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# Sub–Diffraction-Limited Optical Imaging with a Silver Superlens

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Science  22 Apr 2005:
Vol. 308, Issue 5721, pp. 534-537
DOI: 10.1126/science.1108759

## Abstract

Recent theory has predicted a superlens that is capable of producing sub–diffraction-limited images. This superlens would allow the recovery of evanescent waves in an image via the excitation of surface plasmons. Using silver as a natural optical superlens, we demonstrated sub–diffraction-limited imaging with 60-nanometer half-pitch resolution, or one-sixth of the illumination wavelength. By proper design of the working wavelength and the thickness of silver that allows access to a broad spectrum of subwavelength features, we also showed that arbitrary nanostructures can be imaged with good fidelity. The optical superlens promises exciting avenues to nanoscale optical imaging and ultrasmall optoelectronic devices.

Conventional optics suffer from the so-called diffraction limit, because they are only capable of transmitting the propagating components emanating from the source (1). This is because the evanescent waves that carry subwavelength information about the object decay exponentially in a medium with positive permittivity and permeability and are lost before reaching the image plane. To avoid this evanescent decay, a concept of subwavelength imaging through an intimate-contact mask was proposed back in the 1970s (2) and was subsequently demonstrated (3). Conventional immersion lenses that improve image resolution by increasing the index of refraction are limited by the availability of high-index materials. Although scanning near-field optical microscopy detects subwavelength details, it uses point-by-point scanning rather than forming the whole image at once. Interference can also form simple subwavelength patterns (4, 5), but it is not considered to be an imaging method because of the lack of a general bijective conformal mapping between the object and the image.

In contrast, a superlens is predicted to substantially enhance evanescent waves (1), compensating for the evanescent loss outside the superlens and thus restoring an image below the diffraction limit. This unusual lens takes the form of a thin slab of material with negative permittivity or permeability, or both (1, 610). Metamaterials (615), an emerging class of artificially designed and structured materials, have shown unprecedented electromagnetic properties in microwave or terahertz regimes, which provide a basis for the conjecture of the superlens. Although metamaterials and photonic crystals have recently shown beam bending (8, 13, 14) and refocusing (6, 7, 9, 10, 16) at microwave frequencies, achieving superlensing at optical frequencies is challenging partly because of the diminishing magnetic susceptibility of natural materials. Only recently have metamaterials shown magnetic responses in terahertz and infrared regimes (11, 12). However, in the near field, the electric and magnetic responses of materials are decoupled; therefore, for transverse magnetic (TM) waves, only the permittivity needs to be considered (1). This makes noble metals such as silver natural candidates for optical superlensing, because negative permittivity is easily attainable in them as a consequence of the collective excitation of conduction electrons. Let us consider a superlens consisting of a silver slab separated from an object by a spacer layer, and coated on the opposite side with an imaging material. By designing the thin metal slab so that the surface current oscillations (the surface plasmons) match the evanescent waves from the object, the superlens is able to substantially enhance the amplitude of the field. This key precursor for superlensing—the enhancement of evanescent waves by surface plasmons—was observed on silver films (17). Recently, numerical simulations have been conducted to understand the details of the silver superlens (1822). However, experimental attempts reported diffraction-limited images, probably resulting from the use of thick silver films that hinder the enhancement of evanescent waves (20).

As surface charges accumulate at the interface between the silver and the imaging medium, the normal component of an electric field is found at resonance when a proper thickness of silver is selected and the permittivity of the silver and that of the adjacent medium are equal and of opposite sign. Such a delicate resonance is essential to ensure the evanescent enhancement across the slab (1, 22). For enhanced transmission of evanescent waves (23), it is found that an asymptotic impedance match (kzii + kzjj = 0) has to be met at the surface of the silver, known as the surface plasmon excitation condition (kzi, cross-plane wave vector in silver; ϵi, permittivity of silver; kzj, cross-plane wave vector in dialectric; and ϵj, permittivity of dialectric). It is widely known in metal optics that when the two media take the opposite sign in permittivity and |ϵi| ≫ ϵj, only surface plasmons at the narrow range of in-plane wave vector (kx) that are close to k0 can be resonantly coupled. However, less well known is that when |ϵi| ∼ ϵj and they are of opposite sign, the excitable surface plasmon band of kx is significantly broadened, resulting in the superlensing effect (1).

Figure 1 shows a set of objects inscribed onto a chrome screen. The objects, placed about 40 nm away from the 35-nm silver film, are imaged onto the photoresist on the other side of the silver film under ultraviolet (UV) illumination (at a wavelength of 365 nm). Using focused ion beam (FIB) lithography, the chrome objects are patterned on quartz and then planarized, using a 40-nm-thick layer of polymethyl methacrylate (PMMA). The chrome masks are approximated as a binary object because in the UV, chromium (permittivity = –8.55 i8.96) is away from the plasmon resonance + and possesses low skin depth (∼15 nm) (24). Subsequently, a 35-nm-thick layer of silver, the superlens, is evaporated over the PMMA spacer layer, followed by coating with a 120-nm-thick negative photoresist [NFR105G, Japan Synthetic Rubber Microelectronics (JSR Micro)] to record the near-field image. The substrate is then flood-exposed under an I-line (365-nm) mercury lamp (25). The exposure flux is 8 mW/cm2, and an optimal exposure time of 60 s is applied. It is essential to reduce the surface root mean square modulation below 1 nm for both the silver and PMMA surfaces (Fig. 2E); otherwise, the dispersion characteristics of the superlens would be modified and would in turn smear the details of the recorded image (19). The optical image is converted into topographic modulations by developing the negative photoresist and is mapped using atomic force microscopy (AFM). The image of an array of 60-nm-wide nanowires on a 120-nm pitch is shown in Fig. 2A. The Fourier-transformed spectrum shows a sharp peak, corresponding to a pitch of 126 ± 7 nm (Fig. 3A, bottom panel). With careful control of the surface morphology of the PMMA and silver surface, we recorded the photoresist images with typical average height modulations of 5 to 10 nm (Fig. 2C). The result indicates sub–diffraction-limited imaging with half-pitch resolution down to 60 nm, or λ/6, using a silver superlens. The control experiments in which the silver film is replaced by 35-nm-thick PMMA show no evidence of imaging contrast from the subwavelength object, regardless of the optimization of imaging processes (Fig. 2, B and D). Our observation is further verified by a simple analysis of the evanescent decay of these subwavelength features. For a line-array object of period a, the intensity of evanescent waves decays with a characteristic length Z, given by $Math$ (26). With the permittivity of the surrounding media ϵ ∼ 2.4, a decay length of 11 nm is estimated for the 60-nm half-pitch. Without a superlens to enhance and transmit evanescent waves, it is difficult to resolve a 60-nm half-pitch object from a distance of 75 nm away, as we observed in the control experiments.

For the perfect lens originally proposed by Pendry, the entire Fourier spectrum of the image should be transferred uniformly without loss or distortion. However, a slab lens made of real materials with dispersive negative permittivity (such as silver) or permeability inevitably has losses and only asymptotically approaches a perfect lens at the quasi-static limit. Yet, such a lens system greatly enhances the essential portion of the evanescent spectrum, allowing subwavelength imaging resolution. We term such system a superlens, in comparison to an ideally perfect lens. Superlensing requires rather stringent conditions to maximize the enhancement over a broad band of evanescent waves. It is crucial to find a wavelength range where the wavelength-dependent permittivity of silver is nearly equal to and opposite that of the adjacent medium, which is the PMMA spacer and photoresist in this experiment. The resolving power of this system can be measured by the optical transfer function, defined as the ratio of image field to object field, |E|img/|E|obj, with given lateral wave vector kx. Using the Fresnel formula of a stratified medium (18), we computed the optical transfer function of a silver superlens system, taking into consideration the absorption in silver and in the adjacent media (Fig. 3). From Fig. 3A, we estimate that a range of evanescent components from 2 to 4 k0 can be efficiently enhanced and recovered by surface plasmon excitations, which is much broader than the conventional narrow resonance (typically <10% of k0). The calculation shows that the slight absorptions from PMMA and the photoresist have only negligible effects on the imaging quality.

Although the illumination is normal to the plane of the object, the subwavelength object scatters the incident radiation in different directions. Two types of polarization for the scattered waves in reference to the plane of the silver superlens are classified: (i) waves with a magnetic field component parallel to the plane have TM polarization, and (ii) waves with an electric field parallel to the plane have transverse electric (TE) polarization. Whereas a broad band of TM evanescent waves are resonantly coupled over the 35-nm silver superlens to form a sub–diffraction-limited image, the TE fields are significantly damped out (Fig. 3A), which is consistent with theoretical estimations of the image resolution calculated against the loss of natural silver (18, 19). Even though the PMMA and the photoresist slightly detune the surface plasmon resonance at the interfaces, the finite thickness of the silver slab ensures that they will be excited (22), allowing enhanced transfer of a broad evanescent spectrum. Because the 60-nm half-pitch object carries fundamental wave vectors that fall within the broad band of enhancement by the superlens (Fig. 3A, top panel), the corresponding spectrum peak is clearly observed in the recorded image, as seen in our experiment (Fig. 3A, bottom panel). In Fig. 3B, we calculated the transfer function of the 60-nm half-pitch object for various silver film thicknesses. Assisted by surface plasmon excitation, a maximum enhancement of the selected subwavelength feature was reached for a 35-nm-thick silver slab. Above a thickness of 40 nm, the enhancement was damped by material absorption, destroying the superlensing effect. Such a critical thickness gives a measure for the efficient coupling of the evanescent modes at two interfaces of the silver film. The existence of this critical thickness is in good agreement with our previous finding (15).

The silver superlens can also image arbitrary nanostructures with sub–diffraction-limited resolution (Fig. 4). The recorded image “NANO” in Fig. 4B shows that we can faithfully reproduce the fine features from the mask (Fig. 4A) in all directions with good fidelity. As previously discussed, only the scattered TM evanescent waves from the object are coupled into the surface plasmon resonance of the silver film, and they become a primary component for restoring a sub–diffraction-limited image. For comparison, Fig. 4C displays the control experiment performed on the same mask, with “NANO” embedded in 75-nm planarized PMMA. With the same exposure condition, we observed the image of “NANO” with much wider lines, even with the extended development time (>1 min). Because the lines are a few micrometers apart, the subwavelength openings can be treated as isolated line sources, with a broad band of Fourier spectrum: The larger Fourier components decay strongly, and only the smaller Fourier components reach the imaging plane, resulting in a diffraction-limited image as shown in Fig. 4C. In contrast, with a silver superlens, we can resolve an average line width of 89 nm (Fig. 4D), which is much smaller than that of the diffraction-limited image. With natural and structured plasmons (2831) in metals and phonon polaritons in semiconductors, a potential low-loss, high-resolution superlens is achievable.

Supporting Online Material

Materials and Methods

Figs. S1 to S5

Table S1

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