Invisibility devices commonly play a role in science-fiction scenarios. However, the recently formulated theory of transformation optics1–3 establishes a correspondence between coordinate transformations and material parameters (permeability and permittivity) that actually enables us to design invisibility cloaks that exclude electromagnetic (EM) waves in certain regions. Such invisibility cloaks can conceal an object by steering waves around an enclosed domain so that any object located inside the domain is hidden from observation. However, the hidden object will be ‘blind,’ since no outside light can reach into the cloaked domain. It would thus be desirable to design an ’external invisibility device’ that leaves the concealed object out in the open so that it can ‘see’ its surroundings.4 The key idea behind our newly designed device is the concept of complementary media,5 as illustrated in Figure 1. In Figure 1(a), we present a schematic diagram of a dielectric cylinder (with radius r < a). It scatters an incident EM wave and is thus visible: see Figure 1(b). Figure 1(c, d) shows the equivalent schematic diagram and resulting (scattered) electric-field distribution for a cylindrical shell (with inner and outer radii a < r < b) composed of a specific negative refractive-index material designed on the basis of transformation optics. Figure 1(e, f) shows that when the cylinder and shell are combined, they produce no scattering and the dielectric core can therefore be made invisible by the negative refractive-index shell. However, these results can also be interpreted differently. The cylindrical shell can be regarded as optically canceling a shell of air (with inner and outer radii b < r < c) outside of it, as outlined by the dotted line in Figure 1(e). It can be proved that the domain bounded by a < r < b and b < r < c is optically equivalent to a space that is optically void. This means that light does not change phase when it passes through the domain a < r < c. However, tomake a region invisible it must optically behave like air. Since an optical void Figure 1. (a) Dielectric cylinder (green) with permittivity e′′ = 16e0 and permeability μ′′ = 1μ0, where e0 and μ0 are the electric and magnetic constants (i.e., the permittivity and permeability of free space, respectively). (b) The cylinder scatters a plane wave incident from the left (arbitrary size units). (c) Negative refractive-index shell (black), designed using transformation optics. (d) Scattering pattern of the shell in panel (c). (e) The combined core and shell do not scatter electromagnetic waves, as shown in panel (f).