Collimating lenses from non-Euclidean transformation optics

Based on the non-Euclidean transformation optics, we design a thin metamaterial lens that can achieve wide-beam radiation by embedding a simple source (a point source in three-dimensional case or a line current source in two-dimensional case). The scheme is performed on a layer-by-layer geometry to convert curved surfaces in virtual space to flat sheets, which pile up and form the entire lens in physical space. Compared to previous designs, the lens has no extreme material parameters. Simulation results confirm its functionality.Comment: 12 pages, 6 figure

Perfect imaging with geodesic waveguides

Transformation optics is used to prove that a spherical waveguide filled with an isotropic material with radial refractive index n=1/r has radial polarized modes (i.e. the electric field has only radial component) with the same perfect focusing properties as the Maxwell Fish-Eye lens. The approximate version of that device using a thin waveguide with a homogenous core paves the way to experimentally prove perfect imaging in the Maxwell Fish Eye lens

Snell's Law from an Elementary Particle Viewpoint

Snell's law of light deflection between media with different indices of refraction is usually discussed in terms of the Maxwell electromagnetic wave theory. Snell's law may also be derived from a photon beam theory of light rays. This latter particle physics view is by far the most simple one for understanding the laws of refraction.Comment: ReVTeX Format 2 *.eps figure

Perfect imaging: they don't do it with mirrors

Imaging with a spherical mirror in empty space is compared with the case when the mirror is filled with the medium of Maxwell's fish eye. Exact time-dependent solutions of Maxwell's equations show that perfect imaging is not achievable with an electrical ideal mirror on its own, but with Maxwell's fish eye in the regime when it implements a curved geometry for full electromagnetic waves

Notes on Conformal Invisibility Devices

As a consequence of the wave nature of light, invisibility devices based on isotropic media cannot be perfect. The principal distortions of invisibility are due to reflections and time delays. Reflections can be made exponentially small for devices that are large in comparison with the wavelength of light. Time delays are unavoidable and will result in wave-front dislocations. This paper considers invisibility devices based on optical conformal mapping. The paper shows that the time delays do not depend on the directions and impact parameters of incident light rays, although the refractive-index profile of any conformal invisibility device is necessarily asymmetric. The distortions of images are thus uniform, which reduces the risk of detection. The paper also shows how the ideas of invisibility devices are connected to the transmutation of force, the stereographic projection and Escheresque tilings of the plane

Analytical, numerical, and experimental investigation of a Luneburg lens system for directional cloaking

In this study, the design of a directional cloaking based on the Luneburg lens system is proposed and its operating principle is experimentally verified. The cloaking concept is analytically investigated via geometrical optics and numerically realized with the help of the finite-difference time-domain method. In order to benefit from its unique focusing and/or collimating characteristics of light, the Luneburg lens is used. We show that by the proper combination of Luneburg lenses in an array form, incident light bypasses the region between junctions of the lenses, i.e., the "dark zone." Hence, direct interaction of an object with propagating light is prevented if one places the object to be cloaked inside that dark zone. This effect is used for hiding an object which is made of a perfectly electric conductor material. In order to design an implementable cloaking device, the Luneburg lens is discretized into a photonic crystal structure having gradually varying air cylindrical holes in a dielectric material by using Maxwell Garnett effective medium approximations. Experimental verifications of the designed cloaking structure are performed at microwave frequencies of around 8 GHz. The proposed structure is fabricated by three-dimensional printing of dielectric polylactide material and a brass metallic alloy is utilized in place of the perfectly electric conductor material in microwave experiments. Good agreement between numerical and experimental results is found. © 2019 American Physical Society

A demonstration of 'broken' visual space

It has long been assumed that there is a distorted mapping between real and ‘perceived’ space, based on demonstrations of systematic errors in judgements of slant, curvature, direction and separation. Here, we have applied a direct test to the notion of a coherent visual space. In an immersive virtual environment, participants judged the relative distance of two squares displayed in separate intervals. On some trials, the virtual scene expanded by a factor of four between intervals although, in line with recent results, participants did not report any noticeable change in the scene. We found that there was no consistent depth ordering of objects that can explain the distance matches participants made in this environment (e.g. A > B > D yet also A < C < D) and hence no single one-to-one mapping between participants’ perceived space and any real 3D environment. Instead, factors that affect pairwise comparisons of distances dictate participants’ performance. These data contradict, more directly than previous experiments, the idea that the visual system builds and uses a coherent 3D internal representation of a scene

Plasmonic Luneburg and Eaton Lenses

Plasmonics is an interdisciplinary field focusing on the unique properties of both localized and propagating surface plasmon polaritons (SPPs) - quasiparticles in which photons are coupled to the quasi-free electrons of metals. In particular, it allows for confining light in dimensions smaller than the wavelength of photons in free space, and makes it possible to match the different length scales associated with photonics and electronics in a single nanoscale device. Broad applications of plasmonics have been realized including biological sensing, sub-diffraction-limit imaging, focusing and lithography, and nano optical circuitry. Plasmonics-based optical elements such as waveguides, lenses, beam splitters and reflectors have been implemented by structuring metal surfaces or placing dielectric structures on metals, aiming to manipulate the two-dimensional surface plasmon waves. However, the abrupt discontinuities in the material properties or geometries of these elements lead to increased scattering of SPPs, which significantly reduces the efficiency of these components. Transformation optics provides an unprecedented approach to route light at will by spatially varying the optical properties of a material. Here, motivated by this approach, we use grey-scale lithography to adiabatically tailor the topology of a dielectric layer adjacent to a metal surface to demonstrate a plasmonic Luneburg lens that can focus SPPs. We also realize a plasmonic Eaton lens that can bend SPPs. Since the optical properties are changed gradually rather than abruptly in these lenses, losses due to scattering can be significantly reduced in comparison with previously reported plasmonic elements.Comment: Accepted for publication in Nature Nanotechnolog

Transformational Plasmon Optics

Transformation optics has recently attracted extensive interest, since it provides a novel design methodology for manipulating light at will. Although transformation optics in principle embraces all forms of electromagnetic phenomena on all length scales, so far, much less efforts have been devoted to near-field optical waves, such as surface plasmon polaritons (SPPs). Due to the tight confinement and strong field enhancement, SPPs are widely used for various purposes at the subwavelength scale. Taking advantage of transformation optics, here we demonstrate that the confinement as well as propagation of SPPs can be managed in a prescribed manner by careful control of the dielectric material properties adjacent to a metal. Since the metal properties are completely unaltered, it provides a straightforward way for practical realizations. We show that our approach can assist to tightly bound SPPs over a broad wavelength band at uneven and curved surfaces, where SPPs would normally suffer significant scattering losses. In addition, a plasmonic waveguide bend and a plasmonic Luneburg lens with practical designs are proposed. It is expected that merging the unprecedented design flexibility based on transformation optics with the unique optical properties of surface modes will lead to a host of fascinating near-field optical phenomena and devices.Comment: 17 pages, 6 figure