Higher Order Modes Research Articles

End-Capping Hollow-Core Fibers With Suppressed Coupling Into Higher-Order Modes

End-Capping Hollow-Core Fibers With Suppressed Coupling Into Higher-Order Modes

Low Sidelobe Level, High-Gain Patch Antennas Operating at Higher-Order Modes

Low Sidelobe Level, High-Gain Patch Antennas Operating at Higher-Order Modes

Measurements of microwave transmission mode in HL-3 tokamak relevant ECH corrugated waveguides transmission line

The transmission modes of high-power millimeter wave in corrugated waveguides transmission line (TL) are crucial, especially for the long-pulse operation for long-distance TL. The microwave transmission mode in the TL on HL-3 tokamak relevant the electron cyclotron heating system are studied for the purpose according to the phase retrieval method based on intensity distribution measured by an infrared camera at several different locations away from the outlet of TL. A specific high power test platform with about 40-meter TL is established and the mode contents in the middle and the end of the TL are analyzed. In the middle of the TL, the proportion of main transmission mode LP01 mode is about 97% and other high-order modes contents are less than 3%. In the end of the TL, the main mode purity is about 94%, and the high-order mode, LP11 even mode is excited about 4.6%. These mode analysis results indicate that the high-power and long-pulse millimeter wave corrugated waveguides TL are designed and machined well, and the alignment method for long distance transmission line installation is highly useful for high-purity wave mode transmission.

Unveiling non-monochromatic modes and nonlinearity in Piet Hein quantum semiconductor waveguides

We investigate the propagation characteristics of transverse electric (TE) and transverse magnetic (TM) modes in a semiconductor quantum plasma-filled coaxial waveguide with a Piet Hein cross-section. The unique geometry of the Piet Hein cross-section offers intriguing possibilities for tailoring modal properties and exploiting novel nonlinear phenomena. Using analytical and numerical methods, we unveil the non-monochromatic behaviour of TE and TM modes, characterized by distinct peaks and troughs in their field components. The Ez\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{z}$$\\end{document} component of the TM mode exhibits a suppressed field within the central core and higher concentration in the cladding region, potentially minimizing energy loss within the waveguide. The Eρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\rho }$$\\end{document} component exhibits pronounced oscillations near the waveguide boundaries, suggesting constructive and destructive interference patterns. The Eξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{\\xi }$$\\end{document} component displays a non-monotonic behaviour with multiple pits and bumps, highlighting the interplay between the TE mode, the Piet Hein geometry, and the semiconductor quantum plasma properties. The Bρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{\\rho }$$\\end{document} component of the TM mode exhibits a non-monochromatic behaviour with multiple maxima and minima, attributed to the complex interactions between propagating waves with different phase shifts. The Bξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{\\xi }$$\\end{document} component exhibits a non-uniform distribution with distinct pits and bumps, with a resurgence towards the waveguide edges potentially due to higher-order mode contributions and local field enhancement effects. Our findings pave the way for the development of novel photonic devices with enhanced functionalities based on Piet Hein semiconductor quantum plasma waveguides.

Modal phase-matching in thin-film lithium niobate waveguides for efficient generation of entangled photon pairs

Thin-film lithium niobate (TFLN) waveguides have emerged as a pivotal platform for on-chip spontaneous parametric down-conversion (SPDC), serving as a crucible for the generation of entangled photon pairs. The periodic poling of TFLN, while capable of generating high-efficiency SPDC, demands intricate fabrication processes that can be onerous in terms of scalability and manufacturability. In this work, we introduce a novel approach to the generation of entangled photon pairs via SPDC within TFLN waveguides, harnessing the principles of modal phase-matching (MPM). To address the challenge of efficiently exciting pump light typically in a higher-order mode, we have engineered a mode converter that couples two asymmetrically dimensioned waveguides. This converter adeptly transforms the fundamental mode into a higher-order mode, demonstrating a conversion loss of 1.55 dB at 785 nm with a 3 dB bandwidth exceeding 30 nm. Subsequently, we have showcased the device’s capabilities by characterizing the pair generation rate (PGR), coincidences-to-accidentals ratio (CAR), and spectral profile of the entangled photon source. Our findings present a simplified and versatile method for the on-chip generation of entangled photon sources, which may pave the way for the application in the realms of quantum information processing and communication technologies.

Time-resolved x-ray imaging of nanoscale spin-wave dynamics at multi-GHz frequencies using low-alpha synchrotron operation

Time-resolved x-ray microscopy is used in a low-alpha synchrotron operation mode to image spin dynamics at an unprecedented combination of temporal and spatial resolution. Thereby, nanoscale spin waves with wavelengths down to 70 nm and frequencies up to 30 GHz are directly observed in ferromagnetic thin film microelements with spin vortex ground states. In an antiparallel ferromagnetic bilayer system, we detect the propagation of both optic and acoustic modes, the latter exhibiting even a strong non-reciprocity. In single-layer systems, quasi-uniform spin waves are observed together with modes of higher order (up to the 4th order), bearing precessional nodes over the thickness of the film. Furthermore, the effects of magnetic material properties, film thickness, and magnetic fields on the spin-wave spectrum are determined experimentally. Our experimental results are consistent with numerical calculations from a micromagnetic theory even on these so-far unexplored time- and length scales.

A position-based method for detecting orbital angular momentum modes

Abstract Due to the inherent limitations of current Orbital Angular Momentum (OAM) mode detection methods and constraints posed by the physical size of receiving antennas, accurately identifying higher-order OAM modes represents a significant challenge. Therefore, there is a pressing necessity to overcome these hurdles. This paper introduces a new approach to OAM mode detection that exploits positional information. Our methodology ascertains the OAM mode by examining the phase and position data of the electric field at any two randomly chosen points within the energy's spatial distribution radiated by vortex electromagnetic waves. This innovation promises not only to precisely detect higher-order OAM modes but also grants greater versatility in the placement of receiving antennas. Moreover, the study delves into the correlation between the electric field phase of vortex electromagnetic waves, the azimuth angle, and the receiving distance. The validity of our approach is confirmed through both simulation outcomes and experimental data derived from physical tests.

Double localized surface plasmon‒enhanced-second-harmonic generation behavior of equilateral triangular aluminum nanoprisms

Abstract This paper presents second-harmonic generation (SHG) behaviors for different-sized equilateral triangular aluminum nanoprisms. These behaviors were observed under the double localized surface plasmon (LSP) resonance condition. The SHG conversion efficiency was substantially enhanced when the excitation and SHG wavelengths were simultaneously tuned to the LSP-resonance wavelengths. The fundamental and higher-order LSP modes could be used to enhance the SHG conversion efficiency. The nonlinear light‒matter interaction associated with the double LSP resonance was numerically analyzed while focusing on the spatial overlap of the near-field distributions between the excitation and SHG wavelengths. The double LSP resonance enhanced SHG behaviors have been realized by using several elegantly designed plasmonic metal nanostructures consisting of the multi-elements. Our present study demonstrates this double LSP resonance enhanced SHG behavior from single, simple-shape triangular aluminum nanoprism.

Features that matter: Evolutionary signatures can predict viral transmission routes.

Routes of virus transmission between hosts are key to understanding viral epidemiology. Different routes have large effects on viral ecology, and likelihood and rate of transmission; for example, respiratory and vector-borne viruses together encompass the majority of rapid outbreaks and high-consequence animal and plant epidemics. However, determining the specific transmission route(s) can take months to years, delaying mitigation efforts. Here, we identify the vial features and evolutionary signatures which are predictive of viral transmission routes and use them to predict potential routes for fully-sequenced viruses in silico and rapidly, for both viruses with no observed routes, as well as viruses with missing routes. This was achieved by compiling a dataset of 24,953 virus-host associations with 81 defined transmission routes, constructing a hierarchy of virus transmission encompassing those routes and 42 higher-order modes, and engineering 446 predictive features from three complementary perspectives. We integrated those data and features to train 98 independent ensembles of LightGBM classifiers. We found that all features contributed to the prediction for at least one of the routes and/or modes of transmission, demonstrating the utility of our broad multi-perspective approach. Our framework achieved ROC-AUC = 0.991, and F1-score = 0.855 across all included transmission routes and modes, and was able to achieve high levels of predictive performance for high-consequence respiratory (ROC-AUC = 0.990, and F1-score = 0.864) and vector-borne transmission (ROC-AUC = 0.997, and F1-score = 0.921). Our framework ranks the viral features in order of their contribution to prediction, per transmission route, and hence identifies the genomic evolutionary signatures associated with each route. Together with the more matured field of viral host-range prediction, our predictive framework could: provide early insights into the potential for, and pattern of viral spread; facilitate rapid response with appropriate measures; and significantly triage the time-consuming investigations to confirm the likely routes of transmission.

Broadband conversion between high-order angular modes based on double-sided exposure long-period fiber grating

Broadband high-order mode converters play a fundamental and crucial role in mode division multiplexing systems. Unfortunately, there have been no reports on achieving broadband mutual conversion between high-order modes using long-period fiber gratings (LPFGs). In this paper, based on the concept of “stepwise” progressive conversion (SPC), a double-sided exposure fabrication method of LPFGs to achieve broadband mutual conversion between high-order modes is proposed and demonstrated. Based on the proposed method, broadband mode conversion from LP11 to LP21, from LP21 to LP31 and from LP31 to LP41 with low insertion loss are achieved by utilizing low exposure power and shortened device lengths. The 10 dB bandwidths of the three converters are measured to be 80 nm, 110 nm, and 90 nm, respectively, and their insertion losses are all less than 0.2 dB. Theoretically, this method can achieve broadband conversion of even higher-order modes, providing a novel solution for the fabrication of stable broadband mode converters. More generally, such mode converters can convert between any two modes and are essential for building advanced MDM networks that require routing and mode switching.

A Novel Fractional High-Order Sliding Mode Control for Enhanced Bioreactor Performance

This research introduces a fractional high-order sliding mode control (FHOSMC) method that utilises an inverse integral fractional order, 0<β<1, as the high order on the FHOSMC reaching law, exhibiting a novel contribution in the related field of study. The application of the proposed approach into a bioreactor system via diffeomorphism operations demonstrates a notable improvement in the management of the bioreactor dynamics versus classic controllers. The numerical findings highlight an improved precision in tracking reference signals and an enhanced plant stability compared to proportional–integral–derivative (PID) controller implementations within challenging disturbance scenarios. The FHOSMC effectively maintains the biomass concentration at desired levels, reducing the wear of the system as well as implementation expenses. Furthermore, the theoretical analysis of the convergence within time indicates substantial potential for further enhancements. Subsequent studies might focus on extending this control approach to bioreactor systems that integrate sensor technologies and the formulation of adaptive algorithms for real-time adjustments of β-type fractional-orders.

Advanced terahertz refractive index sensor in all-dielectric metasurface utilizing second order toroidal quasi-BIC modes for biochemical environments

We present a novel design for an all-dielectric metasurface ultra-sensitive refractive index (RI) sensor, characterized by a high-quality factor (Qf) and figure of merit (FOM). This design incorporates two high-order toroidal modes, including electric toroidal quadrupole (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document}​) and magnetic toroidal quadrupole (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{m}$$\\end{document}​) based on quasi‑bound states in the continuum (q-BIC) resonances. Our findings demonstrate the feasibility of switching between \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document} and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{m}$$\\end{document}​ through various symmetry-breaking mechanisms. To excite these high-order toroidal modes, we explored several symmetry-breaking strategies, including complex structural designs, symmetry disruption, and variations in the incident wave angle. Symmetry breaking in the structure induces new modes in the transmission spectrum, which are highly advantageous for sensing applications due to the presence of dark modes. The designed metasurface exhibits the capability to sense a broad range of RI in diverse environments, particularly in biochemical fields. Sensitivity (S) is significantly enhanced by the excitation of new resonance modes and adjustments in the incidence angle, increasing from 217 GHz/RIU in a symmetrical structure to 512.3 GHz/RIU for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document}​. The FOM improves from 197 RIU 1 to 8538 RIU− 1 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document}​ and 152,395 RIU− 1 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{m}$$\\end{document}​. Additionally, the Qf rises from 872 to 17,983 and 921,351 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document}​ and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{m}$$\\end{document}​, respectively.

High Peak Power Mini-array Quantum Cascade Lasers Operating in Pulsed Mode

Abstract Broad area quantum cascade lasers (BA QCLs) have significant applications in many areas, but suffer from demanding pulse operating conditions and poor beam quality due to heat accumulation and generation of high order modes. A structure of mini-array is adopted to improve the heat dissipation capacity and beam quality of BA QCLs. The active region is etched to form a multi emitter and the channels are filled with InP: Fe, which acts as a lateral heat dissipation channel to improve the lateral heat dissipation efficiency. A device with λ~4.8 μm, a peak output power of 122 W at 1.2% duty cycle with a pulse of 1.5 μs is obtained in room temperature, with far-field single-lobed distribution. This result allows BA QCLs to obtain high peak power at wider pump pulse widths and higher duty cycle conditions, promotes the application of the mid-infrared laser operating in pulsed mode in the field of standoff photoacoustic chemical detection, space optical communication and so on.

Random Raman Lasing in Diode-Pumped Multi-Mode Graded-Index Fiber with Femtosecond Laser-Inscribed Random Refractive Index Structures of Various Shapes

Diode-pumped multi-mode graded-index (GRIN) fiber Raman lasers provide prominent brightness enhancement both in linear and half-open cavities with random distributed feedback via natural Rayleigh backscattering. Femtosecond laser-inscribed random refractive index structures allow for the sufficient reduction in the Raman threshold by means of Rayleigh backscattering signal enhancement by +50 + 66 dB relative to the intrinsic fiber level. At the same time, they offer an opportunity to generate Stokes beams with a shape close to fundamental transverse mode (LP01), as well as to select higher-order modes such as LP11 with a near-1D longitudinal random structure shifted off the fiber axis. Further development of the inscription technology includes the fabrication of 3D ring-shaped random structures using a spatial light modulator (SLM) in a 100/140 μm GRIN multi-mode fiber. This allows for the generation of a multi-mode diode-pumped GRIN fiber random Raman laser at 976 nm with a ring-shaped output beam at a relatively low pumping threshold (~160 W), demonstrated for the first time to our knowledge.

A Series of Ultra-low Permittivity ALaP4O12 (A = Li, Na, K) Metaphosphate Microwave Dielectric Ceramics for Ultra-wideband Dielectric Resonant Antenna Application.

The employment of ultra-low permittivity materials in the configuration of antennas has been demonstrated to augment the antenna bandwidth and diminish signal delay effectively. This study presents three ultra-low permittivity metaphosphate microwave dielectric ceramics (MWDCs). The ALaP4O12 (A = Li, Na, K) metaphosphate ceramics, which all belong to the monoclinic crystal system, exhibit extremely low permittivity (εr ≈ 5) and excellent quality factor (Q·f > 10,000 GHz) at a low sintering temperature (T < 950 °C). Terahertz time-domain spectroscopy indicates that the εr of ALaP4O12 at terahertz frequencies is comparable to that observed in the microwave band and its value remains stable over an extensive frequency range. Furthermore, the relationship between the crystal structure and the dielectric properties of ALaP4O12 has been analyzed through the lens of chemical bond theory. The highest Q·f value observed for LiLaP4O12 can be attributed to the high chemical bond strength and stability of its crystal structure. The lowest ionic polarizability per unit volume is exhibited by NaLaP4O12, which results in the lowest pore-corrected permittivity. The thermal expansion of the chemical bonds within KLaP4O12 is considerable, resulting in the highest coefficient of thermal expansion. Finally, the performance of a LiLaP4O12-based dielectric resonator antenna (DRA) excited by slot-coupled microstrip lines was designed and optimized by using different ceramic radius-to-height (RH) ratios. It was found that when the RH ratio of DRA reached 1.85, both the fundamental mode (HEM11δ) and the higher-order mode (HEM12δ) of DRA were simultaneously excited. The two modes overlap significantly, resulting in an ultra-wideband (UWB) of 46.8% (bandwidth = 7.93 GHz). Concurrently, the maximum radiation efficiency and gain of the DRA, obtained from the simulation, are 97.9% and 7.92 dBi, respectively. The findings of this study may inform the investigation of ultra-low permittivity phosphorus-based MWDCs and UWB DRAs.

Localization of elastic surface waves based on defect modes in non-Bragg structures

Abstract The non-Bragg defect mode (NBDM) of elastic surface waves is experimentally investigated by inserting a defect in the middle of an antisymmetric periodic corrugated aluminum plate, which has been known as the non-Bragg structures since the observed band gaps are different from the traditional Bragg ones. Generally, the non-Bragg band gaps, existing away from the Bragg ones in a perfectly periodic waveguide, are created by the resonances of different transverse guided modes. The transmission spectra of elastic surface waves in antisymmetric structures with defects reveal the presence of defect modes within the non-Bragg gaps. Notably, the NBDM exhibits significant distribution characteristics in comparison to the traditional Bragg defect mode, including more complex elastic wave higher-order modes and localized wave energy near the defect. Consequently, the NBDM observed in the antisymmetric periodic waveguide with defects holds potential for utilization in other elastic wave functional devices, including filters and wave intensifiers.&amp;#xD;

Mode conversion in graded-index few-mode fiber via hollow cylindrical long-period fiber gratings.

We demonstrate the realization of mode conversion using hollow cylindrical long-period fiber gratings (LPFGs) inscribed in graded-index few-mode fibers (FMFs) by a femtosecond laser. By precisely shaping the refractive index modulation into a hollow cylindrical structure, we enable efficient coupling from the fundamental mode to high-order modes (LP11, LP02, LP21, LP12, LP31, LP03, and LP22 modes). The method achieves high-efficiency and low-loss mode conversion across various mode groups, marking a first for graded-index FMFs with different grating periods. The influence of the hollow cylindrical LPFG radius on mode conversion efficiency and spectral characteristics is thoroughly investigated. Additionally, incorporating a linear polarizer allowed for distinguishing between LP modes within a mode group, enhancing the tunability of the mode converter. These mode conversion devices have significant potential for applications in mode gain equalization and mode scrambling for mode division multiplexing (MDM) systems.

Characterizing temporal stability of supercontinuum generation in higher-order modes supported by liquid-core fibers

The generation of tailored supercontinua is essential for studying ultrafast light-matter interactions and for a variety of practical applications requiring broadband light. Liquid-core fibers (LCFs) have emerged as an innovative nonlinear photonic platform, demonstrating high efficiency in nonlinear frequency conversion. In this study, we showcase that LCFs provide a stable platform for ultrafast supercontinuum generation in a selected higher-order vector mode at 1.55μm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.55\\;\\upmu \\hbox {m}$$\\end{document}. Specifically, we demonstrate soliton fission and double-dispersive wave generation using a radially polarized mode in a CS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CS}_{2}$$\\end{document}-silica liquid-core fiber. The experiments were performed in a temperature-controlled laboratory, showing excellent stability with no evidence of fiber degradation, material degradation, or drift-induced changes in mode excitation over extended periods under standard environmental conditions. Our results confirm that liquid-core fibers are a reliable platform for nonlinear photonics, suitable for applications such as computationally tailored supercontinuum generation, single pulse spxectroscopy, and tailored light sources, all of which rely on consistent and stable nonlinear frequency conversion.

The jump filter in the discontinuous Galerkin method for hyperbolic conservation laws

When simulating hyperbolic conservation laws with discontinuous solutions, high-order linear numerical schemes often produce undesirable spurious oscillations. In this paper, we propose a jump filter within the discontinuous Galerkin (DG) method to mitigate these oscillations. This filter operates locally based on jump information at cell interfaces, targeting high-order polynomial modes within each cell. Besides its localized nature, our proposed filter preserves key attributes of the DG method, including conservation, L2 stability, and high-order accuracy. We also explore its compatibility with other damping techniques, and demonstrate its seamless integration into a hybrid limiter. In scenarios featuring strong shock waves, this hybrid approach, incorporating this jump filter as the low-order limiter, effectively suppresses numerical oscillations while exhibiting low numerical dissipation. Additionally, the proposed jump filter maintains the compactness of the DG scheme, which greatly aids in efficient parallel computing. Moreover, it boasts an impressively low computational cost, given that no characteristic decomposition is required and all computations are confined to physical space. Numerical experiments validate the effectiveness and performance of our proposed scheme, confirming its accuracy and shock-capturing capabilities.

Spatial momentum separation for optical vortex via phase-assembled metasurfaces

Expanding the spatial degrees of freedom is regarded to be the most innovative and effective solution for optical vortex encoding/decoding technology. A phase-assembled metasurface is proposed here to separate the momentum of the optical vortex into different spatial locations, and the incident high-order optical vortex is encoded in 18 channels. By combining both the propagation phase and the Pancharatnam-Berry (PB) phase, the fundamental Gaussian mode (solid spot) positions and other higher-order orbital angular momentum modes (hollow mode spots) positions at different channels are used to achieve the encryption of all-optical information. The scheme of grouping the mode spots on different channels into solid and hollow points greatly reduces the difficulty of encoding/decoding a high-order optical vortex. In this way, the combination of 2 incident high-order optical vortexes can represent 256 hexadecimal numbers from 00 to FF. We envision this work will open avenues for information encryption, multidimensional data storage, wavefront manipulation, and advanced orbital angular momentum detection technologies.