Monochromatic Plane Wave Research Articles

Comparative analysis of exact and approximate solutions of the plane electromagnetic wave scattering from a discrete parabolic reflector made of parallel circular PEC wires

Numerical analysis of the scattering of a plane monochromatic electromagnetic wave from a discrete parabolic reflector made of parallel cylinders (wires) with perfect electric conductivity is carried out in the exact and approximate formulations, the latter neglecting all interactions between the wires. Both the TE and the TM polarizations of the incident field are considered. It is shown that the difference between the exact and approximate solutions strongly depends on the frequency of the incident wave and that the TM-polarized plane wave is focused better by the discrete reflector than the TE-polarized wave. The field in the vicinity of the geometrical focus is investigated. It is found that the focusing ability, oscillating, gradually decreases with frequency. This behavior is in stark contrast to a solid perfectly electrically conducting parabolic reflector.

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

A polynomial approach is adopted to simulate the optical-electrical response of a multilayer thin film subjected to an applied transverse voltage. Each layer in the thin film is modelled by a propagation matrix, while the coupling between any two adjacent layers at an interface is modelled by an interface matrix. Each layer in the multilayer thin film in the present approach is treated as a capacitor coupled to the next so that the multilayer film is modelled as an effective capacitor which is constructed by a series of coupled capacitors. The electric charges accumulated at the interface between adjacent ‘capacitors’ can be modulated by the transverse voltage. The model is constructed to describe only lossless and nonmagnetic materials. The reflection and transmission of multilayer MgO/CaF2 thin films with a selected number of layers and structure, subjected to a tunable transverse potential, are simulated with a home-grown code implementing the model. The numerical results indicate that non-trivial optical responses can be conveniently predicted with the code, providing a handy simulator for designing and optimizing desired optical functionality of an arbitrary lossless multilayer thin film by tuning the transverse potential and the geometrical and electrical parameter of the structure.

Metasurface virtual absorbers: unveiling operative conditions through equivalent lumped circuit model

Virtual absorption concept has been recently introduced as a new phenomenon observed in electromagnetics and optics consisting of theoretically unlimited accumulation of energy within a finite volume of material without dissipation. The anomalous behaviour is achieved by engaging the complex zero scattering eigenmodes of the virtual absorbing system by illuminating it with a proper complex frequency ω = ω r + jω i , whose value is strictly determined by the system characteristics. In this paper, we investigate on the position of the zero-pole scattering pairs in the complex frequency plane as a function of the input impedance of the metasurface-based lossless virtual absorber. We analytically derive the conditions under which a properly modulated monochromatic plane wave can be virtually absorbed by the system and stored within its volume. The analysis is developed by modelling the propagation of a normally impinging plane wave through its equivalent transmission line model terminated in an arbitrary reactive load, which in turn models the input impedance of the metasurface-based system under consideration. The study allows to determine a priori whether the metasurface-based system can support the virtual absorption or not by evaluating the time-constant from its equivalent circuit.

Вакуумное двулучепреломление в поле плоской электромагнитной волны

We study the process of vacuum birefringence in a strong electromagnetic field: a probe photon changes its polarization while traversing a counterpropagating laser beam. To describe this phenomenon, we calculate the polarization tensor in the field of a plane monochromatic wave to leading order with respect to its amplitude. The main goal of the study is to compare the results with the data obtained within the locally constant field approximation (LCFA). Here we identify the domain of the LCFA applicability in the case of a plane-wave external background. It is shown that the frequency of the probe photon and that of the external field are symmetrically involved in the relative uncertainty. The exact treatment of the spatiotemporal dependence beyond the LCFA becomes necessary at the energy scale 0.1-1 MeV.

Рассеяние наклонно падающей плоской звуковой волны упругим цилиндром с неоднородным покрытием, находящимся вблизи плоской поверхности

В статье рассматривается задача о рассеянии плоской монохроматической звуковой волны, падающей произвольным образом на упругий круговой цилиндр с радиальнонеоднородным покрытием в присутствии плоской поверхности (абсолютно жесткой и акустически мягкой). Методом мнимых источников с применением теорем сложения для цилиндрических волновых функций получено аналитическое решение задачи. Волновые поля в содержащей среде и однородном упругом цилиндре находятся в виде разложений по волновым цилиндрическим функциям, а для нахождения полей смещений в неоднородных покрытиях построена краевая задача для системы обыкновенных дифференциальных уравнений второго порядка.Проведены численные расчеты частотных и угловых характеристик рассеянного поля для упругих однородных цилиндров с покрытием и без него, находящихся вблизи подстилающей плоскости. Выявлено существенное влияние непрерывно-неоднородных упругих покрытий на звукоотражающие свойства упругих цилиндрических тел.

Microwave Method for Measuring Electrical Properties of the Materials

The article is about the development of a new non-destructive microwave method for measuring the electrophysical properties of materials, based on the method of transmission and reflection of a plane monochromatic wave through layered materials. The method has been verified by the results of numerical and field experiments. A data processing technique is described for obtaining complex values of dielectric and magnetic permeability based on an original measurement scheme. Based on the results of mathematical calculations, the laboratory model was created using an ultra-wideband antenna and a parabolic mirror. The optimal distance of the antenna from the parabolic mirror for focusing the electromagnetic field has been determined based on the simulation. Testing was carried out in the frequency range 3–13 GHz on two samples of materials (plexiglass and textolite) with known electrophysical properties. The obtained results showed the reliability of the developed method and its applicability. The measurement error was less than 2%.

Space-time nonseparable pulses: Constructing isodiffracting donut pulses from plane waves and single-cycle pulses

Maxwell's equations can be satisfied not only by plane electromagnetic waves, but also by more exotic space-time nonseparable electromagnetic pulses which cannot be represented as a product of time- and space-dependent functions. A family of such pulses with finite energy was identified by Ziolkowski [Phys. Rev. A 39, 2005 (1989)]. Later, Hellwarth and Nouchi [Phys. Rev. E 54, 889 (1996)] highlighted a subset of Ziolkowski's pulses, now known as flying donuts, a formation of polarization singularities of toroidal topology traveling at the speed of light. Spurred by recent advances in ultrafast and topological optics, space-time nonseparable electromagnetic excitations are now becoming the focus of growing experimental efforts as they hold promise for topological information transfer, probing and inducing transient excitations in matter such as anapole and toroidal modes. Here we demonstrate that the flying donut can be constructed from an ensemble of monochromatic plane waves with continuous spatial and frequency spectrum and hence can be generated by converting broadband conventional transverse electromagnetic pulses.

Internal acoustic energy of fluid scattering centers: Application to metamaterials

From its origins, scattering theory seeks to understand the way scattering patterns are related to scattering centers, in the far-field region. However, important information about the scattering object can be obtained via near and/or internal fields. Here, we calculate analytically the amount of energy stored inside fluid spheres and cylinders upon the single scattering of an incident monochromatic plane wave. First, we compute the internal scattering coefficients of the wave inside the scattering center, which can be a sphere or cylinder. Second, using this quantity, along with well established formulas, we calculate the potential and kinetic energy inside the scatterer. We expect to set up a method for theoretically obtaining standard parameters when measuring stability and structural nature of several types of scattering materials. Using scattering theory as means to study properties of materials, we expect to help further developing of acoustic metamaterials and improving the technological advances of this field.

Plasma-covered long cylindrical non-isotropic dielectric lenses for targeted control of energy distribution

In this paper, a long column lens with a circular cross section made of two transversely non-isotropic dielectric parts covered by an isotropic plasma layer, is studied. The response of the mentioned object to the presence of plane monochromatic electromagnetic waves will be investigated. The finite element method has been used to calculate the field equations and the amplitudes of scattered waves in this research. This structure can be purposefully used as a device to focus electromagnetic wave energy in a specific area that its operation will be discussed by scattering theory. The electromagnetic responses of this structure have been simulated for two modes TE, TM of the incident wave, separately. Since in this lens a plasma region exists, the plasma can be considered as transparent or non-transparent states, with variations of plasma frequency in a fixed incident wave frequency. Here we consider the mentioned states too.

Polarization-sensitive transfer matrix modeling for displacement measuring interferometry

The use of polarizing optics for both beam steering and phase measurement applications in displacement measuring interferometer designs is almost universal. Interferometer designs that employ polarizing optics in this manner are particularly sensitive to the effects of unwanted optical cavities that form within the optics due to polarization leakage and back reflections from material interfaces. Modeling techniques commonly employed in the design of such interferometers are poorly suited to the analysis of multiple passes through polarizing optics. A technique, along with an accompanying software implementation, is presented here that is capable of modeling the propagation of monochromatic plane waves through an arbitrary network of linear planar optical components.

Static and optical anapole magnetizabilities and polarizabilities.

The anapolar response of a molecule exposed to a nonhomogeneous magnetic field B with spatially uniform curl C = ∇ × B is rationalized via second-rank tensors, a nonsymmetric aαβ, and a symmetric bαβ, referred to as static anapole magnetizabilities, which can be evaluated by quantum-mechanical Rayleigh-Schrödinger perturbation theory or allowing for the definitions of electronic current densities JB(r) and JC(r) induced in the electron cloud. The isotropic part of bαβ is even under the fundamental symmetry operations of charge conjugation C, parity P, and time reversal T and does not vanish for all matter and antimatter. The isotropic part of aαβ is even under C and T, but odd under P, and is exhibited only by chiral compounds. In the presence of optical fields, represented for simplicity by a monochromatic plane wave of frequency ω, dynamic anapole magnetizabilities and various anapole polarizabilities are taken into account. Assuming, within the electric quadrupole approximation for the impinging wave, that the electric field at the origin of the coordinate system is E(0), with uniform gradient ∇E, and magnetic field is B, the anapolar response is interpreted by second-rank aαβ(ω), aαβ '(ω), fαβ(ω), fαβ '(ω) and third-rank gα,βγ(ω), gα,βγ '(ω) frequency-dependent tensors. The same basic definitions are arrived at introducing frequency-dependent electronic current densities JB(r, ω) and JC(r, ω). As the frequency-dependent anapole susceptibilities depend on the origin of the coordinate system, relationships connecting them for two different origins are reported.

Propagation of electromagnetic waves through very thin non-Hermitian slabs

A theoretical model is proposed to study the propagation of monochromatic electromagnetic plane waves through very thin slabs having gain or loss. The analysis is based on solving the differential equations directly and applying the appropriate boundary conditions. The optical response of the slabs is considered in the linear and nonlinear regimes with a Kerr-type nonlinearity. A number of relations between the real and imaginary parts of the dielectric function are derived in order that useful effects related to the non-Hermiticity of the system be presented. The transmission of plane waves through a system consisting of two thin slabs satisfying the condition of Parity-Time symmetry is also considered.

Active control of the sound power scattered by a locally-reacting sphere.

Active control of the sound power scattered by a sphere is theoretically investigated using spherical harmonic expansions of the primary and secondary fields. The sphere has a surface impedance that is uniform, real, and locally reacting while being subjected to an incident monochromatic plane wave. The scattered power is controlled with a number of monopole sources, initially on the surface of the sphere, and is expressed as the sum of squared amplitudes of the spherical harmonics due to both the scattered and control fields. This quadratic function is minimized to identify the optimal strengths for different numbers of control sources. At low frequencies, the scattered field is dominated by the first few spherical harmonic terms, and its power can be significantly reduced with a single controlling monopole for a soft or absorbent sphere and with two monopoles for a hard sphere. The number of secondary sources required to significantly attenuate the scattered field at higher frequencies is found to be proportional to the square of the frequency, and the attenuation also falls off rapidly if the secondary sources are moved away from the surface of the sphere, no matter what its surface impedance.

Invariants of the Reflection Coefficient

The reflection coefficient of a plane monochromatic wave from a three-layer structure is analyzed in detail in the case in which the wave is linearly polarized in the plane of incidence. The inverse ellipsometry problem for a three-layer structure is solved. The occurrence of two invariants of the reflection coefficient for a plane-parallel plate is shown. A set of three measurable parameters is proposed, which have not been used previously, that make it possible to retrieve the material parameters of the layer. Analytical expressions are obtained for the reflection coefficient and the angles of incidence for a number of important particular cases, as well as for the direct calculation of the dielectric permittivity and the layer thickness from the measured values of the observed parameters.

Resonant Breit-Wheeler process in an external electromagnetic field

The contemporary research scrutinizes the resonant Breit-Wheeler process in the field of a plane monochromatic electromagnetic wave. Implementing the weak external field condition the processes of electron-positron pair production advances pre-eminently with participation of restrictively two field photons. Thus, within the resonant state the represented process effectively splits into two first-order processes with respect to the fine-structure constant. In details, the effect indicates the single photon pair production with consequent absorption of gamma quantum by an electron (positron) in the field of the wave. We analyze the resonance kinematics precisely. The study determines specific regions in which the interference of resonant amplitudes is absent. Additionally, the computation obtains a resonant differential cross section for the described areas. The corresponding resonant differential cross section significantly exceeds the correlating Breit-Wheeler cross-section without an external field. Various scientific facilities of pulsed laser radiation may experimentally verify the results of these calculations (SLAC, FAIR, XFEL, ELI, XCELS).

Modulational instability of dust-ion acoustic waves in the presence of generalized (r, q) distributed electrons

We have investigated the modulational instability (MI) of dust-ion acoustic waves in a dusty plasma model containing warm ions fluid, generalized (r, q) distributed electrons, and immobile dust grains. Using the Krylov-Bogoliubov-Mitropolsky method, the amplitude modulation of a monochromatic plane wave is analyzed through derivation of a nonlinear Schrödinger equation. The MI condition is calculated. Moreover, the effects of the plasma parameters such as the ion-to-electron temperature ratio, the wavenumber, and the unperturbed dust-to-electron number density ratio as well as the electron distribution dual parameters (r, q) are discussed. Our investigations have shown that the unstable region is bounded by two stable regions, i.e., two critical wavenumbers [kcl(lower) and kch(higher)] are found. The applications of the present theoretical study are briefly discussed in space physics whether positive or negative dust grains are enclosed.

Инварианты коэффициента отражения

A detailed analysis of the reflection coefficient of linearly polarized in plane of incidence of a plane monochromatic wave from a three-layer structure is carried out. Solved the reverse problem ellipsometry for a three-layer structure. The existence of two reflection factor invariants for the flat-parallel plate is shown. A set of three observable parameters not previously used is proposed, which allows to restore the material parameters of the layer. Analytical expressions are obtained both for the reflection coefficient and incidence angles for a number of important particular cases, and for the direct calculation of the dielectric constant and layer thickness from the measured values of the observed parameters.

Analytical methods for perfect wedge diffraction: A review

The subject of diffraction of waves by sharp boundaries has been studied intensively for well over a century, initiated by groundbreaking mathematicians and physicists including Sommerfeld, Macdonald and Poincaré. The significance of such canonical diffraction models, and their analytical solutions, was recognised much more broadly thanks to Keller, who introduced a geometrical theory of diffraction (GTD) in the middle of the last century, and other important mathematicians such as Fock and Babich. This has led to a very wide variety of approaches to be developed in order to tackle such two and three dimensional diffraction problems, with the purpose of obtaining elegant and compact analytic solutions capable of easy numerical evaluation.The purpose of this review article is to showcase the disparate mathematical techniques that have been proposed. For ease of exposition, mathematical brevity, and for the broadest interest to the reader, all approaches are aimed at one canonical model, namely diffraction of a monochromatic scalar plane wave by a two-dimensional wedge with perfect Dirichlet or Neumann boundaries. The first three approaches offered are those most commonly used today in diffraction theory, although not necessarily in the context of wedge diffraction. These are the Sommerfeld–Malyuzhinets method, the Wiener–Hopf technique, and the Kontorovich–Lebedev transform approach. Then follows three less well-known and somewhat novel methods, which would be of interest even to specialists in the field, namely the embedding method, a random walk approach, and the technique of functionally-invariant solutions.Having offered the exact solution of this problem in a variety of forms, a numerical comparison between the exact solution and several powerful approximations such as GTD is performed and critically assessed.

Physical possibilities of suppressing the sound transmission through a circular aperture covered by the two identical clamped circular plates

The problem of sound transmission suppression has been reconsidered in this study. The plane monochromatic wave impinges from the upper hemisphere onto the upper receiving plate. The wave is then transmitted through the fluid inside the circular aperture and reaches the lower transmitting plate. Further, the wave propagates in the lower hemisphere. The two plates are controlled by a limited number of excitation actuators in such a way that the transmitted acoustic power is minimized at the lowest resonance frequencies. The detailed rules for such control are presented. They are based mainly on the dominant mode principle. The radial modes are used to improve the accuracy and efficiency of the numerical results. Although similar problems were addressed earlier, this study proposes a relatively simple and efficient alternative solution.

Speed of structured light pulses in free space

A plane monochromatic wave propagates in vacuum at the velocity c. However, wave packets limited in space and time are used to transmit energy and information. Here it has been shown based on the wave approach that the on-axis part of the pulsed beams propagates in free space at a variable speed, exhibiting both subluminal and superluminal behaviours in the region close to the source, and their velocity approaches the value of c with distance. Although the pulse can travel over small distances faster than the speed of light in vacuum, the average on-axis velocity, which is estimated by the arrival time of the pulse at distances z ≫ ld (ld is the Rayleigh diffraction range) and z > cτ (τ is the pulse width) is less than c. The total pulsed beam propagates at a constant subluminal velocity over the whole distance. The mutual influence of the spatial distribution of radiation and the temporal shape of the pulse during nonparaxial propagation in vacuum is studied. It is found that the decrease in the width of the incident beam and the increase in the central wavelength of the pulse lead to a decrease in the propagation velocity of the wave packet.