Tomáš Tyc

Broadband Invisibility by Non-Euclidean Cloaking

Invisibility and negative refraction are both applications of transformation optics where the material of a device performs a coordinate transformation for electromagnetic fields. The device creates the illusion that light propagates through empty flat space, whereas in physical space, light is bent around a hidden interior or seems to run backward in space or time. All of the previous proposals for invisibility require materials with extreme properties. Here we show that transformation optics of a curved, non-Euclidean space (such as the surface of a virtual sphere) relax these requirements and can lead to invisibility in a broad band of the spectrum.

An omnidirectional retroreflector based on the transmutation of dielectric singularities

Transformation optics is a concept used in some metamaterials to guide light on a predetermined path. In this approach, the materials implement coordinate transformations on electromagnetic waves to create the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here, on the basis of transformation optics, we implement a microwave device that would normally require a dielectric singularity, an infinity in the refractive index. To fabricate such a device, we transmute a dielectric singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility from all directions. Our method is robust, potentially broadband and could also be applied to visible light using similar techniques.

Continuous-variable quantum-state sharing via quantum disentanglement

Quantum-state sharing is a protocol where perfect reconstruction of quantum states is achieved with incomplete or partial information in a multipartite quantum network. Quantum-state sharing allows for secure communication in a quantum network where partial information is lost or acquired by malicious parties. This protocol utilizes entanglement for the secret-state distribution and a class of quantum disentangling protocols for the state reconstruction. We demonstrate a quantum-state sharing protocol in which a tripartite entangled state is used to encode and distribute a secret state to three players. Any two of these players can collaborate to reconstruct the secret state, while individual players obtain no information. We investigate a number of quantum disentangling processes and experimentally demonstrate quantum-state reconstruction using two of these protocols. We experimentally measure a fidelity, averaged over all reconstruction permutations, of F=0.73 +/- 0.02. A result achievable only by using quantum resources.

Evidence for subwavelength imaging with positive refraction

The resolution of lenses is normally limited by the wave nature of light. Imaging with perfect resolution was believed to rely on negative refraction, but here we present experimental evidence for subwavelength imaging with positive refraction.

How to share a continuous-variable quantum secret by optical interferometry

We develop the theory of continuous-variable quantum secret sharing and propose its interferometric realization using passive and active optical elements. In the ideal case of infinite squeezing, a fidelity F of unity can be achieved with respect to reconstructing the quantum secret. We quantify the reduction in fidelity for the (2,3) threshold scheme due to finite squeezing and establish the condition for verifying that genuine quantum secret sharing has occurred.

Spherical media and geodesic lenses in geometrical optics

This paper presents a general approach to solving the problems of inverse scattering in three-dimensional isotropic media with a spherically symmetric refractive index distribution. It is based on equivalence of the central section of an inhomogeneous medium and corresponding geodesic lens, which is a non-Euclidean surface with constant refractive index. We use this approach for solving the Luneburg inverse problem and also for the derivation and design of absolute instruments that provide perfect imaging within the frame of geometrical optics. In addition, we solve the generalized Luneburg inverse problem, which leads to the discovery of a new class of magnifying lenses.

Invisibility cloaking without superluminal propagation

Conventional cloaking based on Euclidean transformation optics requires that the speed of light should tend to infinity on the inner surface of the cloak. Non-Euclidean cloaking still needs media with superluminal propagation. Here we show by giving an example that this is no longer necessary.

Absolute instruments and perfect imaging in geometrical optics

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.

Superantenna made of transformation media

We show how transformation media can make a superantenna that is either completely invisible or focuses incoming light into a needle-sharp beam. Our idea is based on representing three-dimensional space as a foliage of sheets and performing two-dimensional conformal maps on each sheet.

Forum Optics: Perfect lenses in focus

Materials that refract light backwards are thought to be required for making super-resolution lenses. An alternative proposal — that conventional, positively refracting media can do the job — has met with controversy. Two experts from either side of the debate lay out their views on the matter.