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# Magnifying Superlens in the Visible Frequency Range

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Science  23 Mar 2007:
Vol. 315, Issue 5819, pp. 1699-1701
DOI: 10.1126/science.1138746

## Abstract

We demonstrate a magnifying superlens that can be integrated into a conventional far-field optical microscope. Our design is based on a multilayer photonic metamaterial consisting of alternating layers of positive and negative refractive index, as originally proposed by Narimanov and Engheta. We achieved a resolution on the order of 70 nanometers. The use of such a magnifying superlens should find numerous applications in imaging.

Optical microscopy is an invaluable tool for studies of materials and biological entities. Imaging tools with ever-increasing spatial resolution are required if the current rate of progress in nanotechnology and microbiology is to continue. However, the spatial resolution of conventional microscopy is limited by the diffraction of light waves to a value on the order of 200 nm. Thus, viruses, proteins, DNA molecules, and many other samples are impossible to visualize with a regular microscope. One suggested way to overcome this limitation is based on the concept of a superlens (1), which relies on the use of materials or metamaterials that have negative refractive index in the visible frequency range. Near-field superlens imaging was recently demonstrated (2, 3), but the technique is limited by the fact that the magnification of the planar superlens is equal to 1. Thus, a thin planar superlens cannot be integrated into a conventional optical microscope to image objects smaller than the diffraction limit.

We describe the realization of a magnifying superlens (Fig. 1A) and demonstrate its integration into a regular far-field optical microscope. Our design is based on the theoretical proposals of an “optical hyperlens” (4) and “metamaterial crystal lens” (5) and on the recently developed plasmon-assisted microscopy technique (6), and in particular on the unusual optics of surface plasmon polaritons (SPPs). The properties of these two-dimensional optical modes and convenient ways to excite them are described in detail in (7). The wave vector of the SPPs is defined by the expression $Math$(1) where ϵm(ω) and ϵd(ω) are the frequency-dependent dielectric constants of the metal and the dielectric, respectively, and c is the speed of light. Above the resonant frequency ω described by the condition $Math$(2) the SPP group and phase velocities may have opposite signs (Fig. 1B). The internal structure of the magnifying superlens (Fig. 2A) consists of concentric rings of poly(methyl methacrylate) (PMMA) deposited on a gold film surface. For the SPP dispersion law for the gold-vacuum and gold-PMMA interfaces (Fig. 1B) in the frequency range marked by the box, PMMA has negative refractive index n2 < 0 as perceived by plasmons (the group velocity is opposite to the phase velocity). The width of the PMMA rings d2 is chosen so that n1d1 = –n2d2, where d1 is the width of the gold-vacuum portions of the interface. Although the imaging action of our lens is based on the original planar superlens idea, its magnification depends on the fact that all the rays in the superlens tend to propagate in the radial direction when n1d1 = –n2d2 (Fig. 1A). This behavior was observed in the experiment upon illumination of the lens with λ = 495 nm laser light (bottom portion of Fig. 2B) for which n1d1 = –n2d2. The narrow beam visible in the image is produced by repeating self-imaging of the focal point by the alternating layers of materials with positive and negative refractive index. On the other hand, if 515-nm light is used, the lens becomes uncompensated and the optical field distribution inside the lens reproduces the field distribution in the normal “plasmonic lens” as described in (8) (top portion of Fig. 2B). However, in the complete theoretical description of the magnifying superlens, the ray optics picture presented in Fig. 1A may need to be supplemented by the anisotropic effective medium theory presented in (4, 5).

The magnifying action of the superlens is demonstrated in Figs. 3 and 4. Rows of two or three PMMA dots were produced near the inner ring of the superlens (Fig. 3, B and C). These rows of PMMA dots had 0.5-μm periodicity in the radial direction, so that phase matching between the incident laser light and surface plasmons could be achieved (Fig. 1A). Upon illumination with an external laser, the three rows of PMMA dots in Fig. 3B gave rise to three radial divergent plasmon “rays,” which are clearly visible in the plasmon image in Fig. 3D obtained with a conventional optical microscope. The cross-sectional analysis of this image across the plasmon “rays” (Fig. 3F) indicates resolution of at least 70 nm, or ∼λ/7. The lateral separation between these rays increased by a factor of 10 as the rays reached the outer rim of the superlens. This increase allowed visualization of the triplet by conventional microscopy. In a similar fashion, the two radial rows of PMMA dots shown in Fig. 3C gave rise to two plasmon rays, which are visualized in Fig. 3E.

The composite image in Fig. 4 is a superposition of the atomic force microscopy (AFM) image from Fig. 3A and the corresponding optical image obtained by conventional optical microscopy. It illustrates the imaging mechanism of the magnifying superlens: The passage of plasmon rays through the concentric alternating layers of materials with positive and negative refractive index increases the lateral separation of the three rays (marked by arrows at lower right). Near the edge of the superlens, the separation is large enough to be resolved with a conventional optical microscope, thus demonstrating a magnifying superlens in the visible frequency range.

The theoretical resolution of such a microscope may reach the nanometer scale (1, 4). It thus has the potential to become an invaluable tool in medical and biological imaging, where far-field optical imaging of individual viruses and DNA molecules may become a reality. It allows very simple, fast, robust, and straightforward image acquisition.

We expect that unusual optical metamaterials may be designed and implemented using the principle of our magnifying superlens. Because (d1 + d2) and the d1/d2 ratio (Fig. 2A) are easy to vary locally, the effective anisotropic refractive index of the multilayer material may be varied continuously from large negative to large positive values. Thus, unusual nanophotonic devices may be created in the visible frequency range, such as the recently suggested (9, 10) and demonstrated (11) “invisibility cloak.”