Shifty invisibility cloaks.

We recently presented what we believe are new cloaking strategies [Belín et al., Opt. Express27, 37327 (2019)10.1364/OE.27.037327], abstracted from the properties of an ideal-lens cloak that exists in theory only. Key to the cloaking strategies is that objects on the cloak's inside are imaged to its outside. In the simplest case, interior objects appear simply shifted, forming a "shifty cloak". Here we connect our work to several previous investigations of shifty cloaks and other shifty devices, designed using standard transformation optics, thereby bringing our cloaking strategies closer to experimental realization. We investigate to the best of our knowledge novel combinations of shifty cloaks, specifically Janus devices and optical wormholes. Finally, we demonstrate an experimental realization of a paraxial shifty cloak.

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.

H-plane horn antenna with enhanced directivity using conformal transformation optics.

Conformal transformation optics is employed to enhance an H-plane horn's directivity by designing a graded-index all-dielectric lens. The transformation is applied so that the phase error at the aperture is gradually eliminated inside the lens, leading to a low-profile high-gain lens antenna. The physical space shape is modified such that singular index values are avoided, and the optical path inside the lens is rescaled to eliminate superluminal regions. A prototype of the lens is fabricated using three-dimensional printing. The measurement results show that the realized gain of an H-plane horn antenna can be improved by 1.5-2.4 dB compared to a reference H-plane horn.

Directivity enhancement of a cylindrical wire antenna by a graded index dielectric shell designed using strictly conformal transformation optics.

A transformation-optical method is presented to enhance the directivity of a cylindrical wire antenna by using an all-dielectric graded index medium. The strictly conformal mapping between two doubly connected virtual and physical domains is established numerically. Multiple directive beams are produced, providing directive emission. The state-of-the-art optical path rescaling method is employed to mitigate the superluminal regions. The resulting transformation medium is all-dielectric and nondispersive, which can provide broadband functionality and facilitate the realization of the device using available fabrication technologies. The realization of the device is demonstrated by dielectric perforation based on the effective medium theory. The device's functionality is verified by carrying out both ray-tracing and full-wave simulations using finite-element-based software COMSOL Multiphysics.

Memory effect assisted imaging through multimode optical fibres.

When light propagates through opaque material, the spatial information it holds becomes scrambled, but not necessarily lost. Two classes of techniques have emerged to recover this information: methods relying on optical memory effects, and transmission matrix (TM) approaches. Here we develop a general framework describing the nature of memory effects in structures of arbitrary geometry. We show how this framework, when combined with wavefront shaping driven by feedback from a guide-star, enables estimation of the TM of any such system. This highlights that guide-star assisted imaging is possible regardless of the type of memory effect a scatterer exhibits. We apply this concept to multimode fibres (MMFs) and identify a 'quasi-radial' memory effect. This allows the TM of an MMF to be approximated from only one end - an important step for micro-endoscopy. Our work broadens the applications of memory effects to a range of novel imaging and optical communication scenarios.

Combinations of generalized lenses that satisfy the edge-imaging condition of transformation optics.

We recently introduced the edge-imaging condition, a necessary condition for all generalized lenses (glenses) [J. Opt. Soc. Am. A33, 962 (2016)JOAOD60740-323210.1364/JOSAA.33.000962] in a ray-optical transformation-optics (RTO) device that share a common edge [Opt. Express26, 17872 (2018)OPEXFF1094-408710.1364/OE.26.017872]. The edge-imaging condition states that, in combination, such glenses must image every point to itself. Here we begin the process of building up a library of combinations of glenses that satisfy the edge-imaging condition, starting with all relevant combinations of up to three glenses. As it grows, this library should become increasingly useful when constructing lens-based RTO devices.

Ideal-lens cloaks and new cloaking strategies.

Previously [Courtial et al., Opt. Express 26, 17872 (2018)] we presented the theory of transformation optics (TO) with ideal lenses and demonstrated an example, an omnidirectional lens. Here we interpret this omnidirectional lens in two different parameter regimes as ideal-lens cloaks that employ different cloaking strategies: a standard "shrink cloak" in which objects appear smaller (ideally zero) and a novel "abyss cloak" in which interior physical-space positions are mapped to the exterior and thus are visible only from certain directions. We proceed to combine two nested abyss cloaks into another novel, omnidirectional, "bi-abyss cloak." Our work significantly extends the arsenal of cloaking strategies.

Controlling refractive index of transformation-optics devices via optical path rescaling.

We present a general method of designing optical devices based on optical conformal mapping and rescaling the optical path along a given bunch of rays. It provides devices with the same functionality as those based purely on conformal mapping, but enables to manipulate the refractive index to a great extent-for instance, eliminate superluminal regions of space as well as reduce the refractive index in other regions significantly. The method is illustrated in two examples, a waveguide coupler and a plasmonic bump cloak, and numerical simulations confirm its functionality.

Conformal optical devices based on geodesic lenses.

Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann sheets, hence compromising the functionalities. To deal with that, we present a special method for conformal transformation optics based on geodesic lenses with special closed surfaces. The requirement is a continuous refractive index profile of dielectrics, which shows the almost perfect performance of designed devices. We demonstrate such a proposal by achieving conformal transparency (invisibility without cloaking region) and reflection. We can further achieve conformal invisible cloaks by two methods with perfect conductors. The conformal transformation optics method based on geodesic lenses may also find applications in other waves that obey the Helmholtz wave equation in two dimensions.

Ray-optical transformation optics with ideal thin lenses makes omnidirectional lenses.

We present the theory of ray-optical transformation optics (RTO) with ideal thin lenses and show that ideal-thin-lens RTO devices are omnidirectional lenses. Key to designing such devices are two theorems, the loop-imaging theorem, and the edge-imaging theorem, which ensure that the interior physical space is distorted in the same way for all viewing directions. We discuss the possibility of realising such devices using lens holograms or Fresnel lenses, as both are in principle capable of changing the directions of rays incident from a specific point precisely like an ideal thin lens, thereby enabling macroscopic and broad-band RTO devices that work for at least one viewing position. Even when restricted in this way, our work opens up new possibilities in ray optics. Our devices have the potential to form the basis of new microscope objectives, virtual-reality headsets, and medical spectacles.

Experimental demonstration of ray-rotation sheets.

We have built microstructured sheets that rotate, on transmission, the direction of light rays by an arbitrary, but fixed, angle around the sheet normal. These ray-rotation sheets comprise two pairs of confocal lenticular arrays. In addition to rotating the direction of transmitted light rays, our sheets also offset ray position sideways on the scale of the diameter of the lenticules. If this ray offset is sufficiently small so that it cannot be resolved, our ray-rotation sheets appear to perform generalized refraction.

Robustness of Light-Transport Processes to Bending Deformations in Graded-Index Multimode Waveguides.

Light transport through a multimode optical waveguide undergoes changes when subjected to bending deformations. We show that optical waveguides with a perfectly parabolic refractive index profile are almost immune to bending, conserving the structure of propagation-invariant modes. Moreover, we show that changes to the transmission matrix of parabolic-index fibers due to bending can be expressed with only two free parameters, regardless of how complex a particular deformation is. We provide detailed analysis of experimentally measured transmission matrices of a commercially available graded-index fiber as well as a gradient-index rod lens featuring a very faithful parabolic refractive index profile. Although parabolic-index fibers with a sufficiently precise refractive index profile are not within our reach, we show that imaging performance with standard commercially available graded-index fibers is significantly less influenced by bending deformations than step-index types under the same conditions. Our work thus predicts that the availability of ultraprecise parabolic-index fibers will make endoscopic applications with flexible probes feasible and free from extremely elaborate computational challenges.

Omnidirectional transformation-optics cloak made from lenses and glenses.

We present a design for an omnidirectional transformation-optics (TO) cloak comprising thin lenses and glenses (generalized thin lenses) [J. Opt. Soc. Am. A33, 962 (2016)1084-7529JOAOD610.1364/JOSAA.33.000962]. It should be possible to realize such devices in pixelated form. Our design is a piecewise nonaffine generalization of piecewise affine pixelated-TO devices [Proc. SPIE9193, 91931E (2014)PSISDG0277-786X10.1117/12.2061404; J. Opt18, 044009 (2016)]. It is intended to be a step in the direction of TO devices made entirely from lenses, which should be readily realizable on large length scales and for a broad range of wavelengths.

Ray optics of generalized lenses.

We study the ray optics of generalized lenses (glenses), which are ideal thin lenses generalized to have different object- and image-sided focal lengths, and the most general light-ray-direction-changing surfaces that stigmatically image any point in object space to a corresponding point in image space. Gabor superlenses [UK patent541,753 (1940); J. Opt. A1, 94 (1999)JOAOF81464-425810.1088/1464-4258/1/1/013] can be seen as pixelated realizations of glenses. Our analysis is centered on the nodal point. Whereas the nodal point of a thin lens always resides in the lens plane, that of a glens can reside anywhere on the optical axis. Utilizing the nodal point, we derive simple equations that describe the mapping between object and image space and the light-ray-direction change. We demonstrate our findings with the help of ray-tracing simulations. Glenses allow novel optical instruments to be realized, at least theoretically, and our results facilitate the design and analysis of such devices.

Direct stigmatic imaging with curved surfaces.

We study the possibilities of direct (using one intersection with each light ray) stigmatic imaging with a curved surface that can change ray directions in an arbitrary way. By purely geometric arguments we show that the only possible case of such imaging is the trivial one where the image of any point is identical to the point itself and the surface does not perform any change of the ray direction at all. We also discuss an example of a curved surface which performs indirect stigmatic imaging after twice intersecting each light ray.

The Lissajous lens: a three-dimensional absolute optical instrument without spherical symmetry.

We propose a three dimensional optical instrument with an isotropic gradient index in which all ray trajectories form Lissajous curves. The lens represents the first absolute optical instrument discovered to exist without spherical symmetry (other than trivial cases such as the plane mirror or conformal maps of spherically-symmetric lenses). An important property of this lens is that a three-dimensional region of space can be imaged stigmatically with no aberrations, with a point and its image not necessarily lying on a straight line with the lens center as in all other absolute optical instruments. In addition, rays in the Lissajous lens are not confined to planes. The lens can optionally be designed such that no rays except those along coordinate axes form closed trajectories, and conformal maps of the Lissajous lens form a rich new class of optical instruments.

Generalized laws of refraction that can lead to wave-optically forbidden light-ray fields.

The recent demonstration of a metamaterial phase hologram so thin that it can be classified as an interface in the effective-medium approximation [Science 334, 333 (2011)] has dramatically increased interest in generalized laws of refraction. Based on the fact that scalar wave optics allows only certain light-ray fields, we divide generalized laws of refraction into two categories. When applied to a planar cross section through any allowed light-ray field, the laws in the first category always result in a cross section through an allowed light-ray field again, whereas the laws in the second category can result in a cross section through a forbidden light-ray field.

Gouy phase for full-aperture spherical and cylindrical waves.

We investigate the Gouy phase shift for full-aperture waves converging to a focal point from all directions in two and three dimensions. We find a simple interpretation for the Gouy phase in this situation and show that it has a dramatic effect on reshaping sharply localized pulses.