Silicon nanostructure cloak operating at optical frequencies

The ability to render objects invisible using a cloak (such that they are not detectable by an external observer) has long been a tantalizing goal1–6. Here, we demonstrate a cloak operating in the near infrared at a wavelength of 1,550 nm. The cloak conceals a deformation on a flat reflecting surface, under which an object can be hidden. The device has an area of 225 mm and hides a region of 1.6 mm. It is composed of nanometre-size silicon structures with spatially varying densities across the cloak. The density variation is defined using transformation optics to define the effective index distribution of the cloak. The prospect of optical cloaking has recently become a topic of considerable interest. Through the use of transformation optics7–11, in which a coordinate transformation is applied to Maxwell’s equations, several designs for such a device have been created12–23. These designs are based on the idea of manipulating the structure of the cloaking medium so that the trajectory of light after interacting with the cloak is the same as that in an empty medium, without the cloak or the object underneath. The external observer is therefore unaware of the presence of the cloak and the object. Such cloaks were recently experimentally demonstrated in the microwave regime using metamaterial structures with feature sizes in the millimetre to centimetre scale24,25. Pushing this technology to the optical regime would greatly increase the potential application. However, this requires nanometre control of the cloaking structure. Here, we demonstrate a cloak in the optical domain operating at 1,550 nm using sub-wavelength scale dielectric structures. We experimentally demonstrate an optical invisibility cloak that hides an object ‘under a carpet’ with the help of a reflective surface. As outlined in Fig. 1, when an external observer looks at a deformed mirror, the observer detects the deformation in the reflected image (Fig. 1a,b). Following theoretical work by others11,20, we designed and fabricated a cloaking device at optical frequencies that is capable of reshaping this reflected image and providing the observer with the illusion of looking at a plane mirror (Fig. 1c). Objects could therefore be hidden under such deformations without being detected. A similar device has also been demonstrated that was constructed using a different technique26. The cloaking device has a triangular shape with an area of 225 mm2, and is composed of a spatially varying density of subwavelength 50-nm diameter silicon posts embedded in a SiO2 medium. The reflective surface consists of a distributed Bragg reflector (DBR) with a deformation that covers the 1.6-mm2 cloaked region. The distribution of posts induces a variation of the effective index of refraction across the surface through the relation 1eff1⁄4 rSiO21SiO2þ rSi1Si, where r is the volumetric fraction and 1 the effective dielectric constant of each material27. The DBR consists of alternating regions of SiO2 and crystalline silicon. The simulated reflectivity for the ten-period DBR used is larger than 0.999. We fabricated the invisibility cloak in a silicon-on-insulator (SOI) wafer. An etching mask, consisting of a 160-nm layer of Dow Corning XR-1541, was patterned by electron-beam lithography, and the 250-nm top silicon layer etched using a standard Cl2 inductively coupled plasma process. We then clad the device with SiO2. Scanning electron microscope images of the fabricated device before deposition of the SiO2 are shown in Fig. 2. A 450-nm-wide silicon waveguide with a tapered end was arranged to terminate at the mid-point of the edge on the y-axis. The waveguide was used to direct light into the device such that all of the input light was incident on the deformation and not on the plane DBR reflector, thereby maximizing the effect of the deformation. Note, however, that the design, based on transformation optics, does not introduce any constraints on the wave fronts applied to the device20, which means that the cloaking medium operates at all angles of incidence where the reflectance of the DBR is sufficiently high. In Fig. 2b the reduced density of the silicon posts in the low effective index region of the cloak can be observed, as well as some of the silicon sections from which the DBR is composed. The spatial distribution of the 50-nm-diameter posts, that is, the effective refractive index distribution of the cloak, was determined by defining a transformation of coordinates from the perfect triangle in Fig. 2a to one with a Gaussian-shaped deformation along its hypotenuse (behind which an object could in principle be hidden) for transverse magnetic (TM) polarized fields (with the major component of the electric field perpendicular to the device). To minimize the anisotropy in the medium, the transformation of coordinates was realized by the minimization of the modified Liao functional20,28,29 with slipping boundary conditions. The resulting effective index distribution has an anisotropy factor of 1.02 with index values ranging from 1.45 to 2.42 between the index of the SiO2 and that of crystalline silicon, enabling fabrication of the device using standard silicon processes. The complete effective refractive index distribution is shown in Fig. 3. The triangular shape of the device with the deformation along its hypotenuse can be observed. The highest and lowest effective refractive index regions are located around the deformation, and the background index value of the remaining cloaking region is 1.65. The final profile of the cloak contains almost no silicon in the low index regions, whereas in the high index regions it has the largest concentration of posts (see Fig. 2). We simulated the propagation of light in the device using the finite-difference time-domain (FDTD) method. The results show that, owing to the presence of the cloak, the image of the light incident on the deformation (the region under which an object could be hidden) resembles the image of a wave propagating in a homogeneous medium without the deformation. Figure 4a shows a simulation of light propagating through a homogeneous background index of 1.65 and reflected by the DBR. Figure 4b shows the same simulation when the DBR is deformed, and Fig. 4c shows the simulation of light reflected by the deformed DBR (same as Fig. 4b), but with the deformation now covered by the cloak. By comparing Fig. 4a and b, it can