Inhomogeneous Research Articles

Coefficient reconstruction problem for the two-dimensional viscoelasticity equation in a weakly horizontally inhomogeneous medium

Предcтавлена обратная задача последовательного определения двух неизвеcтных (одномерного ядра интегрального оператора и двумерной cкороcти раcпроcтранения волн) для уравнения вязкоупругоcти в cлабо горизонтально-неоднородной cреде. Прямая начально-краевая задача для функции cмещения cодержит нулевые начальные данные и граничное уcловие Неймана cпециального вида. В качеcтве дополнительной информации задаетcя образ Фурье функции cмещения точек cреды при $x_3=0$. Предполагаетcя, что иcкомые величины разлагаютcя в аcимптотичеcкий ряд по cтепеням малого параметра. Доказаны теоремы глобальной однозначной разрешимоcти и уcтойчивоcти решения обратной задачи.

Reciprocity and Representations for Wave Fields in 3D Inhomogeneous Parity-Time Symmetric Materials

Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green’s matrix retrieval and Marchenko-type Green’s matrix retrieval in PT-symmetric materials.

Capillary driven fluid flows in microgravity

Safe operation of orbital platforms relies heavily on stability of fluid flows in microgravity, which are strongly affected by capillary forces. This paper describes experiments on capillary imbibition at a station in Earth orbit, as well as during parabolic flights: firstly, experiments on repeated imbibition of an artificial porous medium (glass balls of various diameters) during parabolic flights of the Airbus A300-ZeroG aircraft organized by the European Space Agency; secondly, investigation of capillary driven seepage in soil (80% quartz sand and 20% kaolinite) on the Discovery STS-91 orbiter carried out within the framework of the MIRROR GAS program. The features of the experiments, experimental equipment, post-processing of experimental data are described. The paper considers the features of the fluid flow through an inhomogeneous porous medium, as well as the case when the medium is repeatedly imbibitted. This is possible if the liquid is observed during several successive parabolas during parabolic flight. The paper describes the mathematical model developed by the authors. The results of numerical simulation are compared with experimental data.

Four-vector optical Dirac equation and spin-orbit interaction of structured light

The spin-orbit interaction of light is a crucial concept for understanding the electromagnetic properties of a material and realizing the spin-controlled manipulation of optical fields. Achieving these goals requires a complete description of spin-dependent optical phenomena in the context of vector-wave mechanics. We develop an extended Dirac theory for optical fields in generic media, which was found to be akin to a non-Hermitian chiral extension of massive fermions with anomalous magnetic momenta moving in an external pseudomagnetic field. This similarity allows us to investigate the optical behaviors of a material by effective field-theory methods and can find wide applications in metamaterials, photonic topological insulators, etc. We demonstrate this method by studying the spin-orbit interaction of structured light in a spin-degenerate medium and inhomogeneous isotropic medium, which leads to both spin-orbital Hall effects and spin-to-orbital angular momentum conversion. Of importance, our approach provides simple and clear physical insight into the spin-orbit interaction of light in generic media, and could potentially bridge our understanding of topological insulators between electronic and photonic systems.

Propagation properties of cosh-Airy beams in an inhomogeneous medium with Gaussian PT-symmetric potentials

Abstract We numerically investigate and statistically analyze the impact of medium parameters (modulation depth P, modulation factor ω, and gain/loss strength W 0) and beam parameters (truncation coefficient a and distribution factor χ 0) on the propagation characteristics of a cosh-Airy beam in the Gaussian parity-time (PT)-symmetric potential. It is demonstrated that the main lobe of a cosh-Airy beam is captured as a soliton, which varies periodically during propagation. The residual beam self-accelerates along a parabolic trajectory due to the self-healing property. With increment in P, the period of a trapped soliton decreases almost monotonically, while the peak power of a trapped soliton increases monotonically. With the increase in ω or decrease in the absolute value of W 0, the period and peak power of a trapped soliton decrease rapidly and then almost remain unchanged. Moreover, it is indicated that the period of a trapped soliton remains basically unchanged no matter a and χ 0 increase or decrease. The peak power of a trapped soliton increases with increment of a, but the peak power of a trapped soliton stays relatively constant irrespective of variation in χ 0.

Warp and blur imaging model consistent with the three constraints of imaging through refractive turbulence.

Point spread function (PSF) for imaging through inhomogeneous refractive medium, such as atmospheric turbulence, is bounded by three constraints [Opt. Eng.52, 046001 (2013)OPEGAR0091-328610.1117/1.OE.52.4.046001]. PSF is non-negative, band-limited, and the third constraint, related to the energy conservation principle, warrants the absence of fluctuations in the image of a uniformly bright object. We develop a version of the common warp and blur model for the anisoplanatic image distortions by turbulence that satisfies these three constraints. In order to comply with the third constraint, our model supplements warp and blur by a random PSF power, which was found to be related to the Jacobian of the warp field. We illustrate statistics of the warp and blur using a simple example of anisoplanatic phase screen.

A Novel Embedded Domain Decomposition Method for Electromagnetic Simulation of Structures in Inhomogeneous Medium

A novel embedded domain decomposition method (EDDM) is proposed to simulate electromagnetic scattering from structures in an inhomogeneous medium. In this method, the inhomogeneous medium (e.g., layered substrate) is set as the background subdomain, and the integrated structures (e.g., metallic/dielectric components) with properly defined buffer regions (BRs) are set as the embedded subdomains, where the meshes of two can be completely independent and arbitrarily overlapping. The major contribution of this work lies in the following three aspects. First, to allow for arbitrary inclusion of the embedded subdomains in an inhomogeneous background subdomain, an adaptive BR method is developed. The self-coupling equation is rederived to ensure the consistency of the BR and the inhomogeneous background, and a new mutual-coupling equation is introduced to account for the material and/or conductor differences. Second, the boundary element method (BEM) accelerated by the multilevel fast multipole algorithm (MLFMA) is utilized to truncate the finite-element region so that the computation capability can be enhanced and the extra air box setting of the background subdomain in the original EDDM can be avoided. Third, for structure adjustments such as translations and rotations, we further propose an inherited calculation to avoid mesh regeneration and repeated computation of the self-coupling and preconditioning matrices and also reduce the iteration counts and solution time. Numerical examples have shown the accuracy, robustness, and efficiency of the proposed method.

An implementation of a finite difference time domain method for second-order nonlinear acoustic equations

The framework of the numerical scheme presented in this talk is that of the finite-difference time-domain (FDTD) method published by Sparrow and Raspet [J. Acoust. Soc. Am. 90, 1991]. The method is fourth-order in space and second-order in time when propagating in homogeneous media. Our implementation resides in a Cartesian coordinate system and is meant to be used in inhomogeneous media. In the neighborhood of inhomogeneities the FDTD method is reduced to second-order in space. Of interest to our applications is the simulation of infinite domains, which is achieved using the perfectly matched layer (PML). The particular PML implementation we consider is one that was designed to absorb linear acoustic waves neglecting thermoviscous effects. In this talk, we will give an overview of our FDTD implementation and show one- and two-dimensional examples to illustrate performance in heterogeneous media that include changes in material properties and scattering objects.

Simple Derivation of Transfer Functions in Bistatic Scattering Model

We present a simple derivation of the increment of the scattering and impedance parameters among antennas caused by the scattering from a target in an inhomogeneous nonmagnetic reciprocal medium. Although these formulas have been published in the literature, we provide a straightforward and elegant derivation using the electromagnetic (EM) reciprocity theorem and the circuit theory. In this way, we provide a deeper physical insight into the formulas crucial for most microwave imaging (MWI) algorithms.

Representation of random media in acoustic scattering calculations

Turbulence, internal waves, surface roughness, and other environmental variations in the atmosphere and ocean randomly scatter sound. Realistic representation of these variations is important for numerical wave propagation calculations. In principle, there are two primary approaches to create these representations: (1) physics-based, dynamical models for the atmosphere or ocean and (2) kinematic synthesis of random fields with prescribed statistical properties that do not necessarily capture the medium dynamics. The most common kinematic approach involves synthesizing fields from randomly phased Fourier modes. For statistically inhomogeneous media, the Fourier modes generalize to empirical orthogonal functions. An alternative kinematic approach, called filtered Poisson processes, distribute spatially localized functions with randomized positions and orientations. Quasi-wavelets (QWs) are a filtered Poisson process intended for turbulence and other self-similar media. While both the Fourier and QW approaches can be formulated to reproduce specified second moments of the random field, if the representations are constructed too sparsely, higher-order moments such as the kurtosis will be unrealistic. The kinematic approaches also underlie phase screen methods, which can be quite useful when the Markov approximation is valid.

Solution of the Radiative Transfer Equation for Vertically Inhomogeneous Media by Numerical Integration Solvers: Comparative Analysis

An efficiency of the singular value decomposition (SVD) method and ordinary differential equation (ODE) solvers in finding the reflection matrix are compared. A reflection matrix can be found by solving the one-dimensional radiative transfer equation. The latter’s solution based on the discrete ordinate method leads to the singular value decomposition (SVD) method. Alternative approach consists in transforming the original problem into a matrix Riccati equation written specifically for the reflection matrix. The matrix Riccati equation is solved using numerical integration techniques for ordinary differential equations (ODEs). It is found that for a single layer case, the SVD approach is faster than the ODE solvers by an order of magnitude. Yet as the number of layers increases, the ODE solvers become more efficient than the SVD approach. In addition, they outperform the SVD method when a solution for a set of optical thicknesses of the medium should be found or when retrieval of optical thickness should be performed. The comparison between different ODE solvers is performed, as well.

Traveling Waves in Nondispersive Strongly Inhomogeneous Media

Traveling Waves in Nondispersive Strongly Inhomogeneous Media

Parabolic equation with arbitrary variations in the sound speed and Mach numbers of the medium velocity

Among computational techniques in atmospheric and ocean acoustics and other fields such as seismic wave propagation, the parabolic equation (PE) approach is one of most popular now. The PE is well suited to small computers, large domains, and high frequencies. It can handle many complicated phenomena such as atmospheric and ocean stratification and refraction, scattering by turbulence, internal waves, and other inhomogeneities, ground impedance and ocean bottom interactions, and propagation over slowly varying terrain and ocean bathymetry. PEs are usually formulated for small variations in the sound speed and small Mach numbers of the medium velocity. However, these assumptions might result in significant phase errors of propagating sound waves. In this presentation, a PE is formulated for arbitrary variations in the sound speed and arbitrary Mach numbers. This new PE is surprisingly simple and can be used in various fields of acoustics and physics. It can be implemented numerically with minimal modifications to existing Crank-Nicholson PE solvers described in Section 11.2 of Ostashev and Wilson, Acoustics in Moving Inhomogeneous Media, Second Edition (2015).

Magnetic-field-modulated radiotherapy (MagMRT) in inhomogeneous medium and its potential applications

Objective. To study the effects of magnetic field gradients on the dose deposition in an inhomogeneous medium and to present the benefits offered by magnetic-field-modulated radiotherapy (MagMRT) under multiple radiation beams. Approach. Monte Carlo simulations were performed using the Geant4 simulation toolkit with a 7 MV photon beam from an Elekta Unity system. A water cuboid embedded with material slabs of water, bone, lung or air was used to study the effects of MagMRT within inhomogeneous medium. Two cylindrical water phantoms, with and without a toroidal lung insert embedded, were used to study the effects of MagMRT under single, opposing or four cardinal radiation beams. Optimized magnetic field variations in the form of a wavelet were used to induce dose modulation within the material slabs or at the iso-center of the phantoms. Main results. The magnitudes of the dose enhancement and reduction induced by the magnetic field gradients become more prominent in a medium of lower density. A maximum dose increase of 6.5% and a decrease of 4.8% were found inside bone, while an increase of 20.4% and a decrease of 13.9% were found in lung tissue. Under multiple radiation beams, the dose enhancement can be induced at the iso-center while the dose reduction occurs in regions around the tumor. For the case with four cardinal beams irradiating a homogeneous water cylinder, an 8.4% of dose enhancement and a 2.4% of dose reduction were found. When a toroidal lung insert was embedded, a maximum dose enhancement of 9.5% and a reduction of 17.0% were produced for anterior-posterior opposing fields. Significance. With an optimized magnetic field gradient, MagMRT can induce a dose boost to the target while producing a better sparing to the surrounding normal tissue, resulting in a sharper dose fall-off in all directions outside the target volume.

Customized Vectorial Optical Fields in Homogeneous and Inhomogeneous Media

The ability to generate structured light in different media is important for various applications, such as optical trapping, imaging, and data communication, but is technically difficult. This study uses ideas from the calculus of variations to develop a simplified, consistent framework that can be used to generate the required customized optical fields. The proposed approach is easily generalized, extending its applicability beyond optics to other wave-related phenomena and subjects, such as acoustics.

Controllable optical rogue waves in inhomogeneous media

This paper investigates new rogue wave solutions of the nonlinear Schrödinger equation with variable coefficients, utilizing the self-similar transformation method. A new rogue wave family is introduced, which displays different wave structures. When one chooses appropriate variable coefficients, a series of first-order, second-order, and third-order rogue waves are obtained. We explore the generation and interaction of rational polynomial rogue waves in detail, and discuss some characteristics of their structures. The paper provides theoretical basis for studying the dynamic behavior of optical rogue wave in inhomogeneous media, and presents potential application value for control of rogue waves in fibers, plasmas and other fields of physics.

Semiclassical theory for plasmons in spatially inhomogeneous media

Recent progress in experimental techniques has made the quantum regime in plasmonics accessible. Since plasmons correspond to collective electron excitations, the electron–electron interaction plays an essential role in their theoretical description. Within the Random Phase Approximation, this interaction is incorporated through a system of equations of motion, which has to be solved self-consistently. For homogeneous media, an analytical solution can be found using the Fourier transform, giving rise to Lindhard theory. When the medium is spatially inhomogeneous, this is no longer possible and one often uses numerical approaches, which are however limited to smaller systems. In this paper, we present a novel semi-analytical approach for bulk plasmons in inhomogeneous media based on the semiclassical (or WKB) approximation, which is applicable when the charge density varies smoothly. By solving the equations of motion self-consistently, we obtain the expressions of Lindhard theory with a spatially varying Fermi wavevector. The derivation involves passing from the operators to their symbols, which can be thought of as classical observables on phase space. In this way we obtain effective (Hamiltonian) equations of motion for plasmons. We then find the quantized energy levels and the plasmon spectrum using Einstein–Brilllouin–Keller quantization. Our results provide a theoretical basis to describe different setups in quantum plasmonics, such as nanoparticles, quantum dots and waveguides.

Finite Element Modelling of a Nonplanar Strike Slip Fault in Vertically Inhomogeneous Viscoelastic Medium

Finite Element Modelling of a Nonplanar Strike Slip Fault in Vertically Inhomogeneous Viscoelastic Medium

Quantifying the breakdown of the rotating-wave approximation in single-photon superradiance

We study quantitatively the breakdown of the rotating-wave approximation (RWA) when calculating collective light emission by quantum emitters, in particular in the weak-excitation limit. Our starting point is a known multiple-scattering formalism where the full light–matter interaction leads to induced inter-emitter interactions described by the classical Green function of inhomogeneous dielectric media. When making the RWA in the light–matter interaction, however, these induced interactions differ from the classical Green function, and for free space we find a reduction of the interatomic interaction strength by up to a factor of two. By contrast, for the corresponding scalar model the relative RWA error for the inter-emitter interaction even diverges in the near field. For two identical emitters, the errors due to the RWA in collective light emission will show up in the emission spectrum, but not in the sub- and superradiant decay rates. In case of two non-identical emitters, also the collective emission rates will differ by making the RWA. For three or more identical emitters, the RWA errors in the interatomic interaction in general affect both the collective emission spectra and the collective decay rates. Ring configurations with discrete rotational symmetry are an interesting exception. Interestingly, the maximal errors in the collective decay rates due to making the RWA occur for finite emitter separations.

A Novel FDTD–PML Scheme for Noise Propagation Generated by Biomimetic Flapping Thrusters in the Ocean Environment

Biomimetic flapping-foil thrusters can operate efficiently while offering desirable levels of thrust required for the propulsion of a small vessel or an Autonomous Underwater Vehicle (AUV). These systems have been studied both as main propulsion devices and for augmenting ship propulsion in waves. In this work, the unsteady hydrofoil loads are used to calculate the source terms of the Ffowcs Williams–Hawkings (FW-H) equation which is applied to model noise propagation in the underwater ocean acoustic environment. The solution provided by a simplified version of the Farassat formulation in free space is extended to account for a bounded domain and an inhomogeneous medium, characterizing the sea acoustic waveguide. Assuming the simplicity azimuthal symmetry of the environmental parameters, a numerical model is developed based on a Finite Difference Time Domain (FDTD) scheme, incorporating free-surface and seabed effects, in the presence of a variable sound speed profile. For the treatment of the outgoing radiating field, a Perfectly Matched Layer (PML) technique is implemented. Numerical results are presented illustrating the applicability of the method.