Linking Diffractive and Geometrical Optics Surface Scattering at a Fundamental Level

Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface;however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface.

The Perturbed Riemann Problem for a Geometrical Optics System

The perturbed Riemann problem for a hyperbolic system of conservation laws arising in geometrical optics with three constant initial states is solved.By studying the interactions among of the delta-shock,vacuum,and contact discontinuity,fourteen kinds of structures of Riemann solutions are obtained.The compound wave solutions consisting of delta-shocks,vacuums,and contact discontinuities are found.The single and double closed vacuum cavitations develop in solutions.Furthermore,it is shown that the solutions of the Riemann problem for the geometrical optics system are stable under certain perturbation of the initial data.Finally,the numerical results completely coinciding with theoretical analysis are presented.

Study of the emissivity of rough surfaces periodic using the method of coupled waves analysis (CWA) compared with method of geometrical optics approximation (GOA)

We present in this paper a numerical study of the validity limit of the geometrical optics approximation compared with a differential method which is established according to rigorous formalisms based on the electromagnetic theory. The precedent studies show that this method is adapted to the study of diffraction by periodic rough surfaces. We determine by two methods the emissivity of gold and tungsten for surfaces with a rectangular or sinusoidal profile, for a wavelength equal to 0.55 microns. The monochromatic directional emissivity of these surfaces clearly depends on the angle of incidence, the surface profile, height, period and the nature of the material. We perform our calculations by a method of coupled wave analysis (CWA) and a geometric optics method (GOA). The latter method is theoretically valid only when the dimensions of the cavities are very large compared to the wavelength, while the CWA is theoretically correct whatever these dimensions. The main purpose of this work is to investigate the validity limit of GOA compared with CWA. The obtained results for a fixed height of the grating, allowed us to delimit the validity domain of the optic geometrical approximation for the treated cases. Finally, the agreement between the emissivity calculated by the differential method and that given on the basis of the homogenization theory is satisfactory when the period is much smaller than the wavelength.

Towards the performance limit of catenary meta-optics via field-driven optimization

Catenary optics enables metasurfaces with higher efficiency and wider bandwidth,and is highly anticipated in the imaging system,super-resolution lithography,and broadband absorbers.However,the periodic boundary approximation without considering aperiodic electromagnetic crosstalk poses challenges for catenary optical devices to reach their performance limits.Here,perfect control of both local geometric and propagation phases is realized through field-driven optimization,in which the field distribution is calculated under real boundary conditions.Different from other optimization methods requiring a mass of iterations,the proposed design method requires less than ten iterations to get the efficiency close to the optimal value.Based on the library of shape-optimized catenary structures,centimeter-scale devices can be designed in ten seconds,with the performance improved by ~15%.Furthermore,this method has the ability to extend catenary-like continuous structures to arbitrary polarization,including both linear and elliptical polarizations,which is difficult to achieve with traditional design methods.It provides a way for the development of catenary optics and serves as a potent tool for constructing high-performance optical devices.

CATIA AIDED RADOME ANALYSIS USING GEOMETRIC OPTICS METHOD

In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance of electric large three-dimensional dielectric radome-enclosed antenna of arbitrary contour shape. The surfaces of the radome are approximated by planar triangular patches, the influences of various number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via an ogive and a conical radome are discussed by the hybrid method. The simulation results indicate that computational error from planar triangular patches can limit in one percent, meeting the engineering application requirements.

Engineering of geometrical configurations in dual-atom catalysts for electrocatalytic applications

Geometrical configurations play a crucial role in dual-atom catalysts(DACs)for electrocatalytic applications.Significant progress has been made to design DACs electrocatalysts with various geometri-cal configurations,but in-depth understanding the relationship between geometrical configurations and metal-metal interaction mechanisms for designing targeted DACs is still required.In this review,the recent progress in engineering of geometrical configurations of DACs is systematically summarized.Based on the polarity of geometrical configuration,DACs can be classified into two different types that are homonuclear and heteronuclear DACs.Furthermore,with regard to the geometrical configurations of the active sites,homonuclear DACs are identified into adjacent and bridged configurations,and heteronuclear DACs can be classified into adjacent,bridged,and separated configurations.Subsequently,metal-metal interactions in DACs with different geometrical configurations are introduced.Additionally,the applications of DACs in different electrocatalytic reactions are discussed,including the oxygen reduction reaction(ORR),oxygen evolution reaction(OER),hydrogen evolution reaction(HER),and other catalysis.Finally,the future challenges and perspectives for advancements in DACs are high-lighted.This review aims to provide inspiration for the design of highly effcient DACs towards energy relatedapplications.

Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.

Iterative Subregion Correction Preconditioners with Adaptive Tolerance for Problems with Geometrically Localized Stiffness

We present a class of preconditioners for the linear systems resulting from a finite element or discontinuous Galerkin discretizations of advection-dominated problems.These preconditioners are designed to treat the case of geometrically localized stiffness,where the convergence rates of iterative methods are degraded in a localized subregion of the mesh.Slower convergence may be caused by a number of factors,including the mesh size,anisotropy,highly variable coefficients,and more challenging physics.The approach taken in this work is to correct well-known preconditioners such as the block Jacobi and the block incomplete LU(ILU)with an adaptive inner subregion iteration.The goal of these preconditioners is to reduce the number of costly global iterations by accelerating the convergence in the stiff region by iterating on the less expensive reduced problem.The tolerance for the inner iteration is adaptively chosen to minimize subregion-local work while guaranteeing global convergence rates.We present analysis showing that the convergence of these preconditioners,even when combined with an adaptively selected tolerance,is independent of discretization parameters(e.g.,the mesh size and diffusion coefficient)in the subregion.We demonstrate significant performance improvements over black-box preconditioners when applied to several model convection-diffusion problems.Finally,we present performance results of several variations of iterative subregion correction preconditioners applied to the Reynolds number 2.25×10^(6)fluid flow over the NACA 0012 airfoil,as well as massively separated flow at 30°angle of attack.

基于OPTICS聚类的电力通信网跨层保护系统设计

电力通信网跨层传输数据时,受到噪声数据影响,导致跨层数据传输耗时长、电流畸变率高。为了保证跨层通信安全,设计基于密度的聚类算法(Ordering Points To Identify the Clustering Structure,OPTICS)的电力通信网跨层保护系统。构建并联有源电力滤波器安全保护电路,保证三相四线制限幅后具有良好谐波补偿效果。通过跨层控制主动切换模块,实现目标通信链路下达指令的主动切换。对电力通信网跨层数据进行OPTICS聚类处理,结合Laplace机制添加对称指数分布噪声,将Laplace噪声添加到聚类簇中,输出添加噪声后结果存储在输出队列中,完成通信网跨层保护。由系统测试结果可知,该系统传输耗时少,且在10 s测试时间内跨层电流畸变率仅为21%,能够起到保护通信网跨层传输的作用。

Special issue:Catenary optics and catenary electromagnetics

As a natural mathematical form,a catenary is the curve that a hanging chain or cable adopts under its own weight when supported at its ends in a homogeneous gravitational field.This unique shape arises from the balance of forces acting on each segment of the chain,resulting in a curve described by hyperbolic cosine functions.Catenary functions play pivotal roles in describing the electromagnetic field,intensity distribution,and dispersion of structured light on the sub-wavelength scale^(1).

Quantification of grain boundary effects on the geometrically necessary dislocation density evolution and strain hardening of polycrystalline Mg-4Al using in situ tensile testing in scanning electron microscope and HR-EBSD

In situ tensile testing in a scanning electron microscope(SEM)in conjunction with high-resolution electron backscatter diffraction(HR-EBSD)under load was used to characterize the evolution of geometrically necessary dislocation(GND)densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg-4Al alloy.The increase in GND density was investigated at plastic strains of 0%,0.6%,2.2%,3.3% from the area including 76 grains and correlated with(i)geometric compatibility between slip systems across grain boundaries,and(ii)plastic incompatibility.We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility,from which uniaxial tensile stress-strain response of polycrystalline Mg-4Al are computed and compared with experimental measurement.The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures.

Solar adaptive optics systems for the New Vacuum Solar Telescope at the Fuxian Lake Solar Observatory

Adaptive optics(AO)is essential for high-quality ground-based observations with large telescopes because it counters the impact of wavefront aberrations caused by atmospheric turbulence.The new vacuum solar telescope(NVST)is one of the most important high-resolution solar observation instruments in the world.Three sets of solar adaptive optics systems have been developed and installed on this telescope:conventional adaptive optics,ground layer adaptive optics,and multi-conjugate adaptive optics.These have been in operation from 2018 to 2023.This paper details the development and application of solar adaptive optics on the NVST and discusses the newest instrumentation.

Influence of manufacturing process-induced geometrical defects on the energy absorption capacity of polymer lattice structures

Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.

INVARIANCE AND STABILITY OF THE PROFILE EQUATIONS OF GEOMETRIC OPTICS

The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.

A historical overview of nano-optics:From near-field optics to plasmonics

Nano-optics is an emergent research field in physics that appeared in the 1980s,which deals with light–matter optical interactions at the nanometer scale.In early studies of nano-optics,the main concern focus is to obtain higher optical resolution over the diffraction limit.The researches of near-field imaging and spectroscopy based on scanning near-field optical microscopy(SNOM)are developed.The exploration of improving SNOM probe for near-field detection leads to the emergence of surface plasmons.In the sense of resolution and wider application,there has been a significant transition from seeking higher resolution microscopy to plasmonic near-field modulations in the nano-optics community during the nano-optic development.Nowadays,studies of nano-optics prefer the investigation of plasmonics in different material systems.In this article,the history of the development of near-field optics is briefly reviewed.The difficulties of conventional SNOM to achieve higher resolution are discussed.As an alternative solution,surface plasmons have shown the advantages of higher resolution,wider application,and flexible nano-optical modulation for new devices.The typical studies in different periods are introduced and characteristics of nano-optics in each stage are analyzed.In this way,the evolution progress from near-field optics to plasmonics of nano-optics research is presented.The future development of nano-optics is discussed then.

Glycerol effects on optical,weight and geometrical properties of skin tissue

Complex study of glycerol effects on the skin tissue was performed.The change in optical,weight and geometrical parameters of the rat skin under the action of the glycerol solutions was studied ex vivo.Possible mechanisms of the skin optical clearing under the action of glycerol solutions of different concentrations were discussed.The results can be helpful for refinement of models developed to evaluate the effective diffusion coefficients of glycerol in tissues.

GEOMETRIC OPTICS FOR 3D-HARTREE-TYPE EQUATION WITH COULOMB POTENTIAL

This article considers a family of 3D-Hartree-type equation with Coulomb potential ｜x｜^-1, whose initial data oscillates so that a caustic appears. In the linear geometric optics case, by using the Lagrangian integrals, a uniform description of the solution outside the caustic, and near the caustic are obtained.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Compact magneto-optical traps using planar optics

Magneto-optical traps (MOTs) composed of magnetic fields and light fields have been widely utilized to cool andconfine microscopic particles. Practical technology applications require miniaturized MOTs. The advancement of planaroptics has promoted the development of compact MOTs. In this article, we review the development of compact MOTs basedon planar optics. First, we introduce the standardMOTs. We then introduce the gratingMOTs with micron structures, whichhave been used to build cold atomic clocks, cold atomic interferometers, and ultra-cold sources. Further, we introducethe integrated MOTs based on nano-scale metasurfaces. These new compact MOTs greatly reduce volume and powerconsumption, and provide new opportunities for fundamental research and practical applications.

Adaptive Threshold Wave Front Sensing for Portable Adaptive Optics System Driven by Hybrid Parallel Technique

Our Portable Adaptive Optics(PAO)system designed for high-contrast imaging of exoplanets with current 2-4 m class telescopes achieves a correction speed of nearly 1000 Hz,utilizing a Shack-Hartmann Wave Front Sensor(WFS)in a 9×9 sub-aperture configuration.As we look towards adapting the PAO system for larger telescopes,an increase in the number of sub-apertures in the WFS and enhanced precision in wave front detection are imperative.Originally programmed in LabVIEW,our initial PAO software is based on a traditional centroid calculation module for nighttime wave front sensing and lacks adaptive processing of background noise.To address these limitations and to boost the PAO system's performance and accuracy in wave front detection,we propose a compressive neural network(Th-Net)combined with a specialized hybrid parallel programming approach for wave front detection.Our experimental results indicate that this hybrid parallel technique and Th-Net significantly enhance the PAO system's operational speed and wave front detection precision under uneven background noise.This work paves the way so that a duplicable and low-cost PAO system can be used for direct imaging of exoplanets with large telescopes.