Bound states in the continuum in divided triangular hole metasurfaces.

We investigate the bound states in the continuum (BICs) in dielectric metasurfaces consisting of a two-part divided triangular hole in the unit cell of a square lattice, with emphasis on the generation, splitting, and merging of BICs. At the smallest height ratio between the upper triangular and the lower trapezoidal holes, the accidental BIC with an extremely large quality factor emerges on an isolated dispersion band at the Brillouin zone center, which is recognized as a polarization singularity (V point) with an integer topological charge. As the height ratio increases, the accidental BIC is split into a pair of circularly polarized states, which are polarization singularities (C points) with half-integer topological charges. The two states depart from each other to a maximum distance, and then approach each other as the height ratio continues to change. They finally merge to another polarization singularity (V point) with an integer topological charge, which is identified as the Friedrich-Wintgen BIC that occurs near the avoided crossing between two interacting dispersion bands.

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.

Bound states in the continuum in anisotropic photonic crystal slabs.

We investigate the bound states in the continuum (BICs) in photonic crystal slabs composed of alternating anisotropic and isotropic dielectric materials. According to the orientation of optical axis plane, three different configurations are proposed for analyzing various types of BICs, associated with extremely large quality factors and vanishing spectral linewidths. In particular, symmetry-protected (SP) BICs exist at the Brillouin zone center for zero rotation angle of the optical axis, which exhibit antisymmetric field patterns that are decoupled from the symmetric radiating fields. Accidental BICs and Friedrich-Wintgen (FW) BICs also occur at the Brillouin zone center for particular rotation angles of the optical axis. The former emerge on isolated bands with quasi-symmetric or quasi-antisymmetric field patterns, while the latter appear near the avoided crossing between two dispersion bands. At off the Brillouin zone center, SP BICs do not exist while accidental BICs and FW BICs appear at particular optical axis rotation angles, with similar features but somewhat more asymmetric field patterns than those at the Brillouin zone center.

Bound states in the continuum in asymmetric dual-patch metasurfaces.

We investigate the bound states in the continuum (BICs) in dielectric metasurfaces consisting of asymmetric dual rectangular patches in the unit cell of a square lattice. Various types of BICs are identified in the metasurface at normal incidence, associated with very large quality factors and vanishing spectral linewidths. In particular, symmetry-protected (SP) BICs occur when the four patches are fully symmetric, which exhibit antisymmetric field patterns that are decoupled from the symmetric incident waves. By breaking the symmetry of patch geometry, the SP BICs degrade to quasi-BICs that are characterized by Fano resonance. Accidental BICs and Friedrich-Wintgen (FW) BICs occur when the asymmetry is introduced in the upper two patches, while holding the lower two patches symmetric. The accidental BICs occur on isolated bands when the linewidth of either the quadrupole-like mode or LC-like mode vanishes by tuning the upper vertical gap width. The FW BICs appear when the avoided crossing is formed between the dispersion bands of dipole-like and quadrupole-like modes by tuning the lower vertical gap width. At a special asymmetry ratio, the accidental BICs and FW BICs may appear in the same transmittance or dispersion diagram, accompanied with the concurrence of dipole-like, quadrupole-like, and LC-like modes.

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.

Photonic Weyl semimetals in pseudochiral metamaterials.

We investigate the photonic topological phases in pseudochiral metamaterials characterized by the magnetoelectric tensors with symmetric off-diagonal chirality components. The underlying medium is considered a photonic analogue of the type-II Weyl semimetal featured with two pairs of tilted Weyl cones 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 vacuum and the pseudochiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes are tangent to both the vacuum light cone and the Weyl cones, which form two pairs of crossing surface sheets that are symmetric about the transverse axes. At the Weyl frequency, the surface modes that connect the Weyl points form four Fermi arc-like states as line segments. Topological features of the pseudochiral metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

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.

Hybrid modes in gold nanoslit arrays on Bragg nanostructures and their application for sensitive biosensors.

In this work, we present high-performance surface plasmonic sensors using gold nanostructures and Bragg photonic structures. The gold film on the Bragg structure provides Tamm plasmon states (TPs). The Fano coupling between higher order TPs and Bloch-wave surface plasmon polariton (BW-SPP) on the gold nanoslit array results in a new hybrid Tamm-plasmon mode. Using finite-difference time-domain calculations, we demonstrate that the hybrid mode has the advantages of high surface sensitivity of BW-SPP mode and high resonant quality of Tamm state. The calculated plasmonic field distribution shows that the hybrid mode has a similar evanescent distribution with BW-SPP mode on gold surface and TPs field in the Bragg structure. The experimental results verify that the hybrid mode has one hundred times higher wavelength sensitivity than the Tamm state. The figure of merit of the hybrid mode is five times better than the BW-SPP mode in conventional nanoslit arrays. The real-time sensorgram further confirms that the hybrid mode has a much higher sensitivity and better signal to noise ratios in the biomolecular interaction measurement.

Dual Gold-Nanoslit Electrodes for Ultrasensitive Detection of Antigen-Antibody Reactions in Electrochemical Surface Plasmon Resonance.

We present the use of surface charges in dual gold-nanoslit electrodes to improve the surface plasmon resonance (SPR) detection limit by several orders of magnitude. The SPR is directly generated by gold-nanoslit arrays in the two electrodes. The SPR shifts for both nanoslit arrays are measured simultaneously with a simple hyperspectral setup. When biomolecules are captured by specific antibodies on the dual electrodes, the surface charge is changed during the electrochemical process due to the increase in surface impedance. The push-pull-type electrodes generate opposite surface charges. Using the differences in both spectral shifts, the change in surface charge is detected sensitively. We demonstrate that using a [Fe(CN)6]3-/4- redox process after antigen-antibody interactions, the dual nanoslit electrodes show an enhancement of the detection limit from 1 µg/mL to 10 pg/mL.

Photonic topological insulators in bianisotropic metamaterials.

We analyze the photonic topological phases in bianisotropic metamaterials characterized by a lossless and reciprocal magnetoelectric tensor. The underlying medium is considered a topological insulator that supports a pair of counterpropagating helical edge states. By introducing the pseudospin basis, the photonic system can be described by 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 bianisotropic media with opposite chirality exist in their common band gap, which are represented by elliptic or hyperbolic equations. In particular, two branches of hyperbolic surfaces are degenerate at the frequency where the chiral nihility occurs, which depict the helical nature of edge states between two distinct topological phases. Topological features of the bianisotropic metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Self-referencing biosensors using Fano resonance in periodic aluminium nanostructures.

Surface plasmon resonance (SPR) is an important technique for real-time and label-free detection of specific binding biomolecules. However, conventional SPR signals come from both the surface binding biomolecules and the variation in the bulk refractive index. This work demonstrates that Fano resonance in an aluminum capped nanoslit array has the ability to remove the signal of bulk refractive index changes from the SPR signal. As compared to gold nanostructures, the aluminum nanostructure provides an asymmetrical Fano resonance with clear peak and dip wavelengths. The peak wavelength is close to the grating resonance condition. The evanescent depth at the peak wavelength is up to several microns. The dip wavelength comes from the SPR effect. The evanescent depth at the dip wavelength is about 300 nm. By simultaneously measuring the shifts of peaks and the dip wavelengths, the variation in the bulk refractive index can be removed and only the biolayer thickness is measured. The finite-difference time-domain calculation shows that the 470 nm-period nanoslit array with 90 and 70 nm slit depths has the optimal thickness sensitivity. In this experiment, a simple multispectral imaging system is developed for multiple bio-interaction measurements. The measured results verify that the bulk refractive index changes can be removed and the surface biomolecular interactions can be directly obtained without the need of a reference channel.

Parity-time phase transition in photonic crystals with [Formula: see text] symmetry.

We investigate the parity-time (PT) phase transition in photonic crystals with [Formula: see text] symmetry, with balanced gain and loss on dielectric rods in the triangular lattice. A two-level non-Hermitian model that incorporates the gain and loss in the tight-binding approximation was employed to describe the dispersion of the PT symmetric system. In the unbroken PT phase, the double Dirac cone feature associated with the [Formula: see text] symmetry is preserved, with a frequency shift of second order due to the presence of gain and loss. The helical edge states with real eigenfrequencies can exist in the common band gap for two topologically distinct lattices. In the broken PT phase, the non-Hermitian perturbation deforms the dispersion by merging the frequency bands into complex conjugate pairs and forming the exceptional contours that feature the PT phase transition. In this situation, the band gap closes and the edge states are mixed with the bulk states.

Photonic topological semimetals in bianisotropic metamaterials.

We analyze the photonic topological phases in bianisotropic metamaterials characterized by a chirality tensor with zero trace. We found that the strength of chirality component determines the topological character of the metamaterial. The underlying medium can be considered as a topological semimetal with the nontrivial band gap in the momentum space. The topological properties are described by the spin-orbit Hamiltonians with spin 1 and characterized by the nonzero topological invariants. In particular, photonic quantum Hall states exist when the longitudinal chirality component exceeds the permittivity, whereas photonic quantum spin Hall states are present when the chiral nihility occurs. Considering the dispersion in the frequency domain, the bianisotropic metamaterial is regarded as a photonic Weyl system that supports the Weyl points and Fermi arcs. The topological features are further illustrated with the robust transport of edge states at an irregular boundary of the metamaterial.

Photonic topological phases in dispersive metamaterials.

We analyze the photonic topological phases in dispersive metamaterials which satisfy the degenerate condition at a reference frequency. The electromagnetic duality allows for the hybrid modes to be decoupled and described by the spin-orbit Hamiltonians with pseudospin 1, which result in nonzero spin Chern numbers that characterize the topological phases. In particular, the combined Hamiltonian of the hybrid modes complies with a fermionic-like pseudo time-reversal symmetry that ensures the Kramers degeneracy, leading to the topological protection of helical edge states. The transverse spin generated by the evanescent surface waves is perpendicular to the wave vector, which exhibits the spin-momentum locking as in the surface states for three-dimensional topological insulators. The topological properties of the helical edge states are further illustrated with the robust transport of a pair of counterpropagating surface waves with opposite polarization handedness at an irregular boundary of the metamaterial.

Chiral surface waves on hyperbolic-gyromagnetic metamaterials.

The existence of surface waves at the boundary of a hyperbolic-gyromagnetic metamaterial is studied. The surface waves, which are analytically formulated in terms of the eigenfields, appear in the spatial gap between two elliptically polarized bulk modes of the metamaterial. The surface waves are chiral in the sense that they propagate unidirectionally along the edge and reverse the propagation direction upon changing sign of the gyrotropic parameter. The topological feature of the chiral surface waves can be characterized by the Berry phases of the bulk modes, showing the bulk-edge correspondence for the underlying medium. The unidirectionality of the chiral surface waves and their immunity to disorder are further demonstrated by the propagation of electromagnetic waves around sharp corners.

Wave propagation in bianisotropic metamaterials: angular selective transmission.

We investigate the basic features of wave propagation in bianisotropic metamaterials characterized by asymmetric magnetoelectric tensors with zero diagonal elements. The wave propagation is described by a biquadratic dispersion relation with two elliptically polarized eigenwaves. In particular, the bianisotropic media may possess a hybrid character of the elliptic and hyperbolic dispersions. For a wave incident from vacuum onto a bianisotropic medium, there exist an ordinary and an inversion critical angle, leading to angular selective transmission. A standard and a complementary type of angular selective transmissions are illustrated with the incidence of Gaussian beams based on Fourier integral formulation.

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.

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.

Spatial dispersion and nonlocal effective permittivity for periodic layered metamaterials.

The feature of spatial dispersion in periodic layered metamaterials is theoretically investigated. An effective medium model is proposed to derive the nonlocal effective permittivity tensor, which exhibits drastic variations in the wave vector domain. Strong spatial dispersion is found in the frequency range where surface plasmon polaritons are excited. In particular, the nonlocal effect gives rise to additional waves that are identified as the bonding or antibonding modes with symmetric or antisymmetric surface charge alignments. Spatial dispersion is also manifest on the parabolic-like dispersion, a non-standard type of dispersion in the medium. The associated negative refraction and backward wave occur even when the effective permittivity components are all positive, which is considered a property not available in the local medium.

Negative refraction and backward wave in pseudochiral mediums: illustrations of Gaussian beams.

We investigate the phenomena of negative refraction and backward wave in pseudochiral mediums, with illustrations of Gaussian beams. Due to symmetry breaking intrinsic in pseudochiral mediums, there exist two elliptically polarized eigenwaves with different wave vectors. As the chirality parameter increases from zero, the two waves begin to split from each other. For a wave incident from vacuum onto a pseudochiral medium, negative refraction may occur for the right-handed wave, whereas backward wave may appear for the left-handed wave. These features are illustrated with Gaussian beams based on Fourier integral formulations for the incident, reflected, and transmitted waves. Negative refraction and backward wave are manifest, respectively, on the energy flow in space and wavefront movement in time.