Broad-Band Giant Circular Dichroism in Metamaterials of Twisted

Article pubs.acs.org/JPCC

Broad-Band Giant Circular Dichroism in Metamaterials of Twisted Chains of Metallic Nanoparticles Sotiris Droulias and Vassilios Yannopapas* Department of Materials Science, University of Patras, GR-26504 Patras, Greece ABSTRACT: By using a discrete-dipole approximation for twodimensional periodic lattices of scatterers, we show that threedimensional layer-by-layer metamaterials consisting of twisted arrays of metal-nanoparticle chains exhibit giant circular dichroism spanning over the entire visible regime. The evident broad-band circular dichroism of the metamaterial is not a result of the intrinsic handeness of the constituent meta-atoms as in mainstream chiral designs but arises from the combined action of the anisotropy of each array of chains of nanoparticles, the gradual rotational twist of the metamaterial, and the strong electromagnetic coupling between adjacent layers of nanoparticle chains. As such, it is shown numerically that the degree of circular dichroism of the twisted metamaterial under study depends strongly on the twist angle between two successive lattices of nanoparticle chains and on the degree of anisotropy of each lattice.

■

INTRODUCTION Metamaterials are man-made structures exhibiting electromagnetic (EM) properties that are not met in naturally occurring materials, such as artificial magnetism, negative refractive index (NRI), near-field amplification, cloaking, and optical illusions. The basic functionalities of metamaterials stem from the occurrence of electric/magnetic resonances wherein the EM field is strongly localized within subwavelength volumes. By combining the strong confinement of the EM field with the introduction of some form of chirality, either as an intrinsic property of each meta-atom1−13 or in the geometrical arrangement of the meta-atoms within the unit cell,14−19 large optical activities surpassing that of natural chiral materials have been achieved. By proper engineering of the dispersion relations and in the limit of low losses, optical chirality can induce a negative refractive index.14,20−30 Optical dichroism may also occur for oblique incidence of an EM wave on planar nonchiral metamaterials with asymmetric unit cell (extrinsic chirality) wherein the wavevector, the normal to the metamaterial and polar vector denoting the asymmetry of the unit cell form a chiral triad.31−36 One of the candidate architectures for chiral metamaterials in the visible regime is that consisting of nonchiral metallic nanoparticles (NPs) arranged in a chiral geometry14−16,37−41 wherein a strong chiral activity is demonstrated as a result of the plasmon−plasmon interactions among the NPs. Chiral metamaterials of NPs can be fabricated via bottom-up processes such as supramolecular self-assembly42−44 as well as peptideand DNA-assisted self-assembly.45−50 In this work, we propose a new metamaterial design exhibiting giant circular dichroism that can be viewed as a plasmonic analog of twisted-nematic (cholesteric) liquid crystals.51,52 Namely, we study theoretically the optical properties of two-dimensional (2D) arrays of chiral © 2012 American Chemical Society

layer-by-layer meta-atoms consisting of mutually twisted linear chains of metallic NPs; i.e., each layer of the meta-atom contains a linear chain of metallic NPs that is rotated relative to the preceding layer by a constant angle ϕ along the symmetry axis of the meta-atom (Figure 1). The metamaterial is a 2D

Figure 1. Side (left panel) and top (right panel) view of the meta-atom of the metamaterial design under study. The meta-atom consists of mutually twisted chains of metallic nanoparticles.

array of the above three-dimensional (3D) meta-atom (Figure 2), and its optical properties are numerically probed by the discrete-dipole approximation extended for periodic arrays of EM scatterers. We note that such a metamaterial can possibly be realized in the laboratory by self-organization of the NPs into chiral arrays after being functionalized with properly designed liquid-crystal mesogens.53−59

■

OUTLINE OF THE CALCULATION METHOD As stated above, the optical properties of the chiral metamaterial under study are calculated by means of the Received: November 8, 2012 Revised: December 14, 2012 Published: December 17, 2012 1130

dx.doi.org/10.1021/jp311075z | J. Phys. Chem. C 2013, 117, 1130−1135

The Journal of Physical Chemistry C

Article

For a generally anisotropic NP characterized by a dielectric tensor ε̃s and immersed within an isotropic host of dielectric constant εh, the polarizability tensor is given by the Clausius− Mossoti formula for anisotropic spheres, i.e., αCM ̃ = Vs

discrete-dipole approximation (DDA)60−63 extended for periodic arrays of EM scatterers.64 Each NP (scattering object in our case) of the metamaterial is considered as a point dipole located at the position r and corresponds to a dipole moment P and a (position-dependent) polarizability tensor α̃ . Because we are dealing with an infinitely periodic structure, a given dipole (NP) is indexed by two indices nν, where n enumerates the unit cells (meta-atoms) and ν enumerates the different NPs within a single unit cell (meta-atom). The lattice of meta-atoms is described by the lattice vectors R n = n1a1 + n2a 2 n1 , n2 = −∞ to + ∞ (1)

α̃ = αCM ̃ [13 − i(2k 0 3/3)αCM ̃ ]−1

■

RESULTS AND DISCUSSION In what follows we apply the method outlined in the previous section to the case of a chiral metamaterial wherein the metaatoms consist of mutually twisted linear chains of metallic NPs. Namely, we consider a 2D square lattice of meta-atoms, i.e., the unit vectors of eq 1 are provided by a1 = a(1, 0)

where Enν is the electric field at the νth dipole of the meta-atom which lies in the nth unit cell. The total wave at each dipole of the meta-atom consists of the incident field plus the field scattered by all the other dipoles of the same or other unit cells (meta-atoms). This provides us with a system of linear equations Nm

∑ Ã νμPμ = Einc ν

j = 1, ..., NC , i = 1, ..., NL

The rest of the elements of the interaction matrix are provided by

∑ (1 − δνμδm0δn0)A nν;mμ exp[ik 0·(R n − R 0)] (5)

with A nν ; mμ =

exp(ikrnν ; mμ) ⎡ 2 ⎢k (rn̂ ν ; mμrn̂ ν ; mμ − 13 ) rnν ; mμ ⎢⎣ +

ikrnν ; mμ − 1 rnν ; mμ

2

⎤ (3rn̂ ν ; mμrn̂ ν ; mμ − 13 )⎥ ⎥⎦

(10)

Obviously, the total number of NPs within each meta-atom is Nm = NC × NL and the height h = 2NLS. We first consider a twisted metamaterial (Figure 2) of gold NPs with radius S = 5 nm whose dielectric function is taken from experiment.66 The meta-atom consists of NL = 11 chains of NPs, mutually twisted by an angle Δϕ = 2π/NL = 2π/11 rad =51°, wherein each chain consists of NC = 7 NPs. The 2D lattice constant is a = 4NCS = 140 nm and the height of the (chiral) meta-atom is h = 2NLS = 110 nm. The 2D surface coverage, i.e., the fraction of the unit cell covered by a single chain of NPs is f = NCπ(S/a)2 = 2.8%. Parts a and b of Figure 3 show the transmittance, reflectance, and absorbance spectra for right-circularly polarized (RCP) (a) and left-circularly polarized (LCP) (b) light incident normally on the twisted metamaterial described above. Evidently, the metamaterial is much transparent due to the low surface coverage ( f = 2.8%) of the metaatoms. Figure 3c shows the circular dichroism (CD) defined as67

(4)

Rn

(9)

R ν = R ij = 2S(j cos ϕi , j sin ϕi , i)

(3)

where the diagonal elements of the interaction matrix are essentially the inverse of the polarizability tensor of each dipole of the meta-atom, i.e.,

Ã νμ =

a 2 = a(0, 1)

where a is the 2D lattice constant. Each meta-atom is built up in a layer-by-layer fashion (Figure 1), i.e., a single layer lies in the xy-plane and consists of a linear chain of touching metallic NPs of radius S. The meta-atom consists of NL layers and each layer is indexed by i = 1, ..., NL. The chain of NPs in each layer is rotated relative to the bottom (first) chain by an angle ϕi = 2πi/NL (by angle Δϕ = 2π/NL relative to the previous chain). If each NP of a given chain is indexed by j = 1, ..., NC, where NC is the number of NPs in each chain, then the position vector Rν of a given NP within the meta-atom is provided by

(2)

Ã νν = [αν̃ ]−1

(8)

where α̃ CM is provided by eq 7. Having solved the system of eq 3, one proceeds to calculate the transmission, reflection and absorption coefficients from a 2D lattice of meta-atoms for an incident EM plane wave.64

where a1, a2 are the unit vectors of the 2D lattice of the metamaterial. The position of the νth NP (dipole) within a meta-atom (unit cell) is denoted by Rν where ν = 1, ..., Nm and Nm is the number of different NPs within the meta-atom. The quantities Pnν and α̃ nν are connected by

μ=1

(7)

where Vs is the volume of the NP. Obviously, a metallic sphere is isotropic and hence ε̃s = εm13 where εm is the dielectric function of the metal. We have also considered the correction due to radiation reaction in the polarizability65

Figure 2. Square lattice of the meta-atoms of Figure 1.

Pnν = αñ ν Enν

3εh [εs̃ − εh13 ][εs̃ + 2εh13 ]−1 4π

(6)

where 13 is the 3 × 3 unit matrix, rnν;mμ = rnν − rmμ, rnν = Rn − Rν, rmμ = Rm − Rμ, r̂nν;mμ = rnν;mμ/|rnν;mμ|. k0 is the wavevector of the incident wave. Ã νμ of eq 5 are calculated by direct summation in real space.64

CD = 2 1131

TRCP − TLCP TRCP + TLCP

(11)



Article

namely, it possesses a high degree of anisotropy that becomes much broader for the entire metamaterial as a result of the strong interaction between adjacent lattices (layers) of NP chains. What actually happens is that the rotational twist taking place when going from layer to layer converts adiabatically the EM modes of linear polarization of each lattice into modes of predominant circular polarization.39 The presence of EM modes of predominant circular-polarization character couple preferentially with incident waves of the same polarization and reflect waves of the opposite one.40 The metamaterial under study is an ambichiral71 layered structure of strongly coupled anisotropic metasurfaces that transforms the anisotropy into magneto-electric coupling as a result of the gradual mutual twist of the metasurfaces.39 The spectral extent and the degree of CD of an ambichiral layered structure such as the one studied here depends on the anisotropy of each layer, on the rotational twist Δϕ as well as on the separation between two successive lattices of NP chains (layers). In the present study, we have fixed the separation between the layers as the chains of NPs are touching. In Figure 4 we show the CD for different values of the number of layers Figure 3. Transmittance, reflectance, and absorbance of light incident normally on a square lattice of twisted chains of NPs of S = 5 nm, with NC = 7 and NL = 11 for right-circularly (a) and left-circularly polarized light (b). The corresponding circular dichroism (CD) is shown in (c). The 2D lattice constant is a = 4NCS = 140 nm.

Evidently, the CD assumes alternating positive and negative values from about 500 to 650 nm, which is the frequency region where surface plasmon (SP) interactions among the gold NPs take place (the calculated SP resonance of a single spherical gold NP is 532 nm). Within the same region the reflectance and absorbance curves for RCP and LCP modes shows a structure that stems from the SP interactions among the NPs.68−70 The CD spectrum shows also a distinct peak at about 800 nm, which is a result of the enhanced reflectance of an LCP incident plane wave relative to an RCP wave, i.e., an incident RCP wave is transmitted preferentially over an LCP wave. Given that the rotational twist of the meta-atom is also righthanded, it seems that the operation of the particular metamaterial is opposite to that of twisted-nematic (cholesteric) liquid crystals that reflect waves with the same handeness as the helical rotation of the liquid-crystal molecules.51,52 Moreover, in the present design, the thickness of the metamaterial (height of the meta-atom) is much smaller than the operating wavelength (e.g., for the 800 nm peak, the thickness is about one-eighth of the wavelength) whereas in twisted-nematic liquid crystals the rotational pitch is comparable to the operating wavelength. Light reflection in twisted-nematic liquid crystals is based on a Bragg condition of wave destructive interference, which leads to the formation of a stop band gap that, however, is of very limited bandwidth. In contrast, the metamaterial design under study exhibits a broad-band circular dichroism spanning over the entire visible spectrum. This broad-band CD functionality of the present metamaterial is not met in other chiral material designs based on metallic NPs15−18,32,48−50 where the reported optical CD is restricted around the SP of the NPs. In our case, the resulting CD is based on a different mechanism. As stated above, the metamaterial under study is essentially a succession of 2D lattices of chain of metallic NPs that are mutually twisted by a rotation angle Δϕ. Each 2D lattice of NP chains has a special functionality on its own;

Figure 4. Circular dichroism (CD) for a square lattice of twisted chains of 5 nm NPs for NC = 7 and for different values of NL (see inset). The 2D lattice constant is a = 4NCS = 140 nm.

(NP chains), i.e., for NL = 11, 16, and 21 corresponding to rotational twist values Δϕ = 51°, 22.5°, and 17°, respectively. Evidently, the CD signal is stronger for Δϕ = 51° (NL = 11), a value that lies within the range of 45−65°, where optimal performance of a twisted metamaterial is achieved.39 The oscillatory behavior of the CD spectra for the thicker slab of NL = 21 layers stem from Fabry−Perot oscillations taking place within the entire metamaterial slab (multiple wave reflections at the edges of the slab). A thorough analysis on Fabry−Perot oscillations in relation to 3D plasmonic metamaterials can be found in ref 68. Oscillations of the same are also found in Figure 6 below. In Figure 5 we have considered a structure with NC = 12. Evidently, reflectance and absorbance are much lower than the corresponding curves of Figue 3. This more or less expected because the value NC = 12 means a much more dilute structure [f = 1.6%] compared to the structure of Figure 2 [f = 2.8%]. As a result, the degree of anisotropy in each layer (lattice of NP chains) is very small, resulting in a very weak CD signal, namely, about 2 orders of magnitude weaker than the average CD of Figure 3. This is a clear manifestation of the fact that the source of optical activity in the proposed metamaterial design is 1132



Article

Figure 6. Same as Figure 2 but for a lattice constant a = 3NCS = 105 nm.

Figure 1), then, the second key factor, i.e., the gradual, layer-bylayer twist is lost and the phenomenon is naturally destroyed. However, some optical dichroism still remains due to the intrinsic chirality of the meta-atom. In this case, however, the system would resemble an isotropic chiral mixture of nanoparticle helices14−16,37−50 where dichroism is present without, however, being broad-band and assuming the very large values reported for the (periodic) metamaterial proposed here.

Figure 5. Same as Figure 3 but for NC = 12.

not the intrinsic chirality of each meta-atom separately but a purely lattice effect as described above. If the former was true, the CD as defined in eq 11 would have been independent of the NP concentration for dilute collections of chiral scatterers, i.e., the CD would essentially project the optical chirality of an isolated object. Figure 6 deals with the same meta-atoms as Figure 3 but for a smaller lattice constant, i.e., a = 3NCS corresponding to a denser structure [f = 5%] with a higher degree of anisotropy. One can observe that reflectance is much higher, on the average, compared to both Figures 3 and 5, especially above 650 nm. The CD spectrum is also broad-band, similar to the corresponding one of Figure 3, while remaining almost everywhere negative due to the preferential transmission of incident LCP waves. Again, similarly to Figure 3, the CD spectrum is greatly enhanced for λ > 650 nm. In general, the CD spectra in both Figures 3 and 6 share the same characteristics, namely, they both assume very high (absolute) values spanning over all the visible spectrum. Finally, a note on the effect of disorder on the chiral properties of the metamaterial under study. As already stated above, two are the key factors responsible for the observed dichroism: the anisotropy of each lattice of nanoparticle chains and the gradual twist of the lattice by going from layer to layer. Therefore, a complete in-plane amorphous arrangement would make each layer isotropic and, naturally, destroy optical chirality. However, if in-plane randomness means that the center of the nanoparticle chains fluctuate from their average positions in the lattice, then the anisotropy is, on the average, conserved and dichroism is preserved to a certain degree. If, instead of the layered metamaterial under study, we have a mixture of randomly oriented meta-atoms in space (those of

■

CONCLUSIONS We have studied theoretically a chiral layered metamaterial formed by twisted arrays of metal−nanoparticle chains. We have shown, in particular, that, even for very dilute realizations of the metamaterial, high values of the circular dichroism can be achieved. As manifested by the corresponding spectra of the circular dichroism, the emergent optical chirality is not a functionality stemming from the intrinsic chirality of the metaatoms but stems from the anisotropy of each lattice of metal− nanoparticle chains and the gradual mutual twist between the lattices which convert the evident anisotropy of each lattice into magneto-electric coupling. The proposed chiral metamaterial design can be realized in the laboratory by proper functionalization of gold nanoparticles with cholesteric liquidcrystal mesogens.57−59

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The research leading to these results has received funding from the European Union’s Seven Framework Programme (FP7/ 1133



Article

(32) Yannopapas, V. Opt. Lett. 2009, 34, 632−634. (33) Plum, E.; Liu, X. X.; Fedotov, V. A.; Chen, Y.; Tsai, D. P.; Zheludev, N. I. Phys. Rev. Lett. 2009, 102, 113902-1−113902-4. (34) Feng, C.; Wang, Z. B.; Lee, S.; Jiao, J.; Li, L. Opt. Commun. 2012, 285, 2750−2754. (35) Maoz, B. M.; Ben-Moshe, A.; Vestler, D.; Bar-Elli, O.; Markovich, G. Nano Lett. 2012, 12, 2357−2361. (36) Cao, T.; Cryan, M. J. J. Opt. 2012, 14, 085101-1−115101-6. (37) Gao, W.; Leung, H. M.; Li, Y.; Chen, H.; Tam, W. Y. J. Opt. 2011, 13, 115101-1−115101-8. (38) Hentschel, M.; Schäferling, M.; Weiss, T.; Liu, N.; Giessen, H. Nano Lett. 2012, 12, 2542−2547. (39) Zhao, Y.; Belkin, M. A.; Alú, A. Nat. Commun. 2012, 3, 870−1− 7. (40) Christofi, A.; Stefanou, N.; Gantzounis, G.; Papanikolaou, N. Phys. Rev. B 2012, 84, 125109-1−125109-7. (41) Christofi, A.; Stefanou, N.; Gantzounis, G.; Papanikolaou, N. J. Phys. Chem. C 2012, 116, 16674−16679. (42) Fan, J. A.; Wu, C.; Bao, K.; Bao, J.; Bardhan, R.; Halas, N. J.; Manoharan, V. N.; Nordlander, P.; Shvets, G.; Capasso, F. Science 2010, 328, 1135−1138. (43) Oh, H. S.; Jee, H.; Baev, A.; Swihart, M. T.; Prasad, P. N. J. Am. Chem. Soc. 2010, 132, 17346−17348. (44) Jones, M. R.; Osberg, K. D.; Macfarlane, R. J.; Langille, M. R.; Mirkin, C. A. Chem. Rev. 2011, 111, 3736−3827. (45) Mastroianni, A. J.; Claridge, S. A.; Alivisatos, A. P. J. Am. Chem. Soc. 2009, 131, 8455−8459. (46) Sharma, J.; Chhabra, R.; Cheng, A.; Brownell, J.; Liu, Y.; Yan, H. Science 2009, 323, 112−116. (47) Tan, S. J.; Campolongo, M. J.; Luo, D.; Cheng, W. Nat. Nanotechnol. 2011, 6, 268−276. (48) Slocik, J. M.; Govorov, A. O.; Naik, R. R. Nano Lett. 2011, 11, 701−705. (49) Shen, X.; Song, C.; Wang, J.; Shi, D.; Wang, Z.; Liu, N.; Ding, B. J. Am. Chem. Soc. 2012, 134, 146−149. (50) Kuzyk, A.; Schreiber, R.; Fan, Z.; Pardatscher, G.; Roller, E. M.; Högele, A.; Simmel, F. C.; Govorov, A. O.; Liedl, T. Nature 2012, 483, 311−314. (51) Khoo, I. C. Liquid Crystals, Wiley: Hoboken, NJ, 2007. (52) Scharf, T. Polarized Light in Liquid Crystals and Polymers, Wiley: Hoboken, NJ, 2007. (53) Cseh, L.; Mehl, G. H. J. Am. Chem. Soc. 2006, 128, 13376. (54) Zeng, X.; Liu, F.; Fowler, A. G.; Ungar, G.; Cseh, L.; Mehl, G. H.; Macdonald, J. E. Adv. Mater. 2009, 21, 1746. (55) Khatua, S.; Manna, P.; Chang, W. S.; Tcherniak, A.; Friedlander, E.; Zubarev, E. R.; Link, S. J. Phys. Chem. C 2010, 114, 7251−7257. (56) Liu, Q.; Cui, Y.; Gardner, D.; Li, X.; He, S.; Smalyukh, I. I. Nano Lett. 2010, 10, 1347−1353. (57) Kanie, K.; Matsubara, M.; Zeng, X.; Liu, F.; Ungar, G.; Nakamura, H.; Muramatsu, A. J. Am. Chem. Soc. 2011, 134, 808−811. (58) Bitar, R.; Agez, G.; Mitov, M. Soft Matter 2011, 7, 8198−8206. (59) Yu, C. H.; Schubert, C. P. J.; Welch, C.; Tang, B. J.; Tamba, M. G.; Mehl, G. H. J. Am. Chem. Soc. 2012, 134, 5076−5079. (60) Purcell, E. M.; Pennypacker, C. R. Astrophys. J. 1973, 186, 705− 714. (61) Draine, B. T. J. Opt. Soc. Am. A 1994, 11, 1491−1499. (62) Flatau, P. J. Opt. Lett. 1997, 22, 1205−1207. (63) Yurkin, M. A.; Hoekstra, A. G. J. Quant. Spectrosc. Radiat. Transfer 2007, 106, 558−589. (64) Draine, B. T.; Flatau, P. J. J. Opt. Soc. Am. A 2008, 25, 2693− 2703. (65) Draine, B. T. Astrophys. J. 1988, 333, 848−872. (66) Johnson, R. B.; Christy, R. W. Phys. Rev. B 1972, 6, 4370−4379. (67) Berova, N., Nakanishi, K., Woody, R. W., Eds. Circular Dichroism: Principles and Applications, 2nd ed.; Wiley-VCH: New York, 2000. (68) Yannopapas, V.; Modinos, A.; Stefanou, N. Phys. Rev. B 1999, 60, 5359−5365.

2007-2013) under Grant Agreement No. 228455-NANOGOLD (Self-organized nanomaterials for tailored optical and electrical properties).

■

REFERENCES

(1) Papakostas, A.; Potts., A.; Bagnall, D. M.; Prosvirnin, S. L.; Coles, H. J.; Zheludev, N. I. Phys. Rev. Lett. 2003, 90, 107404-1−107404-4. (2) Vallius, T.; Jefimovs, K.; Turunen, J.; Vahimaa, P.; Svirko, Y. Appl. Phys. Lett. 2003, 83, 234−236. (3) Kuwata-Gonokami, M.; Saito, N.; Ino, Y.; Kauranen, M.; Jefimovs, K.; Vallius, T.; Turunen, J.; Svirko, Y. Phys. Rev. Lett. 2005, 95, 227401-1−227401-4. (4) Valev, V. K.; Smisdom, N.; Silhanek, A. V.; De Clercq, B.; Gillijns, W.; Ameloot, M.; Moshchalkov, V. V.; Verbiest, T. Nano Lett. 2009, 9, 3945−3948. (5) Rogacheva, A. V.; Fedotov, V. A.; Schwanecke, A. S.; Zheludev, N. I. Phys. Rev. Lett. 2006, 97, 17740-11−177401-4. (6) Plum, E.; Fedotov, V. A.; Schwanecke, A. S.; Zheludev, N. I.; Chen, Y. Appl. Phys. Lett. 2007, 90, 223113-1−223113-3. (7) Kanda, N.; Konishi, K.; Kuwata-Gonokami, M. Opt. Express 2007, 15, 11117−11125. (8) Gansel, J. K.; Thiel, M.; Rill, M. S.; Decker, M.; Bade, K.; Saile, V.; von Freyman, G.; Linden, S.; Wegener, M. Science 2009, 325, 1513−1515. (9) Decker, M.; Ruther, M.; Kriegler, C. E.; Zhou, J.; Soukoulis, C. M.; Linden, S.; Wegener, M. Opt. Lett. 2009, 34, 2501−2503. (10) Zhao, R.; Zhang, L.; Zhou, J.; Koschny, T.; Soukoulis, C. M. Phys. Rev. B 2011, 83, 035105-1−035105-4. (11) Radke, A.; Gissibl, T.; Klotzbücher, T.; von Braun, P.; Giessen, H. Adv. Mater. 2011, 23, 3018−3021. (12) Helgert, C.; Phshenay-Severin, E.; Falkner, M.; Menzel, C.; Rockstuhl, C.; Kley, E. B.; Tünnermann, A.; Lederer, F.; Pertsch, T. Nano Lett. 2011, 11, 4400−4404. (13) Schäferling, M.; Dregely, D.; Hentschel, M.; Giessen, H. Phys. Rev. X 2012, 2, 031010-1−031010-9. (14) Yannopapas, V. J. Phys.: Condens. Matter 2006, 18, 6883−6890. (15) Fan, Z.; Govorov, A. O. Nano Lett. 2010, 10, 2580−2587. (16) Fan, Z.; Govorov, A. O. J. Phys. Chem. C 2011, 115, 13254− 13261. (17) Auguié, B.; Alonso-Gómez, J. L.; Guerrero-Martínez, A.; LizMarzán, L. M. Phys. Chem. Lett. 2011, 2, 846−851. (18) Guerrero-Martínez, A.; Auguié, B.; Alonso-Gómez, J. L.; Džolić, Z.; Gómez-Graña, S.; Ž inić, M.; Cid, M. M.; Liz- Marzán, L. M. Angew. Chem., Int. Ed. 2011, 123, 5613−5617. (19) Guerrero-Martínez, A.; Alonso-Gómez, J. L.; Auguié, B.; Cid, M. M.; Liz- Marzán, L. M. Nano Today 2011, 6, 381−400. (20) Pendry, J. B. Science 2004, 306, 1353−1355. (21) Mackay, T. G.; Lakhtakia, A. Phys. Rev. E 2004, 69, 026602-1− 026602-9. (22) Monzon, C.; Forester, D. W. Phys. Rev. Lett. 2005, 95, 1239041−123904-4. (23) Tretyakov, S.; Shivola, A.; Jylhä, L. Photon. Nanostruct.: Fundam. Appl. 2005, 3, 107−115. (24) Shen, J. Q. Phys. Rev. B 2006, 73, 045113-1−045113-5. (25) Agranovitch, V. M.; Garstein, Y. N.; Zakhidov, A. A. Phys. Rev. B 2006, 73, 045114-1−045114-12. (26) Baev, A.; Samoc, M.; Prasad, P. N.; Krykunov, M.; Autschbach, J. Opt. Express 2007, 15, 5730−5741. (27) Kwon, D. H.; Werner, D. H.; Kildishev, A. V.; Shalaev, V. M. Opt. Express 2008, 16, 11822−11829. (28) Zhou, J.; Dong, J.; Wang, B.; Koschny, T.; Kafesaki, M.; Soukoulis, C. M. Phys. Rev. B 2009, 79, 121104-1−121104-4. (29) Zhang, S.; Park, Y.; Li, J.; Lu, X.; Zhang, W.; Zhang, X. Phys. Rev. Lett. 2009, 102, 023901-1−023901-4. (30) Dong, J.; Zhou, J.; Koschny, T.; Soukoulis, C. M. Opt. Express 2009, 17, 14172−14179. (31) Plum, E.; Fedotov, V. A.; Zheludev, N. I. Appl. Phys. Lett. 2008, 93, 191911-1−191911-3. 1134



Article

(69) Prodan, E.; Radloff, C.; Halas, N. J.; Nordlander, P. Science 2003, 302, 419−422. (70) Cunningham, A.; Mühlig, S.; Rockstuhl, C.; Bürgi, T. J. Phys. Chem. C 2011, 115, 8955−8960. (71) Hodgkinson, I. J.; Lakhtakia, A.; Wu, Q. H.; De Silva, L.; McCall, M. Opt. Commun. 2004, 239, 353−358.

1135


Broad-Band Giant Circular Dichroism in Metamaterials of Twisted

Recommend Documents