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  • Editor: Alan E. Willner
  • Vol. 35, Iss. 10 — May. 15, 2010
  • pp: 1593–1595
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Twisted split-ring-resonator photonic metamaterial with huge optical activity

M. Decker, R. Zhao, C. M. Soukoulis, S. Linden, and M. Wegener  »View Author Affiliations


Optics Letters, Vol. 35, Issue 10, pp. 1593-1595 (2010)
http://dx.doi.org/10.1364/OL.35.001593


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Abstract

Coupled split-ring-resonator metamaterials have previously been shown to exhibit large coupling effects, which are a prerequisite for obtaining large effective optical activity. By a suitable lateral arrangement of these building blocks, we completely eliminate linear birefringence and obtain pure optical activity and connected circular optical dichroism. Experiments around a 100 THz frequency and corresponding modeling are in good agreement. Rotation angles of about 30° for 205 nm sample thickness are derived.

© 2010 Optical Society of America

Optical activity in effective media refers to a difference Δn=nRCPnLCP in the real parts of the refractive indices for left- and right-handed circularly polarized incident light. The Kramers–Kronig relations connect these differences to the imaginary parts of the refractive indices, i.e., to circular dichroism. Optical activity requires a magnetic-dipole response mediated by the electric field of the electromagnetic light wave [1

1. E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009). [CrossRef]

, 2

2. S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, Phys. Rev. Lett. 102, 023901 (2009). [CrossRef] [PubMed]

, 3

3. M. Wegener and S. Linden, Physics 2, 3 (2009). [CrossRef]

]. In natural substances like solutions of chiral molecules, these effects are quite small, i.e., |Δn|1. Strong effective magnetic dipoles can arise from the coupling of Mie-like electric-dipole resonances. Coupled gold crosses have recently been discussed in this context [4

4. M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, Opt. Lett. 34, 2501 (2009). [CrossRef] [PubMed]

, 5

5. J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, Phys. Rev. B 79, 121104 (2009). [CrossRef]

]. Yet stronger coupling effects have been reported for twisted split-ring resonators (SRRs) [6

6. N. Liu, H. Liu, S. Zhu, and H. Giessen, Nat. Photonics 3, 157 (2009). [CrossRef]

]. However, the latter structures exhibit not only strong optical activity but also strong linear birefringence. A clean separation is desirable for both understanding the physics and for applications such as poor-man’s optical isolators [7

7. M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, Adv. Mater. 19, 207 (2007). [CrossRef]

].

Fabrication of the two-layer chiral medium shown in Fig. 1 requires advanced nanofabrication, i.e., two successive electron-beam-lithography steps and an intermediate planarization process via a spin-on dielectric [13

13. G. Subramania and S. Y. Lin, Appl. Phys. Lett. 85, 5037 (2004). [CrossRef]

]. Starting with the first functional layer written by electron-beam lithography, we planarize the sample via a 500-nm-thick spacer layer of commercially available spin-on dielectric (IC1-200, Futurrex, Inc.) and a subsequent thinning via reactive-ion etching (SF6, Plasmalab80Plus, Oxford Instruments). Next, we process the second functional layer of split-ring resonators via another electron-beam-lithography step carefully aligned relative to the first layer via alignment markers. As a result, we achieve an alignment mismatch of the first and the second layer of below 10nm over the entire sample footprint of 100μm×100μm. Electron micrographs of a fabricated structure are shown in Fig. 1b. The two functional layers are separated by a 85-nm-thick spacer layer. All samples are fabricated on a glass substrate covered with a 5nm thin film of indium tin oxide (ITO). Obviously, the sample quality is very high. In particular, no misalignment between the two split-ring resonators in each pair is detectable. The in-plane lattice constant of the set of four SRR pairs of a=885nm is significantly smaller than the resonance wavelengths of about 3μm.

For optical characterization, we use a commercial Fourier-transform microscope spectrometer (Bruker Tensor 27 with Bruker Hyperion 1000) combined with a linear CaF2 High Extinction Ratio holographic polarizer and a super-achromatic MgF2-based quarter-wave plate (Bernhard Halle Nachfl., 2.57.0μm) that can be rotated from the outside of the microscope [14

14. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, Science 325, 1513 (2009). [CrossRef] [PubMed]

]. Furthermore, we have modified the reflective ×36 Cassegrain lens (NA=0.5) by introducing a small diaphragm such that the full opening angle of the light incident onto the sample is reduced to about 5°. The sample is tilted such that we achieve actual normal incidence of light onto the sample [14

14. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, Science 325, 1513 (2009). [CrossRef] [PubMed]

]. Normalization of the transmittance spectra is with respect to the transmittance of the glass substrate, the ITO, and the spacer layer.

The measured transmittance spectra (see Fig. 2 ) for left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light are quite different. Indeed, the observed effects are much stronger compared with our planar chiral metamaterial structure [15

15. M. Decker, M. W. Klein, M. Wegener, and S. Linden, Opt. Lett. 32, 856 (2007). [CrossRef] [PubMed]

] and our twisted-cross metamaterial structure [4

4. M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, Opt. Lett. 34, 2501 (2009). [CrossRef] [PubMed]

]. Precisely, the circular dichroism, i.e., the difference between RCP and LCP transmittance, reaches values of about 33% for the present two-layer twisted SRR metamaterial.

Unfortunately, our experimental setup does not allow for analyzing the emerging polarization of light. To investigate this aspect and to understand the nature of the observed resonances, we perform additional numerical modeling. We use a finite-element frequency-domain approach provided by Comsol MultiPhysics supported by finite-integral time-domain calculations by CST MicroWave Studio. The lateral geometrical parameters of the SRR are L1=380nm, L2=350nm, and w=115nm [see Fig. 1a]. The gold thickness in each layer is 60nm, that of the spacer layer 85nm. The unit cell is arranged in a square lattice with an in-plane lattice constant of a=885nm. The gold optical properties are modeled by a free-electron Drude model with plasma frequency ωpl=2π×2133THz and collision frequency ωcoll=2π×33THz. The refractive indices of the glass substrate and the spin-on dielectric are 1.45 and 1.41, respectively. The thin ITO film is neglected.

The calculated results in Fig. 3a qualitatively agree nicely with our experimental findings in Fig. 2. Furthermore, we find very little intensity conversion (below 105) of circular polarization throughout the entire spectral range, i.e., LCP (RCP) incident light emerges as LCP (RCP) transmitted light. This means that LCP and RCP are very nearly the eigenpolarizations of the Jones matrix of our chiral metamaterial structure. Figure 3b shows the corresponding calculated rotation angle of linearly polarized incident light, that is, the effects of optical activity. This part of the figure also shows the calculated tangent, e=tan(η), of the ellipticity angle η, i.e., the ratio between the semiminor and the semimajor axis of the polarization ellipse. Here e=0 corresponds to linear polarization, e=±1 to circular polarization. Obviously, the rotation angle φ in Fig. 3b exhibits a resonance behavior. In resonance, the ellipticity approaches e=1. For pure optical activity we need e=0. At this zero crossing in Fig. 3 (dashed line), we find a rotation angle of about 30° for a metamaterial thickness of just 205nm. Employing the usual parameter retrieval [16

16. D. H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, Opt. Express 16, 11822 (2008). [CrossRef] [PubMed]

] accounting for the glass substrate leads to the difference between RCP and LCP refractive indices Δn=nRCPnLCP shown in Fig. 3c. Values of |Δn|2 are found. As expected, the spectral shape of the retrieved index difference Δn closely resembles the rotation angle [Fig. 3b] that is directly obtained from the calculated transmission phases.

Finally, we study the nature of the resonances seen in Figs. 2, 3. The calculated axial component of the local magnetic field is illustrated in Fig. 4 . For the low-frequency LCP resonance, the magnetic moments within each SRR pair are obviously parallel. In contrast, for the high-frequency RCP resonance, they are antiparallel. The coupling between the two SRRs in each pair is crucial for the observed optical activity: Without SRR coupling, the frequency splitting between the two modes of the coupled system equals zero. Each individual SRR layer is clearly not chiral; hence no optical activity is observable. Thus, for zero coupling between the two SRR layers, the overall optical response would result from two independent nonchiral layers, leading to an overall nonchiral response. The optimum separation of the two SRR layers results from a trade-off: for too large SRR layer separation, the SRR coupling in each pair vanishes, and so does optical activity. In the other limit, if the two SRR layers lie in the same plane, the structure itself is clearly strictly not chiral [see Fig. 1a]. We have found the SRR separation leading to maximum optical activity by computer simulations. The resulting value of 85nm for the spacer layer has been used in this Letter.

We acknowledge support by the European Commission via the project PHOME and by the Bundesministerium für Bildung und Forschung via the project METAMAT. The research of S. L. is supported through a Helmholtz-Hochschul-Nachwuchsgruppe (VH-NG-232). The PhD education of M. D. is embedded in the Karlsruhe School of Optics & Photonics (KSOP). Work at Ames Lab was supported by the Department of Energy (Basic Energy Sciences), contract no. DE-AC02-07CH11358.

Fig. 1 (a) Illustration of our metamaterial’s chiral unit cell composed of gold SRRs. The lateral dimensions of the SRRs are indicated on the left-hand side. (b) Electron micrographs of a typical fabricated structure. The normal-incidence image illustrates the high alignment accuracy of the two stacked layers. Inset, oblique view onto the sample. The scale bars are 400nm.
Fig. 2 Measured normal-incidence intensity transmittance spectra for LCP and RCP light incident onto the sample shown in Fig. 1b.
Fig. 3 Calculated optical properties. (a) Normal-incidence transmittance spectra that can be directly compared with the experiment shown in Fig. 2. The intensity conversion (not shown) is below 105 for the entire spectral range. (b) Calculated rotation angle φ and tangent e of the ellipticity angle of the transmitted light for linearly polarized incident light. (c) Difference of refractive indices Δn=nRCPnLCP retrieved from the complex transmittance and reflectance spectra.
Fig. 4 False-color plots of the axial component of the local magnetic field in two planes cutting through the SRR layers for (a) LCP incidence at 3.2μm wavelength and (b) for RCP incidence at 2.5μm. Schemes of the corresponding underlying electric currents within the SRR are shown in (c) and (d), respectively.
1.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009). [CrossRef]

2.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, Phys. Rev. Lett. 102, 023901 (2009). [CrossRef] [PubMed]

3.

M. Wegener and S. Linden, Physics 2, 3 (2009). [CrossRef]

4.

M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, Opt. Lett. 34, 2501 (2009). [CrossRef] [PubMed]

5.

J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, Phys. Rev. B 79, 121104 (2009). [CrossRef]

6.

N. Liu, H. Liu, S. Zhu, and H. Giessen, Nat. Photonics 3, 157 (2009). [CrossRef]

7.

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, Adv. Mater. 19, 207 (2007). [CrossRef]

8.

N. Liu and H. Giessen, Opt. Express 16, 21233 (2008). [CrossRef] [PubMed]

9.

X. Xiong, W. H. Sun, Y. J. Bao, M. Wang, R. W. Peng, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, Phys. Rev. B 81, 075119 (2010). [CrossRef]

10.

X. Xiong, W. H. Sun, Y. J. Bao, R. W. Peng, M. Wang, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, Phys. Rev. B 80, 201105 (2009). [CrossRef]

11.

M. Decker, S. Linden, and M. Wegener, Opt. Lett. 34, 1579 (2009). [CrossRef] [PubMed]

12.

M. Decker, S. Burger, S. Linden, and M. Wegener, Phys. Rev. B 80, 193102 (2009). [CrossRef]

13.

G. Subramania and S. Y. Lin, Appl. Phys. Lett. 85, 5037 (2004). [CrossRef]

14.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, Science 325, 1513 (2009). [CrossRef] [PubMed]

15.

M. Decker, M. W. Klein, M. Wegener, and S. Linden, Opt. Lett. 32, 856 (2007). [CrossRef] [PubMed]

16.

D. H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, Opt. Express 16, 11822 (2008). [CrossRef] [PubMed]

OCIS Codes
(160.1585) Materials : Chiral media
(160.3918) Materials : Metamaterials
(220.4241) Optical design and fabrication : Nanostructure fabrication

ToC Category:
Materials

History
Original Manuscript: January 21, 2010
Revised Manuscript: March 24, 2010
Manuscript Accepted: March 31, 2010
Published: May 6, 2010

Citation
M. Decker, R. Zhao, C. M. Soukoulis, S. Linden, and M. Wegener, "Twisted split-ring-resonator photonic metamaterial with huge optical activity," Opt. Lett. 35, 1593-1595 (2010)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-10-1593


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References

  1. E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Phys. Rev. B 79, 035407 (2009). [CrossRef]
  2. S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, Phys. Rev. Lett. 102, 023901 (2009). [CrossRef] [PubMed]
  3. M. Wegener and S. Linden, Physics 2, 3 (2009). [CrossRef]
  4. M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, Opt. Lett. 34, 2501 (2009). [CrossRef] [PubMed]
  5. J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, Phys. Rev. B 79, 121104 (2009). [CrossRef]
  6. N. Liu, H. Liu, S. Zhu, and H. Giessen, Nat. Photonics 3, 157 (2009). [CrossRef]
  7. M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, Adv. Mater. 19, 207 (2007). [CrossRef]
  8. N. Liu and H. Giessen, Opt. Express 16, 21233 (2008). [CrossRef] [PubMed]
  9. X. Xiong, W. H. Sun, Y. J. Bao, M. Wang, R. W. Peng, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, Phys. Rev. B 81, 075119 (2010). [CrossRef]
  10. X. Xiong, W. H. Sun, Y. J. Bao, R. W. Peng, M. Wang, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, Phys. Rev. B 80, 201105 (2009). [CrossRef]
  11. M. Decker, S. Linden, and M. Wegener, Opt. Lett. 34, 1579 (2009). [CrossRef] [PubMed]
  12. M. Decker, S. Burger, S. Linden, and M. Wegener, Phys. Rev. B 80, 193102 (2009). [CrossRef]
  13. G. Subramania and S. Y. Lin, Appl. Phys. Lett. 85, 5037 (2004). [CrossRef]
  14. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, Science 325, 1513 (2009). [CrossRef] [PubMed]
  15. M. Decker, M. W. Klein, M. Wegener, and S. Linden, Opt. Lett. 32, 856 (2007). [CrossRef] [PubMed]
  16. D. H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, Opt. Express 16, 11822 (2008). [CrossRef] [PubMed]

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