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Robust and efficient light coupling into and out of quantum valley-Hall (QVH) topological interfaces within near-infrared frequencies is demanded in order to be integrated into practical two-dimensional (2D) optical chips. Here, we numerically demonstrate efficient light coupling between a QVH interface and a pair of input/output silicon photonic waveguides in the presence of photonic crystal line defects. When the topological QVH interface is directly end-butt coupled to the silicon waveguides, the input-to-output transmission efficiency is lower than 50% and the exterior boundaries associated with a QVH interface also cause inevitable back-reflections and high-order scatterings, further reducing the transmission efficiency. The transmission efficiency is substantially increased to 95.8% (94.3%) when photonic crystal line defects are introduced between the bridge (zigzag) QVH interface and the waveguides. The buffering line defect mode, with an effective group refractive index between the interface state and the waveguide mode will ease their mode profile conversion. The design we present here brings no fabrication complexity and may be used as a guide for future implementation of on-chip 2D topological photonics.

Nowadays flexible high-performance electromagnetic interference (EMI) shielding materials are greatly demanded in military and daily purpose. To yield high shielding effectiveness (SE), the traditional metallic EMI materials always require a large mass of loading in a composite matrix, which is uneconomic and harmful to the mechanical property of the materials. Herein the homogeneous decoration of Ag nanoparticles on a light-weight and robust carbon nanotube sponge (CNTS) based 3D conductive scaffold is introduced. The flexible Ag/CNTS/PDMS composites exhibit an extremely high and tunable EMI shielding performance with improved mechanical strength and high conductivity. The maximum EMI SE is measured to be even greater than 90 dB in the X-band (8–12 GHz) with a low loading of Ag (3%, wt %) and CNTS (4%, wt %). In addition, the 3D inter-connected pore structure enables EM waves to reflect multiple times inside the Ag/CNTS hybrids which results in a strong absorption ability. The total EMI shielding property can be further conveniently controlled by tuning the Ag-deposition parameters as well as the thickness of the sample. The current approach successfully avoids the dispersion problem of the fillers and will be of great importance in development of high-performance EMI shielding materials.

Based on the tight-binding calculations on honeycomb lattice and photonic experimental visualization on artificial graphene (AG), we report the domain-wall-induced gapped topological kink states and topological corner states. In honeycomb lattice, domain walls (DWs) with gapless topological kink states could be induced either by sublattice symmetry breaking or by lattice deformation. We find that the coexistence of these two mechanisms will induce DWs with gapped topological kink states. Significantly, the intersection of these two types of DWs gives rise to topological corner state localized at the crossing point. Through the manipulation of the DWs, we show AG with honeycomb lattice structure not only a versatile platform supporting multiple topological corner modes in a controlled manner, but also possessing promising applications such as fabricating topological quantum dots composed of gapped topological kink states and topological corner states.

Perfectly matched layer (PML) is a virtual absorption boundary condition adopted in numerical simulations, capable of absorbing light from all incident angles, which however is still lacking in practice in the optical regime. In this work, by integrating dielectric photonic crystals and material loss, we demonstrate an optical PML design with near-omnidirectional impedance matching and customized bandwidth. The absorption efficiency exceeds 90% for incident angle up to 80°. Good consistence is found between our simulations and proof-of-principle microwave experiments. Our proposal paves the road to realize optical PMLs, and could find applications in future photonic chips.

Finite-size effect plays a significant role in topology photonics not to mention in reality all experimental setups are in finite-size. A photonic bandgap is opened in the topological edge state dispersion if a topological photonic crystal with finite width is considered, and the bandgap size relies on the finite-size effect. Pseudospin-preserving and pseudospin-flipping processes can be realized when a selectively switch of the pseudospin of edge states are customized by our designs. Our microwave experiments also successfully demonstrate pseudospin switch-on and -off behaviors in a finite-width photonic crystal. By combining photonic crystals with finite widths, a multi-tunneling proposal of topological photonic crystals can also be achieved. Our study of the finite-size effect will provide new approaches and thoughts to improve the development of topological photonic devices in the future.

We report an experimental study of the edge surface superconductivity and the Hall effect in a Nb thin film Hall device. We show that the previously reported anomalous sign reversal of the Hall resistance across the superconducting-normal transition is due to the edge supercurrent. Large anomalous oscillations between the transverse voltage probes are observed in the field range between Hc2 and Hc3, in both the anti-symmetric (Hall) and symmetric (resistive) channels. These oscillations are extremely sensitive to a small tilting of the edge surface relative to the external magnetic field. We suggest that these oscillations may arise from the Aharonov-Bohm interference of the edge supercurrents.

We construct an electrical circuit to realize a modified Haldane lattice exhibiting the phenomenon of antichiral edge states. The circuit consists of a network of inductors and capacitors with interconnections reproducing the effects of a magnetic vector potential. The next nearest neighbor hoppings are configured differently from the standard Haldane model, and as predicted by earlier theoretical studies, this gives rise to antichiral edge states that propagate in the same direction on opposite edges and coexist with bulk states at the same frequency. Using pickup coils to measure voltage distributions in the circuit, we experimentally verify the key features of the antichiral edge states, including their group velocities and ability to propagate consistently in a Möbius strip configuration. Ministry of Education (MOE) This work was supported by the National Natural Science Foundation of China (Grant Nos. 11874274, and 12004425), the Natural Science Foundation of Jiangsu Province (Grant Nos. BK20170058, and BK20200630), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). YiDong Chong was supported by the Singapore MOE Academic Research Fund Tier 3 (Grant No. MOE2016-T3-1-006).

Electromagnetic void space is a medium, while geometrically occupying a finite volume of space, optically equivalent to an infinitesimal point, in which electromagnetic waves do not experience any phase accumulation. Here, we report the first realization of three-dimensional (3D) electromagnetic void space by an all-dielectric photonic crystal possessing vanishing permittivity and permeability simultaneously. The 3D electromagnetic void space offers distinctive functionalities inaccessible to its 2D or acoustic counterparts because of the fundamental changes in topology, which comes from the ascension of dimensionality as well as the transverse nature of electromagnetic waves. In particular, we demonstrate, both theoretically and experimentally, that the transmission through such a 3D void space is unaffected by its inner boundaries, but highly sensitive to the outer boundaries. This enables many applications such as the impurity ``antidoping'' effect, outer-boundary-controlled switching, and 3D perfect wave steering. Our work paves a road toward 3D exotic optics of an optically infinitesimal point.

Two anisotropic exceptional points (EPs) of arbitrarily high order are found in a class of random non-Hermitian systems, where the non-Hermiticity emerges from non-reciprocal hoppings. Both eigenvalues and phase rigidity show different asymptotic forms near the anisotropic EP in two orthogonal directions in the parameter space, making them anisotropic EPs. The critical exponents of phase rigidity follow universal rules near an anisotropic EP, and the exponents depend on the dimension of the Hamiltonian as well as the approaching direction, but are independent of the random configurations. We found multiple ellipses formed by EPs of order two converge to the two high-order EPs in the parameter space. A ring of high-order EPs is formed when all ellipses coalesce for some particular configurations.

In this Letter, we theoretically propose and experimentally demonstrate a three-dimensional soundproof acoustic cage structure, hereby denoted as an acoustic metacage. The metacage is composed of six acoustic metamaterial slabs with open holes and hidden bypass space coiling tunnels connected to the holes. Band structure analysis reveals a novel physical mechanism to open a low-frequency broad partial band gap via the band folding in other directions, which can also be interpreted by an effective medium with indefinite effective mass density and negative effective modulus. Transmission loss in simulations and in the acoustic impedance tube are administered. Strikingly, we prove that the soundproofing effect of the metacage is robust against the airflow perturbation induced by a fan. Our work paves a road for low-frequency airborne soundproof structures in the presence of ventilation.

Topological Photonics: Type-II Dirac points in dielectric crystals Crystalline symmetries can be used to create and tune topological points in photonic crystals. If a material’s structure has energy bands that linearly disperse and touch at a point, quasiparticle can emerge that are described by the relativistic Dirac or Weyl equations. This is true for both electronic and photonic systems, but as light is bosonic—rather than fermionic—in nature, the physics is not directly analogous. An international team of researchers led by Jian-Hua Jiang from Soochow Universty and Hae-Young Kee from the University of Toronto and Canadian Institute for Advanced Research now predict that crystalline symmetries can be used to create different types of Dirac and Weyl points in all-dielectric photonic crystals, similar to those seen in their electronic counterparts, which also provide robust surface states that could be exploited for applications.

Chiroptical responses of helical superstructures are determined by collective behaviors of the individual building blocks. In this paper, we present a full theoretical description of the collective resonance in superstructures. We use the gold nanorods as individual building blocks and arrange them helically along an axis in an end-to-end fashion. Numerical simulations on single-unit cells reveal that the plasmonic coupling between the nanorods produces hybridized resonances, whose intensity is strongly dependent on the excitation light with left- or right-handed circular polarizations (LCP or RCP). A node-mode criterion is proposed on the basis of the microscopic mechanism, which successfully explains the difference between LCP and RCP. We further demonstrate, by repeating the unit cell from 1 to infinity along the helical axis, the multiple hybridized resonances gradually evolve and merge into a single collective resonance, whose energy is also dependent on LCP and RCP. An analytical description is provided for the collective resonance of the helical superstructure on the basis of the coupled dipole approximation method. Our theory shows that n collective resonance modes are present in the helical superstructure with the unit cell consisting of $n$ nanorods. Strikingly, only one resonance can be excited by the incident light with certain circular polarization. We propose a universal selection rule for such selective excitation of the collective resonances by analyzing the symmetry of the helical superstructures. The new insights provided in this work may shed light on future designs and fabrications of helical superstructures using plasmonic building blocks., Comment: 11 pages, 8 figures

An astroid-shaped loop of exceptional points (EPs), comprising four cusps, is found to spawn from the triple degeneracy point in the Brillouin zone (BZ) of a Lieb lattice with nearest-neighbor hoppings when non-Hermiticity is introduced. The occurrence of the EP loop is due to the realness of the discriminant which is guaranteed by the non-Hermitian chiral symmetry. The EPs at the four cusps involve the coalescence of three eigenstates, which is the combined result of the non-Hermitian chiral symmetry and mirror-T symmetry. The EP loop is exactly an astroid in the limit of an infinitesimal non-Hermiticity. The EP loop expands from the $\phantom{\rule{4pt}{0ex}}M$ point with increasing non-Hermiticity and splits into two EP loops at a critical non-Hermiticity. The further increase of non-Hermiticity contracts the two EP loops towards and finally to two EPs at the $\phantom{\rule{4pt}{0ex}}X$ and $\phantom{\rule{4pt}{0ex}}Y$ points in the BZ, accompanied by the emergence of Dirac-like cones. The two EPs vanish at a larger non-Hermiticity. The EP loop disappears and several discrete EPs are found to survive when next-nearest hoppings are introduced to break the non-Hermitian chiral symmetry. A topological invariant called the discriminant number is used to characterize their robustness against perturbations. Both discrete EPs and those on the EP loop(s) are found to show anisotropic asymptotic behaviors. Finally, the experimental realization of the Lieb lattice using a coupled waveguide array is discussed.

Metamaterials have generated considerable research interest in manipulating the polarization state of light, but many proposals suffer from narrow bandwidth or low transmission efficiency. Here researchers show that a classical multiple-beam interference mechanism can be used to modulate the phase dispersion of transmitted waves in metamaterials, which motivates a general strategy to achieve a broadband wave plate by independently controlling the phase dispersion for the two orthogonal polarizations. These findings can stimulate the production of high-performance broadband optical devices based on various metamaterials in different frequency domains, to impact applications in photonics.

A pair of anisotropic exceptional points (EPs) of arbitrary order are found in a class of non-Hermitian random systems with asymmetric hoppings. Both eigenvalues and eigenvectors exhibit distinct behaviors when these anisotropic EPs are approached from two orthogonal directions in the parameter space. For an order-$N$ anisotropic EP, the critical exponents $\nu$ of phase rigidity are $(N-1)/2$ and $N-1$, respectively. These exponents are universal within the class. The order-$N$ anisotropic EPs split and trace out multiple ellipses of EPs of order $2$ in the parameter space. For some particular configurations, all the EP ellipses coalesce and form a ring of EPs of order $N$. Crossover to the conventional order-$N$ EPs with $\nu=(N-1)/N$ is discussed., Comment: Main text contains 14 pages and 4 figures

Directional beaming of electromagnetic waves passing through a subwavelength aperture has attracted considerable interests in photonics, but the traditional approach of utilizing gratings to directionally couple surface waves (SWs) to a desired far-field direction faces the low-efficiency issue owing to high-order diffractions. Here we experimentally demonstrate that directional beaming of light can be realized with very high efficiencies, in which two specifically designed metasurfaces (MTSs) are placed at two sides of the aperture to serve as SW to propagating-wave meta-couplers. Different from the grating couplers, the well-designed phase-gradient meta-couplers can freely select the desired diffraction orders by suppressing the undesired diffraction orders. We design and fabricate MTSs with different phase gradients, and perform both far-field and near-field measurements to verify the predicted high-efficiency on/off-axis directional beaming effects. Experimental results are in good agreement with full wave simulations and theoretical analyses.

Utilizing the robust transport properties of the topological photonic crystal interface, we experimentally realize two-dimensional topological photonic crystal cavities, where discrete whispering gallery modes can propagate unidirectionally along the cavity circumference. Different from traditional cavities, these topological whispering galley modes are insensitive to cavity shapes. Our microwave demonstration has a good agreement with numerical simulations. Using pure dielectrics, by scaling down to the optical wavelength, an optical directional coupler based on the same topological photonic crystal scheme is also proposed. We here show that topological photonics can provide more novel designs for optical devices.

The invisibility cloak, a long-standing fantastic dream for humans, has become more tangible with the development of metamaterials. Recently, metasurface-based invisibility cloaks have been proposed and realized with significantly reduced thickness and complexity of the cloaking shell. However, the previous scheme is based on reflection-type metasurfaces and is thus limited to reflection geometry. In this work, by integrating the wavefront tailoring functionality of transparent metasurfaces and the wave tunneling functionality of zero-index materials, we have realized a unique type of hybrid invisibility cloak that functions in transmission geometry. The principle is general and applicable to arbitrary shapes. For experimental demonstration, we constructed a rhombic double-layer cloaking shell composed of a highly transparent metasurface and a double-zero medium consisting of dielectric photonic crystals with Dirac cone dispersions. The cloaking effect is verified by both full-wave simulations and microwave experimental results. The principle also reveals exciting possibilities for realizing skin-thick ultrathin cloaking shells in transmission geometry, which can eliminate the need for spatially varying extreme parameters. Our work paves a path for novel optical and electromagnetic devices based on the integration of metasurfaces and metamaterials., Optics: Another step closer to an invisibility cloak Chinese scientists have developed an innovative technique for making an invisibility cloak that could pave the way for new optical and electromagnetic devices. Although invisibility cloaks by bending light around an object have been around for some time, they are bulky and complex devices with spatially gradient parameters, limiting their uses. Now, Yun Lai and his colleagues from Nanjing University and Soochow University, in collaboration with researchers from Fudan University, have developed a new technique that combines the properties of metamaterials and metasurfaces to produce an invisibility cloak that is significantly thinner and less complex than currently available. The hybrid device integrates the wavefront tailoring functionality of transparent metasurfaces with the wave tunneling functionality of materials with near-zero-refractive index, and enables a new approach of cloaking by creating the illusion of free space.

We demonstrate experimentally that a photonic crystal made of Al_{2}O_{3} cylinders exhibits topological time-reversal symmetric electromagnetic propagation, similar to the quantum spin Hall effect in electronic systems. A pseudospin degree of freedom in the electromagnetic system representing different states of orbital angular momentum arises due to a deformation of the photonic crystal from the ideal honeycomb lattice. It serves as the photonic analogue to the electronic Kramers pair. We visualized qualitatively and measured quantitatively that microwaves of a specific pseudospin propagate only in one direction along the interface between a topological photonic crystal and a trivial one. As only a conventional dielectric material is used and only local real-space manipulations are required, our scheme can be extended to visible light to inspire many future applications in the field of photonics and beyond.

Two-dimensional photonic crystals, in analogy to AB/BA stacking bilayer graphene in electronic system, are studied. Inequivalent valleys in the momentum space for photons can be manipulated by simply engineering diameters of cylinders in a honeycomb lattice. The inequivalent valleys in photonic crystal are selectively excited by a designed optical chiral source and bulk valley polarizations are visualized. Unidirectional valley interface states are proved to exist on a domain wall connecting two photonic crystals with different valley Chern numbers. With the similar optical vortex index, interface states can couple with bulk valley polarizations and thus valley filter and valley coupler can be designed. Our simple dielectric PC scheme can help to exploit the valley degree of freedom for future optical devices.

Following the seminal work by Dubois et al. (Nat. Commun. 8, 14871 (2017)), we study a double-zero-index acoustic metamaterial with triangular lattice. By varying the height and diameter of air scatterers inside a parallel-plate acoustic waveguide, acoustic dispersion of the first-order waveguide mode can be manipulated and various interesting properties are explored. With accidental degeneracy of monopolar and dipolar modes, we numerically prove the double-zero-index properties of this novel acoustic metamaterial. Acoustic waveguides with tunable and asymmetric transmission are realized with this double-zero-index acoustic metamaterial embedded. Band inversion occurs if the bulk acoustic band diagram of this acoustic metamaterial is tuned. Deterministic interface states are found to exist on the interface between two acoustic metamaterials with inverted band diagrams.

The concept of gauge field is a cornerstone of modern physics and the synthetic gauge field has emerged as a new way to manipulate particles in many disciplines. In optics, several schemes of Abelian synthetic gauge fields have been proposed. Here, we introduce a new platform for realizing synthetic SU(2) non-Abelian gauge fields acting on two-dimensional optical waves in a wide class of anisotropic materials and discover novel phenomena. We show that a virtual non-Abelian Lorentz force arising from material anisotropy can induce light beams to travel along Zitterbewegung trajectories even in homogeneous media. We further design an optical non-Abelian Aharonov-Bohm system which results in the exotic spin density interference effect. We can extract the Wilson loop of an arbitrary closed optical path from a series of gauge fixed points in the interference fringes. Our scheme offers a new route to study SU(2) gauge field related physics using optics., Comment: 14 pages, 4 figures. Supplementary information has been added

By exploiting the scaling invariance of photonic band diagrams, a complementary photonic crystal slab structure is realized by stacking two uniformly scaled double-zero-index dielectric photonic crystal slabs together. The space cancellation effect in complementary photonic crystals is demonstrated in both numerical simulations and microwave experiments. The refractive index dispersion of double-zero-index dielectric photonic crystal is experimentally measured. Using pure dielectrics, our photonic crystal structure will be an ideal platform to explore various intriguing properties related to a complementary medium.

Metasurfaces have been successfully applied to realize cloaking in the reflection geometry recently[1, 2]. We propose a transmission cloaking scheme by using a cloaking shell consisting of a metasurface and a thin layer of zero-index medium. The metasurface is designed to impose a suitable amount of phase change on the incident waves and radiation waves, so as to avoid the total reflection on the surface of zero-index medium and to restore the propagating wave front. The energy flux is tunneled through the zero-index medium. Full-wave simulation results show good cloaking effects for cloaks of almost arbitrary shapes. We design and fabricate a rhombus cloaking shell for operation in the microwave region and the experimental results agree well with the numerical simulations.

We propose an anisotropic photonic crystal (PC) structure with close-to-zero effective parameters. The anisotropic zero-index property of PCs provides complex iso-frequency contours, where their shapes can change from ellipses or hyperbolae to a linear crossing. A mechanism of light beam splitting can be achieved by utilizing the linear crossing shaped iso-frequency curve. The manipulation of light beam propagations is verified by both numerical simulations and microwave experiments. By using pure dielectrics and scaling down to optical wavelengths, we also propose a design of nonperiodic PC structures to achieve optical unidirectional cloaking without size or shape limitation. Our design provides a promising platform for cloaking applications in the optical regime.

Artificial magnetic field in electromagnetism is becoming an emerging way as a robust control of light based on its geometric and topological nature. Other than demonstrating topological photonics properties in the diffractive regime using photonic crystals or arrays of waveguides, it will be of great interest if similar manipulations can be done simply in the long wavelength limit, in which only a few optical parameters can be used to describe the system, making the future optical component design much easier. Here, by designing and fabricating a metamaterial with split dispersion surface, we provide a straight-forward experimental realization of spin-dependent gauge field in the real space using a biaxial material. A "magnetic force bending" for light of desired pseudospins is visualized experimentally by such a gauge field as a manifestation of optical spin Hall effect. Such a demonstration is potentially useful to develop pseudospin optics, topological components and spin-enabled transformation optical devices.

A design of acoustic transmissive cloaking is proposed using a hybrid cloaking shell. The shell consists of one layer of metasurface to manipulate both the incident and exit acoustic wavefronts and one layer of zero-index metamaterial to achieve acoustic energy tunneling. Incident acoustic wave will remain its wavefront after propagating through our hybrid cloaking shell constructed by experimentally realizable acoustic metamaterials. As there is no intrinsic limit to the object to be cloaked, the strategy of our transmissive cloaking geometry has wide potential applications in both airborne sound and underwater ultrasound.

In this talk, we discuss realistic metamaterial structures to realize the concept of real-space gauge field. Light propagation can be modified in conventional optical media by changing the sizes and the shapes of their dispersion surfaces. Alternatively, a real space gauge field approach can also manipulate light propagation by shifting the centers of the dispersion surfaces [1–4]. Such a real space gauge field, together with the associated pseudo magnetic field in real space, has been applied to achieve novel wave phenomena such as negative refraction, one-way waveguide, spin-Hall effect, and one-way topological edge states. Recently, we have also proposed that such a gauge field in real space can be synthesized by a tilted anisotropic metamaterials [5, 6]. With such gauge field metamaterials, spin-dependent optical components such as beam splitter and all-angle wave plate can be designed. We will discuss the underlying metamaterial structures in achieving such a real space gauge field, by realizing the two shifted dispersion surfaces. On one hand, in the ideal case we generally require a 45 degree tilted anisotropic metamaterial with dedicated balance of electric and magnetic responses. This can be realized by a metamaterial unit cell composed of a split-ring resonator and a metal bar which both have 45 degrees rotation from one of the principal axis. The split-ring resonator provides the magnetic response while the metal bar works as a tuning for the detailed balance. On the other hand, we further establish a reduced parameter approximation to simplify experiments. In this case, the metamaterial is still 45 degree tilted anisotropic medium, but the magnetic response is dropped. Only the electric responses in different directions are needed to realize the real space gauge field in a reduced parameter approximation.

Photonic graphene, photonic crystal with honeycomb lattice is studied in the work. Using both finite element simulations and microwave experiments, we studied the existence of the edge modes at different edges of this “photonic graphene”. The edge states are observed experimentally on the bearded interfaces of photonic crystals. The physics of the occurrence of these edge modes are discussed and we hope that the fabrication easiness of photonic crystal makes it a perfect platform for classical simulations of electronic transport properties in graphene.

Ever since the introduction of metamaterials, intriguing applications have been proposed by metamaterial designs. An e = μ = −1 slab will serve as a super lens to break diffraction limit. This slab, whose permittivity and permeability is with the same magnitude but of different sign to air, is the complementary medium to air. Lai et al. proposed the possibility to remote cloaking using complementary medium. However, the metamaterial design to have complementary medium realized is complicated and there are experimental demonstrations are limited. Conical dispersion can exist at the Brillouin zone center of two-dimensional photonic crystals and this dielectric photonic crystal can be regarded has an effective zero permittivity and permeability at the Dirac frequency. Close to the Dirac frequency, effective permittivity and permeability are linear to frequencies. Moreover, because of the scaling property of Maxwell's Equation, if the linear dimensions of the structures in a given dielectric PC are scaled uniformly by a factor of α, the frequency ω and wave vector k should also be scaled according to the relations ω = ω/α and k = k/α [1]. Thus a complementary medium can be realized by stacking two photonic crystal slabs scaled uniformly. Our simulations and microwave experiments give a direct demonstration of the phase compensation effect of the complementary medium. Vortex interface states in complementary medium are experimentally observed and one dimensional remote cloaking is proposed.

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.

The study of interface/surface states in photonic crystals provides new approaches to control the flow of light. In this work, a new type of interface states in two-dimensional photonic crystals is experimentally realized and characterized [1]. The existence of this type of interface states is solely dependent on the reflection properties of the bulk photonic crystals without any surface/interface decorations. Our experimental results have excellent agreement to numerical simulations and the propagation properties of these measured interface states indicate that this new type of interface states will be a good candidate for future optical waveguiding applications. This type of deterministic interface states also exists at the boundary between a dielectric photonic crystal and its “inverted” partner as long as a common gap can be found above the lowest band, which is also experimentally characterized [2].

We show how one may obtain conical (Dirac) dispersions in photonic crystals, and in some cases, such conical dispersions can be used to create a metamaterial with an effective zero refractive index. We show specifically that in two-dimensional photonic crystals with symmetry, we can adjust the system parameters to obtain accidental triple degeneracy at Γ point, whose band dispersion comprises two linear bands that generate conical dispersion surfaces and an additional flat band crossing the Dirac-like point. If this triply degenerate state is formed by monopole and dipole excitations, the system can be mapped to an effective medium with permittivity and permeability equal to zero simultaneously, and this system can transport wave as if the refractive index is effectively zero. However, not all the triply degenerate states can be described by monopole and dipole excitations and in those cases, the conical dispersion may not be related to an effective zero refractive index. Using multiple scattering theory, we calculate the Berry phase of the eigenmodes in the Dirac-like cone to be equal to zero for modes in the Dirac-like cone at the zone center, in contrast with the Berry phase of for Dirac cones at the zone boundary.

We show that by applying accidental degeneracy, we can obtain a triply-degenerate state at the zone center in the band diagram of two dimensional (2D) photonic crystal. The dispersion near the zone center comprises two linear bands and an additional ∞at band crossing at the same frequency. If this triply-degenerate state is formed by the degeneracy of monopole and dipole excitations, we show that the system can be mapped to an efiective medium with permittivity and permeability equal to zero. While \Dirac cone" dispersions can only be meaningfully deflned in 2D systems, the notion of a Dirac point can be extended to three dimensional (3D) classical wave systems. We show that a simple cubic photonic crystal composed of core-shell spheres exhibits a 3D Dirac-like point at the center of the Brillouin zone at a flnite frequency. Using efiective medium theory, we can map our structure to an isotropic zero refractive index material in which the efiective permittivity and permeability are simultaneously zero at the Dirac-like point frequency (!D). The Dirac-like point is six-fold degenerate and is formed by the accidental degeneracy of electric dipole and magnetic dipole excitations, each with three degrees of freedom. We found that 3D Dirac-like points at ~ = 0 can also be found in simple cubic acoustic wave crystals. Difierent from the case in the photonic system, the 3D Dirac-like point in acoustic wave system is four-fold degenerate, and is formed by the accidental degeneracy of dipole and monopole excitations. Using efiective medium theory, this acoustic wave system can also be described as a material which has both efiective mass density and reciprocal of bulk modulus equal to zero at !D. For both the photonic and phononic systems, a subset of the bands has linear dispersions near the zone center, and they give