On-Chip Photonic Localization in Aharonov-Bohm Cages Composed of Microring Lattices.

Flatband localization endowed with robustness holds great promise for disorder-immune light transport, particularly in the advancement of optical communication and signal processing. However, effectively harnessing these principles for practical applications in nanophotonic devices remains a significant challenge. Herein, we delve into the investigation of on-chip photonic localization in AB cages composed of indirectly coupled microring lattices. By strategically vertically shifting the auxiliary rings, we successfully introduce a magnetic flux of π into the microring lattice, thereby facilitating versatile control over the localization and delocalization of light. Remarkably, the compact edge modes of this structure exhibit intriguing topological properties, rendering them strongly robust against disorders, regardless of the size of the system. Our findings open up new avenues for exploring the interaction between flatbands and topological photonics on integrated platforms.

Photonic skin-topological effects in microring lattices.

We investigate the non-Hermitian Hofstadter-Harper model composed of microring resonators, in which the non-Hermitian skin effect (NHSE) is particularly analyzed. The effect is achieved through the interaction between well-designed gain-loss layouts and artificial gauge fields. Remarkably, we reveal the emergence of a hybrid skin-topological effect (HSTE), where only the original topological edge modes convert to skin modes while bulk modes remain extended. By changing the distributions of gauge fields, we show the NHSE can manifest itself in bulk modes and be localized at specific edges. Using the equivalence of sites in the bulk or at boundaries to 1D SSH chains, we analyze the potential cancellation of NHSE in these configurations. Additionally, we demonstrate a new, to the best of our knowledge, type of HSTE in topological insulators which emerge at any gain-loss interfaces. The study may improve the understanding of the NHSE behavior in 2D topological systems and provide a promising avenue for tuning light propagation and localization.

Nonreciprocal topological mode conversion by encircling an exceptional point in dynamic waveguides.

The topology of exceptional points (EPs) has been revealed by taking stationary or dynamical encircling around them, which induces eigenstate exchange or chiral mode conversion. However, the conversions are usually reciprocal obeying restricted transmittances. Here we propose the concept of nonreciprocal encircling of EPs in a dynamic waveguide under complex modulation. The waveguide allows direction-dependent EPs in their quasienergy spectra due to different phase-matching conditions for opposite propagation direction. We design a closed loop that will encircle the EP in the backward direction but not in the forward direction. In this way, a nonreciprocal topological conversion is achieved as the forward transmittance from the even to odd mode significantly exceeds the backward transmittance from the odd to even mode. As a result, the forward propagation produces two modes with equal strength while the backward propagation leads to a specific mode regardless of the input. The structure is promising for making robust optical isolators.

Photonic Möbius topological insulator from projective symmetry in multiorbital waveguides.

The gauge fields dramatically alter the algebraic structure of spatial symmetries and make them projectively represented, giving rise to novel topological phases. Here, we propose a photonic Möbius topological insulator enabled by projective translation symmetry in multiorbital waveguide arrays, where the artificial π gauge flux is aroused by the inter-orbital coupling between the first (s) and third (d) order modes. In the presence of π flux, the two translation symmetries of rectangular lattices anti-commute with each other. By tuning the spatial spacing between two waveguides to break the translation symmetry, a topological insulator is created with two Möbius twisted edge bands appearing in the bandgap and featuring 4π periodicity. Importantly, the Möbius twists are accompanied by discrete diffraction in beam propagation, which exhibit directional transport by tuning the initial phase of the beam envelope according to the eigenvalues of translation operators. This work manifests the significance of gauge fields in topology and provides an efficient approach to steering the direction of beam transmission.

Stabilized Dirac points in one-dimensional non-Hermitian optical lattices.

We demonstrate stable Dirac points (DPs) in low dimensions by taking advantage of non-Hermiticity in an optical lattice composed of two coupled Su-Schrieffer-Heeger chains. The occurrence of DPs stems from the constraints of pseudo-Hermiticity and charge-conjugation parity symmetry, which force the system to support both real bands and orthogonal eigenmodes despite its non-Hermitian nature. The two characteristics hold even at spectral degeneracies of zero energy, giving rise to non-Hermitian DPs. We show that DPs are stable with the variation of dissipation since they are topological charges and can develop into nodal rings in two dimensions. Moreover, we investigate the beam dynamics around DPs and observe beam splitting with stable power evolution. The study paves the way for controlling the flow of light to aid dissipation together with high stability of energy.

Non-Hermitian flat bands in rhombic microring resonator arrays.

We investigate the flat bands in a quasi-one-dimensional rhombic array composed of evanescently coupled microring resonators (MRRs) with non-Hermitian coupling. By changing the relative position of non-Hermitian coupling in each cell, we construct topologically trivial and nontrivial flat bands, where both the real and imaginary parts of energy bands become flat and coalesce into a single band. We show the nontrivial systems are able to support topological boundary modes isolated from the flat bulk bands although there is no band gap. The elusive topology of flat bands can be geometrically visualized by plotting the trajectories of their eigenvectors on Bloch sphere based on Majorana's stellar representation (MSR). Furthermore, we perform a full wave simulation and show the characteristics of flat bands, associated compact localized modes, and boundary modes are reflected from absorption spectra and field intensity profiles. The study may find potential applications in lasers, narrowband filters, and efficient light harvesting.

Efficient Generation of Spectrum-Manipulated Few-Cycle Laser Pulses through Cascaded Dual-Chirped OPA.

The cascaded dual-chirped optical parametric amplification (DC-OPA) is presented for efficient generation of few-cycle infrared (IR) laser pulses. The input pulses are strategically chirped to optimize the phase-matching bandwidth in each nonlinear crystal, and four regions of the signal spectrum are amplified in cascaded crystals with different cutting angles, enabling flexible manipulation of the output spectrum. Broadband gain and high conversion efficiency are simultaneously achieved owing to the cascaded-crystal arrangement, the signal pulse duration of 4.2 cycles is obtained with 11.7-mJ pulse energy, corresponding to a conversion efficiency of 39.0%. The proposed scheme offers a robust and simple approach to pushing the phase-matching bandwidth limits introduced by the nonlinear crystal, which manifests great prospect in various researches involving ultrafast optics and strong-field physics.

Steering non-Hermitian skin modes by synthetic gauge fields in optical ring resonators.

We show that the synthetic gauge fields for photons provide a versatile approach to generate and control the non-Hermitian skin effect. By utilizing indirectly coupled optical ring resonator arrays with long-range couplings and on-site gain and loss, we find that the skin effect appears once the gauge field is not an integer multiple of π. In addition to tunable localization direction, the skin modes display anisotropic behaviors with frequency-dependent decay length, which can be explained by the split subregion of the generalized Brillouin zone (GBZ) and an effective model under adiabatic elimination. Through numerical simulation, we can also demonstrate exotic features in propagation effects enabled by the skin effect, including asymmetric transmission and reconfigurable accumulation interface. Our study paves the way to dynamically steer skin modes, which may find applications in laser, optical switch, and signal processing.

Square-root non-Bloch topological insulators in non-Hermitian ring resonators.

We investigate the topological skin effect in a ring resonator array which can be mapped into the square root of a Su-Schrieffer-Heeger (SSH) model with non-Hermitian asymmetric coupling. The asymmetric coupling is realized by integrating the same amount of gain and loss into the two half perimeters of linking rings that effectively couple two adjacent site rings. Such a square-root topological insulator inherits the properties from its parent Hamiltonian, which has the same phase transition points and exhibits non-Bloch features as well. We show the band closing points for open chain are different from that of periodic chain as a result of the skin effect. Moreover, the square-root insulator supports multiple topological edge modes as the number of band gaps is doubled compared to the original Hamiltonian. The full-wave simulations agree well with the theoretical analyses based on a tight-binding model. The study provides a promising approach to investigate the skin effect by utilizing ring resonators and may find potential applications in light trapping, lasers, and filters.

Efficient Mode Transfer on a Compact Silicon Chip by Encircling Moving Exceptional Points.

Exceptional points (EPs) are branch point singularities of self-intersecting Riemann sheets, and they can be observed in a non-Hermitian system with complex eigenvalues. It has been revealed recently that dynamically encircling EPs by adiabatically changing the parameters of a system composed of lossy optical waveguides could lead to asymmetric (input-output) mode transfer. However, the length of the waveguides had to be considerable to ensure adiabatic evolution. Here we demonstrate that the parameters can change adiabatically along a smaller encircling loop by utilizing moving EPs, leading to significant shortening of the structures compared to fixed EPs. Meanwhile, the mode transmittance is remarkably improved and the transfer efficiency persists at ∼90%. Moving EPs are very promising for applications such as highly integrated broadband optical switches and convertors operating at telecommunication wavelengths.

Topological bound modes in anti-PT-symmetric optical waveguide arrays.

We investigate the topological bound modes in a binary optical waveguide array with anti-parity-time (PT) symmetry. The anti-PT-symmetric arrays are realized by incorporating additional waveguides to the bare arrays, such that the effective coupling coefficients are imaginary. The systems experience two kinds of phase transition, including global topological order transition and quantum phase transition. As a result, the system supports two kinds of robust bound modes, which are protected by the global topological order and the quantum phase, respectively. The study provides a promising approach to realizing robust light transport by utilizing mediating components.

Giant Goos-Hänchen shifts in non-Hermitian dielectric multilayers incorporated with graphene.

We theoretically investigate the Goos-Hänchen (GH) shifts of optical beam in a defective photonic crystal composed of dielectric multilayers and graphene. The system is non-Hermitian and possesses exceptional points (EPs) as the scattering matrix becomes defective at the zero points of reflection. The reflective wave at EPs experiences an abrupt phase change and there the eigenvalues of scattering matrix coalesce. The GH shifts are extremely large near EPs in parametric space composed of dielectric refractive index and incident angle. The positive and negative maxima of GH shifts could be as high as 103 times of the incident wavelength. The direction of GH shifts switches at EPs and the EPs position can be readily controlled by the chemical potential of graphene. Moreover, the GH shifts should remarkably change as the incident waves impinge on the structure from opposite directions. The study of GH shifts in the graphene incorporated multilayers may find great applications in highly sensitive sensors.

Topological edge modes in non-Hermitian plasmonic waveguide arrays.

We investigate the topological edge modes of surface plasmon polaritons (SPPs) in a non-Hermitian system composed of graphene pair arrays with alternating gain and loss. The topological edge modes emerge when two topologically distinct graphene arrays are connected. The gain and loss present in the system provide additional ways to control the propagation loss and field distributions of the topological edge modes. Moreover, the existence of the topological edge modes is related to the broken parity-time (PT) symmetry. We show the beam diffraction can be steered by tuning the chemical potential of graphene. Thanks to the strong confinement of SPPs, the topological edge modes can be squeezed into a lateral width of ~λ/70. We also show such modes can be realized in lossy graphene waveguides without gain. The study provides a promising approach to realizing robust light transport and optical switches on a deep-subwavelength scale.

Exceptional points in Fano-resonant graphene metamaterials.

We investigate the optical exceptional points (EPs) in the graphene incorporated multilayer metamaterial manifesting Fano resonance. The system is non-Hermitian and possesses EPs where both the eigenvalues and eigenvectors of the Hamiltonian coalesce. In the aid of Fano resonance, the reflection may reach minimum approaching to zero, resulting in the degeneration of both eigenvalues and eigenvectors and thus the emergence of EPs. The transmission and reflection of light through the metamaterial change sharply by varying slightly the incident wavelength and chemical potential of graphene in the parameter space when encircling the EPs. In addition, the unidirectional invisibility can be achieved at EPs. The study paves a way to precisely controlling the transmission and reflection through metamaterials and may find applications in optoelectronic switches, modulators, absorbers, and optical sensors.

Enhanced plasmonic nanofocusing of terahertz waves in tapered graphene multilayers.

We investigate the plasmonic nanofocusing of terahertz waves in tapered graphene multilayers separated by dielectrics. The nanofocusing effect is significantly enhanced in the graphene multilayer taper compared with that in a single layer graphene taper due to interlayer coupling between surface plasmon polaritons. The results are optimized by choosing an appropriate layer number of graphene and the field amplitude has been enhanced by 620 folds at λ = 50 µm. Additionally, the structure can slow light to a group velocity ~1/2815 of the light speed in vacuum. Our study provides a unique approach to compress terahertz waves into deep subwavelength scale and may find great applications in terahertz nanodevices for imaging, detecting and spectroscopy.

Rabi oscillations of surface plasmon polaritons in graphene-pair arrays.

We investigate the Bloch mode conversion of surface plasmon polaritons in a periodic array of graphene pairs with each consisting of two separated parallel graphene sheets. The employment of graphene pair as a unit cell in the array yields two Bloch modes belonging to different bands. By periodically modulating the permittivity of dielectrics between graphene along the propagation direction, the interband transitions occur and the modes will alternatively couple to each other, similar to traditional Rabi oscillations in quantum systems. The indirect Rabi oscillations can also be observed through introducing transverse modulation momentum. The period of Rabi oscillations can be optimized by taking advantage of the flexible tunability of graphene. The study suggests that the structure have applications in optical switches and mode converters operating on deep-subwavelength scale.

Plasmonic absorption enhancement in periodic cross-shaped graphene arrays.

We present a wavelength tunable absorber composed of periodically patterned cross-shaped graphene arrays in the far-infrared and THz regions. The absorption of the single-layer array can essentially exceed the continuous graphene sheet by increasing the cross-arm width, even for small graphene filling ratio. As chemical potential and relaxation time increase, the absorption can be significantly enhanced. The complementary structure shows higher absorption compared to the original graphene array. Moreover, the wavelength of absorption maximum is angle-insensitive for both TE and TM polarizations. The absorption efficiency can be further improved with double layers of the cross-shaped graphene arrays, which are helpful to design dual-band and broadband absorbers.