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
Metamaterials  have recently attracted considerable attention as an emerging new class of tailored optical materials [2-12], 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 , at 60 THz , at telecommunication [4,6,8] and visible frequencies [6,7,10] has been achieved as well as a negative index of refraction [5,9,11,12]. While these studies based on electron-beam lithography [2,6-12] or focused-ion-beam milling  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 , of magnetic metamaterials around 5-μm wavelength , and of negative-index metamaterials around 2-μm wavelength [5,14]. While the potential for square-centimeter-area metamaterials is clearly there [3,5,14], the large-area homogeneity has not actually been demonstrated so far to the best of our knowledge.
Metamaterial structures that are ideally suited for fabrication via interference lithography have recently been discussed in Refs. [5,8,9]. 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  or a negative refractive index [5,9] 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 [8,15]. 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 [3,5,13,14] (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 .
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.
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 .
Figures 2(a) and (b) show measured (solid curves) and calculated (dashed curves) optical transmittance spectra of a 1D and a 2D structure, respectively. The incident linear polarization is indicated in the insets. The Au and MgF2 layer thicknesses correspond to the experiment (see above). The width of the wires is 260 nm and the relevant axis of the plates is 290 nm, respectively, which fit very well to the data measured from the electron micrographs, namely 280 nm as width of the wires and 290 nm for the relevant axis of the plates. For technical details of the calculations we refer the reader to our previous work [8,17]. In brief, we use a 1D scattering-matrix approach for the 1D structures [18,19] with 201 Bragg orders and a commercial three-dimensional finite-difference time-domain approach (CST MicroWave Studio) for the 2D structures. For both cases, we have checked for numerical convergence.
The experiment-theory comparison in Fig. 2 shows that the measured optical properties meet the theoretical expectation. For a magnetic metamaterial, it is obviously most relevant to retrieve its magnetic permeability μ. The basic idea underlying the retrieval is simple [20,21]: For known complex permittivity ε and permeability μ, it is straightforward to compute the normal-incidence complex field transmittance and reflectance for a slab of (meta)material of thickness d at any given frequency (here d=100 nm). The inversion of this problem, however, is generally not unique and physical conditions have to be imposed [20, 21]. For example, the quantities ε and μ must not reveal discontinuous spectral jumps. Furthermore, for a passive medium, the imaginary part of the refractive index n must not be negative. The magnetic permeability μ versus wavelength shown in Figs. 2(c) and (d) is obtained from the calculated spectra along these lines and reveals regions of negative μ at around 1.25 μm and 1.20 μm wavelength for the 1D and the 2D structures, respectively. It is clear that the metamaterial structure is highly anisotropic. Thus, the retrieved μ exclusively refers to normal incidence. The physics of oblique incidence is discussed in Ref.  and leads to magnetization waves. It is straightforward to shift the magnetic resonance position to longer wavelengths by variation of the roof-top prism or pyramid apex angle, respectively. Shifting to shorter wavelengths is limited by the finite metal plasma frequency . The photograph of a 1D structure in Fig. 3 gives a first overall impression of the achieved large-scale homogeneity of our samples (on 22 mm × 22 mm glass substrate). The blue color arises from Bragg diffraction of the incident white light and is not directly related to the magnetic properties under discussion here. The dim line in the center originates from shadowing due to the upper edge of the roof-top prism. The transmittance spectra taken at four arbitrary spatial locations (as indicated) exhibit a qualitatively similar behavior. This altogether indicates the tremendous potential of interference lithography for mass production of large-area samples.
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.
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
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