Propagation Of Monochromatic Waves Research Articles

Nonlinearized nonlinear electromagnetic guided waves in a circle cylindrical waveguide filled with nonlinear dielectric medium

We consider a problem of propagation of monochromatic electromagnetic waves in a circle cylindrical waveguide filled with nonlinear dielectric medium. The permittivity of the waveguide is described by the Kerr law, which is one of the most important nonlinear dependence in nonlinear optics. In order to find guided waves we develop an original mathematical approach that allows us to prove existence of infinitely many guided waves. In addition, we prove that only a finite number of the founded nonlinear guided waves have linear counterparts; the others are nonlinearizable solutions. Numerical results are also presented.

Metamaterials to control both longitudinal and transverse waves simultaneously

Mechanical metamaterials are used in various applications to control bulk wave propagation through elastic materials. Controlling both the longitudinal and transverse waves at the same time by designing a single phononic device is challenging through theoretical, computational, and experimental perspectives. Suppression of system generated second harmonics due to interaction of monochromatic longitudinal wave and during one-way two-wave mixing of two longitudinal waves by designing effective phononic material is demonstrated in previous work by the author [Ghodake, J. Acoust. Soc. Am. 150, A149 (2021)]. In this talk, the design of linear periodic metamaterials which can control both the longitudinal and transverse waves, their second harmonics during propagation of monochromatic waves, and one-way two-wave mixing between longitudinal and transverse waves, is discussed by solving inverse problems using finite element analysis, effective boundary conditions, and optimization techniques. Along with the widths of periodic elastic materials, the number of repeated periodic cells (N) in a phononic lattice is defined as a design parameter. Different strong and weak contains are implemented so that in every iteration either during or after the iteration N will remain integer. A gradient-free optimization algorithm is used during constrained optimization. Strong constraint solves the inverse problem in a few minutes.

Optical properties of an extended gravitational lens

We continue to study the optical properties of the solar gravitational lens (SGL). The aim is prospective applications of the SGL for imaging purposes. We investigate the solution of Maxwell's equations for the electromagnetic (EM) field, obtained on the background of a static gravitational field of the Sun. We now treat the Sun as an extended body with a gravitational field that can be described using an infinite series of gravitational multipole moments. Studying the propagation of monochromatic EM waves in this extended solar gravitational field, we develop a wave-optical treatment of the SGL that allows us to study the caustics formed in an image plane in the SGL's strong interference region. We investigate the EM field in several important regions, namely i) the area in the inner part of the caustic and close to the optical axis, ii) the region outside the caustic, and iii) the region in the immediate vicinity of the caustic, especially around its cusps and folds. We show that in the first two regions the physical behavior of the EM field may be understood using the method of stationary phase. However, in the immediate vicinity of the caustic the method of stationary phase is inadequate and a wave-optical treatment is necessary. Relying on the angular eikonal method, we develop a new approach to describe the EM field accurately in all regions, including the immediate vicinity of the caustics and especially near the cusps and folds. The method allows us to investigate the EM field in this important region, which is characterized by rapidly oscillating behavior. Our results are new and can be used to describe gravitational lensing by realistic astrophysical objects, such as stars, spiral and elliptical galaxies.

Surface waves in a Goubau line filled with nonlinear anisotropic inhomogeneous medium

The propagation of monochromatic nonlinear symmetric hybrid surface waves in a cylindrical nonlinear anisotropic inhomogeneous metal-dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The setting is reduced to a new type of nonlinear eigenvalue problem and an analytical method of its solution is developed. The propagation modes are found that have not been previously reported in the literature. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Modelling of acoustic waves in homogenized fluid-saturated deforming poroelastic periodic structures under permanent flow

Acoustic waves in a poroelastic medium with periodic structure are studied with respect to permanent seepage flow which modifies the wave propagation. The effective medium model is obtained using the homogenization of the linearized fluid–structure interaction problem while respecting the advection phenomenon in the Navier–Stokes equations. For linearization of the micromodel, an acoustic approximation is introduced which yields a problem for the acoustic fluctuations of the solid displacements, the fluid velocity and pressure. An extended Darcy law of the macromodel involves the permeability and advection tensors which both depend on an assumed stationary perfusion of the porous structure. The monochromatic plane wave propagation is described in terms of two quasi-compressional and two quasi-shear modes. Two alternative problem formulations in the frequency domain are discussed. The one defined in terms of displacement and velocity fields leads to generalized eigenvalue problems involving non-Hermitean matrices whose entries are constituted by the homogenized coefficients depending on the incident wave frequencies, whereby degenerate permeabilities can be accounted for. The homogenization procedure and the wave dispersion analysis have been implemented to explore the influence of the advection flow and the microstructure geometry on the wave propagation properties, namely the phase velocity and attenuation. Numerical examples are reported.

Peculiarities of light pulse propagation in quasi-PT symmetric periodic structures

We study the peculiarities of light pulse propagation in the quasi-parity-time (quasi- P T ) symmetric periodic media in the Bragg geometry. Our focus is the investigation of the competition between the Bragg reflection and the P T symmetry contribution provided different pulse duration. The mechanisms of nonsymmetric interaction between the counterpropagating waves are revealed and the various regimes of the monochromatic and nonmonochromatic wave propagation are determined. It is demonstrated that regardless the gain and loss level, the propagation of so-called long pulses in a quasi- P T -symmetric medium is analogous to monochromatic waves propagation in a “pure” P T -symmetric medium. At the same time, the transmittance of the short pulses is accompanied by strong distortions determined by the gain and loss level.

Finite Difference Schemes for Modelling the Propagation of Axisymmetric Elastic Longitudinal Waves

An efficient finite difference shock-capturing scheme for the solution of direct seismic problems is constructed. Problem formulation is based on equations of the dynamics of elastic medium with axial symmetry. When implementating the scheme on multiprocessor computing systems, the two-cyclic splitting method with respect to spatial variables is used. One-dimensional systems of equations that arise in the context of splitting procedure are represented as subsystems for longitudinal, transverse and torsional waves. The case of longitudinal waves is considered in this paper. The results of simulations with the use of explicit grid-characteristic schemes and implicit schemes of the "predictor–corrector" type with controllable dissipation of energy are compared with exact solutions that describe propagation of monochromatic waves

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.

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.

Complex Waves in Dielectric Layer

The propagation of monochromatic TE-polarized waves in a partially shielded dielectric layer is considered. The existence of infinitely many complex leaky waves is proved as well as the absence of complex surface waves.

Dynamic stress state of underground pipelines at junctions

A one-dimensional statement of unsteady wave problem of a longitudinal monochromatic wave propagation and reflection from a rigid stationary barrier to which an underground pipeline abuts is given. The linear viscoelastic Eyring model, which describes limited creep and limited relaxation, is taken as the pipeline strain law. Eyring model allows us to describe the behavior of underground steel and polymer pipelines under dynamic loading. The problem is solved numerically using the theory of characteristics, followed by the finite difference method in an implicit scheme. Numerical solutions obtained in the form of dependences of plane wave parameters: longitudinal stress, velocity and strain for fixed sections of the pipeline are analyzed in the paper. An analysis of changes in these wave parameters shows that at high frequencies of dynamic load generating the wave, the stress amplitude in the pipeline increases by two or more times compared to the load amplitude. This is due to the superposition of incident and reflected waves in the pipeline and to a high loading rate of the pipeline. At low frequencies of dynamic loading, such an increase is not observed due to the low loading rate. The obtained numerical solutions allow choosing the statement of problems on dynamic stress state of an underground pipeline depending on the frequency of incident wave. It is shown that the greatest longitudinal stress in an underground pipeline arises in points (sections) close to its connection with a rigid stationary solid body.

Effects of an array of widely separated vertical cylinders on time-averaged properties of progressive monochromatic waves

ABSTRACT The design of monopile foundations for offshore wind farms, the estimate of wave loads, and the effect of the structures on the environment usually consider one single vertical cylinder. This choice is based on the size of the ratio cylinder diameter to wavelength, and on the large distances between turbines. However, for large arrays of monopiles, the ensemble effect must be investigated. This study addresses monochromatic wave propagation through a rectangular array of four cylinders 800 m and 300 m apart, considered here as the fundamental geometry for an arbitrary array of monopiles turbines. Results for bottom velocities, mean water level, mass transport, and radiation stress tensor in the presence of the array are compared with those for a single cylinder. The numerical model WAMIT® is used to compute the potential velocity solution. Relevant spatial variations were found, especially for radiation stresses, for different periods and directions of propagation. Diffraction effects on the wave field by the array are significantly stronger than the superposition of individual effects of isolated cylinders under the same conditions. Impacts of the entire wind farm on bottom morphodynamics near the foundations, on the design loads, and on the wave climate past the wind farm are discussed.

Numerical Method for Electromagnetic Wave Propagation Problem in a Cylindrical Anisotropic Waveguide with Longitudinal Magnetization

The propagation of monochromatic electromagnetic waves in metal circular cylindrical dielectric waveguide with longitudinal magnetization filled with anisotropic inhomogeneous waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are obtained using a modification of the projecting methods. The comparison with known exact solutions (for particular values of parameters) are made.

Propagation of Electromagnetic Waves in an Open Planar Dielectric Waveguide Filled with an Nonlinear Medium I: TE Waves

A nonlinear eigenvalue problem on an interval is considered. The nonlinearity in the equation is specified by a nonnegative monotonically increasing function, and the boundary conditions nonlinearly depend both on the sought-for functions and on the spectral parameter. The discrete eigenvalues are defined using an additional (local) condition at one end of the interval. This problem describes the propagation of monochromatic (polarized) electromagnetic TM waves in a planar dielectric waveguide filled with a nonlinear medium. The nonlinearity covers a wide range of laws of nonlinear optics corresponding to self-interaction effects. Results on the solvability of the problem and the properties of the eigenvalues are obtained.

A microstretch description of electroelastic solids with application to plane waves

A continuum microstretch model is introduced for electroelastic media on the basis of a biaxial stretch deformation including microrotation. Strain measures, microinertia and electric multipoles are expressed in terms of angle and axis of microrotation and a couple of stretch variables. The linearization of balance laws allows us to state a differential system for seven field variables, as occurs in the simpler micropolar case. This approach is applied to the propagation of plane monochromatic waves adopting two geometric configurations, where an applied electric field is orthogonal to the wavenumber vector. The dispersion equations are obtained in both cases. In addition to the classical purely longitudinal or transverse waves, a set of coupled microstructural modes is found, which show the dependence on the microinertia, electric quadrupole and the orientational angle of the axis of microrotation. A numerical example is shown to discuss wave properties and their occurrence on finite or unbounded wavenumber ranges.

VLF Transmitters as Tools for Monitoring the Plasmasphere

AbstractContinuous burst mode very low frequency (VLF) measurements were recorded on the Van Allen Probes satellites and are analyzed to detect pulses from the Russian Alpha (RSDN‐20) ground‐based navigational system between January and March 2016. Based on the wave characteristics of these pulses and on the position of the spacecraft, the signals propagated mostly in ducted mode in the plasmasphere. Knowledge of the propagation path allowed us to carry out a monochromatic wave propagation inversion to obtain plasmaspheric electron densities. We compared the obtained densities with independent in situ measurements on the spacecraft. The results show good agreement, validating our inversion process. This contributes to validating the field‐aligned density profile model routinely used in the inversion of whistlers detected on the ground. Furthermore, our method can provide electron densities at regimes where no alternative measurements are available on the spacecraft. This raises the possibility of using this method as an additional tool to measure and monitor plasmaspheric electron densities.

Electromagnetic Non-Polarized Symmetric Hybrid Wave Propagation in a Plane Waveguide with Nonlinear Anisotropic Permittivity

Paper focuses on the propagation of monochromatic nonlinear symmetric hybrid waves in a planar dielectric waveguide filled with nonlinear anisotropic medium. The wave propagation problem is reduced to a transmission eigenvalue problem. Eigenvalues of the problem depend on an additional parameter and correspond to propagation constant. Using a perturbation method, it is theoretically proved the existence of a finite number of isolated eigenvalues and, therefore, guide waves. Numerical results are presented.

On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium

Propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear inhomogeneous metal–dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations where spectral parameters are the wave propagation constants. The setting under study is reduced to a new type of nonlinear eigenvalue problem. An analytical method for solving this problem is elaborated. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

An exact solution of the Helmholtz equation u xx + u yy + u zz + k2u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.

On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular dielectric waveguide filled with nonlinear isotropic homogeneous medium

The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The problem is reduced to the new type of nonlinear eigenvalue problem. The analytical method of solving this problem is presented. New propagation regime is found.