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Parity‐time (PT) and anti‐parity‐time (anti‐PT) symmetries have provided important guiding principles in the research of non‐Hermitian physics. However, realizations of anti‐PT symmetry in photonic systems usually rely on optical nonlinearities and indirect‐coupling approaches. Here, they apply the channel interference principle mediated by synthetic gauge‐flux biasing in open‐cavity systems to construct anti‐PT symmetries. It is shown that a specific π‐flux biasing into a looped‐resonator array can force a frequency degeneracy between pairwise Bloch modes therein. By further coupling the array into two external waveguides with tailored positions of ports, the system near the degeneracy point can be described by an anti‐PT‐symmetric Hamiltonian. When a real gauge‐flux detuning is introduced, the system undergoes a spontaneous transition between anti‐PT and anti‐PT‐broken phases, through which the two extreme cases of complete channel‐drop tunneling and complete tunneling suppression can be switched. Finally, by superimposing a PT‐symmetric term onto the anti‐PT‐symmetric Hamiltonian via applying an imaginary gauge‐flux biasing, extreme channel‐drop amplifying effects can be further realized by exciting the "lasing" mode under the critical‐coupling condition. The work bridges the physical connection between synthetic gauge field and anti‐PT symmetry. This paradigm may also find many applications from optical routing, and switching to buffering and amplifying on a chip–scale platform. [ABSTRACT FROM AUTHOR]

Dynamic localization (DL) refers to a wavefunction confinement effect of electrons in periodic lattices under an ac electric field driving. Recent studies have transplanted DLs from electronic to photonic systems using periodically curved waveguide lattices, where the ac electric field is mimicked by the waveguide's bending curvature. However, due to the severe limitations of bending losses and poor tunability for highly curved, arbitrarily shaped waveguides, present studies mainly focus on DL under the simplest sinusoidal‐wave driving; its extension to an arbitrary‐wave driving remains challenging. Here, by constructing a synthetic temporal lattice with a coupled fiber‐loop circuit, the limitations of spatially curved waveguides are circumvented and generalized DLs are experimentally demonstrated under arbitrary‐wave driving. First, by applying band‐collapse criteria, the general conditions for the driving field's symmetry to achieve DLs are revealed. Then, two representative even‐function driving fields of square‐ and triangle‐waveforms are chosen, and wave‐packet revivals are observed as signatures of DLs. As a counter‐example, the breakdown of DL is also verified using odd‐function driving field of sawtooth‐waveform. The work reveals the conditions for realizing generalized DLs and experimentally verifies them using synthetic lattice schemes. This paradigm may find potential applications in versatile temporal‐waveform reshaping, pulse manipulations for optical communications, and signal processing. [ABSTRACT FROM AUTHOR]

The rapid acquisition of high-resolution spatial distribution of soil organic matter (SOM) at the field scale is essential for precision agriculture. The UAV imaging hyperspectral technology, with its high spatial resolution and timeliness, can fill the research gap between ground-based monitoring and remote sensing. This study aimed to test the feasibility of using UAV hyperspectral data (400–1000 nm) with a small-sized calibration sample set for mapping SOM at a 1 m resolution in typical low-relief black soil areas of Northeast China. The experiment was conducted in an approximately 20 ha field. For calibration, 20 samples were collected using a 100 × 100 m grid sampling strategy, while 20 samples were randomly collected for independent validation. UAV captured hyperspectral images with a spatial resolution of 0.05 × 0.05 m. The extracted spectra within every 1 × 1 m were then averaged to represent the spectra of that grid; this procedure was also performed across the whole field. Upon applying various spectral pretreatments, including absorbance conversion, multiple scattering correction, Savitzky–Golay smoothing filtering, and first-order differentiation, the absolute maximum values of the correlation coefficients of the spectra for SOM increased from 0.41 to 0.58. Importance analysis from the optimal random forest (RF) model showed that the characterized bands of SOM were located in the 450–600 and 750–900 nm regions. When the RF model was used, the UAV hyperspectra data (UAV-RF) were able to successfully predict SOM, with an R2 of 0.53 and RMSE of 1.48 g kg−1. The prediction accuracy was then compared with that obtained using ordinary kriging (OK) and the RF model based on proximal sensing (PS-RF) with the same number of calibration samples. However, the OK method failed to predict the SOM accuracy (RMSE = 2.17 g kg−1; R2 = 0.02) due to a low sampling density. The semi-covariance function was unable to describe the spatial variability of SOM effectively. When the sampling density was increased to 50 × 50 m, OK successfully predicted SOM, with RMSE = 1.37 g kg−1 and R2 = 0.59, and its results were comparable to those of UAV-RF. The prediction accuracy of PS-RF was generally consistent with that of UAV-RF, with RMSE values of 1.41 g kg−1 and 1.48 g kg−1 and R2 values of 0.57 and 0.53, respectively, which indicated that SOM prediction based on UAV-RF is feasible. Additionally, compared with the PS platforms, the UAV hyperspectral technology could simultaneously provide spectral information of tens or even hundreds of continuous bands and spatial information at the same time. This study provides a reference for further research and development of UAV hyperspectral techniques for fine-scale SOM mapping using a small number of samples. [ABSTRACT FROM AUTHOR]

In many areas, such as plains and gently undulating terrain, easy-to-measure soil-forming factors such as landform and vegetation do not co-vary with soil conditions across space to the level that they can be effectively used in digital soil mapping. A challenging problem is how to develop a new environmental variable that co-varies with soil spatial variation under these situations. This study examined the idea that change patterns (dynamic feedback patterns) of the land surface, such as those captured daily by remote sensing images during a short period (6-7 d) after a major rain event, can be used to differentiate soil types. To examine this idea, we selected two study areas with different climates: one in northeastern China and the other in northwestern China. Images from the Moderate Resolution Imaging Spectrotadiometer (MODIS) were used to capture land surface feedback. To measure feedback dynamics, we used spectral information divergence (SID). Results of an independent-samples t-test showed that there was a significant difference in SID values between pixel pairs of the same soil subgroup and those of different subgroups. This indicated that areas with different soil types (subgroup level) exhibited significantly different dynamic feedback patterns, and areas within the same soil type have similar dynamic feedback patterns. It was also found that the more similar the soil types, the more similar the feedback patterns. These findings could lead to the development of a new environmental covariate that could be used to improve the accuracy of soil mapping in low-relief areas. Abbreviations: MODIS, Moderate Resolution Imaging Spectroradiometer; NDVI, normalized difference vegetation index; SID, spectral information divergence. doi: 10.2136/sssaj2009.0411

This paper presents a knowledge discovery approach to extracting knowledge from area-class resource maps. Prototype theory forms the basis of the approach which consists of two major components: (1) a scheme for organizing knowledge used in categorizing geographic entities which allows for the modeling of indeterminate boundaries and non-uniform memberships within categories; and (2) a data mining method using the Expectation Maximization (EM) algorithm for extracting such knowledge from area-class maps. A case study on knowledge discovery from a soil map demonstrates the details of the approach. The study shows that knowledge for classifying geographic entities with indeterminate boundaries is embedded in area-class maps and can be extracted through data mining; and that continuous spatial variation of geographic entities can be better modeled if the knowledge discovery process retains knowledge of within-class variations as well as transitions between classes., Introduction The development of geographic knowledge discovery arose out of the need to intelligently and automatically transform geographic data into information and synthesize geographic knowledge (Yuan et al. 2001). Research [...]

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. [ABSTRACT FROM PUBLISHER]

We propose a graphene Ramsey interferometer to study the non-reciprocal phase shift and modulation of surface plasmon polaritons (SPPs). The Ramsey interferometer is constructed by a spatially separated graphene pair that can support two SPP modes. By dynamically modulating the surface conductivity of graphene, the SPP modes will undergo uncompleted cross conversion and an additional phase shift. When adopting two modulation regions in the interferometer, the converted mode will jump back with a nonreciprocal phase shift which can be controlled by the modulation length or phase. The SPP mode of phase shift will interfere with the throughout unconverted one, resulting in arbitrary power arrangement between the two SPP modes. The study may find great applications in plasmonic isolators, phase detectors, and one-way mode converters. [ABSTRACT FROM PUBLISHER]

Critical source areas (CSAs), characterized by severe soil erosion and high sediment yield, are considered to have a high priority for conservation. How to identify CSAs and assess the effectiveness of conservation practices is a key issue in site-specific watershed management. The Soil and Water Assessment Tool (SWAT) model is a useful tool for site-specific conservation practices design and several studies have attempted to identify CSAs based on watershed models. However, limited research has reported about the effectiveness of conservation practices targeting CSAs. The aim of this study was to assess the effectiveness of conservation pracrices targeted on CSAs using the SWAT model. CSA was firstly identified based on the 4-year average yearly erosion of each HRU. Appropriate soil conservation practices were then designed for the CSAs. A scenario with conservation practices for the whole watershed was also established as the contrasting counter parts scheme and then compared to the outcome of CSA-targeted conservation pracrices. The result shows that SWAT can accurately simulate sediment yield in the study area. CSAs were mainly located in slope farmland areas and steep gullies, coinciding with the distribution of land use and slope. The identified CSA covered 20% of the HRUs and contributed on average 44% of sediment yield. Conservation practices targeting CSAs had higher sediment reduction effectiveness (24 115 t km-2 y-1) than conservation practice covering the whole watershed (20 290 t km-2 y-1). Thus conservation practices targeting CSAs are more effective than broad conservation practices. We conclude that soil conservation practices focusing on CSAs do increase sediment reduction effectiveness. Targeting the placement of soil conservation practices based on the CSAs concept will assist water quality control in watersheds. [ABSTRACT FROM AUTHOR]

Many researchers have examined the impact of detailed soil spatial information on hydrological modelling due to the fact that such information serves as important input to hydrological modelling, yet is difficult and expensive to obtain. Most research has focused on the effects at single scales; however, the effects in the context of spatial aggregation across different scales are largely missing. This paper examines such effects by comparing the simulated runoffs across scales from watershed models based on two different levels of soil spatial information: the 10-m-resolution soil data derived from the Soil-Land Inference Model (SoLIM) and the 1:24000 scale Soil Survey Geographic (SSURGO) database in the United States. The study was conducted at three different spatial scales: two at different watershed size levels (referred to as full watershed and sub-basin, respectively) and one at the model minimum simulation unit level. A fully distributed hydrologic model (WetSpa) and a semi-distributed model (SWAT) were used to assess the effects. The results show that at the minimum simulation unit level the differences in simulated runoff are large, but the differences gradually decrease as the spatial scale of the simulation units increases. For sub-basins larger than 10 km2 in the study area, stream flows simulated by spatially detailed SoLIM soil data do not significantly vary from those by SSURGO. The effects of spatial scale are shown to correlate with aggregation effect of the watershed routing process. The unique findings of this paper provide an important and unified perspective on the different views reported in the literature concerning how spatial detail of soil data affects watershed modelling. Different views result from different scales at which those studies were conducted. In addition, the findings offer a potentially useful basis for selecting details of soil spatial information appropriate for watershed modelling at a given scale. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In a spatio-temporal data set, identifying spatio-temporal clusters is difficult because of the coupling of time and space and the interference of noise. Previous methods employ either the window scanning technique or the spatio-temporal distance technique to identify spatio-temporal clusters. Although easily implemented, they suffer from the subjectivity in the choice of parameters for classification. In this article, we use the windowed kth nearest (WKN) distance (the geographic distance between an event and its kth geographical nearest neighbour among those events from which to the event the temporal distances are no larger than the half of a specified time window width [TWW]) to differentiate clusters from noise in spatio-temporal data. The windowed nearest neighbour (WNN) method is composed of four steps. The first is to construct a sequence of TWW factors, with which the WKN distances of events can be computed at different temporal scales. Second, the appropriate values of TWW (i.e. the appropriate temporal scales, at which the number of false positives may reach the lowest value when classifying the events) are indicated by the local maximum values of densities of identified clustered events, which are calculated over varying TWW by using the expectation-maximization algorithm. Third, the thresholds of the WKN distance for classification are then derived with the determined TWW. In the fourth step, clustered events identified at the determined TWW are connected into clusters according to their density connectivity in geographic-temporal space. Results of simulated data and a seismic case study showed that the WNN method is efficient in identifying spatio-temporal clusters. The novelty of WNN is that it can not only identify spatio-temporal clusters with arbitrary shapes and different spatio-temporal densities but also significantly reduce the subjectivity in the classification process. [ABSTRACT FROM AUTHOR]

When two spatial point processes are overlaid, the one with the higher rate is shown as clustered points, and the other one with the lower rate is often perceived to be background. Usually, we consider the clustered points as feature and the background as noise. Revealing these point clusters allows us to further examine and understand the spatial point process. Two important aspects in discerning spatial cluster features from a set of points are the removal of noise and the determination of the number of spatial clusters. Until now, few methods were able to deal with these two aspects at the same time in an automated way. In this study, we combine the nearest-neighbour (NN) method and the concept of density-connected to address these two aspects. First, the removal of noise can be achieved using the NN method; then, the number of clusters can be determined by finding the density-connected clusters. The complexity for finding density-connected clusters is reduced in our algorithm. Since the number of clusters depends on the value of k (the k th nearest neighbour), we introduce the concept of lifetime for the number of clusters in order to measure how stable the segmentation results (or number of clusters) are. The number of clusters with the longest lifetime is considered to be the final number of clusters. Finally, a seismic example of the west part of China is used as a case study to examine the validity of our method. In this seismic case study, we discovered three seismic clusters: one as the foreshocks of the Songpan quake ( M = 7.2), and the other two as aftershocks related to the Kangding-Jiulong ( M = 6.2) quake and Daguan quake ( M = 7.1), respectively. Through this case study, we conclude that the approach we proposed is effective in removing noise and determining the number of feature clusters. [ABSTRACT FROM AUTHOR]

• We study theoretically and numerically both commensurate and incommensurate AAH graphene lattices and realize the topological edge modes of SPPs and localization transition from extended to all-localized wavefunctions, respectively. • The graphene systems can enable flexible and efficient modulation for constructing AAH lattice, thus circumventing the drawbacks of limited modulation depths in all dielectric AAH waveguide systems. • The topological edge states and localization transitions for graphene SPPs may be utilized for developing plasmonics devices operating in deep subwavelength scale on fully flat and compact platforms. By using rational and irrational on-site modulation in graphene waveguide arrays, we construct both commensurate and incommensurate Aubry-André-Harper (AAH) models and achieve the topological edge states and localization transition for graphene surface plasmon polaritons (SPPs). We show that when the commensurate AAH graphene array is truncated, topological edge states emerge, which are immune to the random perturbation of modulation depth in each individual graphene sheet. While for an incommensurate AAH array, localization transition for SPPs modes have also been achieved when the modulation depth reaches a critical value. Our work points out that graphene waveguide array provides a promising platform for robust light transport and compact localization within a fully deep subwavelength scale. [ABSTRACT FROM AUTHOR]

Bloch oscillations (BOs) in a parity-time (PT)-symmetric Su-Schrieffer-Heeger (SSH) waveguide array are theoretically investigated. We show that the BOs are amplified or damped even for the systems to exhibit entirely real energy bands. The amplified and damped BOs stem from the complex Berry phase and closely relate to the topological properties of the lattice. For the topological nontrivial lattice, the amplification and attenuation of BOs are much more prominent than the trivial case and the output Bloch mode can be selected. Furthermore, we propose an experimental scheme and perform a numerical simulation based on a bent waveguide array. Our work uncovers the impact of the topological properties on the dynamics of the bulk Bloch modes and unveils a horizon in the study of non-Hermitian physics. The mode selection induced by the complex Berry phase may also find application in integrated photonic devices such as the mode filter.

Here we propose an effective method to construct a higher-dimensional synthetic frequency lattice with an optical waveguide under dynamic modulation. By applying the traveling-wave modulation of refractive index modulation with two different frequencies that are not mutually commensurable, a two-dimensional frequency lattice could be formed. The Bloch oscillations (BOs) in the frequency lattice is demonstrated by introducing a wave vector mismatch of the modulation. We show that the BOs are reversible only as the amounts of wave vector mismatch in orthogonal directions are mutually commensurable. Finally, by employing an array of waveguides with each under traveling-wave modulation, a 3D frequency lattice is formed and its topological effect of one-way frequency conversion is revealed. The study offers a versatile platform for exploring higher-dimensional physics in concise optical systems and may find great application in optical frequency manipulations.

Photonic gauge potentials, including scalar and vector ones, play fundamental roles in emulating photonic topological effects and for enabling intriguing light transport dynamics. While previous studies mainly focus on manipulating light propagation in uniformly distributed gauge potentials, here we create a series of gauge-potential interfaces with different orientations in a nonuniform discrete-time quantum walk and demonstrate various reconfigurable temporal-refraction effects. We show that for a lattice-site interface with the potential step along the lattice direction, the scalar potentials can yield total internal reflection (TIR) or Klein tunneling, while vector potentials manifest direction-invariant refractions. We also reveal the existence of penetration depth for the temporal TIR by demonstrating frustrated TIR with a double lattice-site interface structure. By contrast, for an interface emerging in the time-evolution direction, the scalar potentials have no effect on the packet propagation, while the vector potentials can enable birefringence, through which we further create a "temporal superlens" to achieve time-reversal operations. Finally, we experimentally demonstrate electric and magnetic Aharonov-Bohm effects using combined lattice-site and evolution-step interfaces of either scalar or vector potential. Our work initiates the creation of artificial heterointerfaces in synthetic time dimension by employing nonuniformly and reconfigurable distributed gauge potentials. This paradigm may find applications in optical pulse reshaping, fiber-optic communications, and quantum simulations.

Landau-Zener tunneling (LZT), i.e., the nonadiabatic transition under strong parameter driving in multilevel systems, is ubiquitous in physics, providing a powerful tool for coherent wave control both in quantum and classical systems. While previous works mainly focus on LZT between two energy bands in time-invariant crystals, here, we construct synthetic time-periodic temporal lattices from two coupled fiber loops and demonstrate dc- and ac-driven LZTs between periodic Floquet bands. We show that dc- and ac-driven LZTs display distinctive tunneling and interference characteristics, which can be harnessed to realize fully reconfigurable LZT beam splitter arrangements. As a potential application to signal processing, we realize a 4-bit temporal beam encoder for classical light pulses using a reconfigurable LZT beam splitter network. Our work introduces and experimentally demonstrates a new class of reconfigurable linear optics circuits harnessing Floquet LZT, which may find versatile applications in temporal beam control, signal processing, quantum simulations, and information processing.

Here we use a four-wave mixing time lens to demonstrate the spectral self-imaging effect for a frequency comb. The time lens is built by imposing a temporal quadratic phase modulation onto the input signal pulses, which corresponds to a frequency comb in the Fourier spectrum. The modulation is implemented by a Gaussian pump pulse propagating in an external single-mode fiber. Both the signal and pump pulses are injected into a highly nonlinear fiber and four-wave mixing Bragg scattering occurs. We observe periodic revivals of the input frequency comb as the pump pulse propagates periodic distances. The comb-spacing is squeezed at fractional ratios to its original value. Meanwhile, the central-frequency undergoes redshifts and blueshifts subject to the scattered frequencies. We also find that the envelope width of input pulses has an effect on the output spectrum width. The study may find great applications in spectral reshaping and frequency metrology used for optical communication and signal processing.

A waveguide coupler under both phase and intensity modulation is proposed to generate a non-Hermitian Su-Schrieffer-Heeger lattice in frequency dimension. By varying the modulation period and phase, we can manipulate the on-site potential of the lattice and realize anisotropic coupling of the supermodes in waveguides. The artificial electric field associated with the modulation phase can also be introduced simultaneously. Zener tunneling is demonstrated in the non-Hermitian system and manifests an irreversibly unidirectional conversion between odd and even supermodes. The conversion efficiency can be optimized by varying the on-site potential of the waveguides. The study provides a versatile platform to explore non-Hermitian multiband physics in synthetic dimensions, which may find great application in chiral mode converters and couplers.

By creating a synthetic frequency dimension with dynamic modulation in a 2D honeycomb waveguide array, we construct both Type-I and Type-II Weyl semimetals (WSMs) and utilize the WSM phase transition to control the frequency evolutions of topological surface states. We show that Type-I WSMs and Type-II WSMs manifest opposite and same band slopes for the two surface states, which give rise to the bidirectional and unidirectional frequency shifts, respectively. Moreover, by cascading Type-I Weyl lattices and Type-II Weyl lattices together, we also achieve the time-reversed evolution of frequency, such as frequency negative refraction, bandwidth expansion-compression, and perfect imaging. The Letter may find applications in robust signal transmission and processing with synthesized topological states.

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.

Here we investigate the Bloch oscillations (BOs) in a photonic spectral lattice created with four-wave mixing Bragg scattering (FWM-BS). By injecting a signal and two pumps with different frequencies into a silicon nitride waveguide, a spectral lattice can be created for the generated idlers through successive FWM-BS. The phase-mismatch during FWM-BS acts as an effective force that induces BOs in the spectral lattice. Both the oscillation period and amplitude are determined by the magnitude of the effective force. With cascaded FWM-BS processes, the spectrum of idlers experiences a directional shift as the phase differences of pumps are modulated. Additionally, introducing long-range couplings in the spectral lattice will change the trajectory of BOs within each period. The pattern of BOs for a single frequency input can also be tailored. This Letter provides a new platform to realize BOs in the frequency dimension and paves a promising way for broadband frequency control with all-optical schemes.

By using a fiber loop with a phase modulator, we simulate the refraction and reflection effects of optical pulses at the heterointerface in the time domain, which is formed by abruptly varying the modulation depth or frequency. When the variation is periodically imposed on the optical pulse, the heterointerface is vertical and may lead to total internal reflection. The temporal refraction can be controlled by setting different Bloch wave vectors at incidence. As the variation occurs at a specific moment during the pulse propagation, a horizontal interface appears, and the negative refraction and pulse splitting in the time domain could be observed. We also show that the combination between the straight and tilted lattice could provide another way to control the temporal refraction. The study may find great applications in signals processing and optical communication.

It is of fundamental interest to control light diffraction in discrete optical systems. However, photon hopping in discrete systems is dominated by the nearest-neighbor coupling, limiting the realization of nonlocal diffraction phenomena. Here, we generalize the discrete diffraction from spatial to the frequency domain using optical phase modulators. By inducing long-rang couplings in the frequency lattice through periodic modulation signals, we find the lattice band structure can be artificially engineered, giving rise to the realization of arbitrary frequency diffraction. Particularly, we create linear, bilinear and semicircular band structures using sawtooth, triangular and semicircular modulation waveforms and realize the directional, bidirectional, omnidirectional frequency diffraction as well as the spectral "superlens". We also revisit frequency discrete Talbot effect and generalize the allowed incident period to arbitrary integers through band structure engineering. Moreover, as the frequency transition also carries a wave vector mismatch, an effective electric field will emerge, through which we can realize frequency Bloch oscillations that manifest the effects of arbitrary spectral routing and self-imaging. The study paves a promising way towards versatile spectrum management for both optical communications and signal processing.

We investigate the topological phase transition between Type-I and Type-II Weyl points (WPs) in a composite three-dimensional lattice composed of a two-dimensional brick-wall waveguide array and a synthetic frequency dimension created by dynamic modulation. By imposing different modulation amplitudes and phases in the two sublattices, we can break either parity or time-reversal symmetry and realize the phase transition between Type-I and Type-II WPs. As the array is truncated to have two edges, two Fermi-arc surface states will emerge, which propagate in opposite directions for Type-I WPs while in same directions for Type-II WPs, accompanied by bidirectional and unidirectional frequency shifts for the optical modes. Particularly at the phase transition point, we find that one of two bands becomes flat with a vanished group velocity along frequency axis in the vicinity of WPs. The study paves a way towards realizing different topological phases in the same photonic structure, which offers new opportunities to control wave transportation both in spatial and frequency domains.

We investigate the discrete temporal Talbot effect in a synthetic mesh lattice by employing two coupled fiber loops with different lengths. The lattice consists of the round-trip number and time delay of pulse trains propagating in the fiber loops. The Talbot effect occurs only as the incident pulse train in one loop has a temporal period that is 1, 2, or 4 folds of time interval corresponding to the length difference of the two loops. By varying the splitting ratio of coupler connecting the two loops, the lattice band structure can be engineered and so do the Talbot distance, which can be further tuned by imposing an initial linear phase distribution on the incident pulse train. In addition, the incident periods for Talbot effect can also be fractional fold by using time multiplexing. The study may find applications in temporal cloaking, passive amplifying, and pulse repetition rate multiplication.

By using optical phase modulators in a fiber-optical circuit, we theoretically and experimentally demonstrate large control over the spectrum of an impinging signal, which may evolve analogously to discrete diffraction in spatial waveguide arrays. The modulation phase acts as a photonic gauge potential in the frequency dimension, realizing efficient control of the central frequency and bandwidth of frequency combs. We experimentally achieve a 50 GHz frequency shift and threefold bandwidth expansion of an impinging comb, as well as the frequency analogue of various refraction phenomena, including negative refraction and perfect focusing in the frequency domain, both for discrete and continuous incident spectra. Our study paves a promising way towards versatile frequency management for optical communications and signal processing using time modulation schemes.

We investigate the nonlinear supermodes of surface plasmon polaritons in graphene multilayers with arbitrary number of graphene layers. Apart from the symmetric and anti-symmetric supermodes which exist in linear multilayer graphene waveguides, more asymmetric supermodes emerge in the nonlinear counterparts as the field symmetry is broken. The number of asymmetric supermodes relies largely on the layer number of graphene. There is a certain threshold of field intensity for the emergence of each individual asymmetric supermode. The threshold increases as the incident wavelength or chemical potential of graphene increases. The study may find applications in building all-optical mode converters and switches.

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.

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.

We investigate the supermodes in arbitrary layers of graphene sheets, which are collective guided modes formed by coupling of surface plasmon polaritons (SPPs) in each graphene sheet. In terms of the dispersion relation, we analyse the effective indexes and mode profiles of the supermodes. Numerical simulations reveal that the supermodes can be well approximated by linear superposition of SPPs in individual graphene sheets. Among all the possible supermodes, there is an interesting one possessing both lowest propagation loss and shortest mode wavelength. The loss of the supermode decreases as the number of layers increases and saturates at about 5 layers. The graphene multilayers may find potential applications in low-loss plasmonic waveguides and so constructed optical devices.