Surface-enhanced Raman spectroscopy (SERS) offers high sensitivity for biomolecular detection, but its performance is often constrained by noise arising from signal non-uniformity across substrates. Here, we introduce a noise-management-oriented design strategy for hybrid SERS substrates composed of gold nanoparticles (AuNP) and two-dimensional (2D) materials (graphene, MoS2, and WSe2). Compared with conventional AuNP substrates, the hybrids exhibit markedly improved spectral uniformity and signal-to-noise ratio (SNR), with the AuNP/graphene platform reducing noise by ∼67% and increasing SNR by ∼279%. Full-wave simulations based on Maxwell's equations corroborated the experimental results and reveal that optical constants of the 2D material and nanoparticle distribution jointly govern noise characteristics. SNR dependence on nanoparticle density distributions, refractive index (n), and extinction coefficient (k) is further established. As a practical demonstration, the AuNP/graphene substrate enabled detection of the receptor binding domain protein at a limit of detection (LOD) of 10-9 M, representing a ten-fold improvement over the 10-8 M LOD of AuNP substrates. These results establish AuNP/2D hybrids as effective platforms for noise-managed SERS, offering enhanced sensitivity for biosensing.

Inverse-designed nanophotonic devices offer promising solutions for analog optical computation, where high-density photonic integration is critical for scaling computational complexity. Here, we present an inverse-designed photonic neural network (PNN) accelerator, enabling ultra-compact and energy-efficient optical computing. Using a wave-based inverse-design method based on three-dimensional finite-difference time-domain simulations, we exploit the linearity of Maxwell's equations to reconstruct arbitrary spatial fields through optical coherence. Each subwavelength voxel serves as a trainable degree of freedom, yielding a computational density of approximately 400 million parameters per mm². By decoupling the forward-pass process into linearly separable simulations, our approach is highly amenable to computational parallelism. We experimentally demonstrate two inverse-designed PNN accelerators, achieving on-chip MNIST and MedNIST classification accuracies of 89% and 90% respectively, within footprints of 20 × 20 µm² and 30 × 20 µm². Our results establish a scalable, energy-efficient platform for photonic computing, bridging inverse nanophotonic design with high-performance optical information processing.

Abstract This paper aims at developing exactly energy-conservative and structure-preserving finite volume schemes for the discretisation of first-order symmetric-hyperbolic and thermodynamically compatible (SHTC) systems of partial differential equations in continuum physics. Due to their thermodynamic compatibility the class of SHTC systems satisfies an additional conservation law for the total energy and many PDE in this class of equations also satisfy stationary differential constraints (involutions). First, we propose a simple semi-discrete cell-centered HTC finite volume scheme that employs collocated grids and that is compatible with the total energy conservation law, but which does not satisfy the involutions. Second, we develop a fully discrete semi-implicit finite volume scheme that conserves total energy and which can be proven to satisfy also the involution constraints exactly at the discrete level. This method is a vertex-based staggered semi-implicit scheme that preserves the basic vector calculus identities $$\nabla \cdot \nabla \times \textbf{A}= 0$$ ∇ · ∇ × A = 0 and $$\nabla \times \nabla \phi = 0$$ ∇ × ∇ ϕ = 0 for any vector and scalar field, respectively, exactly at the discrete level and which is also exactly totally energy conservative. The main key ingredient of the proposed implicit scheme is the fact that it uses a discrete version of the symmetric-hyperbolic Godunov-form of the governing PDE system. This leads naturally to sequences of symmetric and positive definite linear algebraic systems to be solved inside an iterative fixed-point method used in each time step. We apply our new schemes to three different SHTC systems. In particular, we consider i) the equations of nonlinear acoustics, ii) the nonlinear Maxwell equations in the absence of charges, and iii) a nonlinear version of the Maxwell-GLM system. We also show some numerical results to provide evidence of the stated properties of the proposed schemes.

Preasymptotic Error Estimates of Linear EEM and CIP-EEM for the Time-Harmonic Maxwell Equations with Large Wave Number

The influence of the optical axis orientation on the features of the plasmon-polariton (PP) gap in photonic heterostructures is investigated. To this end a one-dimensional layered system embedded in vacuum and formed by stacking alternate layers of anisotropic metamaterial and air is thoroughly analyzed. Within the formalism of Maxwell's equations and transfer matrix techniques we show the existence of the PP-gap at normal incidence. Furthermore, by tuning the frequency of the incident wave in the neighborhood of this gap, the otherwise usual elliptic dispersion relation, becomes hyperbolic.

Abstract We consider Maxwell’s equations for Kerr-type optical materials, which are magnetically inactive and have a nonlinear response to electric fields. This response consists of a linear plus a cubic term, which are both inhomogeneous with bounded coefficients. The cubic term is temporally retarded while the linear term has instantaneous and retarded contributions. For slab waveguides we show existence of breathers, which are time-periodic, real-valued solutions that are localized in the direction perpendicular to the waveguide, and moreover they are traveling along one direction of the waveguide. We find these breathers using a variational method which relies on the assumption that an effective operator related to the linear part of Maxwell’s equations has a spectral gap about 0. We also give examples of material coefficients, including nonperiodic materials, where such a spectral gap is present.

Abstract This paper deals with the kinetic equations and Lagrangians of vector bosons and spinor fermions. Its goals are mainly pedagogical and methodological, and no claim of novelty is made. But the relevant equations are here derived from the fundamental Lorentz invariants, namely the two Casimir operators for a massive particle with spin-1/2 and spin-1. Special attention is paid to the chiral symmetry and its effects on the Lorentz transformation. A new road leading to the Dirac equation and its polarization spinors is thus shown. Using the spin matrices stemming from the vectorial Lorentz transformation permits one to determine directly the polarization of vector bosons and to establish their Lagrangian including these spin matrices. This approach permits one to rederive also the Maxwell equations, but more importantly to determine the origin of its spin for the massive vector boson. The kinetic helicity of the particles plays a key role in these calculations.

The research presents a new computational system which allows researchers to examine piezoelectric plate structural stability and dynamic performance in landscape design projects that need to withstand wind loads and use energy-harvesting systems. The researchers create wind conditions for their research by using two atmospheric parameters which include the wind attack angle and the average wind speed to simulate outdoor conditions that affect piezoelectric plate performance. The plates are assumed to rest on viscoelastic–concrete auxetic foundations which provide landscape-integrated structures with improved damping abilities and unique deformation patterns. A power-law material model enables the creation of piezoelectric plate material properties which simulate functional gradients that exist throughout the thickness of the material. The research uses higher order shear deformation theory (HSDT) to establish a precise method for examining transverse shear effects which does not require shear correction factors. The electromechanical coupling mechanisms find their complete description through Maxwell's equations while Hamilton's principle serves as the basis for deriving the equations which govern motion because it ensures energy conservation. The harmonic differential quadrature method uses Chebyshev polynomial grid points to achieve spatial discretization of coupled partial differential equations which results in high numerical accuracy and efficient computational performance. The primary solution method uses Physics-informed deep neural networks (PIDNNs) as an Artificial intelligence technique to address the deficiencies which traditional numerical solvers experience during complex multi-physics simulations. The PIDNN framework enables prediction of stability boundaries and vibration characteristics plus electromechanical responses through its integration of governing physical laws into the loss function. The proposed method successfully analyzes smart piezoelectric plate systems which operate in wind-sensitive landscape design applications.

Superoscillation (SO) refers to the phenomenon in which a wavefield locally oscillates at a rate exceeding its highest spatial or temporal Fourier component. SO has enabled light to be focused into arbitrarily small hotspots, forming the basis of superresolution imaging and metrology far beyond the Abbe-Rayleigh diffraction limit. Here we show that spatial and temporal superoscillations can occur simultaneously at the same point in space-time, a phenomenon we term space-time superoscillation (STSO). We demonstrate STSOs ina band-limitedversion of supertoroidal light pulses, a recently introduced family of space-time nonseparable finite-energy solutions of Maxwell's equations. Our results reveal a new regime of extreme spatiotemporal field structuring, with implications for ultrafast metrology, light-matter interactions, and deep-subwavelength control of electromagnetic waves.

This Letter focuses on a remarkable simulation tool for the photothermal properties of the metallic nanostructures. A fully coupled method is established based on Maxwell's equations and the law of heat conduction in the time domain. This method is different from the conventional co-simulation scheme with a steady-state optical field and a transient thermal field, offering a more versatile approach for analyzing photothermal characteristics. To effectively evaluate the photothermal coupling effect, the discontinuous Galerkin technique is utilized. Furthermore, the time-scaling approach is introduced to address the multiscale nature of the temporal responses between the light and heat fields. Thus, an efficient numerical solver for the photothermal properties of metallic nanostructures is developed. Numerical examples demonstrate the remarkable accuracy and efficiency of the proposed method. Therefore, this approach can provide an essential theoretical tool for designing dynamically reconfigurable nano-devices.

We introduce a general approach for probing nonlinear x-ray propagation by imaging secondary fluorescence emitted transverse to the driving field. When a short, intense x-ray pulse excites a deep 1 s core orbital, subsequent K α emission from spin-orbit-split 2 p states can undergo stimulated amplification. This nonlinear process reshapes the relative populations of the 2 p 1 / 2 and 2 p 3 / 2 levels along the propagation path, leaving distinct signatures in the delayed L-edge fluorescence. By solving the coupled density-matrix and Maxwell equations, we show that these fluorescence signals provide a direct and experimentally accessible probe of x-ray amplification dynamics. We demonstrate the concept for argon atoms and extend it to molecular systems containing third-row elements, where competing effects of lifetimes, transition intensities, and nonresonant absorption determine the efficiency of stimulated emission. Our results establish L-edge fluorescence as a broadly applicable diagnostic of nonlinear x-ray phenomena, opening opportunities for studying light-matter interactions in regimes where direct detection of amplified x-ray signals is technically challenging.

The emission of electromagnetic waves from solids encompasses a wide range of processes, including incandescence, fluorescence, electroluminescence, scintillation, cathodoluminescence and light emission from inelastic tunnelling. Different models can be used to describe them; for example, thermal emission from hot bodies is computed using statistical physics, photon emission from an excited electron is treated with quantum mechanics and emission from a current in an antenna is quantitatively described by Maxwell's equations. However, most emitting systems involve statistical ensembles of excited electrons interacting with complex electromagnetic environments, so a blend of the three approaches is needed. The purpose of this Review is to provide a unified framework that combines recent theoretical works that have been developed to quantitatively account for light emission processes in solids. We begin with an overview of the electrodynamics approach used to model incandescence. This framework is then extended to describe light emission from optically or electrically pumped semiconductors. Finally, we generalize the procedure to strongly non-equilibrium systems and illustrate its application through several examples.

Hot electrons and holes generated from the decay of localizedsurfaceplasmons (LSPs) in aluminum nanostructures have significant potentialfor applications in photocatalysis, photodetection, and other optoelectronicdevices. Here, we present a theoretical study of hot-carrier generationin aluminum nanospheres using a recently developed modeling approachthat combines a solution of the macroscopic Maxwell equation withlarge-scale atomistic tight-binding simulations. Different from standardplasmonic metals, such as gold or silver, we find that the energeticdistribution of hot electrons and holes in aluminum nanoparticlesis almost constant for all allowed energies. Only at relatively highphoton energies, a reduction of the generation rate of highly energeticholes and electrons close to the Fermi level is observed, which isattributed to band structure effects suppressing interband decay channels.We also investigate the dependence of hot-carrier properties on thenanoparticle diameter and the environmental dielectric constant. Theinsights from our study can inform experimental efforts toward highlyefficient aluminum-based hot-carrier devices.

We examine two models for electromagnetism, the usual Lorentz invariant electromagnetism and the Galilei invariant version represented by the magnetic model proposed in [1]. For every inertial frame we define two coordinate systems: the Galilei and the Lorentz systems, that accommodate both models. We show that the Lorentz transformation for the fields and the 4-current are induced from the corresponding Galilei transformation, which does not arise as the low velocity limit of the Lorentz transformation. In addition we show the Maxwell equations for the electromagnetic fields and the 4-current induce a family of Galilei invariant equations depending on a parameter β such that in the limit β → 0 they become the Maxwell equations.

We analyze the formal equivalence between the electromagnetic energy conservation law derived from Maxwell’s equations in an optical microcavity and the conservation of a probability fluid associated with the de Broglie–Bohm theory for an effective massive particle describing a photon in this cavity. This work is part of a critical analysis of recent experiments by Sharoglazova et al. carried out with a view to refuting the de Broglie–Bohm theory. Furthermore, the consequences of our analysis for microphotonics go far beyond these experiments. In particular, extensions that take into account photon spin and stochastic aspects associated with radiative or absorption losses are considered. From the point of view of symmetries and probability current, here the effective photon behaves like a spin-1/2 particle.

We present a theoretical analysis of geodesic motion, thermodynamic properties, and field perturbations in anti-de Sitter black hole spacetimes within Kalb-Ramond gravity sourced by ModMax nonlinear electrodynamics. This framework incorporates both Lorentz-violating effects and nonlinear electromagnetic interactions, extending beyond classical black hole solutions. We examine the dynamics of neutral and charged test particles in this modified spacetime, demonstrating how ModMax nonlinearity, electric charge, cosmological constant, Lorentz-violating corrections, and black hole mass significantly alter particle trajectories compared to standard Schwarzschild and RN solutions. Through effective potential analysis, we show how these parameters shift the locations of innermost stable circular orbits and influence orbital stability. We investigate optical properties including photon trajectories, photon spheres, and black hole shadows, revealing parameter dependencies that offer potential observational constraints. Our thermodynamic analysis derives key quantities including Hawking temperature, Bekenstein-Hawking entropy, and explores Joule-Thomson expansion processes within the extended phase space framework. The analysis reveals rich phase structures with distinct cooling and heating regions influenced by all geometric parameters. We examine scalar and electromagnetic field perturbations through the Klein-Gordon and Maxwell equations, deriving perturbative potentials and computing greybody factors that quantify wave transmission probabilities.

Residual tensile stresses in welded joints negatively affect the fatigue strength, corrosion resistance, and dimensional accuracy of metal structures. Treatment with a pulsed electromagnetic field allows for optimization of the stress state and metal microstructure of the welded joints, thereby contributing to enhanced reliability and longevity of structures, and consequently extending their operational lifespan. The aim of this work is to determine, through mathematical modeling, the distribution of the electromagnetic field and magnetic forces within the volume of a weld seam in an aluminum alloy plate with isotropic parameters during its treatment by the magnetic field of an inductor with pulsed current. A three-dimensional mathematical model of the induction system was developed to calculate the electromagnetic field equations. The calculation of pulsed current in the inductor winding conductors along with the electromagnetic field of the entire induction system was performed using electrical circuit equations based on Kirchhoff's second law and electromagnetic field equations based on Maxwell's equation system. A comparison of magnetic forces, field strength, and eddy current density in the weld seam area was conducted for plates with thicknesses of 6 mm and 3 mm. The 6 mm plate can be interpreted as two 3 mm plates, one with a weld seam and the other acting as a screen, which allowed investigation of such screening effect on force and current distribution. A study was conducted of the vector quantities of field strength, current density, and magnetic forces in the volume of the weld seam area being treated, as a function of time. Based on the developed methodology, experimental studies were performed to assess the impact of magneto-pulse treatment on residual welding stresses and the metal microstructure of welded joints made of AMg6 aluminum alloy. It was demonstrated that treating the weld metal during or after welding contributes to reducing residual tensile stresses and dispersing the microstructure of the weld metal. References 16, figures 11, tables 2.

Neutron star magnetospheres are well described in the two extreme cases of a vacuum field and a plasma-filled force-free regime. However, neither of these descriptions allows for magnetic field dissipation into particle kinetic energy and thus high-energy radiation. Some physical processes must be invoked to produce observational signatures typical of pulsars. In this paper, we compute a full set of neutron star magnetosphere structures from the basic vacuum regime to the dissipation-less force-free regime by implementing a resistive prescription for the plasma. A comparison to the radiation reaction limit is also discussed. We investigated the impact of these resistive magnetospheres on the multi-wavelength emission properties based on the polar cap model for radio wavelengths, the slot gap model for X-rays, and the striped wind model for γ-rays. We performed time-dependent pseudo-spectral simulations of the full Maxwell equations including a resistive Ohm's law. We deduced the polar cap shape and size, the Poynting flux, the magnetic field structure, and the current sheet surface, depending on magnetic obliquity ̊chi and conductivity σ. We found that the geometry of the magnetosphere close to the stellar surface is not impacted by the amount of resistivity. Polar cap rims remain very similar in shape and size. However, the Poynting flux varies significantly, as well as the magnetic field sweep-back in the vicinity of the light cylinder. This bending of field lines reflects in the γ-ray pulse profiles, changing the γ-ray peak separation Δ as well as the time lag δ between the radio pulse and γ-ray peaks. X-ray pulse profiles are also drastically affected by resistivity. A full set of multi-wavelength light curves can be compiled for future comparison with the third γ-ray pulsar catalogue. This systematic study will help constrain the amount of magnetic energy that flows into particle kinetic energy and is shared by radiation.

The Lorentz transformations (LT) are conventionally derived from the requirement of interval invariance in Minkowski spacetime. However, this requirement alone is insufficient to uniquely determine the LT. Through straightforward matrix analysis, we demonstrate that an infinite family of transformations — including real, complex, and special Galilean forms — also leave the interval invariant. The physical and mathematical meaning of these transformations is clarified by distinguishing between alibi (active) and alias (passive) interpretations, corresponding respectively to Galilean translations in 3D space and rotations in 4D spacetime. We show that the LT emerge as a special case when the time coordinate is formally taken as imaginary, which simplifies the description of Maxwell's equations but does not impose a fundamental speed limit. Thus, the LT should be understood as a convenient alias transformation projecting 3D Galilean motion into a 4D formalism, rather than as a unique consequence of interval invariance.

ABSTRACT The field generated by a time‐harmonic pure irrotational current distributed in a finite region of free space is derived analytically. Only an electric field is produced and is nonzero even merely within the finite interior of the current distribution, though the problem space itself is infinite. To consider the obtained field solution nonphysical according to our current physical concepts, however, lacks evidence or reasoning. It satisfies the original first‐order Maxwell's equations (MEs) and the related continuity conditions exactly, hence cannot be rejected mathematically. It is also shown that a conceptual denial of such a different kind of solution based on physical interpretations of other known solutions of the same MEs is logically not acceptable. A direct experiment study is necessary to conclude convincingly whether or not the above solution is physical. The completeness problem of MEs and their consistency with the Lorentz force law and the equation of motion are discussed. Free space MEs are incomplete or underdetermined due to the absence of a curl equation for the current density. If the solution is nonphysical, ME‐based electromagnetic (EM) theory is not self‐consistent. On the other hand, if it is physical, this type of inconsistency within the frame of the ME‐based EM theory disappears, yet it is inconsistent with the Lorentz force law and the equation of motion in this case.