Ideal Unconventional Weyl Point in a Chiral Photonic Metamaterial

Surface potential-adjusted surface states in 3D topological photonic crystals

Surface potential in a topological matter could unprecedentedly localize the waves. However, this surface potential is yet to be exploited in topological photonic systems. Here, we demonstrate that photonic surface states can be induced and controlled by the surface potential in a dielectric double gyroid (DG) photonic crystal. The basis translation in a unit cell enables tuning of the surface potential, which in turn regulates the degree of wave localization. The gradual modulation of DG photonic crystals enables the generation of a pseudomagnetic field. Overall, this study shows the interplay between surface potential and pseudomagnetic field regarding the surface states. The physical consequences outlined herein not only widen the scope of surface states in 3D photonic crystals but also highlight the importance of surface treatments in a photonic system.

Twisted photonic Weyl meta-crystals and aperiodic Fermi arc scattering

As a milestone in the exploration of topological physics, Fermi arcs bridging Weyl points have been extensively studied. Weyl points, as are Fermi arcs, are believed to be only stable when preserving translation symmetry. However, no experimental observation of aperiodic Fermi arcs has been reported so far. Here, we continuously twist a bi-block Weyl meta-crystal and experimentally observe the twisted Fermi arc reconstruction. Although both the Weyl meta-crystals individually preserve translational symmetry, continuous twisting operation leads to the aperiodic hybridization and scattering of Fermi arcs on the interface, which is found to be determined by the singular total reflection around Weyl points. Our work unveils the aperiodic scattering of Fermi arcs and opens the door to continuously manipulating Fermi arcs.

Real higher-order Weyl photonic crystal

Higher-order Weyl semimetals are a family of recently predicted topological phases simultaneously showcasing unconventional properties derived from Weyl points, such as chiral anomaly, and multidimensional topological phenomena originating from higher-order topology. The higher-order Weyl semimetal phases, with their higher-order topology arising from quantized dipole or quadrupole bulk polarizations, have been demonstrated in phononics and circuits. Here, we experimentally discover a class of higher-order Weyl semimetal phase in a three-dimensional photonic crystal (PhC), exhibiting the concurrence of the surface and hinge Fermi arcs from the nonzero Chern number and the nontrivial generalized real Chern number, respectively, coined a real higher-order Weyl PhC. Notably, the projected two-dimensional subsystem with kz = 0 is a real Chern insulator, belonging to the Stiefel-Whitney class with real Bloch wavefunctions, which is distinguished fundamentally from the Chern class with complex Bloch wavefunctions. Our work offers an ideal photonic platform for exploring potential applications and material properties associated with the higher-order Weyl points and the Stiefel-Whitney class of topological phases.

Photonic helicoid-like surface states in chiral metamaterials

We investigate the photonic topological phases in chiral metamaterials characterized by the magnetoelectric tensors with diagonal chirality components. The underlying medium is considered a photonic analogue of the topological semimetal featured with a Weyl cone and a cylindrical surface in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system can be rearranged as two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in the form of spin-orbit Hamiltonians of spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the chiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes form a pair of spiral surface sheets wrapping around the Weyl cone, resembling the helicoid surface states that occur in topological semimetals. At the Weyl frequency, the surface modes contain two Fermi arc-like states that concatenate to yield a straight line segment.

Intrinsic Triple Degeneracy Point Bounded by Nodal Surfaces in Chiral Photonic Crystal

In periodic systems, band degeneracies are typically protected and classified by spatial symmetries. However, in photonic systems, the Γ point at zero frequency is an intrinsic degeneracy due to the polarization degree of freedom of electromagnetic waves. For chiral photonic crystals, such an intrinsic degeneracy carries ±2 chiral topological charge while having linear band dispersions, different from the general perception of charge-2 nodes being associated with quadratic dispersions. Here, we show that these topological characters originate from the spin-1 Weyl point at zero frequency node of triple degeneracy, due to the existence of an electrostatic flat band. Such a topological charge at zero frequency is usually buried in bulk band projections and has never been experimentally observed. To address this challenge, we introduce space-group screw symmetries in the design of chiral photonic crystal, which makes the Brillouin zone boundary an oppositely charged nodal surface enclosing the Γ point. As a result, the emergent Fermi arcs are forced to connect the projections of these topological singularities, enabling their experimental observation. The number of Fermi arcs then directly reveals the embedded topological charge at zero frequency.

Topological antichiral surface states in a magnetic Weyl photonic crystal

Chiral edge states that propagate oppositely at two parallel strip edges are a hallmark feature of Chern insulators which were first proposed in the celebrated two-dimensional (2D) Haldane model. Subsequently, counterintuitive antichiral edge states that propagate in the same direction at two parallel strip edges were discovered in a 2D modified Haldane model. Recently, chiral surface states, the 2D extension of one-dimensional (1D) chiral edge states, have also been observed in a photonic analogue of a 3D Haldane model. However, despite many recent advances in antichiral edge states and chiral surface states, antichiral surface states, the 2D extension of 1D antichiral edge states, have never been realized in any physical system. Here, we report the experimental observation of antichiral surface states by constructing a 3D modified Haldane model in a magnetic Weyl photonic crystal with two pairs of frequency-shifted Weyl points (WPs). The 3D magnetic Weyl photonic crystal consists of gyromagnetic cylinders with opposite magnetization in different triangular sublattices of a 3D honeycomb lattice. Using microwave field-mapping measurements, unique properties of antichiral surface states have been observed directly, including the antichiral robust propagation, tilted surface dispersion, a single open Fermi arc connecting two projected WPs and a single Fermi loop winding around the surface Brillouin zone (BZ). These results extend the scope of antichiral topological states and enrich the family of magnetic Weyl semimetals.

Acoustic Higher-Order Weyl Semimetal with Bound Hinge States in the Continuum

Higher-order topological phases have raised widespread interest in recent years with the occurrence of the topological boundary states of dimension two or more less than that of the system bulk. The higher-order topological states have been verified in gapped phases, in a wide variety of systems, such as photonic and acoustic systems, and recently also observed in gapless semimetal phase, such as Weyl and Dirac phases, in systems alike. The higher-order topology is signaled by the hinge states emerging in the common band gaps of the bulk states and the surface states. In this Letter, we report our first prediction and observation of a new type of hinge states, the bound hinge states in the continuum (BHICs) bulk band, in a higher-order Weyl semimetal implemented in phononic crystal. In contrast to the hinge state in gap, which is characterized by the bulk polarization, the BHIC is identified by the nontrivial surface polarization. The finding of the topological BHICs broadens our insight to the topological states, and may stimulate similar researches in other systems such as electronic, photonic, and cold atoms systems. Our Letter may pave the way toward high-Q acoustic devices in application.

Asymmetry spin-polarization Fermi arc and topological chiral beam splitter with the triply degenerate point in metamaterial

Dirac points (DPs) and Weyl points (WPs) have received much attention in photonic crystals (PhCs) and three-dimensional (3D) metamaterials research due to the robust surface states and Fermi arcs. In this work, two pairs of triply degenerate points (TDPs) have been proposed in a 3D metamaterial by breaking the time reversal symmetry (T) with an external magnetic field. Based on these TDPs, two pairs of asymmetric surface states with spin-polarization are revealed, and a topological chiral beam splitter is demonstrated showing the different propagating directions of the right-handed polarization (RCP) and left-handed polarization (LCP) lights. Remarkably, we can achieve unidirectional propagation with RCP or LCP even excited by a linear source owing to the asymmetry surface state. Our work provides a new, to the best of our knowledge, platform to study spin-polarization surface states and the enhanced spin photonic Hall effect in the metamaterials.

Photonic topological phases in Tellegen metamaterials

We investigate the photonic topological phases in Tellegen metamaterials characterized by the antisymmetric magnetoelectric tensors with real-valued quantities. The underlying medium is considered a photonic analogue of the topological semimetal featured with a displaced Weyl cone in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two Tellegen metamaterials with opposite sign of the magnetoelectric parameter exist at their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, two types of surface modes are tangent to or wrapping around the Weyl cones, which form a pair of bended and a pair of twisted surface sheets. At the Weyl frequency, the surface modes contain a typical and two open Fermi arc-like states that concatenate to yield an infinite straight line. Topological features of the Tellegen metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Discovery of a maximally charged Weyl point

The hypothetical Weyl particles in high-energy physics have been discovered in three-dimensional crystals as collective quasiparticle excitations near two-fold degenerate Weyl points. Such momentum-space Weyl particles carry quantised chiral charges, which can be measured by counting the number of Fermi arcs emanating from the corresponding Weyl points. It is known that merging unit-charged Weyl particles can create new ones with more charges. However, only very recently has it been realised that there is an upper limit - the maximal charge number that a two-fold Weyl point can host is four - achievable only in crystals without spin-orbit coupling. Here, we report the experimental realisation of such a maximally charged Weyl point in a three-dimensional photonic crystal. The four charges support quadruple-helicoid Fermi arcs, forming an unprecedented topology of two non-contractible loops in the surface Brillouin zone. The helicoid Fermi arcs also exhibit the long-pursued type-II van Hove singularities that can reside at arbitrary momenta. This discovery reveals a type of maximally charged Weyl particles beyond conventional topological particles in crystals.

All-angle reflectionless negative refraction with ideal photonic Weyl metamaterials

Negative refraction, an unnatural optical phenomenon in which the incident and the refracted waves reside on the same side of the surface normal, has been demonstrated with the invention of negative index media based on artificially engineered photonic structures called metamaterials. It has received wide attention due to its potential applications in imaging, nonlinear optics, and electromagnetic cloaking. However, it is highly challenging to realize negative refraction operating at all angles and with the perfect transmission. In this work, leveraging the recent development in topological photonics, we propose to realize reflectionless negative refraction for all incident angles with a topological metamaterial. The proposed metamaterial possesses two Weyl points of opposite topological charges. By interfacing the metamaterial with a perfect electric conductor (PEC) or a perfect magnetic conductor (PMC), the Fermi arc connecting the two Weyl points can take the form of a half-circle possessing a positive or a negative refractive index. Importantly, due to the topological protection, there is no reflection at the interface between the PEC and PMC covered areas, leading to the observation of all-angle negative refraction without reflection at the boundary. Our work provides a new platform for manipulating the propagation of surface waves, which may find applications in the construction of integrated photonic devices.

Photonic topological semimetals in bigyrotropic metamaterials

We investigate the photonic topological phases in bigyrotropic metamaterials characterized by the gyroelectric and gyromagnetic parameters. The underlying medium is considered a photonic analogue of the topological semimetal featured with a pair of Weyl cones separated by a distance in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two bigyrotropic metamaterials with opposite sign of the gyrotropic parameters exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, two types of surface modes are tangent to or wrapping around the Weyl cones, which form a bent and two twisted surface sheets. At the Weyl frequency, the surface modes contain a typical and two open Fermi arc-like states that concatenate to yield an infinite straight line. Topological features of the bigyrotropic metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Research on the reflection-type ELC-based optomechanical metamaterial

In this paper, we propose a new kind of optomechanical metamaterial based on a planar ELC-type absorbing structure fabricated on the low-loss flexible substrate. The nonlinear coupling mechanism and nonlinear response phenomenon of the proposed optomechanical metamaterial driven by electromagnetic induced force are analyzed theoretically. The mechanical deformation/displacement and the mechanical resonance frequency shift of the metamaterial unit deposed on the flexible substrate are also numerically and experimentally demonstrated to reveal the coupling phenomenon of electromagnetic field and mechanical field. These results will help researchers to further understand the multi-physics interactions of optomechanical metamaterials and will promote the developments of new type of metasurface for high-efficiency dynamic electromagnetic wave controlling and formatting.

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.

Band engineering method to create Dirac cones of accidental degeneracy in general photonic crystals without symmetry

Symmetry usually plays a key role in the formation of the Dirac cone in the band structure of triangular or hexagonal systems. In this work, we demonstrate a systematic method to create Dirac cones of accidental degeneracy in general photonic crystals without symmetry. With this method, a band gap can be closed gradually through a series of modification to the unit structure based on the eigenfields of the band edges, and consequently a Dirac point is formed with Dirac conical dispersions in its vicinity. The validity of this approach is demonstrated by three examples. We further show that the Dirac cones of accidental degeneracy have the same properties as the symmetry-induced Dirac cones, such as finite group velocity and pseudo-diffusive transmission. Our finding opens a route for the engineering of accidental degeneracy in general photonic crystals beyond the scope of high-symmetry ones.

Flatness and boundness of photonic drumhead surface state in a metallic lattice

Nodal chain (NC) semi-metals have the degeneracy of interlacing rings in their band structure in momentum space. With the projection of degenerate rings towards crystal boundaries, there is a special type of surface dispersion appearing at surface Brillouin zone and termed drumhead surface state (DSS). Previously, experimental investigations on photonic NC and DSS have been done on metallic photonic crystals at microwave frequencies. However, far-field detection of DSS and its coupling to radiative modes in free space have not been studied. In the work, we analyze the photonic DSS in a metallic lattice by angle-resolved far-field reflection measurement and numerical simulation at terahertz (THz) frequencies, and reveal its flatness and boundness in band structure, even in the radiation continuum. Particularly, the DSS band can be tuned being from negatively dispersive via flat to positively dispersive by a single surface parameter, and the DSS at Γ point in surface Brillouin zone is in fact a symmetry-protected bound state in the continuum. Our results might have some potential applications towards THz photonics.