy, and we shall not repeatinterferometric experiments here. We have previ-ously published various interferometric experimentsthree times.6–8Figure 2 compares measured and calculatednormal-incidence transmittance and reflectance spec-tra for the two orthogonal linear incident polariza-tions indicated at the top and for N=1, N=2, and N=3functional layers. Three functional layers correspondto seven actual layers, i.e., to the sequence mdmd-Fig. 1. Scheme of the metamaterial with N=1 functionallayer under investigation. (a) Top view on one unit cell, (b)side view. The geometrical parameters are indicated andare given by ax=ay=645 nm, wx=318 nm, wy=173 nm, =8°, t=31 nm, s=21 nm, and ex=ey=14 nm. (c) Snapshot ofthe H field (linear scale) for N=3 and a wavelength of1430 nm (compare Figs. 2 and 3) for the plane indicated bythe dashed horizontal line in (a). (d) E field (linear scale)for the same plane and wavelength.mdm on top of the glass substrate. Horizontal polar-ization will lead to a negative refractive index (seebelow); vertical polarization merely serves as a con-sistency check. The overall agreement between ex-periment and theory in Fig. 2 is very good—even forthe rather complex three-functional-layer sample.Notably, the transmittance for this sample around awavelength of 1410 nm, where a negative real part ofthe refractive index occurs (see below), is as large as60%. Furthermore, the present result for the one-functional-layer sample are consistent with our pre-vious work. Note that we have used a strictly identi-cal parameter set for the three cases N=1,2,3 in ourcalculations, i.e., identical wx, wy, ax, ay, , s, t, ex, ey,as well as identical optical parameters and identicalDrude parameters. Thus, the following retrieval,based on the same theory and parameters, can beconsidered very trustworthy.We retrieve the effective optical parameters asusual.12 These parameters refer to a fictitious homo-geneous film with a thickness corresponding to thetotal thickness d of the metamaterial stack (d=83,135,187 nm for N=1, 2, 3, respectively) on theglass substrate and with complex field-transmittanceand field-reflectance spectra strictly identical tothose of the metamaterial. Figure 3 shows that theshape of the retrieved real part of the complex refrac-tive index hardly changes with the number of func-tional layers N for N=1,2,3. The negative real partof n for N=2,3 results from the combination of anegative real part of the electric permittivity  (notFig. 2. Measured (solid) and calculated (dashed) normal-incidence transmittance (red) and reflectance (blue) spectrafor the relevant horizontal incident polarization in the left-hand column. For completeness and as a consistency check,the vertical polarization is shown in the right-hand col-umn. The first, second, and third rows correspond to N=1,2,3 functional layers, respectively. Insets, correspond-ing electron micrographs with 400 nm scale bar.March 1, 2007 / Vol. 32, No. 5 / OPTICS LETTERS 553shown) and a negative real part of the magnetic per-meability . The increase of the figure of merit(FOM) given by FOM=−Ren / Imn with N towarda maximum of FOM2.5 at a wavelength of 1410 nmshould not be taken too seriously, as the detailed be-havior depends on for what value of N the responsehas been optimized. Here we have optimized it forN=3. The blueshift of the resonance with increasingN simply results from the trapezoidal shape, i.e.,from the finite angle  [see Fig. 1(b)], which directlyinfluences the magnetic resonance frequency. Onemight have expected three magnetic resonances atthree different spectral positions for N=3 or a hugeinhomogeneous broadening—if the three functionallayers were independent. The numerical calculationsin Fig. 3 clearly show that this behavior does not oc-cur. The magnetic dipole moment of one functionallayer stems from the antisymmetric current oscilla-tion in the two metal layers surrounding one dielec-tric spacer. Thus one might have naively expectedthat the magnetic-dipole moments of adjacent func-tional layers would cancel to some extent. The nu-merical calculations in Figs. 1(c) and 3 show that thisbehavior does not occur either. We conclude that in-teraction effects among the different functional lay-ers are of crucial importance. This conclusion is notsurprising in view of the subwavelength distance ofthe functional layers that introduces a strong cou-pling via the light field. Furthermore, adjacent func-tional layers share one common metal layer. Thesetwo aspects lead to a cooperative behavior that isvery favorable for performance. In particular, itFig. 3. Effective refractive index n (top) and magnetic per-meability  (bottom) retrieved from the calculated complextransmittance and reflectance spectra for the same param-eters as in Fig. 2; horizontal incident polarization. Realparts, solid, imaginary parts, dashed. The number of func-tional layers N is indicated.makes the structure robust against varying indi-vidual resonance frequencies, i.e., robust against fab-rication tolerances.In conclusion, we have realized a negative-indexphotonic metamaterial with three functional layers(rather than just one functional layer). These resultsare very encouraging in that the measured perfor-mance is still close to theory and in that the retrievedoptical parameters do not change too much with thenumber of functional layers—as expected for an idealmetamaterial. Also, for the design presented here,the effective-medium limit is well fulfilled, as the rel-evant wavelength of light is 27 times larger than thelattice constant in the propagation direction. It iscurrently not quite clear, however, whether the men-tioned cooperative effects will prevail for structuresthat are many wavelengths in thickness. While ourresults are a first step toward three-dimensional pho-tonic metamaterials, it should be clear that it is stilla long way to truly three-dimensional isotropicnegative-index metamaterials at optical frequencies.We thank Costas M. Soukoulis for discussions andfor exciting us about the field of metamaterials. Weacknowledge support by the Deutsche Forschungsge-meinschaft (DFG) and the State of Baden-Württemberg through the DFG-Center for Func-tional Nanostructures (CFN) within subproject A1.5.The research of S. Linden is further supportedthrough a Helmholtz–Hochschul–Nachwuchsgruppe(VH-NG-232). The work is performed within theKarlsruhe School of Optics & Photonics (KSOP). G.Dolling’s e-mail address is gunnar.dolling@physik.uni-karlsruhe.de.References1. T. J. Yen, W. J. Padilla, N. Fang, D. C Vier, D. R.Smith, J. B. Pendry, D. N. Basov, and X. Zhang,Science 303, 1494 (2004).2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T.Koschny, and C. M. Soukoulis, Science 306, 1351(2004).3. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M.Soukoulis, and S. Linden, Opt. Lett. 30, 3198 (2005).4. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M.Osgood, and S. R. J. Brueck, Phys. Rev. Lett. 95,137404 (2005).5. V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K.Sarychev, V. P. Drachev, and A. V. Kildishev, Opt. Lett.30, 3356 (2005).6. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis,and S. Linden, Science 312, 892 (2006).7. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis,and S. Linden, Opt. Lett. 31, 1800 (2006).8. G. Dolling, M. Wegener, C. M. Soukoulis, and S.Linden, Opt. Lett. 32, 53 (2007).9. N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S.Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou,T. Koschny, and C. M. Soukoulis, Opt. Lett. 30, 1348(2005).10. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C.Panoiu, and R. M. Osgood, Opt. Express 13, 4922(2005).11. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M.Osgood, and S. R. J. Brueck, Opt. Express 14, 6778(2006).12. D. R. Smith, S. Schultz, P. Marko, and C. M. Soukoulis,Phys. Rev. B 65, 195104 (2002).

Realization of a three-functional-layer negative-index photonic metamaterial

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Realization of a three-functional-layer negative-index photonic metamaterial

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