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We investigate the excitation of surface plasmon polaritons (SPPs) using a metallic nanoaperture array illuminated by circularly polarized Laguerre-Gaussian (LG) vortex beams. The direction of SPP excitation is tunable by changing the circular polarization and topological charge of LG beams. The left- or right-handed circular polarization determines SPP propagation on either side of the nanoaperture array. Furthermore, varying the topological charge of LG beam will result in beam splitting of SPPs. We also utilize a composite nanoaperture array with different periods to achieve unidirectional excitation of SPPs. The study provides an interesting approach to control the excitation direction of SPPs and may find great applications in SPP generators and optical switches.

We study the plasmonic second-order topological modes in nanowire waveguides which are covered by monolayer graphene. The waveguide arrays are arranged in the kagome lattice. In a triangle-shaped lattice, the topological modes are localized at the corner of the triangle by tuning the spatial spacing between the different waveguides. The corner modes also depend on the corner shape, which only exist at one corner in a rhombic lattice. In addition to the corner modes, both structures also support the topological edge mode. We show that the corner modes experience a smaller modal wavelength, longer propagation distance, and smaller mode volume than the edge modes. The study may be utilized to explore the topological bound modes at the nanoscale.

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.

We investigate the topological interface modes of surface plasmon polaritons in a multilayer system composed of graphene waveguide arrays. The topological interface modes emerge when two topologically distinct graphene multilayer arrays are connected. In such multilayer system, the non-trivial topological interface modes and trivial modes coexist. By tuning the configuration of the graphene multilayer arrays, the associated non-trivial interface modes present robust against structural disorder. The total number of topological modes is related to that of graphene layers in a unit cell of the graphene multilayer array. The results provide a new paradigm for topologically protected plasmonics in the graphene multilayer arrays. The study suggests a promising approach to realize light transport and optical switching on a deep-subwavelength scale.

We investigate the light propagation in a double-waveguide coupler with imaginary-valued coupling coefficient. The imaginary coupling is realized by incorporating an additional waveguide between the coupled waveguides and considering both gain and loss. Both symmetric and asymmetric couplers with imaginary coupling are analyzed. The coupling strength can be controlled by varying the dielectric gain and loss. As the coupling is imaginary, the energy of the system is no longer conserved and the light intensities in individual waveguides should oscillate in phase. It is also found that the exceptional points can emerge in the asymmetric couplers, which are reflected from the beat length of the intensity oscillation. The study may find great applications in optical switches and splitters.

We investigate the topological bound modes in a binary waveguide array with alternating positive and negative couplings. The negative coupling is realized by incorporating additional waveguides into the bare array and suitably tuning the refractive index. We show the band structures close and Dirac point emerges at the Brillouin zone center when the absolute values of real and negative couplings are equal, indicating topological phase transition. The topological bound modes emerge at the edge of topological non-trivial arrays or at the interface of two arrays with different topologies. Moreover, we show the topological bound mode can be isolated from the trivial defect mode by tuning the coupling strength, which is reflected from wave propagation. The study provides a promising approach to realizing robust light transport.

We theoretically investigate the time-domain dynamics in a non-Hermitian electric circuit network with anti-parity-time (anti-PT) symmetry, which is consisted of amplified resonant LRC circuits connected by resistors. The effective coupling strength and on-site potential can be flexibly tuned via controlling the resistance value and resonant frequencies of LRC circuits, respectively. Therein, we are able to realize all three symmetry phases of the system, including anti-PT symmetric, intermediate, and broken phases, which are distinguished from their band structures. We show the time evolution of the envelope of voltage is analogous to discrete diffraction as a single injection stimulates more and more channels over time. Specifically, the system exhibits constant intensity diffraction at the boundary between intermediate and broken phases as the voltages at different channels are of the same value during the evolution. The reason lies in the dispersionless band structure near exceptional points (EPs) and the related linear energy amplification. The results enrich the study of discrete diffraction and are helpful to further exploration of topological phenomena in anti-PT-symmetric systems.

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.

We investigate the exceptional points (EPs) in a non-Hermitian system composed of a pair of graphene sheets with different losses. There are two surface plasmon polaritons (SPPs) modes in the graphene waveguide. By varying the distance between two graphene sheets and chemical potential of graphene, the EPs appear as the eigenvalues, that is, the wave vectors of the two modes coalesce. The cross conversion of eigenmodes and variation of geometric phase can be observed by encircling the EP in the parametric space formed by the geometric parameters and chemical potential of graphene. At the same time, a certain input SPP mode may lead to completely different output. The study paves a way to the development of nanoscale sensitive optical switches and sensors.

We investigate the spatial Goos–Hanchen (GH) shifts in one-dimensional defective photonic lattices by modulating the imaginary part of refractive index, namely, the imaginary modulation. The reflection spectra possess two singular points under imaginary modulation when the reflectance is infinite or vanishing. These two points correspond to the coherent-perfect-absorption-laser (CPA-LP) point and defect mode (MD) in the parameter space composed of the incident angle and refractive index. We show the spatial GH shifts are extremely giant in the vicinity of CPA-LP and MD as the phase of reflection coefficients dislocate. Moreover, the GH shifts are sensitive to the incident angle and the refractive index of defect. The sensitivity coefficients can reach as high as 106. The study may find potential applications in highly sensitive sensors.

We studied the topological properties of an extended Su&ndash, Schrieffer&ndash, Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.

We investigate the energy transfer of surface plasmon polaritons (SPPs) based on adiabatic passage in a non-Hermitian waveguide composed of three coupled graphene sheets. The SPPs can completely transfer between two outer waveguides via the adiabatic dark mode as the waveguides are lossless and the coupling length is long enough. However, the loss of graphene can lead to breakdown of adiabatic transfer schemes. By utilizing the coupled mode theory, we propose three approaches to cancel the nonadiabatic coupling by adding certain gain or loss in respect waveguides. Moreover, the coupling length of waveguide is remarkably decreased. The study may find interesting application in optical switches on a deep-subwavelength scale.

We investigate the mode conversion in a dielectric waveguide under spatially complex modulation, which refers to modulating both the real and imaginary parts of the dielectric permittivity. The complex modulations are applied separately in two distinct regions in the waveguide. The mode conversion can be controlled by adjusting the initial phase difference of the modulations in the two cascaded regions and by varying the phase difference of real and imaginary modulations in each region. The former is analogous to an Aharonov–Bohm (AB) phase and the latter suggests a symmetric propagation phase. Comparing to one modulated region, the cascaded modulations could benefit to realizing laser, coherent perfect absorber, and bidirectional invisibility. The study may contribute to the applications in optical switches and mode converters.

We investigate the exceptional points (EPs) in plasmonic waveguide arrays, including metallic waveguide arrays (MWAs) and graphene sheet arrays (GSAs). The EPs emerge at the boundary of strong and weak coupling ranges in both systems. The cross conversion of Bloch modes and variation of geometric phase can be observed by encircling an EP in the parametric space. We also show the Bloch modes exhibit strong absorption in the vicinity of EPs in GSAs, which originates from the enhanced longitude electric field along the propagation direction. The abnormal absorption and field enhancement also arise in ultrathin MWAs and disappear when the thickness of metal film increases. Our results may find applications in optical switches and sensors at the nanoscale.

We investigate the lateral shift of optical beam in complex dielectric multilayers with nearly parity–time (PT) symmetry. The gain and loss of dielectrics are modulated to achieve nearly PT symmetry. As light impinges on the multilayers, a laser point (LP) and exceptional points (EPs) appear in the parameter space composed of the incident angle and refractive index. The phase of reflection dislocates at the LP and EPs, inducing large lateral shift around these points. The shift can be positive and negative, and the polarities of the lateral shift convert at the LP and EPs. The shift, which is sensitive to the incident angle and refractive index of dielectrics, could be tuned flexibly. The study may find potential applications in highly sensitive sensors.

We theoretically investigate the Goos-Hanchen (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.

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.

We investigate the switching between two surface plasmon polariton modes in a non-Hermitian system composed of a pair of graphene sheets using topological operations. The topological operation is implemented by suitably designing the waveguide geometry and the chemical potential of graphene, which is equivalent to changing the system parameters along a closed loop in the parameter space. Efficient and robust mode switching takes place as the loop encloses an exceptional point and the wave experiences a sufficiently large propagation length. Moreover, we show this mode switching is chiral, in the sense that the output modes are different for choosing different loop directions. The study provides a promising approach to robust mode switching on a deep-subwavelength scale.

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.

We explored exceptional points (EPs) in one dimensional non-Hermitian photonic crystals incorporated with a defect. The defect was asymmetric with respect to the center. Two EPs could be derived by modulating the normalized frequency and the gain-loss coefficient of defect. The reflection coefficient complex phase changed dramatically around EPs, and the change in complex phase was &pi, at EPs. The electric field of EPs was mainly restricted to the defect, which can induce a giant Goos&ndash, H&auml, nchen (GH) shift. Moreover, we found a coherent perfect absorption-laser point (CPA-LP) in the structure. A giant GH shift also existed around the CPA-LP. The study may have found applications in highly sensitive sensors.

We investigate the topological bound modes of surface plasmon polaritons (SPPs) in a graphene pair waveguide array. The arrays are with uniform inter-layer and intra-layer spacings but the chemical potential of two graphene in each pair are different. The topological bound modes emerge when two arrays with opposite sequences of chemical potential are interfaced, which are analogous to Jackiw-Rebbi modes with opposite mass. We show the topological bound modes can be dynamically controlled by tuning the chemical potential, and the propagation loss of topological bound modes can be remarkably reduced by decreasing the chemical potential. Thanks to the strong confinement of graphene SPPs, the modal wavelength of topological bound modes can be squeezed as small as 1/70 of incident wavelength. The study provides a promising approach to realizing robust light transport beyond diffraction limit.

We investigate the optical bistability of graphene in parity-time-symmetric (PT-symmetric) photonic lattices incorporated with a defect at terahertz frequencies. The field localization of the defect mode can strengthen the nonlinearity of graphene to achieve low-threshold bistability. The nonlinearity is further enhanced, and the bistability threshold decreases, by increasing the gain-loss factor in the PT-symmetric structure. The interval of upper and lower bistability thresholds is broadened as the exceptional points split. Moreover, we show the phase transition between bistability and nonbistability by modulating the incident wavelength and chemical potential of graphene. The study may find great applications in all-optical switches and optical storage.

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.

We investigate the frequency conversion in a waveguide by dynamically modulating the real and imaginary parts of permittivity, namely, the complex modulation. A single frequency of incident light could convert into many discrete frequencies with equivalent intervals, which is analogous to discrete diffraction in spatial waveguide arrays. We develop a coupled mode theory to analyze the frequency conversion process and show the complex modulation results in a complex-valued coupling coefficient between adjacent frequency channels. The coupling strength can be flexibly tuned by controlling the modulation amplitudes. Moreover, the complex coupling becomes asymmetric with increasing the modulation phase difference between the real and imaginary parts of permittivity. The capability to control the complex coupling leads to new features in discrete diffraction in the frequency dimension, including the unidirectional transport and equalization of light intensities at different channels. The study may find interesting applications in frequency comb generators and frequency controllers.

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.