1. Introduction

The advent of metamaterials and their development over the past decade has revolutionized the research fields of electrodynamics and photonics, giving a new perspective to classical interaction of light with matter and enabling scores of unparalleled physical phenomena [1–3]. Among most fascinating proposed metamaterials’ applications, bridging the gap between science fiction and reality, are the sub-diffraction imaging [1,4–8] and invisibility cloaking [9,10]. Despite of recent tremendous progress in both theory and experiment, the research field of metamaterials is hindered by a lack of inexpensive large-size three-dimensional media. One way to overcome this problem is to utilize bulk dielectric templates, which nanoporous space can be filled with metals or other dielectrics [11–14].

Recently, we have demonstrated [14] that an array of silver nanowires embedded into a flat alumina membrane matrix with 35nm-diameter pores behaves as a metamaterial with hyperbolic dispersion, characterized by dielectric permittivity components of opposite signs in two perpendicular directions. Negative refraction in a similar metamaterial has been demonstrated in [12].

It has been theoretically predicted that a metamaterial with hyperbolic dispersion realized in curvilinear coordinates (with radial or azimuthal anisotropy of metallic inclusions) has a property of a hyperlens – the device allowing for sub-diffraction imaging in a far field [4,5], Figs. 1a and 1b. Hyperlenses with coaxial and concentric geometries (resembling that in Fig. 1a) have been demonstrated in [6–8]. The structure with a hair brush morphology of metallic nano-needles embedded into a dielectric host (conceptually similar to that in Fig. 1b, but with different from a hyperlens radial distribution of electric permittivity) has been predicted to have a functionality of non-magnetic optical cloak [10], Fig. 1c.

 

Fig. 1 Proposed design of a hyperlens with azimuthal (a) and radial (b) distribution of metallic inclusions [4] and (c) hair brush morphology of metallic nano-needles in a non-magnetic optical cloak [10] (Reprinted by permission from Macmillan Publishers Ltd: [Nature Photonics] W. Cai et al., “Optical cloaking with metamaterials,” Nature Photonics 1, 224–227 (2007), copyright (2007)).

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Hyperbolic metamaterials based on arrays of nanowires (Fig. 1c) are inherently much less lossy than those based on lamellar or multi-layered metal-dielectric structures (Fig. 1a) and, correspondingly, they are much more attractive for hyperlens and transformation optics applications. At the same time, the technology of curvilinear nanoporous templates and arrays of nanowires with radial or hair brush morphologies remains to be largely unexplored.

In this work, we have developed inexpensive non-lithographic techniques aimed at fabrication of curvilinear hyperbolic metamaterials, which morphology resembles those of a hyperlens or an optical cloak. Three targeted geometries nick-named as hair brush, folded sheet, and urchin are depicted in Figs. 2a , 2b, and 2c.

 

Fig. 2 Explored metamaterials’ morphologies: hair brush (a), folded sheet (b), and urchin (c).

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We show that versatility and flexibility of the developed methods allow one to fabricate three-dimensional curvilinear metamaterials of practically any desired size and shape, Fig. 3 .

 

Fig. 3 Alumina membranes of three different targeted shapes – folded sheet (a), swiss roll (b) and urchin (c) grown from folded, rolled and indented aluminum foil sheets under anodic bias in oxalic acid. The resolution of the images is not sufficient to see the pores.

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Two major technological phases involving (i) fabrication of curved nanoporous alumina templates and (ii) filling the pores with silver nanowires are discussed below.

2. Fabrication and Characterization

Aluminum foils (99.99%) with the thicknesses of 25 μm and 100 μm and aluminum wires (99.99%) with the diameters equal to 50 µm and 500 µm have been acquired from Alfa Aesar. At the first step of the process, aluminum samples were rolled, folded, pressed, or micro-indented to obtain desired shapes and curvatures, Fig. 3. At the second step, the samples were annealed for four hours at 450°C in order to enlarge aluminum polycrystalline grain sizes. This was required for uniform anodization as discussed below. Then the specimens were electrochemically polished for three minutes in a mixture of perchloric acid and ethanol (volume ratio 1:4) to obtain mirror-finished surfaces. After that, a two-stage anodization was carried out in 0.3 M oxalic acid (used as an electrolyte) at constant DC voltage of 40 V. One hour of anodization was followed by removal of the grown porous oxide (via overnight soaking the specimen in the mixture of diluted phosphoric and chromic acids), after which the anodization was repeated for another four hours. This two-stage process converted aluminum to alumina and produced hexagonally arranged nanopores of high quality and uniformity, Fig. 4a . At the last step, pores of fabricated curvilinear alumina membranes were filled with silver nanowires (Fig. 5 ) using standard AC electroplating technique [15]. The mixture of aqueous solutions of silver nitrate (0.2M) and boric acid (0.05M) was used as an electrolyte, graphite rod served as a counter electrode, and a gold film deposited on the membrane’s surface or remaining thin aluminum layer (which was not converted to alumina) served as a working electrode. The process continued for one hour at applied voltage equal to 10 V and AC frequency equal to 200 Hz.

 

Fig. 4 (a) Image of a typical honeycomb nanoporous structure in an alumina membrane (top view). (b) Cross-section of radially oriented nanoporous in an urchin geometry. (c) Radially oriented nanopores formed around the defect (void) in an aluminum metal.

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Fig. 5 Etched edge of the folded sheet curvilinear alumina membrane filled with silver nanowires (a). A thin layer of aluminum, which was not converted to alumina in the process of anodization (b), was used as an electrode at electroplating.

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Structural characterization of fabricated samples was done by using field emission scanning electron microscope (FESEM, Hitachi 5700), scanning electron microscope (SEM, JEOL JSM 5900LV), atomic force microscope (AFM, Multiview 4000, Nanonics), optical microscope with x7000 magnification (HIROX), as well as an optical microscope with lower resolution.

3. Results and Discussion

As nanopores grow perpendicular to the material’s surface, radially oriented channels can be readily produced in urchin and folded sheet geometries as well as around voids in aluminum metal, Figs. 4b, 4c, and 5, As follows from Fig. 3a, the ratio of the outer and inner radii of the fabricated curvilinear alumina matrix is approximately equal to ten.

This ratio would determine the magnification of a hyperperlens with the same geometry. Many fabricated alumina matrixes were succesfully filled with silver (Fig. 5), resulting in structures morphologically similar to those proposed for a hyperlens and optical cloak, Figs. 1 b and 1c. Anodization and electroplating have been realized in aluminum wire (not shown) mimiking a hair brush architecture of Figs. 1c and 2a. Demonstration of a principle possibility to fabricate metamaterials with morphological resemblence and potentional functionality of a hyperlens and an optical cloak is the central result of this work.

4. Conclusion

We have demonstrated the feasibility and flexibility of a porous alumina membrane nano-template approach toward fabrication of curvilinear highly anisotropic and hyperbolic metamaterials. This inexpensive synthetic route opens a door to design and fabrication of large, three-dimensional bulk metamaterials for a number of practical applications ranging from optical cloaking to broad band sub-wavelength imaging.