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Although negative refraction has been demonstrated at microwave frequencies in a quasi-homogeneous metamaterial4, imaging by a flat lens is severely constrained because of large dissipation5,6 and anisotropy in the metamaterial. Plane-wave negative refraction at specific incident angles has been demonstrated at microwave frequencies by using a metallic photonic crystal prism7 and a dielectric photonic crystal8. However, to focus a diverging beam from a point source, the material must exhibit all-angle negative refraction2 as well as low absorption.

Figure 1a shows the image of a microwave point source of frequency 9.3 GHz (wavelength, 3.22 cm) placed 2.25 cm from a two-dimensional flat lens made of a photonic crystal fabricated from an array of cylindrical alumina rods (see supplementary information). On the far side, a high-quality image is seen at a distance of 2.75 cm. Note that there is an image of similar size for the sub-wavelength source. This image is observed only in a narrow frequency range, between 9.0 and 9.4 GHz, with the best focus at 9.3 GHz. Outside this narrow band, at all other frequencies between 2 and 12 GHz, a single focus point is not seen.

Figure 1: Imaging by a flat lens.
figure 1

a, Microwave electric-field-intensity map on a cross-sectional view of the two-dimensional source–image (left–right) system for the flat lens. b, Displacement of the image by 4 cm when the source is moved up by the same distance. Both panels correspond to dimensions of 37.5 × 30.0 cm. The intensity scale on the source side varies from −20 dB (yellow) to −48 dB (black), and on the image side from −30 dB to −75 dB.

Full size image

These observations can be understood by examining the band structure of the photonic crystal and the corresponding equi-frequency surfaces, from which an effective refractive index, neff, can be defined and calculated9. In our geometry, the central axis of the diverging beam is along the (1,0) direction of the square lattice crystal. Just below the top of the second band, between 9.0 and 9.4 GHz, the equi-frequency surfaces move inwards with increasing frequency, consistent with negative neff. The condition for negative refraction, neff(θ) < 0, holds for a diverging beam of sufficiently large angle, enabling the image to be formed. Figure 1 therefore also demonstrates wide-angle negative refraction by a photonic crystal.

The value of neff is necessarily angle-dependent. Inside the crystalline lens, the electromagnetic field is highly modulated and simple ray diagrams applicable in homogeneous media cannot be used. However, upon emerging, the waves create a focus of the divergent beam emanating from the point object.

Conventional optical systems have a single optical axis and limited aperture, and cannot focus light onto an area smaller than a square wavelength1. In contrast, our flat lens does not have a unique optical axis and is not restricted by aperture size. We have demonstrated both of these features by moving the source up by 4 cm: the image moves a corresponding distance in the same direction (Fig. 1b).

The unique properties of our flat lens provide new perspectives on imaging. A particular advantage of the photonic crystalline material is its scalability to submicrometre dimensions for possible applications from microwave to optical frequencies.