It is known that there exist a limited number of analytic potentials with the unusual property that any bound quantum state therein will be periodic in time. This is known as a perfect quantum state revival. Examples of such potentials are the infinte well, quantum harmonic oscillator, and the P & ouml;schl-Teller potentials; here, we present a general method of designing such potentials. A key requirement is that their energy eigenvalues have integer spacings (up to a prefactor). We first analyze the required conditions which permit quantum state revivals for potentials in general, and then we use techniques of iterated Hamiltonian intertwining to construct potentials exhibiting perfect quantum revivals. Our method can readily be extended to multiple dimensions.

The remarkable advancements in our capacity to synthesise structured light have facilitated the generation of any desired optical landscapes and even controlling the spatial distribution of light propagating through optically complex media such as multimode fibres. The availability of precisely defined structured light at the extremity of an exceedingly narrow and flexible cable holds the potential to stimulate a diverse range of highly sought-after applications, encompassing rapid communication, quantum computing, and, notably, imaging. What we lack in reaching these aspirations is the resilience of such light transport to deformations of the waveguide. Although recent theoretical investigations have delineated the attributes of ideal multimode fibres capable of deformation-enduring conveyance of structured light, tangible fibres possessing this indispensable trait to a practical extent remain elusive. Our study takes a deep dive into the precision of commercially available multimode fibres with the highest probability of demonstrating the phenomenon. We identified minuscule imperfections in their refractive index distribution, examined how these affect light transport when the fibre is deformed, and studied their implications for imaging applications. Our investigation has confirmed that these imperfections are indeed responsible for the undesirable alterations introduced into the output structured light fields during bending. Finally, as an alternative to standard graded-index fibres, manufactured by drawing silica-based preforms, we present narrow multimode waveguides in which the refractive-index profile has been established by ion exchange. These waveguides indeed exhibit previously unseen resilience of structured light transport even under severe deformation conditions and aptly fulfil the requirements of imaging applications.

Trojan beams, which are optical counterparts of Trojan asteroids that maintain stable orbits alongside planets, have been successfully showcased in experiments, opening up possibilities for transporting light in unconventional settings.

We analyze the dynamics of a quantum particle on a force-free surface of a cube. Employing the methods of group theory, we divide the solutions of the stationary Schr & ouml;dinger equation (the modes) into classes based on irreducible representations of the symmetry group of the cube and for each class we reduce the problem to finding the modes on a square with special boundary conditions. We analyze the properties of the resulting modes, present them visually, and discuss the possibility of quantum state revivals on the cube.

We recently presented what we believe are new cloaking strategies [Bělín 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.

A rotationally symmetric all-dielectric lens antenna is designed by defining the phase function inside the dielectric directly via a closed-form series formula. The refractive index of the lens is modified using state-of-the-art optical path rescaling to keep the refractive index within practical values. The lens optimization is done using the genetic algorithm in MATLAB, where each case is evaluated by conducting linked ray tracing and full -wave electromagnetic simulation in COMSOL. A lens prototype is shown to provide a directivity enhancement of 5.1 dB compared to the optimal conical horn antenna, an improvement of 2 dB compared to the Luneburg lens, and an improvement of 3.8 dB compared to a reference graded index lens. All the examined cases shared a similar length of for the center frequency of 10 GHz. The prototype lens antenna has a maximum refractive index of 2.1, a reflection coefficient of -22 dB, and a side-lobe level of -25 dB at the center frequency of 10 GHz. The lens' performance is consistent in the 9-11 GHz band supported by the standard circular waveguide. The results from a prototype with a discretized refractive index simulated in CST Studio Suite are in excellent agreement with the ones with a continuous refractive index profile simulated in COMSOL.

To completely hide an object within a transformation optics (TO) cloak, a light ray may not leave the cloaked area. A possible realisation of this uses closed-loop light ray trajectories to trap the rays within the device. By investigating these for an ideal lens TO device, we found areas within a cloak that will cause light rays to follow a closed-loop trajectory. Similarly, there are areas which a closed-loop light ray cannot cross. Utilising these, we created a new nested ideal lens cloak which performs omnidirectional cloaking.

A double-layer lens consists of a pair of rotationally symmetric index profiles or geodesic lens shapes connected by a reflecting mirror partially covering their common periphery. Such a lens can provide a focus in each layer, and a wave travelling between the foci explores both layers. Here, we concentrate on the case with one layer being homogeneous or flat, and derive a general solution for the lens profiles by solving a Luneburg-like inverse problem with pre-specified foci inside or outside the lens, and different background indices in two layers. We demonstrate four examples of interest in ray-tracing plots. These lenses may find application in communications, sensing, and imaging from millimeter waves up to the optical bands.

In this paper, we present a new treatment of cloaking strategies proposed by Belın et. al., in their work on Ideallens Cloaks. By calculating material properties we design a metamaterial structure that acts as an invisibility cloak, based on the principle of an Abyss Cloak, which is a device that shifts the image of the cloaked object to the exterior position. The use of this approach comes with a better affinity for experimental realization. To support this claim, we execute a simple experiment, using a setup consisting of four optical wedges. Our work significantly stretches the arsenal of transformation optics devices, as the presented devices can be employed not only as invisibility cloaks, but also as building blocks for other devices, e.g. optical analogues of celestial mechanics.

This paper presents a quasi-conformal transformation optics (QCTO) based three-dimensional (3D) retroreflective flattened Luneburg lens for wide-angle millimeter-wave radio-frequency indoor localization. The maximum detection angle and radar cross-section (RCS) are investigated, including an impedance matching layer (IML) between the lens antenna and the free-space environment. The 3D QCTO Luneburg lenses are fabricated in alumina by lithography-based ceramic manufacturing, a 3D printing process. The manufactured structures have a diameter of 29.9 mm ( $4 \lambda _{0}$ ), showing a maximum realized gain of 16.51 dBi and beam steering angle of ±70° at 40 GHz. The proposed QCTO Luneburg lens with a metallic reflective layer achieves a maximum RCS of −20.05 dBsqm at 40 GHz with a wide-angle response over ±37°, while the structure with an IML between the lens and air improves these values to a maximum RCS of −15.78 dBsqm and operating angular response between ±50°.

Light transport in a highly multimode fiber exhibits complex behavior in space, time, frequency and polarization, especially in the presence of mode coupling. The newly developed techniques of spatial wavefront shaping turn out to be highly suitable to harness such enormous complexity: a spatial light modulator enables precise characterization of field propagation through a multimode fiber, and by adjusting the incident wavefront it can accurately tailor the transmitted spatial pattern, temporal profile and polarization state. This unprecedented control leads to multimode fiber applications in imaging, endoscopy, optical trapping and microfabrication. Furthermore, the output speckle pattern from a multimode fiber encodes spatial, temporal, spectral and polarization properties of the input light, allowing such information to be retrieved from spatial measurements only. This article provides an overview of recent advances and breakthroughs in controlling light propagation in multimode fibers, and discusses newly emerging applications.

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 design method for graded-index lens antennas is proposed. The method consists of proposing a phase function in a region of space that meets the boundary conditions of the design and rescaling the optical path. The latter allows us to adjust the lens’s refractive index. The designed lens has a length of 6λ, an aperture width of 8.7λ. The highest required refractive index is 1.6. A directivity value of 25.4 dB, and a -24 dB side-lobe level are attained. The design functionality is verified using COMSOL.

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.

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.

Lenses are of interest for the design of directive antennas and multi-optics instruments in the microwave, terahertz and optical domains. Here, we introduce an optical problem defined as the complement of the well-known generalized Luneburg lens problem. The spherically symmetric inhomogeneous lenses obtained as solutions of this problem transform a given sphere in the homogeneous region outside of the lens into a virtual conjugate sphere, forming a virtual image from a real source. An analytical solution is proposed for the equivalent geodesic lens using the analogy between classical mechanics and geometrical optics. The refractive index profile of the corresponding inhomogeneous lens is then obtained using transformation optics. The focusing properties of this family of lenses are validated using ray-tracing models, further corroborated with full-wave simulations. The numerical results agree well with the predictions over the analyzed frequency bandwidth (10–30 GHz). This virtual focusing property may further benefit from recent developments in the fields of metamaterials and transformation optics.

We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Möbius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds.

We present unusual lens combinations which can be applied as building blocks of transformation-optics devices as well as tools for optical simulations of the movement in a gravitational field.

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.

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.