General Bound States in the Continuum in Momentum Space.

Polarization singularities including bound states in the continuum (BICs) and circularly polarized states have provided promising opportunities in the manipulation of light waves. Previous studies show that BICs in photonic crystal slabs are protected by C_{2}T symmetry and hence normally exist on the high-symmetry lines of momentum space. Here, we propose an approach based on graph theory to study these polarization singularities in momentum space, especially in the region off the high-symmetry lines. With a polarization graph, it is demonstrated for the first time that BICs can stably exist off the high-symmetry lines of momentum space for both one-dimensional and two-dimensional photonic crystal slabs. Furthermore, two kinds of interesting processes, including the merging involved with this newly found BICs both on and off the high-symmetry lines, are observed by changing the geometrical parameters of photonic crystal slabs while keeping their symmetry. Our findings provide a new perspective to explore polarization singularities in momentum space and render their further applications in light-matter interaction and light manipulation.

Bound states in the continuum based on the total internal reflection of Bloch waves.

A photonic-crystal slab can support bound states in the continuum (BICs) that have infinite lifetimes but are embedded into the continuous spectrum of optical modes in free space. The formation of BICs requires a total internal reflection (TIR) condition at both interfaces between the slab and the free space. Here, we show that the TIR of Bloch waves can be directly obtained based on the generalized Fresnel equations proposed. If each of these Bloch waves picks up a phase with integer multiples of 2π for traveling a round trip, light can be perfectly guided in the slab, namely forming a BIC. A BIC solver with low computational complexity and fast convergence speed is developed, which can also work efficiently at high frequencies beyond the diffraction limit where multiple radiation channels exist. Two examples of multi-channel BICs are shown and their topological nature in momentum space is also revealed. Both can be attributed to the coincidence of the topological charges of far-field radiations from different radiation channels. The concept of the generalized TIR and the TIR-based BIC solver developed offer highly effective approaches for explorations of BICs that could have many potential applications in guided-wave optics and enhanced light-matter interactions.

Generation of Bessel beams with tunable longitudinal electric and magnetic fields using an all-dielectric metasurface.

Optical beams with a pure longitudinally polarized field are of great interest for their unique properties and promising applications in various fields such as optical trapping and three-dimensional microscopy. Here, an all-dielectric metasurface is proposed to directly generate Bessel beams with tunable longitudinally polarized electric and magnetic fields under a simple incidence of linear polarization. Under the incidence of horizontal polarization, a Bessel beam with a pure longitudinally polarized electric field can be generated, which can be turned to a beam with a pure longitudinally polarized magnetic field when the incidence is switched to vertical polarization. More importantly, it is further demonstrated that the longitudinal components of the electric and magnetic fields can be accurately manipulated between zero and the maximum by simply changing the polarization angle of incident light. The simplicity and flexibility of this proposed metasurface may provide new possibilities in ultracompact photonic devices for optical trapping, optical storage, and related fields.

Interface states and bound states in the continuum in photonic crystals with different lattice constants.

The existence of interface states at the boundary of two semi-infinite photonic crystals (PhCs) with different lattice constants are investigated systematically. Compared to the interface states in the two PhCs with the same period, a band folding effect is observed for the interface states inside the common band gap of the two PhCs with different lattice constants. We demonstrate that these interface states can be predicted by the surface impedance of the two PhCs. The dispersion of interface states can be determined by the condition of impedance matching combined with the band folding effect. Moreover, some part of the folded interface states penetrates the region of projected bulk bands, and they usually leak to the bulk and form resonant states. However, the interface state at the Γ point can be perfectly localized and becomes a bound state in the continuum (BIC) due to the symmetry mismatch. These findings may provide a general scheme for designing BICs in the PhC structures based on the interface states.

Coexistence of a new type of bound state in the continuum and a lasing threshold mode induced by PT symmetry.

Some photonic systems support bound states in the continuum (BICs) that have infinite lifetimes, although their frequencies and momenta are matched to vacuum modes. Using a prototypical system that can be treated analytically, we show that each of these BICs always splits into a pair of new type BIC and lasing threshold mode when a parity-time (PT)-symmetric perturbation is introduced. The radiation loss at the lasing threshold is exactly balanced by the net gain of the particles. These PT symmetry-induced BICs are different from ordinary BICs, as they can be excited by an external source but do not radiate, and they carry a different quality factor divergence rate from that of the ordinary BICs. While most of the attention of PT-symmetric systems is captured by the coalescence of modes at exceptional points, the splitting of ordinary BICs is a new phenomenon that illustrates the rich physics embedded in PT-symmetric systems.

Near-field analysis of bound states in the continuum in photonic crystal slabs.

Bound states in the continuum (BICs) can be derived from a generalized waveguide condition in which the total internal reflection is substituted by coherent perfect reflection. Coherent perfect reflection can occur in the truncated photonic crystal (PhC) due to the interference of different Bloch modes. Based on the coherent reflection, BICs can be constructed by the bulk Bloch modes of PhC slabs. In contrast to the determination of BICs from the topological vortices of far-field radiation, this interpretation from coherent reflection can give the spatial field profile in detail in the near field. We show that the BICs can be characterized by the indices (or number of nodes) of their constituent Bloch modes. Moreover, all the guided resonances in addition to BICs can also be labelled by these mode indices. It is found that for the guided resonances the mode indices can change suddenly on the same frequency band. Our results may have potential applications in guided-wave optics and enhanced light-matter interaction.

Angle-dependent optical response of the plasmonic nanoparticle clusters with rotational symmetry.

Plasmonic nanoparticle clusters are widely considered experimentally and numerically. In the clusters consisting of one central particle and N satellite particles, not only the magnetic modes but also the toroidal modes can exist. Here, the eigenmodes of such clusters and the corresponding excitation efficiency under the illumination of a plane wave are studied analytically by using the eigen-decomposition method. The angular dependence of the optical response of these clusters is clearly demonstrated. The behavior of excitation efficiency is dependent on both the value and the parity of N, the number of satellite particles. Our results may provide a guide for the selective excitation of plasmonic modes in the plasmonic nanoparticle clusters.

Direct observation of valley-polarized topological edge states in designer surface plasmon crystals.

The extensive research of two-dimensional layered materials has revealed that valleys, as energy extrema in momentum space, could offer a new degree of freedom for carrying information. Based on this concept, researchers have predicted valley-Hall topological insulators that could support valley-polarized edge states at non-trivial domain walls. Recently, several kinds of photonic and sonic crystals have been proposed as classical counterparts of valley-Hall topological insulators. However, direct experimental observation of valley-polarized edge states in photonic crystals has remained difficult until now. Here, we demonstrate a designer surface plasmon crystal comprising metallic patterns deposited on a dielectric substrate, which can become a valley-Hall photonic topological insulator by exploiting the mirror-symmetry-breaking mechanism. Topological edge states with valley-dependent transport are directly visualized in the microwave regime. The observed edge states are confirmed to be fully valley-polarized through spatial Fourier transforms. Topological protection of the edge states at sharp corners is also experimentally demonstrated.

Unidirectional scattering induced by the toroidal dipolar excitation in the system of plasmonic nanoparticles.

The interference between conventional multipoles (e.g., electric and magnetic dipole, electric quadrupole, etc.) is known as the cause of unidirectional backward and forward scattering of nanoparticles. However, an unconventional multipole moment, toroidal dipole moment is generally overlooked in the unidirectional scattering. In this work, we systematically investigate the unidirectional scattering in the system of plasmonic nanoparticles. It is found that the toroidal dipole moment can play a significant role in the unidirectional backward scattering. The structural tunability of the unidirectional scattering is also demonstrated. Our results can find applications in the design of nanoantennas.

Broadband light absorption in graphene ribbons by canceling strong coupling at subwavelength scale.

We theoretically investigate the broadband light absorption in the THz range by canceling the strong coupling in an array of graphene ribbons at subwavelength scale. A series of resonators with different absorption frequencies can achieve a broadband absorber, however, the suppression of absorption always accompanies since the mutual coupling between resonators cause the mode splitting. By adjusting the near- and far-field coupling between the plasmon resonances of the graphene ribbon array to the critical point, the absorption linewidth is broadened for almost one magnitude larger than that of individual graphene ribbon, to be ~1 THz. Our study provides not only insight understanding but also new approaches towards the broadband graphene absorber.

Topological interface states in multiscale spoof-insulator-spoof waveguides.

The spoof-insulator-spoof (SIS) structure can serve as a waveguide for spoof surface plasmon polaritons (spoof SPPs). If a periodic geometry modulation in the wavelength scale is introduced to the SIS waveguide, this multiscale SIS (MSIS) waveguide possesses band gaps for spoof SPPs analogous to the band gaps in a photonic crystal. Inspired by the topological interface states found in photonic crystals, we construct an interface by connecting two MSIS waveguides with different topological properties (inverted Zak phases of bulk bands). The topological interface states in the MSIS waveguides are observed experimentally. The measured decay lengths of the interface states agree excellently with the numerical results. These localized interface states may find potential applications in miniaturized microwave devices.

Coexistence of Scattering Enhancement and Suppression by Plasmonic Cavity Modes in Loaded Dimer Gap-Antennas.

Plasmonic nanoantenna is of promising applications in optical sensing and detection, enhancement of optical nonlinear effect, surface optical spectroscopy, photoemission, etc. Here we show that in a carefully-designed dimer gap-antenna made by two metallic nanorods, the longitudinal plasmon antenna mode (AM) of bonding dipoles can compete with the transverse plasmonic cavity modes (CMs), yielding dramatically enhanced or suppressed scattering efficiency, depending on the CMs symmetry characteristics. More specifically, it is demonstrated that an appropriately loaded gap layer enables substantial excitation of toroidal moment and its strong interaction with the AM dipole moment, resulting in Fano- or electromagnetically induced transparency (EIT)-like profile in the scattering spectrum. However, for CMs with nonzero azimuthal number, the spectrum features a cumulative signature of the respective AM and CM resonances. We supply both detailed near-field and far-field analysis, showing that the modal overlap and phase relationship between the fundamental moments of different order play a crucial role. Finally, we show that the resonance bands of the AM and CMs can be tuned by adjusting the geometry parameters and the permittivity of the load. Our results may be useful in plasmonic cloaking, spin-polarized directional light emission, ultra-sensitive optical sensing, and plasmon-mediated photoluminescence.

Topological edge modes in multilayer graphene systems.

Plasmons can be supported on graphene sheets as the Dirac electrons oscillate collectively. A tight-binding model for graphene plasmons is a good description as the field confinement in the normal direction is strong. With this model, the topological properties of plasmonic bands in multilayer graphene systems are investigated. The Zak phases of periodic graphene sheet arrays are obtained for different configurations. Analogous to Su-Schrieffer-Heeger (SSH) model in electronic systems, topological edge plasmon modes emerge when two periodic graphene sheet arrays with different Zak phases are connected. Interestingly, the dispersion of these topological edge modes is the same as that in the monolayer graphene and is invariant as the geometric parameters of the structure such as the separation and period change. These plasmonic edge states in multilayer graphene systems can be further tuned by electrical gating or chemical doping.

Determination of the quantized topological magneto-electric effect in topological insulators from Rayleigh scattering.

Topological insulators (TIs) exhibit many exotic properties. In particular, a topological magneto-electric (TME) effect, quantized in units of the fine structure constant, exists in TIs. Here, we theoretically study the scattering properties of electromagnetic waves by TI circular cylinders particularly in the Rayleigh scattering limit. Compared with ordinary dielectric cylinders, the scattering by TI cylinders shows many unusual features due to the TME effect. Two proposals are suggested to determine the TME effect of TIs simply by measuring the electric-field components of scattered waves in the far field at one or two scattering angles. Our results could also offer a way to measure the fine structure constant.

Nonlocal optical properties in periodic lattice of graphene layers.

Based on the effective medium model, nonlocal optical properties in periodic lattice of graphene layers with the period much less than the wavelength are investigated. Strong nonlocal effects are found in a broad frequency range for TM polarization, where the effective permittivity tensor exhibits the Lorentzian resonance. The resonance frequency varies with the wave vector and coincides well with the polaritonic mode. Nonlocal features are manifest on the emergence of additional wave and the occurrence of negative refraction. By examining the characters of the eigenmode, the nonlocal optical properties are attributed to the excitation of plasmons on the graphene surfaces.

Unusual electromagnetic scattering by cylinders of topological insulator.

Topological insulators (TIs) show unusual optical responses resulting from a topological magnetoelectric (TME) effect. In this paper, we study theoretically the scattering of electromagnetic waves by circular TI cylinders. In certain configurations, the bulk scattering can be suppressed, leading to strong scattering in the backward direction in both Rayleigh and Mie scattering regimes due to the TME effect. At antiresonances, an interesting filed trapping phenomenon is found which is absent in conventional dielectric cylinders.

Additional waves in the graphene layered medium.

We investigate the features of additional waves that arise in the graphene layered medium, within the framework of nonlocal effective medium model. The additional wave is manifest on the biquadratic dispersion relation of the medium and represents as a distinctive nonlocal character at long wavelength. In particular, the reflection and transmission coefficients for the nonlocal medium are underdetermined by Maxwell's boundary conditions. An additional boundary condition based on modal expansions is proposed to derive the generalized Fresnel equations, based on which the additional wave in the graphene layered medium is determined. The additional wave tends to be significant near the effective plasma frequency, near which the graphene plasmons are excited inside the medium.

Coherent fluorescence emission by using hybrid photonic-plasmonic crystals.

The spatial and temporal coherence of the fluorescence emission controlled by a quasi-two-dimensional hybrid photonic-plasmonic crystal structure covered with a thin fluorescent-molecular-doped dielectric film is investigated experimentally. A simple theoretical model to describe how a confined quasi-two-dimensional optical mode may induce coherent fluorescence emission is also presented. Concerning the spatial coherence, it is experimentally observed that the coherence area in the plane of the light source is in excess of 49 µm2, which results in enhanced directional fluorescence emission. Concerning temporal coherence, the obtained coherence time is 4 times longer than that of the normal fluorescence emission in vacuum. Moreover, a Young's double-slit interference experiment is performed to directly confirm the spatially coherent emission. This smoking gun proof of spatial coherence is reported here for the first time for the optical-mode-modified emission.

Plasmonic analog of electromagnetically induced transparency in nanostructure graphene.

Graphene has shown intriguing optical properties as a new class of plasmonic material in the terahertz regime. In particular, plasmonic modes in graphene nanostructures can be confined to a spatial size that is hundreds of times smaller than their corresponding wavelengths in vacuum. Here, we show numerically that by designing graphene nanostructures in such deep-subwavelength scales, one can obtain plasmonic modes with the desired radiative properties such as radiative and dark modes. By placing the radiative and dark modes in the vicinity of each other, we further demonstrate electromagnetically induced transparency (EIT), analogous to the atomic EIT. At the transparent window, there exist very large group delays, one order of magnitude larger than those offered by metal structures. The EIT spectrum can be further tuned electrically by applying a gate voltage. Our results suggest that the demonstrated EIT based on graphene plasmonics may offer new possibilities for applications in photonics.

Wideband trapping of light by edge states in honeycomb photonic crystals.

We study theoretically light propagations at the zigzag edge of a honeycomb photonic crystal consisting of dielectric rods in air, analogous to graphene. Within the photonic band gap of the honeycomb photonic crystal, a unimodal edge state may exist with a sharp confinement of optical fields. Its dispersion can be tuned simply by adjusting the radius of the edge rods. For the edge rods with a graded variation in radius along the edge direction, we show numerically that light beams of different frequencies can be trapped sharply in different spatial locations, yielding wideband trapping of light.