Tailoring whispering-gallery fields in optical black hole cavities.

The ability to confine light has great significance in both fundamental science and practical applications. Optical black hole (OBH) cavities show intriguing zero radiation loss and strong field confinement. In this work, we systematically explore the whispering gallery mode (WGM) in a group of generalized OBH cavities, featuring bound states and strong field confinement. The field confinement in generalized OBH cavities is revealed to be enhanced with the increase of index-modulation factors, resulting from the increase of a potential barrier. Furthermore, we reveal the anomalous external resonant modes, exhibiting fascinating field enhancement in the low-index region far beyond the cavity boundary. These anomalous WGMs are attributed to the potential bending effect and above-barrier resonance. Our work may shed light on tailoring WGM fields in gradient-index cavities and find potential applications in light coupling and optical sensing.

Geodesic conformal gradient device based on a torus.

In recent years, optical fields on non-Euclidean geometry have become a hot topic. The geodesic conformal transformation theory, linking curved surfaces with planar gradient refractive indices, holds unique advantages in controlling curved optical fields. However, this theory has not yet addressed surfaces with non-trivial topology with a certain genus. In this work, we design a gradient planar device based on the geodesic conformal transformation theory for toroidal surfaces, which can achieve Gaussian beam focusing. Unlike traditional angle-preserving geodesic theories, the non-zero genus results in the one-to-two discontinuous boundaries in the device, and we utilize inversion transformations to rectify this drawback.

Multiple hyperbolic waves.

This study presents a conceptual design for a hyperbolic material utilizing transformation optics. This material is designed to produce multiple hyperbolic wave fields or polaritons excited by a point source. The design dictates key parameters including branch number, propagation range, and overall propagation direction of deflection. Through this approach, the hyperbolic material demonstrates new effects compared to traditional hyperbolic materials. These advancements offer possibilities for the design and applications of photonic devices in other degrees of freedom.

Mirrored transformation optics.

A mirrored transformation optics (MTO) approach is presented to overcome the material mismatch in transformation optics. It makes good use of the reflection behavior and introduces a mirrored medium to offset the phase discontinuities. Using this approach, a high-performance planar focusing lens of transmission type is designed, which has a larger concentration ratio than the other focusing lens obtained by the generalized Snell's law. The MTO will not change any functionality of the original lens and has promising potential applications in imaging and light energy harvesting.

Analogy of the interior Schwarzschild metric from transformation optics.

In this paper, we make an analogy of the interior Schwarzschild metric from transformation optics (we call the method transformation cosmology). It is shown that a simple refractive index profile is sufficient to capture the behavior of the metric to bend light. There is a critical value of the ratio of the radius of the massive star to the Schwarzschild radius, which is exactly related to the condition of collapsing into a black hole. We demonstrate the light bending effect for three cases from numerical simulations as well. Especially, we find that a point source at the photon sphere will form an image inside the star approximately, and the equivalent lens is like Maxwell's fish-eye lens. This work will help us to explore the phenomena of massive stars with laboratory optical tools.

Perfectly matched layer for biaxial hyperbolic materials.

Hyperbolic materials have attracted considerable interest for their unique open hyperbolic dispersion properties. These materials support high-momentum propagating modes and strong light confinement, leading to a wide range of applications including super-resolution technologies, negative refraction and long-life propagation. Even with these wonderful optical properties, hyperbolic materials, however, cause problems when applying perfectly matched layer (PML) boundary conditions in numerical simulation software such as COMSOL Multiphysics. Due to the unfit embedded attenuation function, the built-in PML of simulation software would result in a mass of reflections in the computational domain when the background medium is hyperbolic materials. Here, we take advantage of an imaginary coordinate mapping and the complex coordinate stretching of transformation optics theory to design a PML for biaxial hyperbolic materials, which avoids any reflections and can be tuned flexibly. The proposed recipe can provide antidote and new insights for hyperbolic material studies.

Simulation of the expanding universe in hyperbolic metamaterials.

The particle horizon represents the boundary between observable and unobservable regions of the universe, which changes as the universe expands. Based on transformation optics, hyperbolic electromagnetic metamaterials can be utilized to simulate metrics with different signs due to their unique anisotropic properties. In this paper, we use hyperbolic metamaterials to visually depict the variation of the particle horizon under three models of an expanding universe (open, flat, and closed) by substituting one-dimensional time with one-dimensional space. The good agreement between theory and simulation confirms that hyperbolic metamaterials are excellent for simulating space-times, suggesting their potential as a new platform for cosmological analogies.

540-degree deflecting lens and its general version.

We demonstrate an isotropic device called 540-degree deflecting lens, which has symmetric refractive index and can deflect parallel beam by 540 degrees. The expression of its gradient refractive index is obtained and generalized. We discover it's an optical absolute instrument with self-imaging characteristic. Using conformal mapping, we deduce its general version in one-dimensional space. We also introduce a combined lens called the generalized inside-out 540-degree deflecting lens similar to the inside-out Eaton lens. Ray tracing and wave simulations are used to demonstrate their characteristics. Our study expands the family of absolute instruments and provides new ideas to design optical systems.

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.

Shear polaritons from transformation optics.

Natural in-plane hyperbolic crystals (such as α-MoO3) and natural monoclinic crystals (such as ß-Ga2O3) have recently drawn great research focus. Despite their obvious similarities, however, these two kinds of materials are usually studied as separate topics. In this Letter, we explore the intrinsic relationship between materials like α-MoO3 and ß-Ga2O3 under the framework of transformation optics, providing another perspective to understand the asymmetry of hyperbolic shear polaritons. It is worth mentioning that we demonstrate this novel, to the best of our knowledge, method from theoretical analysis and numerical simulations, which maintain a high degree of consistency. Our work not only combines natural hyperbolic materials with the theory of classical transformation optics, but also opens new avenues for future studies of various natural materials.

Tailoring Topological Transitions of Anisotropic Polaritons by Interface Engineering in Biaxial Crystals.

Polaritons in polar biaxial crystals with extreme anisotropy offer a promising route to manipulate nanoscale light-matter interactions. The dynamic modulation of their dispersion is of great significance for future integrated nano-optics but remains challenging. Here, we report tunable topological transitions in biaxial crystals enabled by interface engineering. We theoretically demonstrate such tailored polaritons at the interface of heterostructures between graphene and α-phase molybdenum trioxide (α-MoO3). The interlayer coupling can be modulated by both the stack of graphene and α-MoO3 and the magnitude of the Fermi level in graphene enabling a dynamic topological transition. More interestingly, we found that the wavefront transition occurs at a constant Fermi level when the thickness of α-MoO3 is tuned. Furthermore, we also experimentally verify the hybrid polaritons in the graphene/α-MoO3 heterostructure with different thicknesses of α-MoO3. The interface engineering offers new insights into optical topological transitions, which may shed new light on programmable polaritonics, energy transfer, and neuromorphic photonics.

Anomalous wavefront control of third-harmonic generation via graphene-based nonlinear metasurfaces in the terahertz regime.

Freely controlling wavefronts with metasurfaces has been widely studied in linear optical systems. By constructing phase gradient meta-atoms with nonlinear responses, the wavefronts of high-harmonic fields in nonlinear metasurfaces can be arbitrarily steered by following nonlinear generalized Snell's law (NGSL). However, for incident angles above the critical angle, NGSL fails to predict the generated nonlinear waves. In this work, by involving the reciprocal lattice effect of the nonlinear metasurface, we show a modified diffraction law to completely describe the nonlinear diffraction phenomena. This law is numerically demonstrated and confirmed by designed graphene-based nonlinear metasurfaces in the terahertz regime. Moreover, based on the diffraction law, we designed a nonlinear retroreflector and realized tunable control over a nonlinear wavefront in a single nonlinear metasurface. Our work provides a way to manipulate nonlinear waves and provides a better design of functional nonlinear metadevices.

Giant 2D-chiroptical response in an achiral metasurface integrated with black phosphorus.

In this work, we proposed a black phosphorus (BP) achiral metasurface and theoretically study the chiroptical response arising from extrinsic 2D-chirality in the mid-infrared regime. The achiral metasurface is composed of a monolayer BP sheet sandwiched by a silver ring array and dielectric spacer stacking on a silver substrate. The giant circular conversion dichroism (CCD) of the achiral metasurface is allowed at oblique incidence for the cooperative interaction of BP anisotropic surface plasmon modes and localized surface plasmons in metal rings, and the integrated BP can dynamically modulate the chiroptical response by controlling the doping concentration of BP. Furthermore, we found that a multiband phenomenon for CCD response occurs when tuning the thickness of the spacer. The proposed hybrid achiral metasurface provides more flexible opportunities to realize active polarization modulator, biosensor and chiral detection.

Criterion for photonic topological transition in two-dimensional heterostructures.

The anisotropic van der Waals material α-MoO3 has recently attracted considerable attention because of the ability to support ellipse and hyperbolic phonon polaritons with extreme field confinement and long lifetimes, which can be used in topological transition and transformation polaritonics. However, the dispersion theory of some phonon polaritons in complex heterojunctions often requires tedious computation, which makes it difficult to simply judge and analyze the physical process of the photonic topological transition. Here we obtain the equivalent permittivity distribution of two-dimensional (2D) heterostructures by the effective medium theory and analyze the rotation-induced topological transitions and stack-dependent topological transitions of phonon polaritons. Unlike the previous discussion, we can predict the topological transition points by a parameter ɛx/y(i.e., the permittivity ratio along the in-plane crystal axis of the equivalent medium) and design precisely the phonon polaritons in the stacked materials by controlling the equivalent permittivity after simple calculation. The feasibility of the effective medium theory is verified based on the 2D approximation model and the non-2D approximation model under the limit of an ultrathin slab. Meanwhile, we compare the field distributions and dispersions of the 2D heterostructures and the corresponding equivalent structure. The simulation suggests that the elliptic/hyperbolic responses of the stacked materials depend on the sign of ɛx/y. The new, to the best of our knowledge, method not only provides an easier and clearer criterion for the study of photonic topological transition in anisotropic polaritons, but also shows great potential in designing some multilayer 2D heterostructures.

Broadband achromatic aberration general conformal Luneburg lens with quasi-far-field highly efficient super-focusing.

Super-focusing light using metamaterials and metasurfaces is of paramount importance in several applications, from integrated optics to microwave engineering and sensing. However, there are still some difficulties to realize broadband achromatic aberration highly efficient super-focusing from the far field to far field or quasi far field. In this Letter, based on conformal transformation optics, we propose a generalized conformal Luneburg lens (GCLL), which provides a new, to the best of our knowledge, strategy for quasi-far-field super-focusing with broadband (0.9-1.3 THz) achromatic aberration and high efficiency (above 60%). A relatively high numerical aperture (NA of 0.63) and sub-diffraction-limited resolution (FWHM of 0.45λ) are also obtained. The sample of the GCLL was designed using gradient metamaterials. The numerical simulation results verify that the focusing effects of the designed samples are consistent with the performance of the ideal GCLL.

Tunable Cherenkov radiation based on a van der Waals semiconductor α-MoO3 and graphene hybrid.

In this Letter, we explore the Cherenkov radiation properties of α-phase molybdenum trioxide (α-MoO3). We demonstrate that the asymmetric, forward, and reverse Cherenkov radiation can simultaneously exist by rotating the α-MoO3 slab at the same working frequency and structure. In addition, thanks to the tunable functionalities of graphene, the conversion of forward and reverse Cherenkov radiation can be actualized by altering the Fermi level of graphene. These dynamically adjustable features provide a novel, to the best of our knowledge, and intuitive way for tunable Cherenkov radiation in the mid-infrared range, which opens up new opportunities in designing and manufacturing tunable radiation sources in future.

Water Wave Polaritons.

We find that a one-dimensional groove array can be equivalent to a negative water depth and excite unidirectional surface polaritons for water waves. We explain this phenomenon through theoretical analysis, numerical simulations, and experiments. This phenomenon shows that the propagation direction of water waves can be manipulated through such simple structures, which will be very important in offshore transportation and environmental protection.

Observation of Topological p-Orbital Disclination States in Non-Euclidean Acoustic Metamaterials.

Disclinations-topological defects ubiquitously existing in various materials-can reveal the intrinsic band topology of the hosting material through the bulk-disclination correspondence. In low-dimensional materials and nanostructure such as graphene and fullerenes, disclinations yield curved surfaces and emergent non-Euclidean geometries that are crucial in understanding the properties of these materials. However, the bulk-disclination correspondence has never been studied in non-Euclidean geometry, nor in systems with p-orbital physics. Here, by creating p-orbital topological acoustic metamaterials with disclination-induced conic and hyperbolic surfaces, we demonstrate the rich emergent bound states arising from the interplay among the real-space geometry, the bulk band topology, and the p-orbital physics. This phenomenon is confirmed by clear experimental evidence that is consistent with theory and simulations. Our experiment paves the way toward topological phenomena in non-Euclidean geometries and will stimulate interesting research on, e.g., topological phenomena for electrons in nanomaterials with curved surfaces.

Ultra-compact reconfigurable device for mode conversion and dual-mode DPSK demodulation via inverse design.

The mode multiplexing/de-multiplexing devices are key components for mode-division multiplexing (MDM) technology. Here, we propose an ultra-compact and reconfigurable mode-conversion device via inverse design, which can selectively implement multichannel mode conversion controlled by input phase shifts (Δφ). The device can transform input TE0 (TE1) mode to TE4 (TE3) mode at Δφ=0, or from TE0 (TE1) to TE1 (TE2) at Δφ=π spanning the wavelength range of 1525-1565 nm. We further demonstrate an integrated monolithic module based on the mode conversions to directly demodulate the dual-mode difference phase shift keying (DPSK) signal which significantly reduces the device size and benefits for future dense integrations in MDM systems.

Ideal type-II Weyl points in twisted one-dimensional dielectric photonic crystals.

We proposed an one-dimensional layer-stacked photonic crystal using anisotropic materials to realize ideal type-II Weyl points. The topological transition from Dirac to Weyl points can be clearly observed by tuning the twist angle between layers. Also, on the interface between the photonic type-II Weyl material and air, gapless surface states have been demonstrated in an incomplete bulk bandgap. By breaking parameter symmetry, these ideal type-II Weyl points would transform into the non-ideal ones, exhibiting topological surface states with single group velocity. Our work may provide a new idea for the realization of photonic semimetal phases by utilizing naturally anisotropic materials.