Expansion Of Electromagnetic Field Research Articles

Scattering properties of dual Bessel beams on chiral layered particle

The paper investigates the scattering analytical solution of arbitrary direction double zero-order Bessel beams (ZOBBs) incident on a non-uniform layered chiral sphere. Using the generalized Lorenz-Mie theory (GLMT), the electromagnetic field expansion expression of the double ZOBBs is obtained through the vector superposition of the spherical vector wave functions (SVWFs). Analytical solutions of the scattering on chiral layered particles by dual Bessel beams are derived based on the boundary condition. The iterative coefficient equations are constructed to obtain the expansion coefficients of the SVWFs in each region of the multi-layer chiral sphere. The variation of radar cross section (RCS) with angular distribution is numerically simulated, and the scattering results of layered chiral spheres degenerated into isotropic layered spheres are compared with the literature, which verifies the correctness of the theory and program. The effects of incident angle, polarization angle, cone angle and chiral parameters on the scattering characteristics of far region and internal field of the layered chiral particle are analyzed in detail. The theory and results can offer significant assistance in studying the optical properties of non-uniform chiral particles and complex biological cells irradiated by multiple beams and may also provide important practical value in the micromanipulation of multi-layered biological structures.

The time-domain Cartesian multipole expansion of electromagnetic fields

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are computationally intensive and require significant memory. Semi-analytical solutions (e.g., series expansion), such as those provided by the current theoretical framework of the multipole expansion, can be discouraging for practical case studies. This paper shows how sophisticated mathematical tools standard in modern physics can be leveraged to find semi-analytical solutions for arbitrary localized time-varying current distributions thanks to the novel time-domain Cartesian multipole expansion. We present the theory, apply it to a concrete application involving the imaging of an intricate current distribution, verify our results with an existing analytical approach, and compare the proposed method to a finite-difference time-domain numerical simulation. Thanks to the concept of current “pixels” introduced in this paper, we derive time-domain semi-analytical solutions of Maxwell’s equations for arbitrary planar geometries.

Novel Numerical Basis Sets for Electromagnetic Field Expansion in Arbitrary Inhomogeneous Objects.

We investigated how to construct low-order subspace basis sets to accurately represent electromagnetic fields generated within inhomogeneous arbitrary objects by radio-frequency sources external to a Huygen's surface. The basis generation relies on the singular value decomposition of Green's functions integro-differential operators which makes it feasible to derive a reduced-order yet stable model. We present a detailed study of the theoretical and numerical requisites for generating such basis, and show how it can be used to calculate performance limits in magnetic resonance imaging applications. Finally, we propose a novel numerical framework for the computation of characteristic modes of arbitrary inhomogeneous objects. We validated accuracy and convergence properties of the numerical basis against a complete analytical basis in the case of a uniform spherical object. We showed that the discretization of the Huygens's surface has a minimal effect on the accuracy of the calculations, which mainly depended on the electromagnetic solver resolution and order of approximation.

Light scattering and absorption by two-dimensional arrays of nano and micrometer monodisperse spherical silver particles

The problem of light scattering and absorption is considered for a free-standing two-dimensional array (monolayer) of nano- and micrometer spherical silver particles. To solve this problem for short- and imperfect long-range ordered arrays the statistical theory of multiple scattering of waves is used. The key points of the developed semi-analytical method are described. The method is based on the quasicrystalline approximation and the multipole expansion of electromagnetic fields and the dyadic Green's function in terms of vector spherical wave functions. Results for the angular distribution of scattered light, the coefficients of coherent transmission and reflection, incoherent scattering, and absorption of a monolayer are obtained for a spectral range corresponding to the nanoparticle plasmonic resonance. Some features of light propagation through two-dimensional arrays of particles with different spatial order are investigated and discussed. The results are in close agreement with the existing experimental data for a partially ordered array and the calculations for a regular array obtained under the extended low-energy electron diffraction theory.

Convergence analysis of various factorization rules in the Fourier-Bessel basis for solving Maxwell equations using modal methods.

The choice of factorization rule can strongly affect the convergence of solutions to Maxwell equations based on the orthogonal expansion of electromagnetic fields. While this issue has already been investigated thoughtfully for the Fourier basis (plane-wave expansion), for other bases it has not yet received much attention. Although there are works showing that, in the case of the Fourier-Bessel basis (cylindrical-wave expansion), the use of an inverse factorization rule can provide faster convergence than Laurent's rule, these works neglect the fact that other rules are also possible. Here, I mathematically demonstrate four different factorization rules for solving Maxwell equations in cylindrical coordinates using the Fourier-Bessel expansion in both infinite and finite domains. I compare their convergence for a step-index fiber (which has a known exact solution and thus enables the absolute numerical error to be determined), as well as for several VCSEL structures. I show that the cylindrical-wave expansion differs from the plane-wave expansion and that the application of an inverse factorization rule for the electric field component perpendicular to the discontinuities can result in deterioration of numerical convergence. Finally, I identify the factorization rule that gives the fastest convergence of the modal method using the Fourier-Bessel basis.

Modal approach to the method of calculating axisymmetric array antennas taking into account interaction of slot elements based on the electromagnetic field expansion in terms of the eigenfunctions of the outer region of the antenna surface

Modal approach to the method of calculating axisymmetric array antennas taking into account interaction of slot elements based on the electromagnetic field expansion in terms of the eigenfunctions of the outer region of the antenna surface

On the pole expansion of electromagnetic fields.

In several publications, it has been shown how to calculate the near- or far-field properties for a given source or incident field using the resonant states, also known as quasi-normal modes. As previously noted, this pole expansion is not unique, and there exist many equivalent formulations with dispersive expansion coefficients. Here, we approach the pole expansion of the electromagnetic fields using the Mittag-Leffler theorem and obtain another set of formulations with constant weight factors for each pole. We compare the performance and applicability of these formulations using analytical and numerical examples. It turns out that the accuracy of all approaches is rather comparable with a slightly better global convergence of the approach based on a formulation with dispersive expansion coefficients. However, other expansions can be superior locally and are typically faster. Our work will help with selecting appropriate formulations for an efficient description of the electromagnetic response in terms of the resonant states.

Design of terahertz fibers using polymer tube bundles and their guided mode and propagation loss analyses

Flexible terahertz fibers were designed for terahertz wave applications. In this paper, new terahertz fiber structures using polymer tube bundles were proposed. A triangle structure fiber with three-tube core and a hexagonal structure fiber with mono-tube core were considered. Mode field distributions in the proposed terahertz fibers and their propagation losses were numerically calculated using the finite element method. It was found that lower propagation loss was obtained for longer operating wavelength and smaller thickness of polymer tube due to the fraction increment of electromagnetic field propagating in the air. It was also clarified that lower propagation loss was brought by introducing the core tube material with lower absorption coefficient, where the propagation loss increased for longer wavelength due to the electromagnetic field expansion into the cladding region with larger absorption coefficient compared with the core material.

On some behavioral peculiarities of magneic type eigenmodes of a spherical particle with arbitrarily valued material parameters

Subject and Purpose. The spectral characteristics (eigenfrequencies, eigenmodes, Q-factors) of a spherical particle with arbitrarily valued permittivity and permeability are considered to take a further look into some important features of their behavior. The real and imaginary parts of the material parameters of the particle can be both positive and negative. The emphasis is on magnetic type modes. Methods and Methodology. The spectral problem is solved using the electromagnetic field expansion in vector spherical wave functions. Results. The first eigenfrequencies of a spherical particle have been calculated depending on its relative permittivity e 1 and relative permeability m 1 whose real and imaginary parts can take both positive and negative values. The eigenmodes split into two, internal and external, eigenmode families. The internal eigenmodes bear an independent, associated with eigenmode structure labeling in each quadrant of the plane (m 1 , e 1). The external eigenmodes, on the contrary, have a uniform labeling throughout the whole (m 1 , e 1) plane and bear a structural resemblance to surface plasmon oscillations distributed in the vicinity of the particle surface or outside it. In the first quadrant of the plane (m 1 , e 1), the external eigenmodes repeatedly interact with the internal eigenmodes, leading to either mode hybridization or mode type exchange. In the third quadrant of the plane (m 1 , e 1), the external eigenmodes can interact with one another. The anomalous behavior of the spectral characteristics of a spherical particle corresponds to the already known phenomenon of wave mode coupling described in the scientific literature well enough. Conclusion. The performed study has revealed some new behavioral patterns as to the spectral characteristics of a spherical particle with arbitrarily valued permittivity and permeability

Spatial Order and Absorption of light by Monolayer of Silicon Nano- and Submicrometer-Sized Particles

The effect of the spatial order of a monolayer of monodisperse spherical crystalline silicon nano- and submicrometer-sized particles upon its absorption coefficient is theoretically investigated. The calculation method is based on the quasicrystalline approximation of the theory of multiple scattering of waves and multipole expansion of electromagnetic fields and tensor Green function in terms of vector spherical wave functions. The results can be used for an enhancement of light harvesting in a solar cells design.

Deformations of circularly polarized Bessel vortex beam reflected and transmitted by a uniaxial anisotropic slab.

Bessel vortex beams are widely studied, since their intensity is independent of the propagation distance, and also their original field intensity distribution can be reconstructed after passing through an obstacle. Therefore, such beams are more advantageous for long-distance communication, optical imaging, and other potential applications. Based on the expansion of electromagnetic fields in terms of vector wave functions, in this investigation a method has been proposed to study the reflection and transmission of an incident circularly polarized Bessel vortex beam by a uniaxial anisotropic slab. The expansion coefficients of a circularly polarized Bessel vortex beam are derived by use of the cylindrical vector wave functions. The magnitude profiles of the electric field amplitude and phase, as well as the distribution of orbital angular momentum (OAM) states for both the reflected and transmitted beams, are numerically simulated and discussed. The effects of dielectric tensor and incident angle on the propagation characteristics of a circularly polarized Bessel vortex beam are analyzed. The observed results indicate that the contours of the electric field components cannot retain circularly symmetric structures; the distortion of phase distribution is obvious, and except for the predominant OAM state, other OAM states are derived, particularly for the reflected beam. Although few OAM states emerge in the transmitted beam, the predominant OAM state is still the same as that of the incident Bessel vortex beam.

Leaky-mode expansion of the electromagnetic field inside dispersive spherical cavity

Rigorous justification is presented for a recently introduced method to construct leaky-mode expansions of electromagnetic fields excited inside a spherical cavity filled with a dispersive, lossy medium. In a departure from the traditional approaches, our construction does not rely on Green’s functions, rather it starts from a judiciously chosen auxiliary meromorphic function. Convergence of both the series expansions and of the over-completeness relations for the leaky modes is proven for a realistic model of chromatic dispersion.

Incoherent component of light scattered by a monolayer of spherical particles: analysis of angular distribution and absorption of light.

We have derived an analytical solution for an incoherent component of light scattered by a normally illuminated monolayer of homogeneous spherical particles. It is based on the quasi-crystalline approximation of the theory of multiple scattering of waves as well as on the multipole expansion of electromagnetic fields and tensor Green's function in terms of vector spherical wave functions. We apply the solution to a description of scattering and absorption characteristics of partially ordered monolayers and monolayers with imperfect lattices. The impact of particle size and type of particle spatial order on light absorption is studied. The comparison of calculated and available experimental data is made on the angular and spectral position of the first diffraction order peak for a monolayer with an imperfect triangular lattice from silicon dioxide particles. The theoretical and experimental data are in close agreement.

ELECTROMAGNETIC WAVE DIFFRACTION PROBLEM BY PERIODICAL GRATING IN PLANE WAVEGUIDE

The problem of an electromagnetic wave diffraction by a periodical grating made of thin conducting screens between two conducting planes is reduced to an infinite set of linear algebraic equations. Three-dimensional case was considered when a field depends on all three spatial coordinates. According to the theorem of unique diffraction problem solution if an original wave is Floquet wave, then the desired solution of the Maxwell equations set can also be only the Floquet wave. We used the expansion of the desired functions along the orthogonal system of functions depending on a transverse coordinate, and the representation in the form of a quasiperiodic function along a longitudinal coordinate. The case when a field does not depend on a transverse coordinate is considered separately. From the boundary conditions and the field conjugation conditions in a grating plane, a pair-wise summatory equation is obtained with respect to the coefficients of the electromagnetic field expansion over an eigenwave of a waveguide. This equation is reduced to an infinite set of linear algebraic equations by the method of integral-summatory identity. An infinite set of linear equations is represented in vector-matrix form: the desired values are two-dimensional vectors, and their coefficients are the square matrices of the second order. Its approximate solution can be obtained by truncation.

Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.

Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system.

Comments on “Confluent edge conditions for the electromagnetic wave at the edge of a wedge bounded by material sheets” by Mithat Idemen

It is pointed out some inaccuracies in Idemen’s method [Idemen (2000, 2011)] while having investigated electromagnetic field near the edge of a resistive half-plane. The limiting for the field expansion only to the first power of logarithmic function is not valid and rigorously leads to the trivial solution. It is needed to include the logarithmic functions to the field expansion in any cases when among the solutions of the characteristic equation there are roots that differ from one another by any integer. • Inaccuracies in published papers are commented on. • The inability to represent an electromagnetic field near the edge of resistive half-plane without logarithmic functions. • The importance of taking into account higher order terms in the electromagnetic field expansion is emphasized.

Quasimodal expansion of electromagnetic fields in open two-dimensional structures

A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional open structures. In contrast with the bounded case which has only a discrete spectrum (real in the lossless media case), open resonators show a continuous spectrum composed of radiation modes and may also be characterized by resonances associated to complex eigenvalues (quasimodes). The use of a complex change of coordinates to build perfectly matched layers allows the numerical computation of those quasimodes and of approximate radiation modes. Unfortunately, the transformed operator at stake is no longer self-adjoint, and classical modal expansion fails. To cope with this issue, we consider an adjoint eigenvalue problem whose eigenvectors are biorthogonal to the eigenvectors of the initial problem. The scattered field is expanded on this complete set of modes leading to a reduced order model of the initial problem. The different contributions of the eigenmodes to the scattered field unambiguously appears through the modal coefficients, allowing us to analyze how a given mode is excited when changing incidence parameters. This gives physical insights to the spectral properties of different open structures such as nanoparticles and diffraction gratings. Moreover, the QMEM proves to be extremely efficient for the computation of local density of states.

Multipole expansion of polarised electromagnetic fields

The multipole expansion of a general plane polarised electromagnetic field is derived. This is accomplished by calculating the coefficients of the dynamical multipole expansion of electromagnetic fields, representing generic solutions of the Maxwell equations in a source-free region. The analytical results are confirmed by comparing the suitably terminated expansions to the exact fields.

Measurement-Based Analysis of Spatial Degrees of Freedom in Multipath Propagation Channels

A method of estimating spatial degrees of freedom (DoF) from measured multipath propagation channels in the multiple-input single-output regime is presented. The DoF of the multipath channels on the transmit (Tx) side is derived by means of the spherical-wave expansion of electromagnetic fields radiated from a Tx antenna array having a certain aperture size. The DoF estimates are independent of particular realization of antenna elements on the Tx aperture. For a given aperture size, the DoF provides the number of the Tx antenna elements for efficient improvement of the system performance by utilizing the spatial diversity. Having confirmed the soundness of our DoF estimation method by channel measurements in an anechoic chamber, the DoF of indoor multipath channels is analyzed. The DoF on the Tx side of the considered multipath channels reveals larger values when the antenna aperture size is increased at a fixed frequency, and when the frequency increases for a fixed antenna aperture size. For a fixed frequency, increasing the antenna aperture size is more effective in observing extra DoF in the obstructed and non-line-of-sight channels than in the line-of-sight channels. Furthermore, for a fixed antenna aperture size, the use of the higher frequency brings larger DoFs in many propagation scenarios. The results also show that electrically smaller antennas are more efficient in observing the DoF. Finally, the solid angle of multipath is derived as a Tx antenna-independent metric of the multipath richness. It is defined as an angular range of dominant multipath clusters subtended on a unit sphere. Our analysis method is extendable to the multiple-input multiple-output regime in a straightforward manner.

Generalized Modal Expansion of Electromagnetic Field in 2-D Bounded and Unbounded Media

A generalized modal expansion theory is presented to investigate and illustrate the physics of wave-matter interaction within arbitrary two-dimensional (2-D) bounded and unbounded electromagnetic problems. We start with the bounded case where the field excited by any sources is expanded with a complete set of biorthogonal eigenmodes. In regard to non-Hermitian or nonreciprocal problems, an auxiliary system is constructed to seek for the modal-expansion solution. We arrive at the unbounded case when the boundary tends to infinity or is replaced by the perfectly matched layer (PML). Modes are approximately categorized into two types: trapped modes and radiation modes, which respond differently to environment variations. When coupled with the source, these modes contribute to the modal-expansion solution with different weights, which leads to a reduced modal representation of the excited field in some geometries.