Inhomogeneous Research Articles

Spin Hall effect of radiofrequency waves in magnetized plasmas.

In inhomogeneous media, electromagnetic-wave rays deviate from the trajectories predicted by the leading-order geometrical optics. This effect, called the spin Hall effect of light, is typically neglected in ray-tracing codes used for modeling waves in plasmas. Here, we demonstrate that the spin Hall effect can be significant for radiofrequency waves in toroidal magnetized plasmas whose parameters are in the ballpark of those used in fusion experiments. For example, an electron-cyclotron wave beam can deviate by as large as 10 wavelengths (∼0.1m) relative to the lowest-order ray trajectory in the poloidal direction. We calculate this displacement using gauge-invariant ray equationsof extended geometrical optics, and we also compare our theoretical predictions with full-wave simulations.

Novel applications of local optimization semi-Cartesian grid for the complex band structure analysis of phononic crystals

In this paper, we propose a finite element method based on the Floquet transform and local optimization semi-Cartesian grid to compute the complex band structure of phononic crystals. Floquet transform is applied to transform the elastic wave equation into a quadratic eigenvalue equation. Value-periodic test function independent of the interface is defined to derive the weak formulation. The local optimization semi-Cartesian grid is proposed to improve the quality of triangular elements near the interface. Our results are in good agreement with ones obtained by other mature methods, and the purely propagative mode coincides with the traditional band diagram. In addition to simple scatterer shapes such as circle or square, the proposed method is able to calculate the complex band structures of phononic crystals with complicated scatterer shapes. Numerical experiments demonstrated the effectiveness of this method in the computation of anisotropic inhomogeneous medium. The complex band structures under different lattice types, scatterer shapes, material properties, rotation angle and modes are obtained, and their effects on the width and number of band gaps are analyzed.

Inhomogeneous reduced Maxwell-Bloch system in nonlinear optics: Darboux-transformation and solitonic issues

Studies on nonlinear optics are active, providing the applications in modulators, fiber lasers, optical sensors, etc. In this paper, we investigate an inhomogeneous reduced Maxwell-Bloch system, which could describe the ultra-short optical pulses through an inhomogeneous medium. N-fold Darboux transformation is constructed via an existing Lax pair, where N is a positive integer. Generalized Darboux transformation is obtained via a limit procedure. One- and two-soliton solutions are determined with the aid of the N-fold Darboux transformation. Double-pole soliton solutions are derived via the generalized Darboux transformation. With respect to the electric field, microscopic polarization, phase information, and atomic inversion related to the inhomogeneous medium, one soliton, interaction between the two solitons, and double-pole soliton are graphically depicted. Effects of the coefficients in that system on those solitons are shown via the trigonometric and linear functions.

Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium

Investigations on nonlinear optics are active, with the applications in the modulators, fiber lasers, optical sensors, etc. In this paper, we focus our attention on a system for the ultra-short pulses in an inhomogeneous multi-component nonlinear optical medium. Starting from the existing Lax pair and one-fold Darboux transformation (DT), we construct the N-fold DT of that system, which involves N distinct spectral parameters, where N is a positive integer. The N-fold generalized DT with one spectral parameter is obtained through resorting to the Taylor-series-expansion coefficients of a special solution to that Lax pair. Double-pole soliton solutions of that system are derived via that N-fold generalized DT with N=2. With the aid of the N-fold DT, an N-fold Darboux matrix is constructed, based on which the multi-pole soliton solutions in the determinant form with respect to the electromagnetic field E are determined. Graphically, we find that those double-pole soliton solutions are a kind of the bound-state soliton solutions which represent the elastic interactions between the two solitons. Effects of the coefficients in that system on the double-pole soliton are shown via choosing the trigonometric, linear and quadratic functions. Furthermore, we present the triple-pole soliton and quadruple-pole soliton with respect to E. Our results might be useful in understanding the ultra-short pulses in the nonlinear optical media.

Volume Integral Equations and Single-Trace Formulations for Acoustic Wave Scattering in an Inhomogeneous Medium

AbstractWe study frequency domain acoustic scattering at a bounded, penetrable, and inhomogeneous obstacleΩ−⊂Rd\Omega^{-}\subset\mathbb{R}^{d},d=2,3d=2,3. By defining constant reference coefficients, a representation formula for the pressure field is derived. It contains a volume integral operator, related to the one in the Lippmann–Schwinger equation. Besides, it features integral operators defined on∂Ω−\partial\Omega^{-}and closely related to boundary integral equations of single-trace formulations (STF) for transmission problems with piecewise constant coefficients. We show well-posedness of the continuous variational formulation and asymptotic convergence of Galerkin discretizations. Numerical experiments in 2D validate our expected convergence rates.

A right inverse of curl which is divergence‐free invariant and some applications to generalized Vekua‐type problems

In this work, we investigate the system formed by the equations and in bounded star‐shaped domains of . A Helmholtz‐type decomposition theorem is established based on a general solution of the above‐mentioned div‐curl system. When , we obtain a bounded right inverse of which is a divergence‐free invariant. The restriction of this right inverse to the subspace of divergence‐free vector fields with vanishing normal trace is the well‐known Biot–Savart operator. This right inverse will be restricted to guarantee its compactness and satisfy suitable boundary value problems. Applications to Beltrami fields, Vekua‐type problems, as well as Maxwell's equations in inhomogeneous media are proposed.

Simulation of Linear Non-Hermitian Boundary-Value Problems with Quantum Singular-Value Transformation

We propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the propagation of electromagnetic waves in a one-dimensional system with outgoing boundary conditions. The corresponding measurement procedure is also discussed. Limitations of the QSVT algorithm are identified in connection with the large condition numbers that the dispersion matrices exhibit at weak dissipation.

Theory of Doubly-Shielded Coupled Lines for Directional Couplers of Various Directivity Types With Impedance Transformation

Asymmetric coupled lines (CLs) with double shielding in an inhomogeneous dielectric medium are studied. They have specific properties that allow the creation of impedance-transforming directional couplers with a given directivity type. The proposed models and synthesis techniques take into account both electric asymmetry and dielectric inhomogeneity. Numerical simulations and measurements prove the correctness of the general theory, and the possibility of creating co-, contra-, and trans-directional couplers with impedance-transforming and phase-shifting properties. The results will be useful for finding new design solutions for next-generation microwave circuits.

Seismic and medical ultrasound imaging of velocity and density variations by nonlinear vectorial inverse scattering.

We present an iterative nonlinear inverse scattering algorithm for high-resolution acoustic imaging of density and velocity variations. To solve the multi-parameter nonlinear direct scattering problem, the acoustic wave equation for inhomogeneous media in the frequency domain is transformed into a vectorial integral equation of the Lippmann-Schwinger type for the combined pressure and pressure-gradient field. To solve the multi-parameter nonlinear inverse scattering problem, we use the Newton-Kantorovich method in conjunction with matrix-free representations of the Fréchet derivative operators and their adjoints. The approximate Hessian information that is accounted for in our iterative solution of the (nonlinear) multi-parameter inverse scattering problem is essential for the mitigation of multi-parameter cross talk effects. Numerical examples related to seismic and medical ultrasound breast imaging illustrate the performance of the new algorithm for multi-parameter acoustic imaging.

Wave and Particle Analysis of Z‐Mode and O‐Mode Emission in the Jovian Inner Magnetosphere

AbstractWe report some of the most intense Z‐mode and O‐mode observations obtained by the Juno spacecraft while in orbit about Jupiter in a low to mid‐latitude region near the inner edge of the Io torus. We have been able to estimate the density of the plasma in this region based on the lower frequency cutoff of the observed Z‐mode emission. The results are compatible with the electron density measurements of the Jovian Auroral Distributions Experiment (JADE), on board the Juno spacecraft, if we account for unmeasured cold plasma. Direction‐finding measurements indicate that the Z‐ and O‐mode emission have distinct source regions. We have also used the measured phase space density of the JADE and the Jupiter energetic particle detector instruments to calculate estimated local growth rates of the observed O‐mode and Z‐mode emission assuming a loss cone instability and quasilinear analysis. The results suggest the emissions were observed near, but not within, a source region, and the free energy source is consistent with a loss cone. We have thus carried out the quasilinear wave analysis of the assumed remote Z‐ and O‐mode wave growths. It is shown that the remotely generated waves, propagated through an inhomogeneous medium to the satellite location, may account for the observed wave characteristics. The importance of Z‐mode in accelerating electrons in the inner Jovian magnetosphere makes these new wave mode confirmations at Jupiter of particular interest.

Transient radiative transfer in two graded – index slab adhered by an infinitely thin vacuum via the lattice Boltzmann method

The lattice Boltzmann method is presented to solve the radiative transport of both diffuse and collimated problems in inhomogeneous and semitransparent two – layered slab with graded refractive indices. The two layers are bounded by Fresnel's walls and separated by an infinitely thin vacuum interlayer with negligible thickness to represent the case with surface roughness or assembling of two layers using a transparent binder or intumescent resin. The high – order discrete ordinates is used to simulate the angular redistribution due to variable refractive indices and multiple reflections at the boundaries and interface. The accuracy and efficiency of the methodology is firstly tested for transient and steady state solution in two – layered slab with constant or variable refractive indices. Effects of the distributions of refractive indices and surrounding, scattering albedos, and the optical thicknesses on the transient radiative signals are examined. Calculation results show that, these parameters have a significant influence on radiative transfer and the angular intensities at different few times levels are presented to illustrate the effects of the interface characteristics, and the discontinuous nature of the intensity at the interface is discussed. The developed LBM is a promising, efficient and simple solver to perform the radiative transport in inhomogeneous layered media with graded – index functions.

Generation and Manipulation of Airy Breathing Solitons in an Inhomogeneous Medium with Periodic Potential

The propagation characteristics of Airy beams in an inhomogeneous medium with periodic potential are studied theoretically and numerically. The Gross–Pitaevskii equation was solved with periodic potential using the separating variables method, and a breathing soliton solution and the breathing period were obtained. Further, the propagation properties of an Airy beam, and the interaction between two Airy beams while considering the medium parameters and beam parameters were numerically simulated in detail. First, we discuss the influence of the initial medium parameters (modulation intensity P and modulation frequency ω) on the propagation characteristics. Then, we investigate the effect of the initial beam parameters (initial chirp C and position x0) on the propagation characteristics. Lastly, the interaction of two Airy beams with opposite spatial positions for different phase φ, amplitude A, and initial interval x0 is analyzed. The breathing period and central position of the breathing solitons could be controlled by changing the initial medium parameters. By varying the initial beam parameters, the deflection direction and size, and the maximal intensity of the breathing solitons were manipulated. The breathing solitons of different bound states were formed by changing the phase φ, amplitude A, and initial interval x0 of two Airy beams. The results provide a theoretical basis for the propagation and manipulation of Airy beams.

Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media

The propagation and scattering of electromagnetic waves in dielectric media is of theoretical and experimental interest in a wide variety of fields. An understanding of observational results generally requires a numerical solution of Maxwell equations---usually implemented on conventional computers using sophisticated numerical algorithms. In recent years, advances in quantum information science and in the development of quantum computers have piqued curiosity about taking advantage of these resources for an alternate numerical approach to Maxwell equations. This requires a reformulation of the classical Maxwell equations into a form suitable for quantum computers which, unlike conventional computers, are limited to unitary operations. In this paper, a unitary framework is developed for the propagation of electromagnetic waves in a spatially inhomogeneous, passive, nondispersive, and anisotropic dielectric medium. For such a medium, generally, the evolution operator in the combined Faraday-Ampere equations is not unitary. There are two steps needed to convert this equation into a unitary evolution equation. In the first step, a weighted Hilbert space is formulated in which the generator of dynamics is a pseudo-Hermitian operator. In the second step, a Dyson map is constructed which maps the weighted-physical-Hilbert space to the original Hilbert space. The resulting evolution equation for the electromagnetic wave fields is unitary. Utilizing the framework developed in these steps, a unitary evolution equation is derived for electromagnetic wave propagation in a uniaxial dielectric medium. The resulting form is suitable for quantum computing.

A hybrid implicit-explicit discontinuous Galerkin spectral element time domain (DG-SETD) method for computational elastodynamics

SUMMARY A hybrid implicit-explicit (IMEX) discontinuous Galerkin spectral element time domain (DG-SETD) algorithm is proposed to simulate 3D elastic wave propagation in inhomogeneous media. In this method, the original problem can be divided into a number of well designed subdomains, and the mesh generation of different subdomains is completely independent, thus allowing flexible spatial discretization of complex geometry. The neighboring subdomains are connected by a Riemann transmission condition (RTC), and spectral elements with different interpolation orders can be used in different subdomains to maximize the computational efficiency of multiscale problems to facilitate parallel computing for different subdomains. In particular, the explicit or implicit time iteration scheme can be appropriately selected for a subdomain according to the size of its mesh elements to increase the global time step increment, thus giving higher computational efficiency: For subdomains with coarse meshes, the explicit time integration scheme is used and the time step increment is limited by the Courant−Friedrichs−Lewy (CFL) stability condition; for subdomain with fine structures and thus fine meshes, an implicit time integration scheme is used so that a large time step increment can be used without affecting the stability. In addition, a jump condition of displacement and velocity is introduced to accurately simulating fractures and faults, including lossless and viscous fractures with plane, curve or cross structures. This avoids the volume modeling of the extremely thin fracture structures, and effectively reduces the number of degrees of freedoms (DoFs) in the discretized system without the loss of accuracy. The accuracy, robustness and efficiency of the DG-SETD algorithm are demonstrated by quantitative comparisons of the waveforms with the commercial finite element software COMSOL.

Defect-mediated diffusion of implanted Mg in GaN: Suppressing dopant redistribution by sequential thermal and microwave annealing

The diffusion behavior of Mg in Mg/N co-implanted GaN is investigated in response to a set of annealing conditions and methodologies, namely, 1000 °C/30 min thermal anneal, by high-temperature pulsed gyrotron microwave annealing at 1420 or 1500 °C, or by thermal and microwave annealing, sequentially. After 1000 °C annealing, the diffusion of Mg in GaN is found to be negligible, as measured by secondary ion mass spectrometry. Annealing by gyrotron microwave annealing alone induces the diffusion of Mg at a rate on the order of 10−12 cm2/s. However, the use of a thermal anneal before microwave gyrotron annealing reduces this rate by an order of magnitude to 10−13 cm2/s. We find that a model that considers Mg diffusion from an inhomogeneous medium that contains a defect-rich implanted region near-surface to a relatively pristine region below the implant range better explains the observed diffusion behavior than a conventional model that assumes a homogeneous medium. By analyzing the diffusion behavior using the Boltzmann–Matano method, we present a discussion of reduction in [VGa] by thermal annealing at 1000 °C, leading to a suppressed diffusion coefficient during subsequent high-temperature annealing relative to diffusion after 1420/1500 °C annealing alone. This effect holds potential for improvement in the precision of selectively doped regions for future applications based on the (Al)GaN material system. An improved field profile control in real devices can increase the breakdown and current-handling capabilities in power electronic applications.

Dynamic stress analysis of elliptical inclusions in an inhomogeneous medium with modulus and density variations under the action of shear horizontal (SH) waves

In this paper, in connection with the problem of elastic wave propagation in a continuously inhomogeneous medium, the dynamic stress concentration phenomenon caused by the elliptical inclusions in a complex, continuously inhomogeneous medium under the action of shear horizontal (SH) waves is studied. First, the auxiliary function and the shear modulus function are introduced to construct the wave field function, and the modulus is reduced in order and simplified using a high-order fluctuating wave equation with variable coefficients that has power function variations; then, the auxiliary function and the modulus function are introduced once again to construct the density function; finally, the conformal mapping method is used to carry out coordinate transformation and to solve and obtain the standard form of the Helmholtz equation. Based on this combined problem model, the wave field and the stress field are derived, and the expression for the dynamic stress concentration factor (DSCF) is given. The influence of the inhomogeneous parameters, the ratio of the long and short axes of the elliptical inclusions, and the relative properties of the elliptical inclusions and the matrix on the DSCF around the elliptical inclusions is analyzed through calculation examples.

Exact soliton solutions of a (2+1)-dimensional time-modulated nonlinear Schrödinger equation with cubic-quintic nonlinearity

In the present paper, based on the wave ansatz method, exact bright and dark solitons of a (2+1)-dimensional time variable coefficients nonlinear Schrödinger equation with cubic-quintic nonlinearity term are presented. This model can be used to describe the propagation of optical pulse in inhomogeneous media. These obtained solitons exhibit nonautonomous properties due to the amplitude and velocity of them are time-dependent coefficients. At this time, Tangent and Secant function solutions are also reported.

An Analytical Antenna Modeling of Electromagnetic Wave Propagation in Inhomogeneous Media Using FDTD: A Comprehensive Study.

This paper discusses the challenges in characterizing electromagnetic (EM) waves propagating through inhomogeneous media, such as reinforced cement concrete and hot mix asphalt. Understanding the EM properties of materials, including their dielectric constant, conductivity, and magnetic permeability, is crucial to analyzing the behavior of these waves. The focus of this study is to develop a numerical model for EM antennas using the finite difference time domain (FDTD) method, and to gain a deeper understanding of various EM wave phenomena. Additionally, we verify the accuracy of our model by comparing its results with experimental data. We analyze several antenna models with different materials, including the absorber, high-density polyethylene and perfect electrical conductors, to obtain an analytical signal response that is verified against the experimental response. Furthermore, we model the inhomogeneous mixture of randomly distributed aggregates and voids within a medium. We verify the practicality and reliability of our inhomogeneous models using experimental radar responses on an inhomogeneous medium.

A mixed element scheme for the Helmholtz transmission eigenvalue problem for anisotropic media

In this paper, we study the Helmholtz transmission eigenvalue problem for inhomogeneous anisotropic media with the index of refraction in two and three dimensions. Starting with the nonlinear fourth-order formulation established by Cakoni et al 2009 J. Integral Equ. Appl. 21 203–27, we present an equivalent mixed formulation for this problem with auxiliary variables, followed by finite element discretization. Using the proposed scheme, we rigorously show that the optimal convergence rate for the transmission eigenvalues on both convex and nonconvex domains can be expected. With this scheme, we obtain a sparse generalized eigenvalue problem whose size is too demanding, even with a coarse mesh that its smallest few real eigenvalues fail to be solved by the shift and invert method. We partially overcome this critical issue by deflating nearly all of the eigenvalues with huge multiplicity, resulting in a marked reduction in the matrix size without deteriorating the sparsity. Extensive numerical examples are reported to demonstrate the effectiveness and efficiency of the proposed scheme.

Shadows and strong gravitational lensing by Van der Waals black hole in homogeneous plasma

In this paper, we first analyze the horizon structure of the Van der Waals (VdW) black hole and then investigate its shadow in the absence of a plasma medium as well as the presence of a homogeneous plasma medium. We find that both the Van der Waals parameters a and b have a significant effect on the shadow of the black hole. We also observe that the radius of the shadow in a homogeneous plasma medium increases when parameter σ=ωpω∞ (the ratio of plasma frequency and photon frequency) increases and the radius of the shadow inhomogeneous plasma medium is larger than the vacuum medium. We also discuss the strong gravitational lensing in a homogeneous plasma medium. We observe that the photon sphere radius, deflection limit coefficients and deflection angle in the strong field are highly affected by the presence of a homogeneous plasma medium. We also find that the deflection angle in the strong field limit by the Van der Waals black hole with the homogeneous plasma is greater than that of the Vacuum medium. Further, we discuss the observable quantities angular position θ∞, separation S and magnification rmag by taking the example of a supermassive black hole M87∗ in the context of Van der Waals black hole and compared to the other ordinary black hole such as Schwarzschild Ads black hole in the strong field limit with the effects of homogeneous plasma. It is concluded that the Van der Waals parameters a, b and homogeneous plasma medium have a significant effect on both the shadows and strong gravitational lensing. It is further concluded that the Van der Waals black hole can be quantitatively distinguished from the other ordinary black hole such as Schwarzschild Ads black hole via shadow and strong lensing observations.