LETTER pubs.acs.org/NanoLett
Chiral Metamaterial Composed of Three-Dimensional Plasmonic Nanostructures Christian Helgert,*,†,|| Ekaterina Pshenay-Severin,†,|| Matthias Falkner,† Christoph Menzel,‡ Carsten Rockstuhl,‡ Ernst-Bernhard Kley,† Andreas T€unnermann,†,§ Falk Lederer,‡ and Thomas Pertsch† †
Institute of Applied Physics and ‡Institute of Condensed Matter Theory and Solid State Optics, Abbe Center of Photonics, Friedrich-Schiller-Universit€at Jena, Max Wien Platz 1, 07743 Jena, Germany § Fraunhofer Institute of Applied Optics and Precision Engineering, Albert Einstein Strasse 7, 07745 Jena, Germany
bS Supporting Information ABSTRACT: We introduce a top-down fabricated metamaterial composed of three-dimensional, chiral, plasmonic nanostructures for visible and near-infrared wavelengths. Based on a combined spectroscopic and interferometric characterization, the entire complex transmission response in terms of a Jones matrix is disclosed. Particularly, the polarization output state of light after propagation through the nanostructures can be decoded from the measurements for any excitation configuration. We experimentally found a rotation of the polarization azimuth of linearly polarized light exceeding 50° at wavelengths around 1.08 μm. This corresponds to a specific rotation which is significantly larger than that of any linear, passive, and reciprocal medium reported to date. KEYWORDS: Plasmonic nanostructures, nanophotonics, chirality, photonic metamaterials, optical activity
A
rtificially nanostructured materials may exhibit a topology far off the thermodynamic equilibrium which is their primary difference to natural materials. This has been impressively demonstrated by photonic metamaterials which consist of unit cells comprising planar or stacked planar nanostructures.13 These unit cells are much smaller than the wavelengths of the interacting electromagnetic radiation and are commonly referred to as metaatoms.4 By deliberately breaking their spatial symmetries,57 most notably in stacked thin films,8 new effects occurred, such as asymmetric transmission,911 and natural effects were extraordinarily enhanced, such as optical activity.1214 Currently, the immense potential of metamaterials regarding applications, like plasmonic sensing,15 nanoscale size detectors16 or optical information processing,17 is revealed. However, the lack of controlling the structural variation in the third dimension manifests the quasi two-dimensional character of contemporary metaatoms, considerably restricting their mirror and rotational symmetry properties and thus the degrees of freedom in their design. While few notable exceptions with feature sizes on the micrometer scale have been demonstrated recently,18,19 a further miniaturization of such chiral structures down to the nanoscale remained rather challenging. To date, the exploitation of chiral plasmonic nanostructures is one key factor to drastically enhance optical activity and circular dichroism in the visible wavelength regime when compared to natural chiral molecules.22,23 Furthermore, to discuss the properties of nanostructured materials composed of such complex unit cells, their understanding in terms of effective material parameters is likely inappropriate due to strong spatial dispersion.24 For the same r 2011 American Chemical Society
reason even bianisotropic constitutive relations, regardless of their complexity, may not give an adequate description.25 Thus alternative characterizing quantities need to be introduced to cover all pertinent properties of complexly shaped metaatoms. In this contribution, we demonstrate experimentally a photonic metamaterial composed of submicrometer, three-dimensional, chiral unit cells. We show how an ensemble of such nanoscaled metaatoms, which are not just stacked planar layers, can be fabricated by a dedicated technology that involves multiple lithographic steps. In addition, for the first time we measure all entries of its broadband complex Jones matrix in the visible/ near-infrared (VIS/NIR). With this technique at hand there is no need to resort to numerical simulations for disclosing optical farfield properties of complexly shaped nanostructures. Specifically, the polarization output upon exciting the structure by an arbitrary input can be determined immediately. The proposed measurement scheme is not only applicable to photonic metamaterials but enables the complex far-field characterization of the wide class of generally dispersive and/or optically active media. Finally, based on the acquired data, we prove experimentally that this plasmonic chiral nanostructure exhibits a record-breaking optical activity. In particular, a peak polarization azimuth rotation of linearly polarized light exceeding 50° is found for a wavelength of 1.08 μm. The canonical metaatom under consideration here is the loop-wire structure,20,21 which combines a cut-wire pair and a split-ring resonator Received: July 27, 2011 Published: August 19, 2011 4400
dx.doi.org/10.1021/nl202565e | Nano Lett. 2011, 11, 4400–4404
Nano Letters
LETTER
Figure 1. An array of loop-wire metaatoms along with the definition of the coordinate system. The inset shows a single loop-wire metaaom and its lowest order plasmonic eigenmode associated with the excitation of a dominant magnetic dipole response oscillating parallel to the incoming electric field vector. The yellow-green tube indicates schematically the induced electron current flow.
Figure 2. Fabrication and geometry of the nanostructured material. (ah) Schematic of the fabrication procedure of the loop-wire metaatoms. (i) Two sketches of a single loop-wire metaatom from two different perspectives along with the definition of all geometrical parameters, as used in the simulations: lx1 = 280 nm, lx2 = 290 nm, ly = 420 nm, wx = wy1 = wy2 = 155 nm, h1 = h2 = 50 nm, d = 60 nm, and s = 50 nm. (j) False-colored, tilted view scanning electron microscopy image of the fabricated metaatoms with a periodic lattice of 500 nm in both lateral directions before final embedding. The scale bar is 1 μm. The inset shows a corresponding sketch of the metaatoms without the supportive dielectric grating structure.
and can be fabricated by advanced top-down nanotechnology. It shall be mentioned that the metaatom was denoted as a wire braid by earlier sources.26 In Figure 1 we visualize an ensemble of periodically arranged loop-wire metaatoms and the excitation scheme of its lowest order eigenmode. The design of the metaatom was rationally devised as to simultaneously support hybrid plasmonic resonances.20,21 With the coordinate system of Figure 1, a linearly x-polarized electric field excites this mode by driving in-phase currents in the wires. These currents are coupled to the split-ring (the loop). As a result, the mode exhibits a magnetic dipole moment27 which emits an orthogonally polarized electric field with respect to the incident one. Higher order modes are equally supported, e.g., when the currents in the metaatom bear an increasing number of nodes.28 For example, the next mode that is sustained by the particle under the same excitation conditions at higher frequencies exhibits symmetric currents. In that case the currents in the two arms of the split ring co-oscillate, which renders the emitted radiation to be accompanied by an
effective electric dipole perpendicularly oriented to the incoming x-polarized electric field. Since a notable fraction of the scattered field always possesses an electric component orthogonal to the incident polarization, the metaatom exhibits broadband optical activity, which is observed here as a superposition of circular birefringence and circular dichroism. The top-down fabrication of the nanostructured material involved three steps of electron-beam lithography (EBL), two times metal lift-off, and numerous dry etching steps (Figure 2ah). Basically, two L-shaped gold nanoparticles are placed on top of each other and connected in the vertical direction. They are arranged such that the two long arms are parallel and connected at their terminations, while the two short arms are oppositely oriented. The technological process for the fabrication of a periodic array of loop-wire metaatoms starts with the deposition of a bilayer resist (AR-P 610 and AR-P 671 from Allresist Berlin GmbH, Strausberg Germany) based on polymethyl 4401
dx.doi.org/10.1021/nl202565e |Nano Lett. 2011, 11, 4400–4404
Nano Letters
LETTER
Figure 4. (a) Circular dichroism η and (b) circular birefringence θ extracted from the measured Jones matrix of the loop-wire metaatoms.
Figure 3. Measured and simulated transmission spectra of the fabricated metaatoms. The different colors indicate the four entries of the Jones matrix. (a) Measured transmittances, (b) measured transmission phase delays, (c) simulated transmittances, and (d) simulated transmission phase delays.
methacrylate resist (PMMA) with an overall thickness of 170 nm. In addition, a 10 nm thick gold layer was thermally evaporated to ensure a conducting surface. Standard EBL (Vistec SB350 OS, Jena, Germany), wet chemical removal of the gold layer, PMMA development (Figure 2a), and thermal evaporation of a 50 nm thick gold layer was followed by a lift-off step to obtain the first (bottom) layer with L-shaped nanoparticles made of gold (Figure 2b). Along with the structures, multiple alignment marks were written to allow for a precise lateral alignment of subsequent lithography steps. The layer was planarized with a spin-on glass (xR-1541 from Dow Corning, Midland, MI) which was heated and UV-cured. This spin-on glass was chosen to match the dielectric permittivity of the substrate. The following down-etching with CF4 reactive ion beam etching (RIBE) was stopped at a distance of 110 nm from the plane of the substrate, leaving a quasi-planar surface of the dielectric covering of the bottom L-structures (Figure 2c). After depositions of 20 nm chromium and 200 nm FEP171 resist (Fujifilm Arch, North Kingstown, RI), a second EBL-step was performed to define grooves perpendicular to the long arm of the bottom L-shaped nanoparticles. These grooves were transferred through the chromium via inductively coupled plasma-reactive ion etching (ICP-RIE) and into the spin-on glass via RIBE. The latter etching step was repeated several times until intermediate scanning electron microscope inspections revealed unambiguously that the gold arms of the L-structures were laid open (Figure 2d). Spin coating another bilayer of PMMA-resist covered the whole pattern including the grooves in the spin-on glass (Figure 2e). The third and last EBL step defined L-shaped holes in the PMMA with the shorter arms of the structures directed in the opposite direction (Figure 2f). With the procedure described above, subsequent thermal evaporation and lift-off of another 50 nm gold layer led to the formation of the top L-nanostructures connected to the lower L-nanoparticles at the terminations of their longer arms (Figure 2g). The alignment accuracy between top and bottom L-structures was better than 20 nm. Finally, the whole ensemble was embedded in xR-1541 spin-on glass to ensure a homogeneous dielectric surrounding of the metaatoms (Figure 2h) in order to match the dielectric
permittivity of the substrate to inhibit optical activity stemming from an inhomogeneous background. Atomic force microscopy confirmed the top surface to be almost planar with a reminiscent waviness of about 5 nm only. The entire photonic metamaterial covers a macroscopically large area of 2 2 mm. Figure 2i shows a single metaatom structure together with its geometrical parameters, as obtained from topographical measurements. The oblique incidence scanning electron microscopy image in Figure 2j shows the fabricated loop-wire metaatoms prior to dielectric embedding. To quantitativly describe all transmission properties of our nanostructured material, we resort on the classical Jones calculus.29 Thus the metaatoms are assumed to be optically linear, nondepolarizing, and reciprocal, imposing only weak constraints which were verified retrospectively (see Supporting Information). The transmission of coherent light through such media is entirely characterized by the 2 2 complex and dispersive entries Tij(λ) of in ^ lin. It relates the incident (Ein the Jones matrix T x , Ey ) to the out out transmitted field (Ex , Ey ) according to ! ! ! ! Txx Txy Ein Ein Eout x x x ^ lin ¼T ¼ ð1Þ Eout Ein Tyx Tyy Ein y y y The subscript “lin” indicates a linear (Cartesian) base that decomposes the field into x- and y-polarized components, with z being the principal propagation direction. For the experimental characterization, we measured the entire linear Jones matrix of the loop-wire metamaterial for a broad spectral range from 0.65 to 1.7 μm in two steps. First, spectrally and polarization-resolved transmission measurements with a Lambda950 spectrometer from Perkin-Elmer (Waltham, MA) delivered the transmittances as reported previously.11 The results are displayed in Figure 3a. Second, to access also the respective phase information, we developed a novel experimental technique based on white-light Fourier-transform spectral interferometry.33 The phase measurements were performed with a self-built polarization interferometer34 for wavelengths from 0.65 to 1.7 μm. In this polarization interferometer,35 the light beam was divided by a polarizing beam displacer into two parallel beams referred to as sample and reference arms. The beam recombination was achieved upon a second polarizing beam displacer. Note that both beam displacers additionally worked as two parallel aligned polarizers. The nanostructured material was put in the sample arm and illuminated with linearly polarized light. To eliminate the influence of the substrate, it was equally placed in both the sample and reference arms. For x-polarized incoming electric field (E0x), the general output polarization state after propagation through one layer of loop-wire metaatoms was an 4402
dx.doi.org/10.1021/nl202565e |Nano Lett. 2011, 11, 4400–4404
Nano Letters
LETTER
Figure 5. (ac) Linear output polarization states of x-polarized incoming wave after propagation through the loop-wire metaatoms for selected wavelengths as extracted from the measured Jones matrix. The axes are labeled as the normalized and dimensionless output electric field components, i.e., in 2 in 2 1/2 Ex,y = Eout (see eq 1). The numbers indicate the absolute polarization azimuth rotation. x,y /(|Ex | + |Ey | )
ellipse (E1x,y), which was determined by two of the complexvalued coefficients Tij of the Jones matrix: ! ! Txx E0x E1x ¼ ð2Þ E1y Tyx E0x After placing a linear polarizer only in the sample arm between the nanostructured material and the second polarizing beam displacer, two measurements were performed. The polarizer was rotated under +45° and 45° relative to the incoming polarization, respectively. After recombining the two beams, the electric fields of the sample arm (Esam) and of the reference arm (Eref) give rise to interference terms:
loop-wires (45° E(45°, sam 3 Eref ¼ A 3
Txx ( Txy 2
ð3Þ
where A is a complex coefficient accounting for differences between the interferometer arms. This value was eliminated by two additional measurements in which the nanostructured material was replaced by air (Tair) under otherwise identical polarizing conditions. The according interference terms were Tair ð4Þ 2 The resulting system of four equations allows to calculate the arguments of Txx and Txy. Likewise, upon rotating the loop-wire nanostructures by 90°, the arguments of Tyy and Tyx were measured. The results of the phase measurements are shown in Figure 3b. Taking both the amplitude and the phase information ^ lin as together, the four complex coefficients of the Jones matrix T used in eq 1 could be unambiguously determined for all accessible wavelengths. The emergence and the strength of the observed resonances are due to the interaction among various plasmonic eigenmodes of the three-dimensional nanostructures. It is stressed that for normal incidence all transmission properties of the loop-wire metaatoms are accessible from the measured Jones matrix. Most notably, the output for an arbitrarily polarized input field can be easily predicted. To further confirm the correctness of the measured matrix elements, in addition to an alternative experimental validation (see Supporting Information) they were also compared to numerical simulations. The complex coefficients Tij as shown in Figure 3c and d were computed by the Fourier modal method,30 taking into account the dispersion of gold.31 Comparison of the measured and the simulated data reveals a convincing agreement. Especially the width and the strength of all spectral features are quite well reproduced. Minor deviations may be attributed to an approximate
air (45° E(45°, sam 3 Eref ¼ A 3
description of the complex geometry of the fabricated loop-wire metaatoms in the simulation. Particularly we note that the measured off-diagonal elements Txy and Tyx are generally not equal across the entire spectral domain. This is a signature of broadband asymmetric transmission of linearly polarized light, which is caused by additional asymmetries of the metaatoms in propagation direction.11 Such symmetry breaking in the loop-wire structures is unintentionally present due to fabrication imperfections. To elaborate quantities that describe phenomena linked to ^ lin, optical activity, it is convenient to transform the Jones matrix T ^ circ. In which was measured in a linear base into a circular base T ^ circ relates the amplitudes of circularly polarized analogy to eq 1, T in out incident (Ein + , E) and circularly polarized transmitted light (E+ , out E ). If a linearly polarized wave illuminates the metaatoms, the simultaneous action of circular dichroism η and circular birefringence θ will lead to an elliptically polarized output with a rotated azimuth. Circular dichroism η = |T++|2 |T|2 corresponds to a differential intensity transmission of right- (RCP, +) and lefthanded circularly polarized light (LCP, ). Circular birefringence θ = 1/2[arg(T++) arg(T)] is associated with differential phase delays of RCP and LCP. The plots of η and θ as extracted from the measured Jones matrix are shown in Figure 4. As expected, the vivid spectral dynamics manifests in a strong modification of the incident polarization, stemming from huge values of both circular dichroism and birefringence across the entire accessible spectral range. In Figure 4a two distinct values of η = 0.3 (around λ = 0.9 μm) and 0.45 (around λ = 1.5 μm) specify the contrast extrema between the two diagonal elements of the circular Jones matrix. Even more appealing, the strong dispersion of θ at wavelengths between 1.0 and 1.5 μm allows to access the full angular range of the azimuth of the output polarization ellipse (Figure 4b). In the following we describe conceptually how linear birefringence and linear dichroism originating from the design-related anisotropy of the present metaatoms can be distinguished from optical activity. In principle this anisotropy could be compensated by constructing a C4 symmetric, polarization-independent supercell consisting of four metaatoms with an appropriate inplane rotation.13,18 The off-diagonal elements T+ and T+ of the associated Jones matrix would then be identically zero. If the interaction between adjacent metaatoms was negligible, then the diagonal elements T++ and T would not be affected. It follows that C4 symmetrically oriented loop-wire metaatoms would yield pure azimuth rotation, i.e., azimuth rotation of a linear polarization state without linear birefringence and linear dichroism, of θ = 36.2° at a wavelength around 1.25 μm (Figure 4b). 4403
dx.doi.org/10.1021/nl202565e |Nano Lett. 2011, 11, 4400–4404
Nano Letters It is noteworthy that pure azimuth rotation was also observed for the fabricated loop-wire metaatoms. This was demonstrated by directly determining the polarization state upon transmission through the nanostructured material from ^ lin. The incoming wave was the measured Jones matrix T chosen to be linearly polarized in x-direction. By scanning over all wavelengths (see Supporting Information), it was found that perfectly linear polarization emerges at wavelengths of 0.78, 1.08, and 1.29 μm (Figure 5). The polarization azimuth was rotated by 23.0°, 52.5°, and 19.9°, respectively. The giant rotation at λ = 1.08 μm comes at the expense of high absorption since the metaatoms are resonantly excited. Normalizing it to the metamaterial layer thickness (160 nm) delivers a specific rotation of 3.28 105 °/mm. This striking value outperforms any natural and artificial linear, passive, and reciprocal medium reported to date.13,32 In conclusion, we have demonstrated that a novel, optically active, plasmonic material made of three-dimensional, chiral nanostructures exceeds the quasi two-dimensional character of most contemporary photonic metamaterials. Furthermore and for the first time, we determined experimentally its strongly dispersive complex Jones matrix over a broad optical wavelength range. Based on entirely experimental means, all quantities related to optical activity could be unambiguously extracted, among them, a record-breaking polarization azimuth rotation. We consider this demonstration as a substantial advancement in the current state of nanostructured material description and characterization. Our results open the way to the complex farfield characterization of a very general class of dispersive media and will have important implications for their design, realization, and experimental evaluation. Moreover, the reported concepts and methods can be straightforwardly applied to the realization of miniaturized optical systems based on optically active media.
’ ASSOCIATED CONTENT
bS
Supporting Information. Description of the experimental validation of the measured linear Jones matrix by circularly polarized light and direct visualizations of the polarization eigenstates and polarization output states of the loop-wire metaatoms. The two latter features are supported by two movies showing the spectral dependencies. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. )
Author Contributions
These authors contributed equally.
’ ACKNOWLEDGMENT Financial support by the Federal Ministry of Education and Research (PhoNa and MetaMat), the Thuringian State Government (MeMa) as well as from the German Research Foundation (NanoGuide) is gratefully acknowledged. C.H. wishes to thank W. Gr€af, M. Banasch, H. Schmidt, M. Steinert, H.-J. Fuchs, M. Oliva, and B. Steinbach for technical assistance during the sample fabrication and K. Verch (www.karstenverch.com) for providing us with the artist's view of the experiment.
LETTER
’ REFERENCES (1) Valentine, J.; Zhang, S.; Zentgraf, T.; Ulin-Avila, E.; Genov, D.; Bartal, G.; Zhang, X. Nature 2008, 455, 376–380. (2) Burgos, S.; de Waele, R.; Polman, A.; Atwater, H. Nat. Mater. 2010, 9, 407–412. (3) Burresi, M.; Diessel, D.; van Oosten, D.; Linden, S.; Wegener, M.; Kuipers, L. Nano Lett. 2010, 10, 2480–2483. (4) Rockstuhl, C.; Menzel, C.; M€uhlig, S.; Petschulat, J.; Helgert, C.; Etrich, C.; Chipouline, A.; Pertsch, T.; Lederer, F. Phys. Rev. B 2011, 83, 245119. (5) Christ, A.; Martin, O. J. F.; Ekinci, Y.; Gippius, N. A.; Tikhodeev, S. G. Nano Lett. 2008, 8, 2171–2175. (6) Verellen, N.; Sonnefraud, Y.; Sobhani, H.; Hao, F.; Moshchalkov, V.; Van Dorpe, P.; Nordlander, P.; Maier, S. Nano Lett. 2009, 9, 1663–1667. (7) Mukherjee, S.; Sobhani, H.; Lassiter, J. B.; Bardhan, R.; Nordlander, P.; Halas, N. J. Nano Lett. 2010, 10, 2694–2701. (8) Liu, N.; Langguth, L.; Weiss, T.; K€astel, J.; Fleischhauer, M.; Pfau, T.; Giessen, H. Nat. Mater. 2009, 8, 758–762. (9) Fedotov, V. A.; Schwanecke, A. S.; Zheludev, N. I.; Khardikov, V. V.; Prosvirnin, S. L. Nano Lett. 2007, 7, 1996–1999. (10) Schwanecke, A. S.; Fedotov, V. A.; Khardikov, V. V.; Prosvirnin, S. L.; Chen, Y.; Zheludev, N. I. Nano Lett. 2008, 8, 2940–2943. (11) Menzel, C.; Helgert, C.; Rockstuhl, C.; Kley, E.-B.; T€unnermann, A.; Pertsch, T.; Lederer, F. Phys. Rev. Lett. 2010, 104, 253902. (12) Plum, E.; Zhou, J.; Dong, J.; Fedotov, V.; Koschny, T.; Soukoulis, C. M.; Zheludev, N. I. Phys. Rev. B 2009, 79, 035407. (13) Decker, M.; Zhao, R.; Soukoulis, C. M.; Linden, S.; Wegener, M. Opt. Lett. 2010, 35, 1593–1595. (14) Shadrivov, I. V.; Fedotov, V. A.; Powell, D. A.; Kivshar, Y. S.; Zheludev, N. I. New J. Phys. 2011, 13, 033025. (15) Liu, N.; Weiss, T.; Mesch, M.; Langguth, L.; Eigenthaler, U.; Hirscher, M.; S€onnichsen, C.; Giessen, H. Nano Lett. 2010, 10, 1103–1107. (16) Appavoo, K.; Haglund, R. F., Jr. Nano Lett. 2011, 11, 1025–1031. (17) Artar, A.; Yanik, A. A.; Altug, H. Nano Lett. 2011, 11, 1685–1689. (18) Zhang, S.; Park, Y.; Li, J.; Lu, X.; Zhang, W.; Zhang, X. Phys. Rev. Lett. 2009, 102, 023901. (19) Gansel, J.; Thiel, M.; Rill, M.; Decker, M.; Bade, K.; Saile, V.; von Freymann, G.; Linden, S.; Wegener, M. Science 2009, 325, 1513–1515. (20) Smith, D.; Vier, D.; Padilla, W.; Nemat-Nasser, S.; Schultz, S. Appl. Phys. Lett. 1999, 75, 1425–1427. (21) Rockstuhl, C.; Menzel, C.; Paul, T.; Lederer, F. Phys. Rev. B 2009, 79, 035321. (22) Fan, Z.; Govorov, A. O. Nano Lett. 2010, 10, 2580–2587. (23) Govorov, A. O.; Fan, Z.; Hernandez, P.; Slocik, J. M.; Naik, R. R. Nano Lett. 2010, 10, 1374–1382. (24) Menzel, C.; Paul, T.; Rockstuhl, C.; Pertsch, T.; Tretyakov, S.; Lederer, F. Phys. Rev. B 2010, 81, 035320. (25) Serdyukov, A.; Semchenko, I.; Tretyakov, S.; Sihvola, A. Electromagnetics of Bi-Anisotropic Materials - Theory and Applications; Routledge Chapman & Hall: London, 2001. (26) Jaggard, D. L.; Mickelson, A. R.; Papas, C. H. Appl. Phys. 1979, 18, 211–216. (27) Burresi, M.; van Oosten, D.; Kampfrath, T.; Schoenmaker, H.; Heideman, R.; Leinse, A.; Kuipers, L. Science 2009, 326, 550–554. (28) Boudarham, G.; Feth, N.; Myroshnychenko, V.; Linden, S.; de Abajo, J.; Wegener, M.; Kociak, M. Phys. Rev. Lett. 2010, 105, 255501. (29) Jones, R. C. J. Opt. Soc. Am. 1947, 37, 107–110. (30) Li, J. J. Opt. Soc. Am. A 1997, 14, 2758–2767. (31) Johnson, P. B.; Christy, R. W. Phys. Rev. B 1972, 6, 4370–4379. (32) Hodgkinson, I.; Wu, Q. Adv. Mater. 2001, 13, 889–897. (33) Lepetit, L.; Cheriaux, G.; Joffre, M. J. Opt. Soc. Am. B 1995, 12, 2467–2474. (34) Pshenay-Severin, E.; Setzpfandt, F.; Helgert, C.; H€ubner, U.; Menzel, C.; Rockstuhl, C.; T€unnermann, A.; Lederer, F.; Pertsch, T. J. Opt. Soc. Am. B 2010, 27, 660–666. (35) Francon, M.; Mallick, S. Polarization Interferometers: Applications in Microscopy and Macroscopy; Wiley: London, 1971.
4404
dx.doi.org/10.1021/nl202565e |Nano Lett. 2011, 11, 4400–4404
