Transforming Light

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Science  17 Oct 2008:
Vol. 322, Issue 5900, pp. 384-386
DOI: 10.1126/science.1166079

Recent advances in micro- and nanofabrication methods are presenting opportunities to control light in a way that is not possible with the materials provided to us by nature. Synthetic structures built up from subwavelength elements can now be fabricated with a desired spatial distribution of effective electric permittivity ε and magnetic permeability μ, thereby offering the potential to guide and control the flow of electromagnetic energy in an engineered optical space. These “metamaterials” have opened the door to a number of applications that had been previously considered impossible. No longer are we constrained by the electromagnetic response of natural materials and their chemical compounds. Instead, we can tailor the shape and size of the structural unit of the metamaterial and tune their composition and morphology to provide new functionality.

The field of transformation optics, which is enabled by metamaterials, has inspired a fresh look to be taken at the very foundations of optics. Analogous to general relativity, where time and space are curved, transformation optics shows that the space for light can also be bent in an almost arbitrary way. The ability to design and engineer optical space provides the possibility of controlling the flow of light with nanometer spatial precision. Thus, general relativity may find practical use in a number of novel optical devices based on transformation optics, guiding how, using metamaterials, the space for light can be curved in a predesigned and well-controlled way. The relation between light propagation and effective space-time geometries was considered, for example, in early papers by Tamm (1, 2), with the basics of transformation optics established later (3-5); these important early studies were not fully appreciated and were almost forgotten. Only recently has the field of transformation optics been reestablished (6-10).

Generally, light propagates so that the optical path, which is given by the product of the physical length and the refractive index, is minimized. Thus, by creating a complex distribution for the refractive index n, the geometrical path that minimizes the optical path can be curved in an almost arbitrarily complex way. One might think that such a molding of a light path is possible only in the limit of geometrical optics, which implies a scale much larger than the wavelength. Provided that the basic optical parameters of materials, ε and μ, are also transformed appropriately, and because of the generic invariance of Maxwell's equations, transformation optics makes it possible to mold and control light on all scales, from macroscopic sizes down to the deeply subwavelength scale. By creating a desired distribution of ε and μ, and thus a distribution of refractive index n, one can “curve” the space for light in a nearly arbitrary way, making it possible to propagate light not only in the backward direction (when n is negative) but also along nearly any curved line. As a result, a myriad of fascinating devices are achievable using transformation optics and metamaterials.

One of the most exciting applications is an electromagnetic cloak that can bend light around itself, similar to the flow of water around a stone, making invisible both the cloak and an object hidden inside (6, 11). By excluding light from a certain area of space and bending the light around the space, one can make an object in that area invisible (12) (see the figure, left panel).

Optical transformations.

(Left) Optical cloaking. (Middle left) Light concentrator [adapted from (13)]. (Middle right) Impedance-matched hyperlens [adapted from (18)]. (Right) Planar hyperlens [adapted from (13)].


However, practical applications of transformation optics go far beyond just cloaking. Theory allows the control of light in an extreme and ultimate manner by providing a general recipe for obtaining complex spatial distributions of anisotropic permittivity and permeability. Using these distributions, a “curvilinear” optical space is molded, thereby creating the channel for the desired flow of light. The core challenge here is to approximate the required ideal optical space by manufacturable nanostructured metamaterials, with minimal loss of the required functionality, and thereby move from the theoretical description to actual prototypes.

One cannot only exclude light from some region, as in a cloak, but also do the opposite and concentrate light within a certain area of the space. In such a concentrator, light could be collected from all directions onto an arbitrarily small spot, leading to extremely high intensities [see the figure, middle left panel (13)]. The light concentrator may enable applications such as omnidirectional solar light collection and field-enhanced sensing.

Transformation optics can also enable a magnifying, planar hyperlens, which is probably the most exciting and promising metamaterial application to date. The information about the subwavelength features of an object is carried by evanescent waves that exponentially decay with distance. This decay results in the loss of the subwavelength details in the far-field image and thus limits the imaging resolution. The hyperlens transforms the evanescent fields into propagating waves, producing magnified far-field images of the subwavelength features (14-17).

However, the originally proposed hyperlens suffers from strong reflections at its inner and outer cylindrical surfaces, causing reduced light throughput. With local control of the electromagnetic response of metamaterials, the impedance matching at these boundaries can be improved (18) (see the figure, middle right panel). Moreover, the actual fabrication and use of the hyperlens is extremely challenging, as in its original concept it requires cylindrical symmetry. Such symmetry is needed to slowly increase the electromagnetic mode wavelength as the wave spreads away from the center of the device to the point where propagation in air becomes possible (19). In addition, its cylindrical symmetry limits applications, because placing an object of interest in the hyperlens' inner cylindrical cavity is often impossible. One would be better served by a planar hyperlens—if it were possible.

The approach of “engineering optical space” with local control of a metamaterial's response offers a direct solution to this problem. The process of “slowing down” the evanescent waves required for converting them into propagating waves in air can be achieved by properly varying the dielectric tensor within the hyperlens. Simulations for the proposed flat hyperlens (13) show that it can produce magnified far-field images of sub-λ structures (see the figure, right panel). Such a planar, magnifying hyperlens could eventually become a standard add-on to conventional microscopes. By enabling nanoscale resolution in optical microscopy, metamaterial-based transformation optics could allow one to literally see extremely small objects with the eye, including biological cells, viruses and, possibly, even DNA molecules.

Transformation optics enabled by metamaterials transforms the science of light and opens up many exciting applications that often go beyond what we could imagine until very recently.

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