Selected for a Viewpoint in Physics PHYSICAL REVIEW B 79, 035407 ͑2009͒ Metamaterial with negative index due to chirality E. Plum,1,* J. Zhou,2,3 J. Dong,3,4 V. A. Fedotov,1 T. Koschny,3,5 C. M. Soukoulis,3,5 and N. I. Zheludev1 1Optoelectronics Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom 2Department of Electrical and Computer Engineering and Microelectronics Research Center, Iowa State University, Ames, Iowa 50011, USA 3Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA 4Institute of Optical Fiber Communications and Network Technology, Ningbo University, Ningbo 315211, China 5Institute of Electronic Structure and Laser—FORTH, and Department of Materials Science and Technology, University of Crete, Greece ͑Received 31 July 2008; revised manuscript received 31 October 2008; published 12 January 2009͒ Recently it has been predicted that materials with exceptionally strong optical activity may also possess a negative refractive index, allowing the realization of superlenses for super-resolution imaging and data storage applications. Here we demonstrate experimentally and numerically that a chirality-induced negative index of refraction is possible. A negative index of refraction due to three-dimensional chirality is demonstrated for a bilayered metamaterial based on pairs of mutually twisted planar metal patterns in parallel planes, which also shows negative electric and magnetic responses and exceptionally strong optical activity and circular dichro- ism. Multilayered forms of the metamaterial are found to be suitable for use as ultrathin polarization rotators and circular polarizers for practical applications. DOI: 10.1103/PhysRevB.79.035407 PACS number͑s͒: 78.20.Ek, 41.20.Jb, 42.25.Ja I. INTRODUCTION are confirmed experimentally. Importantly we show for a bi- layered metamaterial consisting of pairs of mutually twisted Optical activity, which is the ability to rotate the plane of rosettes that its negative refractive index arises from the polarization of electromagnetic waves, has always been a structure’s 3D-chiral symmetry. In contrast to conventional phenomenon of great importance to many areas of science, negative index materials, such as split ring wire media, fish- including molecular biology, analytical chemistry, detection net structures, and double crosses,14–16 the negative index is of life forms, optoelectronics, and display applications. Op- not caused by simultaneous negative electric and magnetic tical activity exhibited by natural materials such as quartz, responses. We also found that two layers of mutually twisted however, is quite weak. Consequently artificial gyrotropic metal rosettes show strong polarization rotary power and cir- structures are of interest for polarization control applications cular dichroism, and we study these effects by modeling how in microwave and optoelectronic devices.1–4 Since Pendry5 the polarization state changes as the wave travels through the and Tretyakov6 recently predicted that strong optical activity metamaterial. Finally we find that multilayered versions of may also result in negative refraction, artificial gyrotropic the metamaterial, consisting of four or more layers of ro- materials have started to attract a lot of attention as potential candidates for achieving negative refraction.7–11 With respect (a) (b) 5° to the realization of negative refraction due to optical activ- 1 ity, however, little progress was made until very strong mi- crowave gyrotropy was reported for a single pair of mutually twisted metal patterns in parallel planes. Importantly a sig- nature of circularly polarized backward waves was observed for this structure, indicating that metamaterials based on such mutually twisted metal patterns might have a negative index of refraction.12 Recently a scaled down metamaterial version of this structure was shown to also possess exceptionally strong polarization rotary power in the optical part of the spectrum.13 In this paper we demonstrate experimentally and numeri- cally that metamaterials based on multiple layers of mutually ͑ ͒ twisted planar metal patterns in parallel planes Fig. 1 sup- 2 1.6 m m 15 m m 5 x 15 m m port a wealth of useful electromagnetic properties including 1 giant optical activity and circular dichroism, strong negative FIG. 1. ͑Color online͒ Structure of the metamaterial. ͑a͒ Sche- electric and magnetic responses, and negative refraction. Due matics of the four-layered metamaterial’s unit cell. The rosettes in to their fourfold rotational symmetry, circular polarization neighboring layers have a relative twist of 15°. The structure of conversion due to anisotropy in our three-dimensional ͑3D͒- metamaterials with a different number of layers is analogous. ͑b͒ chiral metamaterials is absent and they have circularly polar- Photograph of part of a bilayered metamaterial sheet. The twisted ized eigenstates. Thus the polarization state of circularly po- rosettes of the second layer can be seen as a shaded area thanks to larized waves is not affected by our structures. These facts partial transparency of the substrate. A unit cell has been marked. 1098-0121/2009/79͑3͒/035407͑6͒ 035407-1 ©2009 The American Physical Society PLUM et al. PHYSICAL REVIEW B 79, 035407 ͑2009͒ B C D A while the weaker high-frequency resonances C and D have 0 ) 3␭/2 current modes. B d -10 ( RCP n “” o -20 i s III. NEGATIVE REFRACTION DUE TO 3D CHIRALITY s i -30 m s So far, negative refraction has been achieved in a variety n 40 - “ a ” r of structures, from split ring wire media to fishnet designs LCP (a) T and double crosses.14–16 All of these structures were designed -50 30 5 7 9 11 13 15 17 3 to superimpose electric and magnetic resonances, which h t ␧ ␮ u separately drove the permittivity and permeability nega- ) g m 15 i e tive in the same frequency region. While these achiral nega- z d a ( tive index materials have attracted a lot of attention, first n n 0 o o i i t experimental evidence of negative refraction due to chirality t a a 5 z t i was seen only in Ref. 12, even though Pendry and r o -15 r 6 a l Tretyakov predicted that negative refraction could be easier o (b) P to achieve in chiral media: for chiral media the refractive 30 - ͱ index is nϮ = ␧␮Ϯ␬, where “+” and “−” refer to the right- 5 7 9 11 13 15 17 3 handed and left-handed circularly polarized eigenstates and ␬ requency (GHz) F is the chirality parameter. This implies that in principle FIG. 2. ͑Color online͒ Circular dichroism and optical activity of strong enough chirality is sufficient to achieve negative re- the bilayered metamaterial. Measurements ͑dark lines͒ and numeri- fraction for one circular polarization. The difficulty here is cal simulations ͑faint lines͒ are shown. ͑a͒ Transmission levels for that if ͱ␧␮ is not very close to zero, then very strong chiral- left-handed ͑blue, LCP, −͒ and right-handed ͑red, RCP, +͒ circularly ity is required indeed. Our bilayered metamaterial shows ex- polarized waves. ͑b͒ Azimuth rotation for linearly polarized waves. ceptionally strong gyrotropic behavior and thus it is an ideal candidate for negative refraction due to chirality. settes, lead to exceptionally strong optical activity and circu- Based on transmission and reflection we calculated the lar dichroism combined with reduced insertion losses, mak- refractive index nϮ, chirality parameter ␬, permeability ␮, ing such structures practical ultrathin polarization rotators or and permittivity ␧ ͑see Appendix B͒ for the bilayered 3D- circular polarizers. chiral metamaterial, and a reference structure in which 3D chirality has been removed by reducing the relative twist between paired rosettes to zero. The results, which are shown II. GIANT OPTICAL ACTIVITY AND CIRCULAR in Fig. 3, show that both chiral and achiral forms of the DICHROISM metamaterial have similar electric and magnetic responses. Particularly in both cases resonance A leads to negative per- Figure 2͑a͒ shows transmission properties of the bilayered meability while resonance B corresponds to negative permit- form of the metamaterial for left-handed ͑LCP͒ and right- tivity. The negative magnetic behavior for A results from handed ͑RCP͒ circular polarizations. The structure shows ex- antisymmetric current oscillations in top and bottom rosettes, ceptionally strong circular dichroism of up to 20 dB. For each pair of rosettes effectively forms a current loop, and linear polarization, azimuth rotation of up to 25° is achieved, thus a magnetic dipole ͓see Fig. 4͑a͔͒. On the contrary the however, in this case the transmitted polarization state be- electric response for B results from in-phase current oscilla- comes elliptical. Pure optical activity, i.e., polarization azi- tions in pairs of rosettes, i.e., here pairs of rosettes act like a muth rotation without any change of ellipticity, is achieved single electric dipole ͓see Fig. 4͑b͔͒. The origin of the nega- between resonances A and B, where the absolute rotation is tive electric and magnetic responses of the bilayered struc- about 7°. These values are substantial considering the mate- ture is of the same nature as for fishnet structures and double rial’s thickness of only 1/30 wavelength ␭ at 6 GHz where crosses.15,16 the strongest effects occur. In terms of rotation per material In contrast to conventional negative index media, how- thickness of one wavelength, the structure’s peak rotary ever, permeability and permittivity become negative in sepa- power and pure optical activity are 780° /␭ and 250° /␭, rate bands and ͱ␧␮ is always positive for both structures. respectively. This is gigantic compared to naturally optically Nevertheless the 3D-chiral metamaterial has a negative re- active crystals such as quartz ͑0.02° /␭ at 400 nm͒ in the fractive index just above resonances A ͑for RCP͒ and B ͑for LCP͒: it is the large contribution from the chirality parameter visible part of the spectrum. The metamaterial also rotates ͱ several times stronger than helix-based artificial structures that drives the refractive index nϮ = ␧␮Ϯ␬ negative.