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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 2 — Jan. 22, 2007
  • pp: 501–507
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Large-area magnetic metamaterials via compact interference lithography

Nils Feth, Christian Enkrich, Martin Wegener, and Stefan Linden  »View Author Affiliations


Optics Express, Vol. 15, Issue 2, pp. 501-507 (2007)
http://dx.doi.org/10.1364/OE.15.000501


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Abstract

Magnetic metamaterials with magnetic-dipole resonances around 1.2-μm wavelength are fabricated using an extremely compact and robust version of two- or three-beam interference lithography for 1D and 2D structures, respectively. Our approach employs a single laser beam at 532-nm wavelength impinging onto a suitably shaped dielectric object (roof-top prism or pyramid) – bringing the complexity of fabricating magnetic metamaterials down to that of evaporating usual dielectric/metallic coatings. The measured optical spectra agree well with theory; the retrieval reveals a negative magnetic permeability. Importantly, the large-scale sample homogeneity is explicitly demonstrated by optical experiments.

© 2007 Optical Society of America

1. Introduction

Metamaterials [1

1. D. R. Smith, J.B. Pendry, and M.C.K. Wiltshire, “Metamaterials and negative refractive index,” Science 305,788–792 (2004). [CrossRef] [PubMed]

] have recently attracted considerable attention as an emerging new class of tailored optical materials [2

2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C.M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306,1351–1353 (2004). [CrossRef] [PubMed]

-12

12. G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31,1800–1802 (2006). [CrossRef] [PubMed]

], allowing for optical properties that are not accessible with natural materials. The basic idea is to fabricate sub-wavelength functional building blocks, “photonic atoms”, which often contain metallic constituent materials, and pack these “photonic atoms” sufficiently dense such that an effective material results. In this fashion, a magnetic-dipole response at 100 THz [2

2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C.M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306,1351–1353 (2004). [CrossRef] [PubMed]

], at 60 THz [3

3. S. Zhang, W. Fan, B.K. Minhas, A. Frauenglass, K.J. Malloy, and S.R.J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94,037402 (2005). [CrossRef] [PubMed]

], at telecommunication [4

4. C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C.M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17,2547–2549 (2005). [CrossRef]

,6

6. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, T. Koschny, and C.M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95,203901 (2005). [CrossRef] [PubMed]

,8

8. G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30,3198–3200 (2005). [CrossRef] [PubMed]

] and visible frequencies [6

6. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, T. Koschny, and C.M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95,203901 (2005). [CrossRef] [PubMed]

,7

7. A.N. Grigorenko, A.K. Geim, H.F. Gleeson, Y. Zhang, A.A. Firsov, I.Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005). [CrossRef] [PubMed]

,10

10. M.W. Klein, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31,1259–1261 (2006). [CrossRef] [PubMed]

] has been achieved as well as a negative index of refraction [5

5. S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, and S.R.J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95,137404 (2005). [CrossRef] [PubMed]

,9

9. V.M. Shalaev, W. Cai, U.K. Chettiar, H. Yuan, A.K. Sarychev, V.P. Drachev, and A.V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30,3356–3358 (2005). [CrossRef]

,11

11. G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312,892–894 (2006). [CrossRef] [PubMed]

,12

12. G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31,1800–1802 (2006). [CrossRef] [PubMed]

]. While these studies based on electron-beam lithography [2

2. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C.M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306,1351–1353 (2004). [CrossRef] [PubMed]

,6

6. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, T. Koschny, and C.M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95,203901 (2005). [CrossRef] [PubMed]

-12

12. G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31,1800–1802 (2006). [CrossRef] [PubMed]

] or focused-ion-beam milling [4

4. C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C.M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17,2547–2549 (2005). [CrossRef]

] are a convincing proof-of-principle, they do not offer a promising avenue for the fabrication of metamaterial layers on the scale of usual optical coatings (i.e., on a cm2-scale ≈ 108 × λ2) at reasonable fabrication cost and time. Interference lithography has a large corresponding potential, is inexpensive, and versatile. Indeed, interference lithography has already successfully been employed in early work on the fabrication of one-dimensional metallic photonic crystal slabs [13

13. H.C. Guo, D. Nau, A. Radke, X.P. Zhang, J. Stodolka, X.L. Yang, S.G. Tikhodeev, N.A. Gippius, and H. Giessen, “Large-area metallic photonic crystal fabrication with interference lithography and dry etching,” Appl. Phys. B 81,271–275 (2005). [CrossRef]

], of magnetic metamaterials around 5-μm wavelength [3

3. S. Zhang, W. Fan, B.K. Minhas, A. Frauenglass, K.J. Malloy, and S.R.J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94,037402 (2005). [CrossRef] [PubMed]

], and of negative-index metamaterials around 2-μm wavelength [5

5. S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, and S.R.J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95,137404 (2005). [CrossRef] [PubMed]

,14

14. W. Fan, S. Zhang, K.J. Malloy, and S.R.J. Brueck, “Large-area, infrared nanophotonic materials fabricated using interferometric lithography,” Jour. Vac. Sci. Tech. B 23,2700–2704 (2005). [CrossRef]

]. While the potential for square-centimeter-area metamaterials is clearly there [3

3. S. Zhang, W. Fan, B.K. Minhas, A. Frauenglass, K.J. Malloy, and S.R.J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94,037402 (2005). [CrossRef] [PubMed]

,5

5. S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, and S.R.J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95,137404 (2005). [CrossRef] [PubMed]

,14

14. W. Fan, S. Zhang, K.J. Malloy, and S.R.J. Brueck, “Large-area, infrared nanophotonic materials fabricated using interferometric lithography,” Jour. Vac. Sci. Tech. B 23,2700–2704 (2005). [CrossRef]

], the large-area homogeneity has not actually been demonstrated so far to the best of our knowledge.

2. Fabrication

Metamaterial structures that are ideally suited for fabrication via interference lithography have recently been discussed in Refs. [5

5. S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, and S.R.J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95,137404 (2005). [CrossRef] [PubMed]

,8

8. G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30,3198–3200 (2005). [CrossRef] [PubMed]

,9

9. V.M. Shalaev, W. Cai, U.K. Chettiar, H. Yuan, A.K. Sarychev, V.P. Drachev, and A.V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30,3356–3358 (2005). [CrossRef]

]. These designs (see Fig. 1(f)) consist of two metallic layers (e.g., Au) separated by a dielectric spacer (e.g., MgF2) on a substrate (e.g., glass). Depending on the in-plane geometry, a negative magnetic permeability μ [8

8. G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30,3198–3200 (2005). [CrossRef] [PubMed]

] or a negative refractive index [5

5. S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, and S.R.J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95,137404 (2005). [CrossRef] [PubMed]

,9

9. V.M. Shalaev, W. Cai, U.K. Chettiar, H. Yuan, A.K. Sarychev, V.P. Drachev, and A.V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30,3356–3358 (2005). [CrossRef]

] have been reported. Here, we focus on magnetic metamaterials which are the magnetic counterpart of usual dielectric layers or coatings. These metamaterials are effective materials composed of sub-wavelength-sized “magnetic atoms”. Their physics has been described in detail [8

8. G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30,3198–3200 (2005). [CrossRef] [PubMed]

,15

15. A.N. Lagarkov and A.K. Sarychev, “Electromagnetic properties of composites containing elongated conducting inclusions,” Phys. Rev B 53,6318–6336 (1996). [CrossRef]

]. In brief, the incident light field can induce an anti-symmetric current oscillation in the coupled system of two metallic wires or plates. This current can be viewed as part of a ring current, which leads to a magnetic dipole moment. For wavelengths above (below) the magnetic-resonance wavelength, this magnetic moment is parallel (anti-parallel) to the incident magnetic-field component of the light, leading to μ>1 (μ<1). For appropriate design and dense packing of these magnetic atoms, μ<0 can be achieved along these lines.

2.1 Principle of interference lithography

The basic principle of interference lithography is simple: A photoresist film, which has been spun onto a substrate, is exposed to a standing wave pattern arising from the interference of at least two non-coaxial laser beams (ideally plane waves). For a positive resist, the regions that are not sufficiently exposed remain on the substrate after the development process. To obtain large-area structures, large optical power as well as longitudinal and transverse coherence of the exposing light fields are of obvious importance. Thus, a transverse and longitudinal single TEM00 mode of a laser is ideal. Today, corresponding continuous-wave, single-mode, solidstate lasers at 532-nm emission wavelength are readily available in many optics laboratories around the world. Unfortunately, all commercially available photoresists are optimized for somewhat shorter exposure wavelengths [3

3. S. Zhang, W. Fan, B.K. Minhas, A. Frauenglass, K.J. Malloy, and S.R.J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94,037402 (2005). [CrossRef] [PubMed]

,5

5. S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, and S.R.J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95,137404 (2005). [CrossRef] [PubMed]

,13

13. H.C. Guo, D. Nau, A. Radke, X.P. Zhang, J. Stodolka, X.L. Yang, S.G. Tikhodeev, N.A. Gippius, and H. Giessen, “Large-area metallic photonic crystal fabrication with interference lithography and dry etching,” Appl. Phys. B 81,271–275 (2005). [CrossRef]

,14

14. W. Fan, S. Zhang, K.J. Malloy, and S.R.J. Brueck, “Large-area, infrared nanophotonic materials fabricated using interferometric lithography,” Jour. Vac. Sci. Tech. B 23,2700–2704 (2005). [CrossRef]

] (typically UV), where laser performance, especially coherence and transverse mode profile, has to be compromised. Our way out of this dilemma is to use a standard photoresist in the extreme long-wavelength tail of its sensitivity maximum. Unfortunately, due to this detuning, the required exposure times increase to the scale of few minutes. On this timescale, free-space setups with different independent beams interfering on the sample are subject to mechanical vibrations, which can severely distort the interference pattern, hence deteriorating the resulting structures. Our solution is to generate the interfering beams by a suitably designed dielectric object, onto which only a single laser beam impinges (Figs. 1(a) and (b)). To generate two partial waves for one-dimensional (1D) structures (Fig. 1(a)), a simple roof-top prism can be used (linear incident s-polarization); to obtain three partial waves for two-dimensional (2D) structures (Fig. 1(b)), a pyramid is employed in conjunction with circular incident polarization. Four partial waves have been discussed previously for fabricating three-dimensional photonic crystal templates [16

16. L. Wu, Y. Zhong, C.T. Chan, K.S. Wong, and G.P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86,241102 (2005). [CrossRef]

].

Fig. 1. Our robust interference-lithography setup employs a dielectric object to generate two or three partial waves from one largely expanded incident laser beam. (a) Roof-top prism for two partial waves leading to 1D structures, (b) pyramid for three partial waves leading to hexagonal 2D structures. (c) and (d) illustrate the corresponding digitized interference patterns, precisely, those areas where the local light intensity exceeds a certain threshold value (light-gray areas above threshold, dark-gray areas below threshold). (e) and (f) show electron micrographs of structures fabricated along these lines. The oblique-incidence view in the inset in (f) reveals the layer sequence: 20-nm Au (golden), 60-nm MgF2 (blue), and 20-nm Au on glass substrate.

Clearly, the desired interference pattern only appears in the region where all partial waves overlap. For the geometries of Figs. 1(a) and (b), the resulting digitized interference patterns are illustrated in Figs. 1(c) and (d), respectively.

2.2 Experimental details

We start with glass cover slides (commonly used for light microscopy) as substrates. Their thickness is 180 μm, their area 22 mm × 22 mm. The substrates are coated with a 5-nm thin film of indium-tin-oxide (ITO) via electron-beam evaporation in a high-vacuum chamber (see below). The ITO serves as an adhesion layer for the gold. Next, we add hexamethyldisilazan (HMDS) as an adhesion layer for the photoresist. For this purpose, the substrate and one drop of HMDS are enclosed in a glass receptacle under ambient conditions for about ten minutes. This step makes the surface sufficiently hydrophobic. Otherwise, a water film could inhibit wetting of the substrate with the photoresist. We use a positive photoresist (AR-P-3120 from AllResist), which is diluted with 30% weight percent PGMEA. This photoresist is optimized for exposure between 308 and 450-nm wavelength. Spinning of the resist at 6100 rotations per minute leads to a film thickness of about 300 nm. The photoresist film is exposed using the following arrangement: The Gaussian output beam of a single-mode Coherent VERDI at 10-W output power and 532-nm emission wavelength is expanded 31-fold by a telescope consisting of a high-quality microscope lens (EPIPLAN 10×, Carl Zeiss, numerical aperture NA=0.2, 16.17-mm focal length) and a large-aperture plano-convex lens (SPX058AR.14, Newport, 50.8-mm diameter, 500-mm focal length). We have calculated that the amplitude of the electric field decreases by about 8% for 1-cm distance from the optical axis behind the telescope. To keep the three-fold symmetry (for the 2D structures), we convert the linearlypolarized laser output into circular polarization by means of an antireflection-coated 532-nm quarter-wave plate. The expanded beam is sent onto a pyramid (see Fig. 1) made from Schott glass NSK-2 with refractive index n=1.61, λ/10 surface quality, and 32-degrees apex angle (custom-made by DoroTek GmbH, Berlin). This apex angle leads to a cone half-opening angle of the three partial waves inside the pyramid of 26 degrees, resulting in a two-dimensional hexagonal lattice with lattice constant a=505 nm. Other lattice constants can easily be obtained by varying the apex angle of the pyramid. Glycerol (C3H8O3) is employed as indexmatching fluid between the glass pyramid and the photoresist. The photoresist is exposed for typically 3-4 minutes under usual ambient laboratory conditions (i.e., not in a clean-room facility) and developed using the developer AR-300-35 from AllResist, diluted 1:5 (water: developer). Thereafter, a layer sequence of 20-nm gold, 60-nm MgF2, and again 20-nm gold is evaporated in a high-vacuum chamber (at <10−6 mbar pressure) using electron-beam evaporation. This is followed by a room-temperature lift-off procedure using acetone and an ultrasonic bath at moderate power for typically 45 seconds. We have not encountered major problems in the lift-off of this 100-nm thick Au-MgF2-Au package with the single photoresist layer. Generally, a lift-off process is to be preferred with respect to (reactive ion) etching, as the latter can potentially deteriorate the constituent material surfaces.

For the one-dimensional (rather than two-dimensional) structures, the pyramid is replaced by a roof-top prism made from BK-7 glass with refractive index n=1.52 and with 27-mm height and λ/10 surface quality (custom-made by DoroTek GmbH, Berlin). For an apex angle of 90 degrees, this leads to a lattice constant of a=590 nm. Again, other lattice constants can easily be obtained by varying the prism apex angle. Here, incident linear s-polarization is used for optimum interference contrast. We have also successfully fabricated structures using 1-W (rather than 10-W) incident average optical power and 30 minutes (rather than 3-4 minutes) exposure time. This again confirms the high mechanical stability of our arrangement.

3. Characterization

Figures 1(e) and (f) exhibit electron micrographs of the resulting 1D and 2D structures, respectively. The inset in Fig. 1(f) reveals an oblique-incidence view of one “magnetic atom” as described above. For both wire pairs and plate pairs and for the parameters used by us here, the vacuum wavelength of the magnetic resonance roughly equals four times the linear dimension of the “magnetic atoms” along the polarization of the incident light – provided that the resonance wavelength is well above the metal plasma wavelength [10

10. M.W. Klein, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31,1259–1261 (2006). [CrossRef] [PubMed]

].

Fig. 2. Measured normal-incidence transmittance spectra (solid curves) of (a) the 1D metamaterial (see Fig. 1(e)) and (b) the 2D metamaterial (see Fig. 1(f)). The dashed curves exhibit calculated spectra for the experimental parameters. (c) and (d) are the retrieved complex magnetic permeabilities μ for the relevant spectral regime.

Fig. 3. Large-scale homogeneity exemplified on the 1D metamaterial (see left-hand side columns in Figs. 1 and 2). The center shows a photograph of the actual structure on a 22 mm × 22 mm glass substrate. The color depends on the viewing angle and stems from Bragg diffraction at visible wavelengths. Infrared transmittance spectra at four well-separated locations are exemplified (compare Fig. 2(a)).

4. Conclusions

In conclusion, using a compact and robust version of interference lithography, we have fabricated and characterized large-area high-quality 1D and 2D negative-μ magnetic metamaterials for photonics. The 2D samples contain on the order of one billion “magnetic atoms”. Our approach does not require expensive nanofabrication equipment, uses a standard 532-nm solid-state laser available in many optics laboratories around the world, and brings the complexity of fabricating magnetic metamaterials down to that of evaporating usual dielectric/metallic layers. It would be straightforward to further increase the resulting sample area to many square inches by up-scaling of the apertures of the optics. Moreover, given the simplicity of fabricating single layers of “magnetic atoms” with our approach, we envision future work aiming at stacking such individual two-dimensional layers to three-dimensional photonic metamaterials – an important step, which has not been accomplished yet.

Acknowledgments

We acknowledge discussions with C.M. Soukoulis and D.C. Meisel, support by the DFG and the State of Baden-Württemberg through CFN subproject A1.5, and support by a “Helmholtz-Hochschul-Nachwuchsgruppe” (VH-NG-232) for S.L. The work is embedded in the “Karlsruhe School of Optics & Photonics (KSOP)”.

References and links

1.

D. R. Smith, J.B. Pendry, and M.C.K. Wiltshire, “Metamaterials and negative refractive index,” Science 305,788–792 (2004). [CrossRef] [PubMed]

2.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C.M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306,1351–1353 (2004). [CrossRef] [PubMed]

3.

S. Zhang, W. Fan, B.K. Minhas, A. Frauenglass, K.J. Malloy, and S.R.J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94,037402 (2005). [CrossRef] [PubMed]

4.

C. Enkrich, F. Pérez-Willard, D. Gerthsen, J. Zhou, T. Koschny, C.M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17,2547–2549 (2005). [CrossRef]

5.

S. Zhang, W. Fan, N.C. Panoiu, K.J. Malloy, R.M. Osgood, and S.R.J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95,137404 (2005). [CrossRef] [PubMed]

6.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, T. Koschny, and C.M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95,203901 (2005). [CrossRef] [PubMed]

7.

A.N. Grigorenko, A.K. Geim, H.F. Gleeson, Y. Zhang, A.A. Firsov, I.Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005). [CrossRef] [PubMed]

8.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30,3198–3200 (2005). [CrossRef] [PubMed]

9.

V.M. Shalaev, W. Cai, U.K. Chettiar, H. Yuan, A.K. Sarychev, V.P. Drachev, and A.V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30,3356–3358 (2005). [CrossRef]

10.

M.W. Klein, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31,1259–1261 (2006). [CrossRef] [PubMed]

11.

G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312,892–894 (2006). [CrossRef] [PubMed]

12.

G. Dolling, C. Enkrich, M. Wegener, C.M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31,1800–1802 (2006). [CrossRef] [PubMed]

13.

H.C. Guo, D. Nau, A. Radke, X.P. Zhang, J. Stodolka, X.L. Yang, S.G. Tikhodeev, N.A. Gippius, and H. Giessen, “Large-area metallic photonic crystal fabrication with interference lithography and dry etching,” Appl. Phys. B 81,271–275 (2005). [CrossRef]

14.

W. Fan, S. Zhang, K.J. Malloy, and S.R.J. Brueck, “Large-area, infrared nanophotonic materials fabricated using interferometric lithography,” Jour. Vac. Sci. Tech. B 23,2700–2704 (2005). [CrossRef]

15.

A.N. Lagarkov and A.K. Sarychev, “Electromagnetic properties of composites containing elongated conducting inclusions,” Phys. Rev B 53,6318–6336 (1996). [CrossRef]

16.

L. Wu, Y. Zhong, C.T. Chan, K.S. Wong, and G.P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86,241102 (2005). [CrossRef]

17.

S. Linden, M. Decker, and M. Megener, “Model system for a one-dimensional magnetic photonic crystal,” Phys. Rev. Lett. ,97,083902 (2006). [CrossRef] [PubMed]

18.

S.G. Tikhodeev, A.L. Yablonskii, E.A. Muljarov, N.A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66,045102(2002). [CrossRef]

19.

D.M. Whittaker and I.S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60,2610–2618 (1999). [CrossRef]

20.

D.R. Smith, D.C. Vier, T. Koschny, and C.M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71,036617 (2005). [CrossRef]

21.

T. Koschny, P. Markos, E.N. Economou, D.R. Smith, D.C. Vier, and C.M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71,245105 (2005). [CrossRef]

22.

G. Dolling, M. Wegener, A. Schädle, S. Burger, and S. Linden, “Observation of magnetization waves in negative-index photonic metamaterials,” Appl. Phys. Lett. 89,231118 (2006) [CrossRef]

OCIS Codes
(160.4760) Materials : Optical properties
(220.3740) Optical design and fabrication : Lithography
(260.5740) Physical optics : Resonance

ToC Category:
Metamaterials

History
Original Manuscript: August 29, 2006
Revised Manuscript: November 17, 2006
Manuscript Accepted: November 29, 2006
Published: January 22, 2007

Citation
Nils Feth, Christian Enkrich, Martin Wegener, and Stefan Linden, "Large-area magnetic metamaterials via compact interference lithography," Opt. Express 15, 501-507 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-501


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