Monochromatic Plane Research Articles

Diffraction tomography for incident Herglotz waves

Abstract Diffraction tomography is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the scattered waves induced from different incident field angles are recorded. In conventional diffraction tomography, the incident wave is assumed to be a monochromatic plane wave, an unrealistic simplification in practical imaging scenarios. In this article, we extend conventional diffraction tomography by introducing the concept of customized illumination scenarios, with a pronounced emphasis on imaging with focused beams. More specifically, we consider incident Herglotz waves and extend the classical Fourier diffraction theorem to this setting. This yields a new two-step reconstruction process which we comprehensively evaluate through numerical experiments.

Negative radiation pressure in the abelian Higgs model

Interactions of small-amplitude monochromatic plane waves with domain walls in (1+1) dimensional abelian Higgs model with a sextic potential were studied. The effective force exerted on a domain wall was derived from a linearized equation and compared with numerical simulations of the original model. It was shown that the domain walls always accelerate in one direction, regardless of the direction of the incoming wave. This implies that in some cases an effect called negative radiation pressure is observed, i.e. instead of pushing, the wave pulls the soliton.

Patterned magnetophotonic crystal for all-optical magnetization precession generation

A magnetophotonic crystal (MPC) with a locally etched magnetic layer is proposed for all-optical excitation of magnetization precession in the confined area. When the sample is illuminated by circularly polarized monochromatic plane wave, the optical MPC mode and the effective magnetic field excited by the inverse Faraday effect are localized inside the etched area. Therefore, the optical impact on the spin system in a magnetically ordered medium becomes confined in both lateral directions on the order of tens of nanometers and along the film thickness serving as a nanoconfined source of spin waves. The dependence of the spatial distribution of the effective magnetic field and magnetization precession amplitude on the depth and dimensions of the etched area are addressed. A proposed design of the MPC can find its applications in the field of magnetization dynamics generation as a compact and stable source of the spin waves that allows compact arrangement of the sources for some complex spin waves excitations.

Phase Retrieval Algorithm for Surface Topography Measurement Using Multi-Wavelength Scattering Spectroscopy

We are currently developing a high-precision and wide-range in-process surface topography measurement system using the laser inverse scattering method. In the laser inverse scattering method, a monochromatic plane wave is illuminated perpendicular to the target surface and the surface topography is measured by retrieving the phase distribution of the reflected light. However, the dynamic range of this method is limited to the sub-micrometer range because of phase wrapping during phase retrieval. In this paper, we propose a laser inverse scattering method using a multi-wavelength light source based on the fact that the phase of light is inversely proportional to the wavelength with the propagation distance as a coefficient. We also constructed a surface profilometer based on the proposed method and measured the profile of a single rectangular groove with a width of 50 µm and a depth of 2 µm. The dimensions of the measured profiles agree well with the nominal dimensions of the rectangular groove.

NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE

Subject and Purpose. Сonsidered are the natural modes and their correspondent eigenfrequencies of a composite structure which is nonuniform along one of the coordinates and consists of a lossy ferromagnetic layer placed in a static magnetic field. The layer involves a perfectly conducting strip grating at one of its boundaries and a graphene monolayer at the other. Methods and Methodology. The above stated problem can be approached within the analytical regularization procedure developed for dual series equations. The latter concern a broad class of diffraction problems which include, in particular, the diffraction of monochromatic plane waves on strip gratings placed at the boundary of a gyromagnetic medium. The amplitudes of the electromagnetic eigenmodes can be obtained from the infinite set of homogeneous linear algebraic equations solvable within a truncation technique. The roots of the system’s determinant represent complex-valued eigenfrequencies of the system under investigation. The material parameters adopted in our computations for the ferromagnetic layer correspond to such of yttrium iron garnet. Results. A number of numerical programs have been developed which permit analyzing the dependences of wave field eigenfunctions and complex eigenfrequencies upon geometrical parameters of the structure (such as grating slot width and period, and thickness of the lossy layer), as well as on electrodynamic parameters of the ferromagnet and graphene characteristics, specifically the chemical potential and relaxation energy of electrons. A number of behavioral regularities have been established, as well as the effect of non-uniformity of ferrite layer parameters upon the structure’s eigenfrequencies and wave field eigenfunctions. Conclusions. The structure under study has been shown to be is an open oscillatory system with a set of complex-valued natural frequencies demonstrating finite points of accumulation. The real parts of these eigenfrequencies lie in a certain interval determined by characteristic frequencies of the ferrite layer, while the imaginary parts are negative, such that the correspondent natural modes show an exponential decay with time. The grating edges represent the mirrors which the natural surface oscillations are reflected from, being supported at that by the ferromagnetic medium. The results obtained in this paper can be useful for creating the elemental base for microwave devices and the devices themselves.

Modulational instability of dust-ion acoustic waves in generalized (r, q) distributed electron dissipative plasmas

The modulational instability of the dust-ion acoustic waves in a dissipative dusty plasma system containing warm ions, generalized ( r , q ) distributed electrons, and immobile dust grains has been studied. The Krylov–Bogoliubov–Mitropolsky (KBM) perturbation method is employed to analyze the amplitude modulation of a monochromatic plane wave through the derivation of a nonlinear Schrödinger equation. This equation is solved analytically to determine the modulational instability region, and the corresponding dissipative rogue wave solution is obtained. The effects of various system parameters, such as the kinematic viscosity of the ions (υ), the wavenumber (k), the ion to electron temperature ratio ( σ i ), the unperturbed ion to electron density ratio (γ) as well as the electron distribution parameters: r and q, are investigated. The dependence of the amplitude of dissipated rogue waves on υ is discussed. It is found that various system parameters have significant effects on the features of dissipated rogue waves. The present investigation can be relevance to the electrostatic rogue structures in various cosmic dust-laden plasmas such as Saturn's F-ring.

Interactions between linear polarized gravitational waves and electromagnetic waves in an electromagnetic analog of gravity

We study the interaction among gravitational and electromagnetic plane waves by means of an analog electromagnetic model of gravity, where the gravitational properties are encoded in the electromagnetic properties of a material in flat space-time. In this setup, the variations in the metric tensor produced by the gravitational waves are codified as space-time-varying electromagnetic properties. We use an in-house code based on the finite-difference time-domain method to conduct numerical experiments, where we find that, when a monochromatic gravitational plane wave interacts with a narrow-band electromagnetic plane wave, an infinite number of sidebands, equally separated between themselves, are induced by the gravitational wave. Finally, we discuss possible future applications of this effect as an alternative method to directly detect gravitational waves.

Relativistic transformations of quasi-monochromatic paraxial optical beams

A monochromatic plane wave recorded by an observer moving with respect to the source undergoes a Doppler shift and spatial aberration. We investigate here the transformation undergone by a generic, paraxial, spectrally coherent quasimonochromatic optical beam (of finite transverse width) when recorded by a moving detector. Because of the space-time coupling intrinsic to the Lorentz transformation, the monochromatic beam is converted into a propagation-invariant pulsed beam traveling at a group velocity equal to that of the relative motion and which belongs to the recently studied class of ``space-time wave packets.'' We show that the predicted transformation from a quasimonochromatic beam to a pulsed wave packet can be observed even at terrestrial speeds.

Diffraction Phenomena in Time-Varying Metal-Based Metasurfaces

This paper presents an analytical framework for the analysis of time-varying metal-based metamaterials. Specifically, we particularize the study to time-modulated metal-air interfaces embedded between two different semi-infinite media that are illuminated by monochromatic plane waves of frequency ${\ensuremath{\omega}}_{0}$. The formulation is based on a Floquet-Bloch modal expansion, which takes into account the time periodicity of the structure (${T}_{s}=2\ensuremath{\pi}/{\ensuremath{\omega}}_{s})$ and integral-equation techniques. It allows us to extract the reflection and transmission coefficients as well as to derive nontrivial features about the dynamic response and dispersion curves of time-modulated metal-based screens. In addition, the proposed formulation has an associated analytical equivalent circuit that gives a physical insight into the diffraction phenomenon. Similarities and differences between space- and time-modulated metamaterials are discussed via the proposed circuit model. Finally, some analytical results are presented to validate the present framework. Good agreement is observed with numerical computations provided by a self-implemented finite-difference time-domain (FDTD) method. Interestingly, the present results suggest that time-modulated metal-based screens can be used as pulsed sources (when ${\ensuremath{\omega}}_{s}\ensuremath{\ll}{\ensuremath{\omega}}_{0}$), beam formers (${\ensuremath{\omega}}_{s}\ensuremath{\sim}{\ensuremath{\omega}}_{0}$) to redirect energy in specific regions of space, and analog samplers (${\ensuremath{\omega}}_{s}\ensuremath{\gg}{\ensuremath{\omega}}_{0}$).

A polynomial model of transmission and reflection of electromagnetic monochromatic plane waves in lossy, non-magnetic multilayer thin films subjected to an external transverse voltage

Simulation of the electrical and optical response of a multilayer thin film composed of lossless material coupled with adjacent lossy material in an alternating arrangement when applying a transverse voltage across the multilayer thin film is conducted using a polynomial approach. The modelling of the lossy–lossless multilayer thin film is a generalization of our previous work on multilayer thin film made up of alternating lossy–lossy materials. It is the propagation matrix of the electromagnetic wave in the thin film that governs its propagation, while the interface matrix represents the coupling between layers at an interface. The present solution models the multilayer thin film as an effective capacitor constructed from a series of coupled capacitors, with every layer being considered as a capacitor coupled to the next. A transverse voltage can affect the amounts of electric charges that accumulate at the interface between adjacent ‘capacitors’. The present model is constructed to describe nonmagnetic, lossy and lossless materials. With the aid of a home-developed code implementing the model, the reflection and transmission of multilayer Ge/MgO thin films are simulated. By tuning the transverse electric potential, geometrical and electrical parameters of an arbitrary lossy–lossless multilayer thin film, the code is capable of predicting nontrivial optical responses in terms of $$T\left(\lambda \right), R\left(\lambda \right), {\phi }_{T}\left(\lambda \right), {\phi }_{R}(\lambda )$$ . The code can serve as a useful tool for designing and optimizing lossless-lossy or lossless-lossless multilayer thin films to deliver desired optical functions.

Accurate Direction–of–Arrival Estimation Method Based on Space–Time Modulated Metasurface

A metasurface (MTS)-based direction of arrival (DoA) estimation method is presented. The method exploits the properties of space–time modulated reflective metasurfaces to estimate in real-time the impinging angle of an illuminating monochromatic plane wave. The approach makes use of the amplitude unbalance of the received fields at broadside at the frequencies of the two first-order harmonics generated by the interaction between the incident plane wave and the modulated metasurface. Here, we first describe analytically how to generate the desired higher order harmonics in the reflected spectrum and how to realize the breaking of the spatial symmetry of each order harmonic scattering pattern. Then, the 1-D omnidirectional incident angle can be analytically computed using +1st- and −1st-order harmonics. The approach is also extended to 2-D DoA estimation by using two orthogonally arranged 1-D DoA modulation arrays. The accuracy of 1-D DoA estimation is verified through full-wave numerical simulations. Compared to conventional DoA estimation methods, the proposed approach simplifies the computation and hardware complexity, ensuring at the same time estimation accuracy. The proposed method may have potential applications in wireless communications, target recognition, and identification.

An Efficient Method for Calculating the Doppler Spectrum of an Arbitrarily Shaped Object in Uniform Motion

In the article, an efficient numerical method for calculating the spectrum of the scattering fields of an arbitrarily shaped object in uniform motion is proposed. This method relies on the frame hopping technique stemming from the special theory of relativity (STR). Firstly, the incident monochromatic plane wave is transformed to the comoving inertial frame in which the object is stationary. Next, the scattering fields of the moving object at the sampling time points are obtained in the comoving frame by solving the electromagnetic (EM) scattering problem with the conventional numerical method in the frequency domain. Then, the spectrum of the scattering fields in the frame in which the observer remains stationary is obtained using the discrete Fourier transform (DFT). The asymptotic expressions for the scattering fields when the moving object is far away from the observation point are derived, by applying which the computation efficiency could be greatly improved.

Observation of Gravitational Waves by Invariants for Electromagnetic Waves

We lay a theoretical foundation in the observation of gravitational waves (GWs) by electromagnetic waves (EMWs) performing a full electromagnetic analysis without any optical approximation. For that, the perturbation of plane EMWs is obtained by solving the perturbed Maxwell equation with GWs in the Minkowski background spacetime. In a GW detector using the EMWs, we propose to measure the electromagnetic invariants that are independent of the motion of the EMW receiver and whose perturbations are gauge-invariant. Imposing a physical boundary condition at EMW emitters, we have analytic results for the perturbations of invariants that can be measured in the EMW receiver. Finally, we show antenna patterns of the detector with monochromatic plane GWs and EMWs.

Proportionality of gravitational and electromagnetic radiation by an electron in an intense plane wave

Accelerated charges emit both electromagnetic and gravitational radiation. Classically, it was found that the electromagnetic energy spectrum radiated by an electron in a monochromatic plane wave is proportional to the corresponding gravitational one. Quantum mechanically, it was shown that the amplitudes of graviton photoproduction and Compton scattering are proportional to each other at tree level. Here, by combining strong-field QED and quantum gravity, we demonstrate that the amplitude of nonlinear graviton photoproduction in an arbitrary plane wave is proportional to the corresponding amplitude of nonlinear Compton scattering. Also, introducing classical amplitudes we prove that the proportionality relies on the semiclassical nature of the electron's motion in a plane wave and on energy-momentum conservation laws, leading to the same proportionality constant in the classical and quantum case. These results deepen the intertwine between gravity and electromagnetism into both a nonlinear and a quantum level.

Connection between cosmological time and the constants of nature

We examine in greater detail the proposal that time is the conjugate of the constants of nature. Fundamentally distinct times are associated with different constants, a situation often found in ``relational time'' settings. We show how in regions dominated by a single constant the Hamiltonian constraint can be reframed as a Schr\"odinger equation in the corresponding time, solved in the connection representation by outgoing-only monochromatic plane waves moving in a ``space'' that generalizes the Chern-Simons functional (valid for the equation of state $w=\ensuremath{-}1$) for other $w$. We pay special attention to the issues of unitarity and the measure employed for the inner product. Normalizable superpositions can be built, including solitons, ``light-rays'' and coherent/squeezed states saturating a Heisenberg uncertainty relation between constants and their times. A healthy classical limit is obtained for factorizable coherent states, both in monofluid and multifluid situations. For the latter, we show how to deal with transition regions, where one is passing on the baton from one time to another, and investigate the fate of the subdominant clock. For this purpose minisuperspace is best seen as a dispersive medium, with packets moving with a group speed distinct from the phase speed. We show that the motion of the packets' peaks reproduces the classical limit even during the transition periods, and for subdominant clocks once the transition is over. Deviations from the coherent/semiclassical limit are expected in these cases, however. The fact that we have recently transitioned from a decelerating to an accelerating Universe renders this proposal potentially testable, as explored elsewhere.

Machine Learning Target Count Prediction in Electromagnetics Using Neural Networks

In this article, we showcase an application of neural networks (NNs) to solve an inverse problem in electromagnetics (EMs). Wires are randomly distributed into an area of known dimensions. The wires are then illuminated with a monochromatic plane wave (PW) at a certain angle of incidence, and the EM field measured at a finite number of uniformly spaced points along the perimeter of the area is then fed into a convolutional neural network (CNN) designed to predict the number of wires. Counting the wires is posed as a supervised classification problem with a known upper limit to the number of wires, and accuracy of 96% has been achieved for the case where the number of the wires is known to be ten or less. A number of approaches have been taken to improve the network performance including frequency variation analysis and illuminating the wire distributions with additional PW angles of incidence. We conclude with an analysis of the network capability to resolve objects based on its performance on known wire distributions, which suggests the existence of a characteristic resolution limit corresponding to the CNN topology.

Optical response of dielectric&metal-core/metal-shell nanoparticles: Near electromagnetic field and resonance frequencies

We study the diffraction of a monochromatic electromagnetic plane wave by a dielectric&metal-core/metal-shell nanoparticle surrounded by a dielectric medium. This problem was solved by using generalized Mie’s theory and both the scattering cross section and the square module of the electric field were calculated as a function of shell thickness. Numerically, the first particles studied were gold-core/silver-shell nanoparticles and their inverse configuration. The gold-core/silver-shell particle presented more variation of their optical properties. The second particles were vacuum-core/metal-shell surrounded by vacuum, symmetric configurations. In this case, the dispersive Drude dielectric function for the metal was used, and a comparative study between the positions of the resonance frequencies obtained from quasi-static limit and electrodynamic theory was performed. Thus, consequently the formula obtained from the quasi-static limit can be used to calculate the positions of the resonance frequencies instead of the electrodynamic theory, when the external radius is smaller than 20 nm.

Origin independent current density vector fields induced by time-dependent magnetic field. I. The LiH molecule.

The electronic current density, induced in a molecule by the optical magnetic field associated with a frequency-dependent monochromatic plane wave, assumed to be spatially uniform within the electric quadrupole approximation, has been studied by using a theoretical method based on a continuous translation of its origin. The induced electronic current density vector field designated by this procedure, invariant of the origin for any point of the molecular domain, is obtained via a computational scheme, formally annihilating the diamagnetic contribution of the conventional common-origin approach based on perturbation theory. In a preliminary application of the theoretical methods outlined in the present work, the simple molecule of lithium hydride has been investigated. Particular attention has been paid to the structure of induced electronic current density for several values of the magnetic field frequency by investigating equilibrium points of four different types, organized in stagnation lines, which constitute its stagnation graph, i.e., a topological fingerprint of the vector field conveying complete information in the condensed form, to verify the fulfillment of fundamental requirements, e.g., the continuity equation and the Poincaré-Hopf theorem on spherical and toroidal surfaces.

Scattering asymmetry and circular dichroism in coupled PT-symmetric chiral nanoparticles

Abstract We investigate the scattering properties of coupled parity-time (PT) symmetric chiral nanospheres with scattering matrix formalism. The exceptional points, i.e., spectral singularities at which the eigenvalues and eigenvectors simultaneously coalesce in the parameter space, of scattering matrix can be tailored by the chirality of the nanospheres. We also calculate the scattering, absorption and extinction cross sections of the PT-symmetric chiral scatter under illumination by monochromatic left- and right-circularly polarized plane waves. We find that the scattering cross section of the nanostructures exhibits an asymmetry when the plane waves are incident from the loss and gain regions, respectively, especially in the broken phase, and the optical cross section exhibits circular dichroism, i.e., differential extinction when the PT-symmetric scatter is endowed with chirality. In particular, under illumination by linearly polarized monochromatic plane waves without intrinsic chirality, the ellipticity of scattered fields in the forward direction, denoting the chirality of light, becomes larger when the scatter is in the PT-symmetry-broken phase. Our findings demonstrate that the gain and loss can control the optical chirality and enhance the chiroptical interactions and pave the way for studying the resonant chiral light–matter interactions in non-Hermitian photonics.

Applicability Conditions for the Approximation Presuming Small Influence of Radiation Damping on the Motion of a Classical Electron in the Field of a Monochromatic Plane Wave

Applicability Conditions for the Approximation Presuming Small Influence of Radiation Damping on the Motion of a Classical Electron in the Field of a Monochromatic Plane Wave