PT Symmetry Induced Rings of Lasing Threshold Modes Embedded with Discrete Bound States in the Continuum

It is well known that spatial symmetry in a photonic crystal(PhC)slab is capable of creating bound states in the continuum(BICs),which can be characterized by topological charges of polarization vortices.Here,we show that when a PT-symmetric perturbation is introduced into the PhC slab,a new type of BICs(pt-BICs)will arise from each ordinary BIC together with the creation of rings of lasing threshold modes with pt-BICs embedded in these rings.Different from ordinary BICs,the Q-factor divergence rate of a pt-BIC is reduced and anisotropic in momentum space.Also,pt-BICs can even appear at off-high symmetry lines of the Brillouin zone.The pt-BICs also carry topological charges and can be created or annihilated with the total charge conserved.A unified picture on pt-BICs and the associated lasing threshold modes is given based on the temporal coupled mode theory.Our findings reveal the new physics arising from the interplay between PT symmetry and BIC in PhC slabs.

Finite barrier bound state

A boundary mode localized on one side of a finite-size lattice can tunnel to the opposite side which results in unwanted couplings.Conventional wisdom tells that the tunneling probability decays exponentially with the size of the system which thus requires many lattice sites before eventually becoming negligibly small.Here we show that the tunneling probability for some boundary modes can apparently vanish at specific wavevectors.Thus,similar to bound states in the continuum,a boundary mode can be completely trapped within very few lattice sites where the bulk bandgap is not even well-defined.More intriguingly,the number of trapped states equals the number of lattice sites along the normal direction of the boundary.We provide two configurations and validate the existence of this peculiar finite barrier-bound state experimentally in a dielectric photonic crystal at microwave frequencies.Our work offers extreme flexibility in tuning the coupling between localized states and channels as well as a new mechanism that facilitates unprecedented manipulation of light.

On-chip single-photon chirality encircling exceptional points

Exceptional points(EPs),which are typically defined as the degener-acy points of a non-Hermitian Hamiltonian,have been investigated in various physical systems such as photonic systems.In particular,the intriguing topological structures around EPs have given rise to novel strategies for manipulating photons and the underlying mechanism is especially useful for on-chip photonic applications.Although some on-chip experiments with the adoption of lasers have been reported,EP-based photonic chips working in the quantum regime largely re-main elusive.In the current work,a single-photon experiment was proposed to dynamically encircle an EP in on-chip photonic waveg-uides possessing passive anti-parity-time symmetry.Photon coinci-dences measurement reveals a chiral feature of transporting single photons,which can act as a building block for on-chip quantum de-vices that require asymmetric transmissions.The findings in the cur-rent work pave the way for on-chip experimental study on the physics of EPs as well as inspiring applications for on-chip non-Hermitian quantum devices.

Dynamically encircling an exceptional point in antiparity-time symmetric systems:asymmetric mode switching for symmetry-broken modes

Dynamically encircling an exceptional point(EP)in parity-time(PT)symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes.The counterpart symmetry-broken modes(i.e.,each eigenmode is localized in one waveguide only),which are more useful for applications such as on-chip optical signal processing,exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching.Here,we solve this problem by resorting to anti-parity-time(anti-PT)symmetric systems and utilizing their unique topological structure,which is very different from that of PT-symmetric systems.We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting point in the PT-broken phase results in chiral dynamics.As a result,symmetry-broken modes can be used for asymmetric mode switching,which is a phenomenon and application unique to anti-PT-symmetric systems.We perform experiments to demonstrate the new wave-manipulation scheme,which may pave the way towards designing on-chip optical systems with novel functionalities.

Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals

It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups.We discover that in an AB-layerstacked photonic crystal composed of anisotropic dielectrics,the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line.The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell’s equations.The bands with a constant kz and iso-frequency surfaces near a nexus point both disperse as a spin-1 Dirac-like cone,giving rise to exotic transport features of light at the nexus point.We show that spin-1 conical diffraction occurs at the nexus point,which can be used to manipulate the charges of optical vortices.Our work reveals that Maxwell’s equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and hence paves the way to finding novel topological nodal structures unique to photonic systems.

Dirac-like cone-based electromagnetic zero-index metamaterials

Metamaterials with a Dirac-like cone dispersion at the center of the Brillouin zone behave like an isotropic and impedance-matched zero refractive index material at the Dirac-point frequency.Such metamaterials can be realized in the form of either bulk metamaterials with efficient coupling to free-space light or on-chip metamaterials that are efficiently coupled to integrated photonic circuits.These materials enable the interactions of a spatially uniform electromagnetic mode with matter over a large area in arbitrary shapes.This unique optical property paves the way for many applications,including arbitrarily shaped high-transmission waveguides,nonlinear enhancement,and phase mismatch-free nonlinear signal generation,and collective emission of many emitters.This review summarizes the Dirac-like cone-based zero-index metamaterials’fundamental physics,design,experimental realizations,and potential applications.

Pseudospin-1 Physics of Photonic Crystals

We review some recent progress in the exploration of pseudospin-1 physics using dielectric photonic crystals(PCs).We show some physical implications of the PCs exhibiting an accidental degeneracy induced conical dispersion at theΓpoint,such as the realization of zero refractive index medium and the zero Berry phase of a loop around the nodal point.Te photonic states of such PCs near the Dirac-like point can be described by an efective spin-orbit Hamiltonian of pseudospin-1.Te wave propagation in the positive,negative,and zero index media can be unifed within a framework of pseudospin-1 description.A scale change in PCs results in a rigid band shif of the Dirac-like cone,allowing for the manipulation of waves in pseudospin-1 systems in much the same way as applying a gate voltage in pseudospin-1/2 graphene.Te transport of waves in pseudospin-1 systems exhibits many interesting phenomena,including super Klein tunneling,robust supercollimation,and unconventional Anderson localization.Te transport properties of pseudospin-1 systems are distinct from their counterparts in pseudospin-1/2 systems,which will also be presented for comparison.

Intrinsic in-plane nodal chain and generalized quaternion charge protected nodal link in photonics

Nodal lines are degeneracies formed by crossing bands in three-dimensional momentum space.Interestingly,these degenerate lines can chain together via touching points and manifest as nodal chains.These nodal chains are usually embedded in two orthogonal planes and protected by the corresponding mirror symmetries.Here,we propose and demonstrate an in-plane nodal chain in photonics,where all chained nodal lines coexist in a single mirror plane instead of two orthogonal ones.Nodal lines are degeneracies formed by crossing bands in three-dimensional momentum space.Interestingly,these degenerate lines can chain together via touching points and manifest as nodal chains.These nodal chains are usually embedded in two orthogonal planes and protected by the corresponding mirror symmetries.Here,we propose and demonstrate an in-plane nodal chain in photonics,where all chained nodal lines coexist in a single mirror plane instead of two orthogonal ones.The chain point is stabilized by the intrinsic symmetry that is specific to electromagnetic waves at theГpoint of zero frequency.By adding another mirror plane,we find a nodal ring that is constructed by two higher bands and links with the in-plane nodal chain.The nodal link in momentum space exhibits non-Abelian characteristics on a C_(2)T-invariant plane,where admissible transitions of the nodal link structure are determined by generalized quaternion charges.Through near-field scanning measurements of bi-anisotropic metamaterials,we experimentally mapped out the in-plane nodal chain and nodal link in such systems.The chain point is stabilized by the intrinsic symmetry that is specific to electromagnetic waves at the r point of zero frequency.By adding another mirror plane,we find a nodal ring that is constructed by two higher bands and links with the in-plane nodal chain.The nodal link in momentum space exhibits non-Abelian characteristics on a C2T-invariant plane,where admissible transitions of the nodal link structure are determined by generalized quaternion charges.Through near-field scanning measurements of bi-anisotropic metamaterials,we experimentally mapped out the in-plane nodal chain and nodal link in such systems.

Photonic crystals and topological photonics

The idea of photonic crystals and photonic band gap was first introduced by both Yablonovitch[1]and John in 1987[2].Photonic crystals are man-made periodic optical media in which the dispersion of light is strongly modified due to the scattering of periodically arranged dielectric or metal inclusions in the unit cell.Photonic band gaps,a frequency range in which light cannot propagate,can form as a consequence of Bragg scattering or the resonance of the inclusions in the unit cell.The existence of band gaps means that photonic crystals can serve as low-loss distributed feedback mirrors and as such,they can confine light and can be used to realize high fidelity resonant cavities that can facilitate the observation of quantum electronics phenomena.The application of such ideas to realize strong coupling between photon and exciton is achieved using planar dielectric Si periodic structures[3].When combined with a gain material,photonic crystals are obviously good platforms to realize lasing and indeed photonic crystal based lasers have attracted great interest in past three decades.The technical challenges and progress in distributed feedback organic lasers based on photonic crystals are discussed and reviewed by Fu and Zhai[4].For practical applications,nonlinear photonic crystals with different superlattices has been successfully used in quasi-phase matching and nonlinear diffraction harmonic generation.This is reviewed by Li and Ma[5].