Invited Paper
Beating the diffraction limit using a 3D nanowires metamaterials nanolens B. D. F. Casse† , Y. J. Huang, W. T. Lu, E. Gultepe, L. Menon, and S. Sridhar‡ Electronic Materials Research Institute and Department of Physics, Northeastern University, Boston, MA 02115, USA. ABSTRACT Super-resolution imaging using a three-dimensional metamaterials nanolens has been recently reported [B. D. F. Casse et al. Appl. Phys. Lett. 96, 023114 (2010)]. This nanolens, consisting of bulk gold nanowires embedded in alumina template, can transport with low-loss object details down to λ/4 (λ, wavelength) length scales, over significant distances of the order of 6λ. Here, we present validation of the super-resolution imaging by the nanolens through extensive control experiments. We also analytically show that the nanowire array medium supports a quasi transverse electromagnetic mode (TEM) with flat isofrequency contours, which is a requirement for superresolution imaging. We numerically compute the optical transfer function to quantify the imaging quality of the lens and show that the theoretical resolution of this nanolens is λ/5. Additionally, we demonstrate the broadband nature of the lens in the spectral region 1510 nm to 1580 nm. Finally, imaging of a large object (∼ 52λ in diameter), with subwavelength features, is presented. Keywords: Super-resolution, Metamaterials, Bulk, Nanowires, Subwavelength, 3D, Superlens
1. INTRODUCTION Optical imaging instruments suffer from Abbe’s diffraction limit1 — object structural details which are less than half the wavelength of light are not resolved by conventional lenses made of positive refractive index materials. This limit in resolution arises because evanescent waves, which carry the fine details of the object, decay exponentially and by the time the waves reach the image plane they are almost completely extinguished. Lenses made of metamaterials with negative parameters promise super-resolution imaging2–9 by either amplifying these decaying evanescent fields or by transporting them with minimal loss. Several prototypes, mostly based on the amplification mechanism, have been realized. However, most of these superlenses are hindered by materials losses, and exhibit narrow spectral bandwidth and other pertinent drawbacks summarized in Refs.2, 10 A superior three-dimensional (3D) metamaterials nanolens, free from the drawbacks mentioned above, has been recently reported by our group.11 The 3D nanolens is capable of transporting fine details of an object down to λ/4 (λ, wavelength), over a significant distance of > 6λ. Here, we validate the experimental observation of superresolution imaging by a series of control experiments. Also, we show that this array of nanowires in dielectric media has flat isofrequency contours, which is a requirement for imaging below Abbe’s diffraction limit. We then compute the optical transfer function of such a system and show that the theoretical resolution approaches λ/5 for near infrared wavelengths. The broadband nature of the lens is demonstrated by mapping the image at various wavelengths from 1510 nm to 1580 nm. Finally, imaging of a large object (∼ 52λ in diameter) with subwavelength features is demonstrated. Further author information: (Send correspondence to S. Sridhar and B. D. F. Casse) S. Sridhar: E-mail:
[email protected] † B. D. F. Casse: E-mail:
[email protected] ‡
Photonic Microdevices/Microstructures for Sensing III, edited by Hai Xiao, Xudong Fan, Anbo Wang, Proc. of SPIE Vol. 8034, 803407 · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.883699 Proc. of SPIE Vol. 8034 803407-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 07/19/2013 Terms of Use: http://spiedl.org/terms
2. EXPERIMENTAL The nanolens was manufactured in a two-steps process: Nanoporous alumina templates were prepared by chemical anodization of aluminum foils and by a subsequent electrochemical process to fill the pores with metal, following an in-house recipe outlined in Ref.12 The anodization process yielded a periodic, hexagonally ordered, 10 μm thick nanoporous layer with pore diameter of 12 nm and with a lattice spacing of 25 nm (filling ratio of 15%), while the electrodeposition process grew a comparable thick layer (10 μm) of gold nanowires inside the vertically arranged pores. A typical nanowire array nanolens obtained is shown in Fig. 1(a). For better visual illustration, the alumina host matrix was removed. Note that the removal of the alumina host matrix causes the wires to slightly agglomerate. As for manufacturing the nanoscale objects for the imaging experiments, void patterns were milled, by a focused ion beam (FEI Nova Nanolab 600), in thin gold metallic film deposited on glass substrate. The object pattern consists of the letters ‘NEU’ (acronym for Northeastern University) with 600 nm wide (0.4λ) arms, as shown in the SEM picture in Fig. 1(b). For the optical characterization, the nanolens was ‘glued’ to the patterned metallic film on glass substrate using methanol and subsequently left to dry. In the experiments, the sample was illuminated from the bottom (glass substrate end) with a continuous wave (CW) tunable semiconductor laser. The optical measurement was performed with a near-field optical microscope, NSOM, (Nanonics MultiView 2000TM) where a tapered fiber probe, with an aperture diameter of 150 nm, was used in collection mode. The fiber tip was raster scanned above the porous alumina surface, allowing us to map the optical intensity. A schematic of the experimental setup is shown in Fig. 1(c). The recovered image of the ‘NEU’ pattern is shown in Fig. 1(d). In this article, the images presented are raw data with a threshold applied to remove background noise. Microscope snapshot images were captured through a high-resolution infrared camera (Hamamatsu C274H-03). Note that several samples were used in this work and the results obtained were fully reproducible. Representative results of the research work are shown in this letter.
Figure 1. (a) Free-standing array of nanowires having diameter of 12 nm and lattice spacing of 25 nm. The wires are 10 μm thick. Note that the alumina host matrix has been removed for better visual illustration. (b) ‘NEU’ void text pattern milled in metallic film. Arms are 600 nm wide (0.4λ). (c) Experimental setup: A CW laser at 1550 nm illuminates the void patterns. The structural details of the object are then transported from the throughout the nanolens and then mapped by a near-field scanning optical microscope (NSOM) at the image plane. (d) Typical image of the text recorded by the NSOM. Here, we note that the subwavelength details have also been recovered.
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For a complete set of control experiments (Fig. 2), we have also attempted to image the “N E U” letters with (1) porous alumina template without the gold nanowires (essentially a pure dielectric), as shown in Fig. 2(b), and (2) 10 μm above the surface of the object in air without the alumina template, as shown in Fig. 2(c). In both cases, the images were almost unrecognizable in the far-field and super-resolution imaging was not achieved, demonstrating that the composite metamaterial behaves as a super-resolution medium. (3) Infrared camera snapshot from a regular microscope objective with resolution of λ/NA [NA = 1.4 and λ = 1550 nm], which shows that the subwavelength ‘NEU’ text cannot be resolved with a diffraction-limited lens (Fig. 2(d)). Furthermore, our experiments corroborate that a 100 nm thick gold film almost completely blocks infrared light (thickness being larger than the skin depth of the metal), so that bulk gold of thickness comparable to the nanowire material (∼10 μm) could not possibly yield the present imaging results.
Figure 2. Comparison of NSOM images obtained with the metamaterial nanolens and control configurations. (a) The image is obtained above the surface of the nanolens. (b) Nanoporous alumina template (10 μm thick) without the gold nanowires. (c) No nanolens (10 microns above the surface). (d) An infrared camera picture from a regular microscope objective with resolution of (λ/NA) [NA = 1.4 and λ = 1550 nm]. In the cases (b), (c) and (d) the “N E U” text is not observed indicating a complete lack of imaging, unlike (a) where the image is clearly seen.
To demonstrate the broadband aspect of the lens, imaging experiments were performed at different wavelengths (1510 nm–1580 nm), limited only by the tunable range of the laser. No significant distortions were observed when the wavelength was varied from 1510 nm to 1580 nm, indicating that some degree of broadband imaging is also realizable with this nanolens (Fig. 3). Theoretically, the nanolens, with its current geometrical as well as material configurations, can operate from the near-infrared to the mid-infrared spectral range, up to a wavelength of 21 μm.13
Figure 3. Broadband imaging: NSOM image maps of the “N E U” object at different wavelengths: (a) 1510 nm, (b) 1530 nm, (c) 1550 nm, (d) 1565 nm and (e) 1580 nm, to demonstrate the broadband nature of the metamaterials nanolens. The image characteristics are robust across the entire spectrum.
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3. THEORETICAL In such metallic rods architecture, imaging with super-resolution requires guided modes with flat isofrequency contours, where the longitudinal wave vector kz (z is in the direction of the nanowires) is nearly independent of the transverse wavevector kx,y . In arrays of metallic rods medium, in which the permittivity of nanowires is sufficiently negative (Reεz < 0), a quasi-TEM (transverse electromagnetic) nearly dispersionless mode capable of guiding evanescent waves is supported.14 To visualize the isofrequency contour of the quasi-TEM mode, we used a non-local homogenization model,13 and described the gold nanowires, arranged on a square lattice with spacing 25 nm, as a Drude metal with plasma frequency 2175 THz and collision frequency 6.5 THz (εAu = −125 + 4.2i at λ = 1.55 μm), while the alumina is modeled as a dielectric with permittivity of 3. With the given geometrical parameters and materials properties, we can observe, as shown in Fig. 4(a), a relatively flat dispersion contour for the quasi-TEM mode at 1.55 μm, thereby satisfying the main requirement for super-resolution imaging. The image quality of this nanolens can be quantified by computing the optical transfer function (OTF), which is defined as the ratio of the image field to the object field for each plane wave component kx,y .15, 16 In general, the OTF of the system has the form (Tobject .Tslab .Timage ), but in the case of the nanolens it can be reduced to the transmission coefficient of the slab Tslab alone, due to the very close proximity of both image and object to the lens (i.e. Tobject = Timage ≈ 1). A critical role of a super-resolution medium is to transmit transverse field components with large spatial frequency kx,y (evanescent modes), with enhanced amplitude. In an OTF plot, this reconstruction of evanescent modes is depicted by the average transmission (TAV G ) being greater √ than the half-intensity criterion∗ transmission (TI/2 ) for kx,y /k0 > 1. TI/2 can be estimated as TI/2 ∼ T / 2 for 0 ≤ kx,y /k0 ≤ 1 (propagating waves). For a 10 microns thick slab of this anisotropic medium, the plot of the transmission coefficient T of the slab, as a function of kx,y /k0 , is shown in Fig. 4(b). As seen from the curve of the transfer function, TAV G > TI/2 (red dotted line) for approximately (kx,y /k0 )max < 2.5. Therefore, the resolution of this slab should be around Δmax = λ/(2 × (kx,y /k0 )max ) = λ/(2 × 2.5), i.e. λ/5, in good agreement with the observed resolution of better than λ/4.
Figure 4. (a) Dispersion contour for the quasi-TEM mode at 1.55 μm wavelength for gold nanowires with square lattice arrangement, lattice spacing of 25 nm and radius of 6 nm. The isofrequency contours are relatively flat, which suggests that guided modes capable of transporting evanescent waves can be excited in the medium. (b) Plot of the optical transfer function (OTF) of the anisotropic slab, with a thickness of 10 μm, at 1.55 μm wavelength (blue curve). Here, the halfintensity criterion transmission TI/2 (red dotted line) is the lower limit of the transmission coefficient for which imaging √ with acceptable distortions occurs, and is mathematically defined as T / 2 for 0 ≤ kx,y /k0 ≤ 1. As seen from the curve of the transfer function, TAV G > TI/2 , kx,y /k0 > 1 (regime of evanescent waves reconstruction) for (kx,y /k0 )max < 2.5. Therefore, the resolution of this slab should be around Δmax = λ/(2 × (kx,y /k0 )max ) = λ/(2 × 2.5), i.e. λ/5, in good agreement with the observed resolution of better than λ/4.
The metamaterial nanolens can also image very large objects with subwavelength features. To demonstrate this capability, we imaged the Northeastern University logo, which is 80 μm wide (∼ 52λ) and is composed of feature sizes down to the order of λ/5 (Fig. 5(a)). The recorded image (Fig. 5(b)) by the lens demonstrates ∗
The half-intensity criterion is the lower limit of the transmission coefficient for which imaging with acceptable distortions occurs.
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that subwavelength features are retained even for large objects, although distortions arising from large scale inhomogeneities are evident. In the case of a conventional microscope, only an outline of the logo can be observed (Fig. 5(c)).
Figure 5. (a) SEM image of the Northeastern University logo milled in metallic film. The logo is a large object, which is 80 μm wide (∼ 52λ) and has subwavelength features down to the order of ∼ λ/5. (b) NSOM scan of the image recovered by the metamaterial nanolens. Note that most of the features of the logo are well resolved. (c) Imaging using a conventional microscope. Here, the image snapshot was captured using an infrared camera. We can see that for the ordinary microscope, the detailed features cannot be observed.
4. CONCLUSION To summarize, the three-dimensional metamaterials nanolens, consisting of bulk metallic nanowires embedded in alumina template, is a viable architecture for super-resolution imaging. Control experiments, analytical computation of the isofrequency contour of the supported quasi-TEM guiding mode by the medium, combined with assessment of the image quality of the lens and test-driving the lens on large structures with deep subwavelength features, reinforce the fact that the nanolens is a robust super-resolution medium. In addition, the nanolens is able to transport both propagating and evanescent waves over very long distances (>> λ) with low-loss and without significant distortions. For the near-infrared region, the nanolens has a theoretical resolution of λ/5, which is in excellent agreement with the resolution determined experimentally.11 Interestingly, by appropriate choice of filling factor and raw material, the nanolens can operate from UV to the mid-infrared spectral range, thereby enabling color imaging. The superior optical properties of the material combined with the capability for large scale production offer the potential for numerous applications in biomedical imaging, plasmonic nanoscale lithography and optical storage devices.
ACKNOWLEDGMENTS The authors would like to thank M. G. Silveirinha, J. Topolancik, S. Savo and F. Camino for useful discussions and comments. This work was financially supported by the Air Force Research Laboratories, Hanscom through FA8718-06-C-0045 and NSF through PHY-0457002. The work was also performed in part at the Kostas Center at Northeastern University and the Center for Nanoscale Systems, a member of NNIN, which is supported by the National Science Foundation under NSF award no. ECS-0335765. Research carried out in part at the Center for Functional Nanomaterials, Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886.
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