Lenses on curved surfaces

Spherical wedge billiard: From chaos to fractals and Talbot carpets

We introduce the spherical wedge billiard, a dynamical system consisting of a particle moving along a geodesic on a closed non-Euclidean surface of a spherical wedge. We derive the analytic form of the corresponding Poincaré map and find very complex dynamics, ranging from completely chaotic to very regular, exhibiting fractal features. Further, we show that upon changing the billiard parameter, the fixed points of the Poincaré map merge in complex ways, which has origin in the spherical aberration of the billiard mapping. We also analyze in detail the regular regime when phase space diagram is closely related to Talbot carpets.

Double-layer geodesic and gradient-index lenses

A double-layer lens consists of a first gradient-index/geodesic profile in an upper waveguide, partially surrounded by a mirror that reflects the wave into a lower guide where there is a second profile. Here, we derive a new family of rotational-symmetric inhomogeneous index profiles and equivalent geodesic lens shapes by solving an inverse problem of pre-specified focal points. We find an equivalence where single-layer lenses have a different functionality as double-layer lenses with the same profiles. As an example, we propose, manufacture, and experimentally validate a practical implementation of a geodesic double-layer lens that is engineered for a low-profile antenna with a compact footprint in the millimeter wave band. Its unique double-layer configuration allows for two-dimensional beam scanning using the same footprint as an extension of the presented design. These lenses may find applications in future wireless communication systems and sensing instruments in microwave, sub-terahertz, and optical domains.

A double-layer lens consists of a first gradient-index/geodesic profile in an upper waveguide, partially surrounded by a mirror that reflects the wave into a lower guide where there is a second profile. A family of such lens profiles are derived.

Partial Maxwell fish-eye lens inspired by the Gutman lens and Eaton lens for wide-angle beam scanning

This paper presents a novel two-dimensional (2-D) partial Maxwell fish-eye (PMFE) lens with the capability of wide-angle beam scanning inspired by the Gutman lens and Eaton lens, which is obtained by cutting a part from the 2-D Maxwell fish-eye (MFE) lens along a straight line. In terms of the refractive index profile, the MFE lens is similar to the Gutman lens near the center and the Eaton lens near the edge, respectively. We demonstrate the potential of the PMFE lens in wide-angle beam scanning based on its Gutman-like focusing and Eaton-like rotating characteristics corresponding to different feed points. As an example, a fully metallic PMFE lens antenna in the Ka-band composed of a bed of nails and a series of linearly arranged waveguide feeders is designed and experimentally verified. The measured results reveal wide-angle scanning ranges, especially about ±90° at 36 GHz, low reflections and low mutual couplings. The frequency scanning due to the dispersion of the lens is also discussed.

A reprogrammable multifunctional chalcogenide guided-wave lens

The transformation optics (TO) technique, which establishes an equivalence between a curved space and a spatial distribution of inhomogeneous constitutive parameters, has enabled an extraordinary paradigm for manipulating wave propagation. However, extreme constitutive parameters, as well as a static nature, inherently limit the simultaneous achievement of broadband performance, ultrafast reconfigurability and versatile reprogrammable functions. Here, we integrate the TO technique with an active phase-change chalcogenide to achieve a reconfigurable multi-mode guided-wave lens. The lens is made of a Rinehart-shaped curved waveguide with an effective refractive index gradient profile through partially crystallizing Ge2Sb2Te5. Upon changing the bias time of the external voltage imparted to the Ge2Sb2Te5 segments, the refractive index gradient profile can be tuned with a transformative platform for various functions for visible light. The electrically reprogrammable multi-mode guided-wave lens is capable of dynamically acquiring various functionalities with an ultrafast response time. Our findings may offer a significant step forward by providing a universal method to obtain ultrafast and highly versatile guided-wave manipulation, such as in Einstein rings, cloaking, Maxwell fish-eye lenses and Luneburg lenses.

Nonresonant modes in plasmonic holey metasurfaces for the design of artificial flat lenses

This Letter discusses nonresonant modes excited on holey metasurfaces and their influence on the properties of spoof plasmonic states supported by the metasurface when a second surface is placed in its proximity. We consider here a metallic surface with periodic holes drilled in it. The field excited on each hole is projected onto a set of nonresonant modes in order to discuss their relative relevance. While previous simpler models assumed only the presence of the fundamental mode, we show that the simultaneous presence of several modes occurs when the surface is placed next to a metallic plate. Therefore, higher-order modes are responsible for the peculiar physical properties of wave propagation of spoof plasmons between two surfaces, which can lead to new gradient-index flat lenses for transceivers for space communications.

Omnidirectional surface wave cloak using an isotropic homogeneous dielectric coating

The field of transformation optics owes a lot of its fame to the concept of cloaking. While some experimental progress has been made towards free-space cloaking in three dimensions, the material properties required are inherently extremely difficult to achieve. The approximations that then have to be made to allow fabrication produce unsatisfactory device performance. In contrast, when surface wave systems are the focus, it has been shown that a route distinct from those used to design free-space cloaks can be taken. This results in very simple solutions that take advantage of the ability to incorporate surface curvature. Here, we provide a demonstration in the microwave regime of cloaking a bump in a surface. The distortion of the shape of the surface wave fronts due to the curvature is corrected with a suitable refractive index profile. The surface wave cloak is fabricated from a metallic backed homogeneous dielectric waveguide of varying thickness, and exhibits omnidirectional operation.

Tunable photonic nanojet formed by generalized Luneburg lens

Nanojet has been emerging as an interesting topic in variety photonics applications. In this paper, inspired by the properties of generalized Luneburg lens (GLLs), a two-dimensional photonic nanojet system has been developed, which focal distance can be tuned by engineering the refractive index profile of GLLs. Simulation and analysis results show that the maximum light intensity, transverse and longitudinal dimensions of the photonic nanojet are dependent on the focal distance of the GLLs, thereby, by simply varying the focal distance, it is possible to obtain localized photon fluxes with different power characteristics and spatial dimensions. This can be of interest for many promising applications, such as high-resolution optical detection, optical manipulation, technology of direct-write nano-patterning and nano-lithography.