Macroscopic Invisibility Cloak made from Natural Birefringent Crystals
Author: Shuang Zhang
Affiliation: School of Physics and Astronomy, University of Birmingham, UK
Making things invisible is certainly appealing to most people - including scientists and magicians. Invisibility cloaks have existed only in movies and science fictions until 2006 when Pendry and Leonhardt independently pointed out ways to scientifically realize them [1, 2]. Transformation optics, the enabling theoretical tool to make this happen, works by optically compressing a spatial region to leave out a niche that cannot be accessed by light, while keeping its outer boundary intact so nothing seems to have happened when light exits the cloak.
This new research field has witnessed rapid progresses. Soon after the theoretical proposal, the first experimental demonstration of invisibility was shown at microwave frequencies in 2007 , and within 2 years, invisibility has reached Near-Infrared, the frequencies normally used for optical communications [4, 5]. These milestone works show that invisibility has become more a reality than fiction. However, all those invisibility cloaks were made from artificially engineered structures with subwavelength feature size, the so called metamaterials. At optical frequencies, the nano- and micro- fabrication of metamaterials limited the achievable invisibility cloak to a few wavelengths.
Recently two independent teams (including us at University of Birmingham, Imperial College London and Technical University of Denmark) have succeeded in scaling up the invisibility cloak to hide things of macroscopic scale [6, 7]. While previous works on optical invisibility have focused on non-uniform isotropic artificial media, we utilize uniform, anisotropic medium to construct the invisibility cloak. Specifically, our invisibility cloak was made from natural birefringent crystals, and therefore they can be easily scaled up to hide things at least thousands of times bigger than optical wavelengths. In addition, the cloaks work in the visible range, therefore the cloaking effect can directly be seen with our naked eyes.
Our macroscopic invisibility cloak consists of two triangular calcite prisms, with carefully designed geometries and crystal orientations, glued together, as shown by Fig. 1. At bottom of the cloak, there is a small triangular indentation, where objects can be hidden from view. The cloak is capable of optically transforming the triangular bump into a flat surface for a specific light polarization; light is guided around the bump without being scattered by it. As a consequence, for someone looking from outside, the bump appears to be flat and it would not be discernible when it sits on top of an opaque surface. Thus, anything that can be fitted in this triangular region of two and half centimeters width and 1.2 millimeters height can be rendered invisible.
Fig. 1: (Left) A photograph of the triangular cloak, which consists of two calcite prisms glued together. The optical axis of each calcite prism is indicated by the red arrow. The dimension of the cloak along z direction is 2 cm. (Right) Ray tracing shows that light is reflected by the bump without being scattered.
The cloak has been tested with laser beams and natural white light, both in air and liquid with carefully designed refractive index. Fig. 2 shows the reflection of an arrow-shaped green laser beam by the triangular bump at the bottom of cloak. Due to the birefringent nature of the cloak, light with different polarizations follow different paths in the cloak. Light of transverse electric (TE) polarization does not experience the cloaking effect; for TE, the cloak is no more than two pieces of glass prisms. The reflection from the bottom bulging surface split the laser beam into two, as shown by the image projected on the screen for the green laser beam (Fig. 2b). While with TM polarization, the reflected beam shows no splitting at all (Fig. 2c), serving as direct evidence that the calcite cloak transforms the protruding bottom surface into a flat mirror. An invisibility cloak should work at all incident angles. This is confirmed by the measurements at three different incident angles, as shown in Fig. 2 (d, e, f), where the central image corresponds to the TM polarization, and the two projected arrow segments images away from the centre correspond to the TE polarization. The projected images of the TM polarized beam at all incident angles show no distortion of the laser pattern.
Fig. 2: Optical characterization of the cloak using green laser beam. (a) The pattern of the laser beam as reflected by a flat surface. The projected arrow image is about 1.2 cm long in the horizontal direction. (b, c) The projected image of the laser beam reflected by the calcite cloak for TE and TM polarizations, respectively. The TM measurement shows that the laser beam is not distorted by reflection by the triangular protruding surface. (d, e, f) the projected images for mixed TE and TM polarizations at incidence angles of 39.5°, 64.5° and 88°, respectively. For all incident angles, the central TM images are not distorted, the cloaked reflective bump appears to be a flat mirror to outside observers.
The macroscopic calcite cloak is further tested by imaging of white-color alphabetic letters printed on a sheet of black paper reflected by the cloak system. For TE polarization (Fig. 3a), the mirror deformation results in distortion of the image collected by the camera, whereas switching the polarization to TM leads to imaging of consecutive letters from the same location as if the bottom surface of the cloak is flat (Fig. 3b). Due to the dispersion of calcite crystal, rainbow can be observed at the edge of the letters. Nonetheless, the overall cloaking effect looks considerably well, confirming the broadband operation of our calcite invisibility cloak.
Fig. 3: Imaging of white-color alphabetic letters (from ‘A’ to ‘Z’) printed on a sheet of black paper reflected by the cloak system. The reflected image captured by the camera for TE (a) and TM (b) polarizations, respectively.
In air, the cloak itself, though transparent, is still visible due to refraction and reflection caused by the mismatch of refractive index at its interface. When the cloak is immersed in a liquid with appropriate refractive index, both refraction and reflection can be eliminated, and the cloak itself can be made invisible as well. Fig. 4 shows the characterization of the invisibility cloak in an index matching oil of index close to 1.53. At the right polarization of light, the calcite cloak can hardly be seen if not for the scattering of light at the edges.
Fig. 4: Characterization of the invisibility cloak in the index matching fluid. (a, b) Reflected images for TE and TM polarizations, respectively, viewed right above the cloak. (c) Reflected image viewed at an oblique angle.
Our work represents the first macroscopic cloak operating at visible frequencies, which transforms a deformed mirror into a flat one from all viewing angles. The cloak is capable of hiding three-dimensional objects three to four orders of magnitudes larger than optical wavelengths. Indeed, the cloak can be further scaled up as it does not require time consuming nanofabrication techniques. Because our work solves several major issues typically associated with cloaking: size, bandwidth, loss, and image distortion, it paves the way for future practical cloaking devices.
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