Wavefront shaping through emulated curved space in waveguide settings

Evolution of optical vortices in gradient media and curved spaces

Light propagation in gradient media and curved spaces induce intriguing phenomena, such as focusing and self-imaging, thus delivering a wide range of applications. However, these systems are limited to excitations without orbital angular momentum, which may produce unforeseen results. Here, we demonstrate the reconstructions (or called imaging to some extent) of optical vortices (OVs) in two-dimensional (2D) gradient media and three-dimensional (3D) curved spaces. We present the evolution of OVs in two types of generalized Maxwell fisheye (GMFE) lenses from the perspective of geometrical and wave optics, and use coherent perfect absorbers (CPAs) to better recover the OVs in the converging position. Furthermore, we also demonstrate such phenomena in two types of 3D compact closed manifolds-sphere and spindle-which are also called geodesic lenses. Surprisingly, the results we obtained in 3D curved spaces can be seen as a strong verification of the Poincaré-Hopf theorem. Our work provides a new, to the best of our knowledge, platform to investigate the evolution of OVs on curved surfaces.

Bound vortex light in an emulated topological defect in photonic lattices

Topology have prevailed in a variety of branches of physics. And topological defects in cosmology are speculated akin to dislocation or disclination in solids or liquid crystals. With the development of classical and quantum simulation, such speculative topological defects are well-emulated in a variety of condensed matter systems. Especially, the underlying theoretical foundations can be extensively applied to realize novel optical applications. Here, with the aid of transformation optics, we experimentally demonstrated bound vortex light on optical chips by simulating gauge fields of topological linear defects in cosmology through position-dependent coupling coefficients in a deformed photonic graphene. Furthermore, these types of photonic lattices inspired by topological linear defects can simultaneously generate and transport optical vortices, and even can control the orbital angular momentum of photons on integrated optical chips.

Propagation properties of finite Airy beams on curved surfaces

Airy beams have provided exciting inspiration in the field of optical communication, particle manipulation, and imaging. We investigate the propagation properties of the exponential truncation Airy beams (ETABs) on constant Gaussian curvature surfaces (CGCSs) in this paper. The analytical expression of the electric field of ETABs propagating on the CGCSs is derived. It shows that the equivalent periodical accelerations of the trajectories of ETABs on the curved surface are always larger than the constant one on the flat surface because the CGCSs have a strong focusing ability. For the same reason, the non-diffraction propagation of ETABs is found when the focusing ability of the CGCSs is strong enough. Moreover, we investigate the self-healing length of ETABs on CGCSs and explore that the ability of self-healing is related to the geometry of CGCSs besides the width of the block and the size of the beam. The self-healing length gets larger with the increase of radius of CGCSs and finally consists with that on the flat surface. These propagation characteristics are different from those in the flat space and are useful for the future applications of ETABs in particle manipulation on waveguides, light-sheet fluorescence microscopy, curved nanophotonics, and so on.

Transformation Metamaterials

Based on the form-invariance of Maxwell's equations under coordinate transformations, mathematically smooth deformation of space can be physically equivalent to inhomogeneous and anisotropic electromagnetic (EM) medium (called a transformation medium). It provides a geometric recipe to control EM waves at will. A series of examples of achieving transformation media by artificially structured units from conventional materials is summarized here. Such concepts are firstly implemented for EM waves, and then extended to other wave dynamics, such as elastic waves, acoustic waves, surface water waves, and even stationary fields. These shall be cataloged as transformation metamaterials. In addition, it might be conceptually attractive and practically useful to control diverse waves for multi-physics designs.

Observation of the acceleration of light in a tapered optical fiber

One of the most fascinating aspects of quantum fields in curved spacetime is the Unruh effect. The direct experimental detection of Unruh temperature has remained an elusive challenge up to now. Gradient optical waveguides manipulating the dispersion of photons are assumed to realize the great acceleration of effective particles, leading to a high effective Unruh temperature. However, experimentally achieving this optical waveguide has not yet been reported. In this work, we exploit a tapered fiber to simulate the accelerated motion of effective particles and obtain an effective Unruh temperature. When light propagating in a tapered fiber is affected by the external high refractive index medium, a leaky phenomenon akin to bremsstrahlung will be observed, and the pattern of leaky radiation is dependent on the acceleration of photons. During the experiments, different accelerations corresponding to different Unruh temperatures are achieved by controlling the shape of the tapered waveguide.

Topological Hyperbolic Lattices

Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general theory of relativity. Notably, an infinite number of regular tessellations in hyperbolic geometry-hyperbolic lattices-are expected to extend Euclidean Bravais lattices and the consequent wave phenomena to non-Euclidean geometry. However, topological states of matter in hyperbolic lattices have yet to be reported. Here we investigate topological phenomena in hyperbolic geometry, exploring how the quantized curvature and edge dominance of the geometry affect topological phases. We report a recipe for the construction of a Euclidean photonic platform that inherits the topological band properties of a hyperbolic lattice under a uniform, pseudospin-dependent magnetic field, realizing a non-Euclidean analog of the quantum spin Hall effect. For hyperbolic lattices with different quantized curvatures, we examine the topological protection of helical edge states and generalize Hofstadter's butterfly, by employing two empirical parameters that measure the edge confinement and defect immunity. We demonstrate that the proposed platforms exhibit the unique spectral-magnetic sensitivity of topological immunity in highly curved hyperbolic planes. Our approach is applicable to general non-Euclidean geometry and enables the exploitation of infinite lattice degrees of freedom for band theory.

Quantum simulation of particle pair creation near the event horizon

Though it is still a big challenge to unify general relativity and quantum mechanics in modern physics, the theory of quantum field related with the gravitational effect has been well developed and some striking phenomena are predicted, such as Hawking radiation. However, the direct measurement of these quantum effects under general relativity is far beyond present experiment techniques. Fortunately, the emulation of general relativity phenomena in the laboratory has become accessible in recent years. However, up to now, these simulations are limited either in classical regime or in flat space whereas quantum simulation related with general relativity is rarely involved. Here we propose and experimentally demonstrate a quantum evolution of fermions in close proximity to an artificial black hole on a photonic chip. We successfully observe the acceleration behavior, quantum creation, and evolution of a fermion pair near the event horizon: a single-photon wave packet with positive energy escapes from the black hole while negative energy is captured. Our extensible platform not only provides a route to access quantum effects related with general relativity, but also has the potentiality to investigate quantum gravity in future.

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.

Definite photon deflections of topological defects in metasurfaces and symmetry-breaking phase transitions with material loss

Combination of topology and general relativity can lead to some profound and farsighted predictions. It is well known that symmetry breaking of the Higgs vacuum field in the early universe possibly induced topological defects in space-time, whose nontrivial effects can provide some clues about the universe’s origin. Here, by using an artificial waveguide bounded with rotational metasurface, the nontrivial effects of a topological defect of spacetime are experimentally emulated. The photon deflection in the topological waveguide has a robust definite angle that does not depend on the location and momentum of incident photons. This is remarkably different from the random optical scattering in trivial space. By including material loss such a topological effect can be well understood from the symmetry breaking of photonic modes. Our technique provides a platform to investigate topological gravity in optical systems. This method can also be extended to obtain many other novel topological photonic devices.

Photonic structures can be used to simulate fundamental physical phenomena like the optical analog of gravity. Here, the authors use metasurface-engineered waveguides to emulate the optical effects of a topological defect on space-time.

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.

Controlling Surface Plasmons Through Covariant Transformation of the Spin-Dependent Geometric Phase Between Curved Metamaterials

General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different frames. In this Letter, we use one-dimensional curved metamaterials to mimic accelerating particles in curved space-times. The different curved shapes of structures are used to mimic different accelerating frames. The different geometric phases along the structure are used to mimic different movements in the frame. Using the covariant principle of general relativity, we can obtain equivalent nanostructures based on space-time transformations, such as the Lorentz transformation and conformal transformation. In this way, many covariant structures can be found that produce the same surface plasmon fields when excited by spin photons. A new kind of accelerating beam, the Rindler beam, is obtained based on the Rindler metric in gravity. Very large effective indices can be obtained in such systems based on geometric-phase gradient. This general covariant design method can be extended to many other optical media.

Controllable multiple plasmonic bending beams via polarization of incident waves

Plasmonic bending beams, which preserve their spatial shapes while propagating along curved trajectories in metal-dielectric interface, offer important applications in the fields of fiber sensor, optical trapping, and micro-nano manipulation. In this work, circular hole array, as a local point-like sources of surface plasmon polaritons, is designed on the metal film to generate multiple plasmonic bending beams. The electric field intensity of multiple plasmonic bending beams is controlled by polarization angle of input light. In addition, the electric filed intensity of multiple plasmonic bending beams relies on circle hole radius. These findings provide guidance in the design and optimization of plasmonic bending beam generators.

Ultra-short beam expander with segmented curvature control: the emergence of a semi-lens

We introduce direct curvature control in designing a segmented beam expander, and explore novel design possibilities for ultra-compact beam expanders. Assisted by the particle swarm optimization algorithm, we search for an optimal curvature-controlled multi-segment taper that maintains width continuity. Counterintuitively, the optimization yields a structure with abrupt width discontinuity and width compression features. Through spatial phase and parameterized analysis, a semi-lens feature is revealed that helps to flatten the wavefront at the output end for higher coupling efficiency. Such functionality cannot be achieved by normal tapers in a short distance. The structure is fabricated and characterized experimentally. By a figure of merit that accounts for expansion ratio, length, and efficiency, this structure outperforms an adiabatic taper by 9 times.

Diffraction-Free Bloch Surface Waves

Here, we demonstrate a diffraction-free Bloch surface wave sustained on all-dielectric multilayers that does not diffract after being passed through three obstacles or across a single mode fiber. It can propagate in a straight line for distances longer than 110 μm at a wavelength of 633 nm and could be applied as an in-plane optical virtual probe both in air and in an aqueous environment. Its ability to be used in water, its long diffraction-free distance, and its tolerance to multiple obstacles make this wave ideal for certain applications in areas such as the biological sciences, where many measurements are made on glass surfaces or for which an aqueous environment is required, and for high-speed interconnections between chips, where low loss is necessary.

Ultratransparent Media and Transformation Optics with Shifted Spatial Dispersions

By using pure dielectric photonic crystals, we demonstrate the realization of ultratransparent media, which allow near 100% transmission of light for all incident angles and create aberration-free virtual images. The ultratransparency effect is well explained by spatially dispersive effective medium theory for photonic crystals, and verified by both simulations and proof-of-principle microwave experiments. Designed with shifted elliptical equal frequency contours, such ultratransparent media not only provide a low-loss and feasible platform for transformation optics devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework.

Fractional nonparaxial accelerating Talbot effect

We demonstrate the fractional Talbot effect of nonparaxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A single nonparaxial accelerating beam possesses duality-it can be viewed as a Talbot effect of itself with an infinite or zero Talbot angle. These results improve the understanding of the nonparaxial accelerating beams and of the Talbot effect among them.