Microdroplets as metamaterial lenses

Current interest in metamaterials and transformation optics is driven by applications such as cloaking and superlenses. In theory, various metamaterial-superlens designs are capable of overcoming the usual diffraction limit of optical devices. However, extreme sophistication of 3D nanofabrication techniques (which are required to realize these metamaterial designs) makes experimental progress very slow. In addition, it is difficult to develop metamaterials with low-loss, broadband performance. These difficulties are particularly severe in the visible frequency range, where good magnetic performance is limited.

Very recently, we developed an alternative experimental realization of optical designs based on metamaterials and transformation optics. Our approach is based on emulating the metamaterial properties by the height of a thin waveguide. We successfully applied this technique to broadband electromagnetic cloaking in the visible range.¹ Here, we demonstrate that a similar technique is applicable to design of metamaterial optics such as Maxwell fish-eye and Eaton lenses,² which may be capable of superlens imaging.³

Maxwell fish-eye and Eaton lens designs require a radial refractive-index distribution that changes from some constant value in the middle to near zero close to the lens edge. These designs are based on the stereographic projection of a sphere onto a plane. Our earlier work on cloaking demonstrated that a thin waveguide near cutoff emulates a refractive index near zero. Therefore, the height profile of a microdroplet, which tapers off near the edge, provides a natural realization of the requisite effective refractive index. Moreover, points near the droplet edge correspond to points located close to the equator of the projected sphere. Therefore, these points are imaged onto points located near the opposite droplet edge (see Figure 1).

Figure 1. Numerical simulations of imaging properties of a fish-eye lens. (a) Two points near the edge of the lens are imaged into opposite points. (b) Refractive-index distribution. (c) Experimental testing of the imaging mechanism. The droplet is illuminated near the edge with a tapered fiber tip of a near-field scanning-optical microscope (NSOM). The NSOM tip is clearly seen at the opposite edge of the droplet.

Eaton lenses have similar imaging properties. In addition, we have demonstrated that Eaton lenses may be deformed to achieve image magnification. Figure 2 clearly shows good agreement between theoretical and experimental images of a deformed Eaton lens obtained at a wavelength of 515nm.

Figure 2. Experimental testing of image magnification of the ‘deformed droplet.’ We moved the NSOM probe tip along the droplet edge. The bottom row shows results of our numerical simulations for one and two point sources. The shape of the ‘deformed droplet’ used in the numerical simulations closely resembles the droplet's actual shape.

To realize better microdroplet/metamaterial lenses, we need to achieve better control of the overall shapes of the microdroplets and study their ultimate resolution limit. Because of their relative simplicity, these microlenses may find numerous applications in microscopy and nanolithography.