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The spherical and parabolic wave functions are calculated for the generalized MIC–Kepler system in the continuous spectrum. It is shown that the coefficients of the parabola–sphere and sphere–parabola expansion are expressed in terms of the generalized hypergeometric function . The quantum mechanical problem of scattering in the generalized MIC–Kepler system is solved. [ABSTRACT FROM AUTHOR]

A system of initially immobile spherical liquid drops placed in another liquid in the field of a propagating acoustic wave is considered. The acoustic radiation force acting on each spherical liquid drop is determined as the function of the incident wave frequency, making use of the solution of a problem of plane harmonic wave scattering on a system of two spherical bodies. The problem is solved by the variable separation method. To satisfy the boundary conditions on spherical surfaces, the expansion of the incident and reflected wave potentials over the spherical wave functions are used. Required constants in the solution are calculated from an infinite system of the algebraic equations, which is solved by a truncation method. It is established that the value of the acoustic radiation force affecting each liquid drop depends significantly on the densities, speed of sound in the outer and internal liquid, as well as on the distance between drops. It is also found that the acoustic radiation force has the same or opposite direction as the incident sound wave depending on its frequency. As result, at different frequencies, the liquid drops can start moving towards or further away from each other. [ABSTRACT FROM AUTHOR]

This study examines the scattering of the orbital angular momentum (OAM) carrying wave by perfect electromagnetic conductor (PEMC) sphere. The incident and scattered electromagnetic fields are expressed using vector spherical wave functions (VSWFs) and unknown field coefficients. A relation between the incident and scattered field coefficients is formulated by implementing the appropriate boundary conditions (BCs) at the surface of the PEMC sphere. Expressions related to the extinction efficiency and scattering asymmetry parameter are derived and computed. The influences of the size parameter of the sphere and the beam waist radius are analyzed. To check the convergence of the proposed work, the numerical results of the scattering efficiency for the vortex electromagnetic (VEM) wave (l = 1) and plane wave (l = 0) for the PEMC sphere are calculated and found to be satisfactory. This investigation provides sufficient information for exploring the electromagnetic scattering mechanism in the OAM domain regarding metamaterial structures. [ABSTRACT FROM AUTHOR]

Near-field acoustic holography (NAH) is an effective tool for realizing accurate sound field reconstruction in three-dimensional space on the prerequisite that appropriate elementary wave functions are selected or constructed to match the characteristics of the sound sources. However, for elongated sources, common wave functions, i.e., plane, cylindrical, or spherical waves, sometimes do not perform well during the sound field projections. To solve this problem, statistically optimized near-field acoustical holography combined with prolate spheroidal wave functions is proposed. In the approach, the sound field is expanded by a series of prolate spheroidal wave functions, whose wavefronts can be set nearly conformal to the elongated sources. Based on these wave functions, fewer expansion terms are required to model the sound field, and the need for regularization can be reduced during the inverse solving process. Therefore, the accuracy of the reconstruction results can be further improved. Numerical simulations are conducted by two types of elongated source models, namely, spatially separated and extended. The results show that the proposed method can effectively reconstruct the sound pressures of elongated sources and perform robustly across a wide frequency range. Simultaneously, a designed experiment is carried out in an anechoic chamber, which demonstrates the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

The exact solution to the axisymmetric acoustic problem of the interaction of a plane wave with a spherical liquid bubble immersed into a dissimilar fluid in a cylindrical cavity is obtained. To satisfy all boundary conditions, the general solution is expanded into a series of normal modes in the coordinate systems fixed to the bubble and cavity, and the expressions of cylindrical wave functions in terms of spherical wave functions are used. The problem is reduced to an infinite system of algebraic equations solved by reduction. The obtained numerical results describe the pressure and velocity fields in the vicinity of the bubble as functions of frequency, fluid characteristics, and geometric parameters of the mechanical system. The strength of acoustic radiation acting on the bubble is calculated and its features at some frequencies of the wave are shown. [ABSTRACT FROM AUTHOR]

An analysis of electromagnetic scattering by perfect electromagnetic conductor (PEMC) sphere using Bessel beam incidence is presented which is based on the generalized Lorenz–Mie theory (GLMT). The PEMC is famous for the generalization of the renowned concept of perfect electric and perfect magnetic conductor (PEC and PMC). The scattering problem is solved by representing the Bessel beam fields i.e., incident and scattered in the context of vector spherical wave functions (VSWFs). The unknown expansion field coefficients can be found out by solving linear equations which are attained from the implementation of boundary conditions (BCs) of PEMC sphere. Computations of the scattering cross-section C sca and the extinction cross-section C ext are performed. The impact on scattering and extinction cross-section for admittance parameter, conical angle, and sphere size parameter are analyzed. Considering a special case for conical angle i.e., α = 0 ∘ , the numerical results of scattering cross-section for Bessel beam and plane wave are same. [ABSTRACT FROM AUTHOR]

We construct the integral transform passing from the space representation to the radial momentum representation for the Hydrogen atom. The resulting wave functions are explicitly given in terms of complex finite expansions of Gegenbauer functions of the first and second kind, or in terms of (elementary) trigonometric functions. We show their symmetry under the S O (4) group, and their equivalence with those of Lombardi and Ogilvie (2020 Chem. Phys. 538 110886). [ABSTRACT FROM AUTHOR]

Antennas for wireless body area networks (WBANs) need to be modeled with adapted methods because the coupling with the body tissue does not allow for a clear separation between antenna and channel. Especially for dynamically varying on-body channels due to changing body poses, e.g., with head-worn antennas, modeling is challenging and design goals for optimal antennas are difficult to determine. Therefore, in this article, the modeling of WBAN channels using spherical wave functions (SWFs) is utilized for antenna de-embedding and for deriving optimal antenna characteristics that maximize the transmission coefficient for the respective channel. It is evaluated how typical factors influencing WBAN channels (different body anatomies, body postures, and varying positions of the communication nodes) can be modeled statistically with SWF. An optimized antenna design is developed based on the derived optimization method, specifically adapted to the channel of on-body links with eye-wear applications. The results with the optimized antenna are compared to other standard antenna designs and validated against measurements. [ABSTRACT FROM AUTHOR]

Partial wave expansions with spherical wave functions are usually employed to describe complex velocity potentials or pressure fields in ultrasonic and acoustic scattering by spherical particles. The expansion coefficients – known as the beam shape coefficients (BSCs) – can be calculated using different approaches which have been largely unexplored in the acoustical literature. Here, we formally present the Finite Series method for the evaluation of BSCs of ultrasonic and acoustic arbitrary-shaped beams. Such a series, which relies on Neumann expansion theorem, is an alternative to quadratures whenever analytical solutions cannot be obtained from direct integration over polar and azimuthal spherical angles. As examples of application, we consider the calculation of BSCs of Bessel, Laguerre–Gauss and Gaussian beams under on-axis configuration, including a discussion on a modified version of the finite series method recently presented in the context of optical fields. • A systematic approach to the finite series is presented for acoustic scattering. • The approach is valid for lossless and inviscid fluids. • Exact beam shape coefficients (BSCs) for beams satisfying the Helmholtz equation. • BSCs of paraxial beams provide approximate remodeling of the velocity potential. • Examples of are given for Bessel, Gaussian and Laguerre–Gauss ultrasonic beams. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherent in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon's fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules. [ABSTRACT FROM AUTHOR]

The Funk‐Hecke type integral relations for vector spherical wave functions are derived. Applying the obtained Funk‐Hecke integral identities, 3D Fourier transforms of vector spherical wave functions Mlmτ and Nlmτ and Llmτ are obtained. On the basis of the Central Slice Theorem, the ray transforms for these vector functions are evaluated. This was found to be a useful tool in the scattering and the vector tomography problems. [ABSTRACT FROM AUTHOR]

We employ the extended boundary condition method (EBCM) that we properly extend so as to describe gyroelectric and gyromagnetic (i.e., gyrotropic) anisotropy and report on the electromagnetic (EM) complex resonances of magnetooptic (i.e., gyroelectric) bodies of revolution (BoRs), as well as on the complex magnetic plasmon resonances (MPRs) of ferrite (i.e., gyromagnetic) BoRs. The proposed extension is based on an alternative scheme for the expansion of the EM field inside a gyrotropic medium, namely, a discrete eigenfunction (DE) expansion in terms of spherical vector wave functions (SVWFs). This approach provides the transition matrix (namely, T-matrix) that allows not only for the direct computation of the scattered field from the incident one, but also for the determination of the complex resonances of open (i.e., situated in free space) gyrotropic BoR resonators. The EBCM is validated on two levels: first, by calculating the EM scattering from various BoRs, including anisotropic spheroids, cylinders, and rods, and comparing with HFSS commercial software; second, by computing the complex eigenfrequency spectrum of gyroelectric spheroidal resonators and comparing with a recently developed rigorous technique for the EM modeling of anisotropic spheroids. [ABSTRACT FROM AUTHOR]

Sound-field reconstruction via the equivalent source method presents an ill-conditioned problem. This paper proposes a method in which traditional monopole equivalent source spherical wave functions are replaced with strong directional wave functions such that an ill-conditioned problem can be improved upon when building the integral equations of a near-field acoustic holography model. Using directional wave functions as an integral kernel function can cause the transfer matrix to be main-diagonally dominant. The accuracy of the proposed method for sound-field reconstruction is verified using numerical simulations, and reconstruction stability in the presence of measurement noise is considered. Furthermore, a method for selecting directional wave functions that are appropriate for various model parameters is introduced. The results show that the proposed method can greatly reduce the condition number of the transfer matrix and improve reconstruction stability. [ABSTRACT FROM AUTHOR]

Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based on expansion in half-space spherical wave functions is proposed. First, the series of half-space spherical wave functions is derived based on the analytical solution of the sound field due to a multipole source located near an impedance plane. Then the sound field in the half-space is approximated by the superposition of a finite number of half-space expansion terms. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching this assumed solution to the total acoustic pressures in the half-space. The free-space radiation can finally be reconstructed via multiplying the free-space spherical wave functions by the corresponding coefficients. Numerical simulation examples of a vibrating sphere and a vibrating baffled plate are demonstrated. The effects of specific acoustic impedance of the boundary and the locations of the measurement points on the accuracy of reconstruction are examined. [ABSTRACT FROM AUTHOR]

The acoustic radiation force on a compressible spheroid is calculated using expansions of the scattered field in terms of both spherical and spheroidal wave functions that are matched analytically in the far field. There is no restriction on the size or impedance of the spheroid, the structure of the incident field, or the orientation of the spheroid with respect to the incident field. The form of the solution is the same as that developed previously for the radiation force on an elastic sphere, which is a summation of terms involving products of the coefficients in spherical wave expansions of the incident and scattered fields. Spheroidal wave expansions are employed to satisfy the boundary conditions and obtain the scattering coefficients. While the scattering coefficients must be obtained numerically for compressible spheroids, explicit expressions in terms of radial wave functions are available for spheroids with rigid or free surfaces. Results are compared with available analytical expressions for various limiting cases. The theoretical framework may be extended to objects of arbitrary shape. [ABSTRACT FROM AUTHOR]

A method for computing the Laue diffraction of an X-ray spherical wave in a single crystal with an inclined step on the exit surface has been developed. The method is based on the use of two approaches to solving the problem: Fourier transformation of the wave function angular dependence in the case of a plane wave incident on a plate-shaped crystal and a numerical solution of the Takagi equations in the step area, where the diffraction parameters depend on the coordinate along the crystal surface. The effect of strong increase in the reflected-beam intensity (by a factor of more than 7 in the maxima) in the transition area, if the step boundary makes a smaller angle with the reflected-beam direction, is predicted based on the numerical calculations. The dependence of the effect on the step-boundary inclination angle is analyzed. [ABSTRACT FROM AUTHOR]

Based on the image theory and addition theorem of spherical vector wave functions, a multiple-reflection solution is described for the electromagnetic scattering by a buried sphere. An iterative process is introduced to obtain the scattered field by enforcing the boundary conditions at the plane interface between free space and an isotropic medium and the spherical surface of a dielectric sphere buried in the isotropic medium. Numerical results for the scattered fields are provided and compared with those obtained by the commercial software FEKO. A good agreement is observed, which verifies the presented formulation. [ABSTRACT FROM AUTHOR]

• The Generalized Source Method is used to develop T-matrix calculation methods: scattering matrix and scattering vector algorithms. • Scattering matrix algorithm provide a new recurrence for T-matrix calculation. • Scattering vector algorithm is highly parallelizable and yields accurate power balance. • A method for consideration of arbitrary polyhedral particles is suggested. The paper presents a scattering matrix and scattering vector methods for calculation of non-spherical particle T-matrices, which are based on the volume integral equation and the spherical vector wave function basis, and rely on the Generalized Source Method rationale. The derivation of the scattering matrix method is based on ideas previously used within the matrix operator method of the radiative transfer theory and the S-matrix method of the grating diffraction theory, and provides a new T-matrix recurrence relation being alternative to the recurrences used within the Invariant Imbedding and the Superposition T-matrix methods. The developed scattering vector algorithm for calculation of T-matrix single columns is shown to have a potential for parallelization and to yield an almost zero power balance for purely dielectric particles. Demonstrated results of electromagnetic scattering simulations include examples for spheroids and a complex non-symmetric polyhedron particle. [ABSTRACT FROM AUTHOR]

Based on the recently proposed power-law spectrum for oceanic turbulence [Opt. Express 26 , 10188 (2018)] and the Rytov approximation, the new and exact theoretical forms for the wave structure function (WSF) of plane and spherical waves propagating in turbulent ocean are derived. To make the results easy to use, the simple formulas for the WSF and the associated spatial coherence radius in certain asymptotic regimes are also developed. Through numerical analysis, it is found that the existing results based on the Nikishov's spectrum predict a higher values for the WSF and thus a lower values for the spatial coherence radius than our results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, a light scattering model for Total Internal Reflection Microscopy (TIRM) is described. The model handles the scattering by an axisymmetric particle of arbitrary orientation situated in the evanescent field near a plane surface, and the imaging of the scattered light via microscope optics. The scattering problem is solved by using the -matrix method and the rotation addition theorem for spherical vector wave functions, while the image of the scattered field is computed by using the Debye diffraction integral. The numerical simulations provide evidence of two working regimes for TIRM: the first regime, corresponding to an incident angle less than the critical angle of total internal reflection, provides information on the size and the orientation of the particle, while the second regime, corresponding to an incident angle larger than the critical angle of total internal reflection, is recommended for measuring the distance between the particle and plane surface. [ABSTRACT FROM AUTHOR]

It is easy to write down entire solutions of the Helmholtz equation: Examples are plane waves and Herglotz wavefunctions. We are interested in the far‐field behaviour of these solutions motivated by the following question: When is it legitimate to split the far field of such an entire solution into the sum of an incoming spherical wave and an outgoing spherical wave? We review the relevant literature (there are disjoint physical and mathematical threads), and then we answer the question for Herglotz wavefunctions, using a combination of the 2‐dimensional method of stationary phase and some explicit examples. [ABSTRACT FROM AUTHOR]

Signal recovery is one of the most important problem in signal processing. This paper proposes a novel signal recovery method based on prolate spherical wave functions (PSWFs). PSWFs are a kind of special functions, which have been proved having good performance in signal recovery. However, the existing PSWFs based recovery methods used the mean square error (MSE) criterion, which depends on the Gaussianity assumption of the noise distributions. For the non-Gaussian noises, such as impulsive noise or outliers, the MSE criterion is sensitive, which may lead to large reconstruction error. Unlike the existing PSWFs based recovery methods, our proposed PSWFs based recovery method employs the maximum correntropy criterion (MCC), which is independent of the noise distribution. The proposed method can reduce the impact of the large and non-Gaussian noises. The experimental results on synthetic signals with various types of noises show that the proposed MCC based signal recovery method has better robust property against various noises compared to other existing methods. [ABSTRACT FROM AUTHOR]

New relations are found between the spheroidal and spherical wave functions, as well as between the spheroidal functions related to different spheroidal coordinate systems. The systems must have a common origin of coordinates and a common symmetry axis of coordinate surfaces. The applicability ranges of the relations obtained are discussed. Numerical test calculations have demonstrated a high efficiency of the relations, specifically those for wave functions including the radial functions of the first kind. As a particular case, relations are considered between prolate and oblate spheroidal wave functions including radial functions of the first and second kinds. These relations are necessary for solving the light scattering problem for nonconfocal layered spheroidal particles. Bibliography: 15 titles. [ABSTRACT FROM AUTHOR]

A passive resonator model for enhancing the low frequency performance of dipole transducers is presented using a spherical wave function model. It is shown that because the near field response of a dipole has the same on-axis low frequency dependence as an equivalent monopole, it can effectively excite a nearby monopole passive resonator and do this with enough strength to significantly modify the response of the system. Sample results are presented to demonstrate the performance enhancement and to illustrate the conversion of the dipole beam pattern to a nearly omni-directional beam pattern. [ABSTRACT FROM AUTHOR]

The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent. [ABSTRACT FROM PUBLISHER]

The work presented in this paper focuses on the reflection and transmission coefficients of an incident plane wave which impinges obliquely a plane of identical spheres arranged periodically in a homogeneous host with infinite extension. The Bloch theorem of periodic structure and the addition theorem of spherical wave functions are used to obtain the total scattering wave from all spherical scatterers periodically arranged in a plane. The total scattering wave in series form of spherical wave functions is then transformed into plane wave form in order to derive the reflection and transmission coefficients. Some numerical examples are given for different size, material constants and array patterns of spherical scatterers, and their influences on the reflection and transmission coefficients of a plane of spheres are discussed based on the numerical results. This study implies that a plane of spheres can be elaborately designed to serve as a sound barrier at a certain frequency range. [ABSTRACT FROM AUTHOR]

This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber. [ABSTRACT FROM AUTHOR]

The expressions for the wave and the phase structure functions of a plane wave and a spherical wave propagating in the natural water turbulence characterized by the recently developed spatial power spectrum (Yao et al., 2020) are evaluated in general and in the limits of large and small separations. The spatial coherence radius for both plane and spherical waves is then deduced. The angle-of-arrival variance of these wavefronts at the collecting lens of the receiving system is also evaluated. In-depth numerical illustrations of the dependence of these quantities on the average temperature/salinity, temperature/energy dissipation rates, and the temperature–salinity gradient ratio are included. Our results are of utmost importance for underwater imaging and sensing technologies. • Wave structure function for plane and spherical wave in underwater turbulent medium is found. • Phase structure function for plane and spherical wave is found. • Angle of arrival fluctuations for plane and spherical wave is found. • Underwater is governed by Oceanic Turbulence Optical Power Spectrum (OTOPS) model. [ABSTRACT FROM AUTHOR]

• The scattering of a non-paraxial Bessel pincer light-sheet by a dielectric sphere of arbitrary size is investigated using GLMT. • The BSCs of the Bessel pincer light-sheet are calculated using ASDM and VSWFs. • The incident, scattering, internal and near-surface fields are numerically analyzed. • The absorption and extinction efficiencies are analyzed. • The influences of the scaling parameter and order of the Bessel pincer light-sheet are discussed. The scattering of a non-paraxial Bessel pincer light-sheet by a dielectric sphere of arbitrary size is studied in the framework of generalized Lorenz-Mie theory (GLMT). The electrical field of the Bessel pincer light-sheet is expanded using the vector angular spectrum decomposition method (VASDM), and its beam shape coefficients (BSCs) are derived using the method of multipole expansion and vector spherical wave functions (VSWF). By this way, the incident field, scattering field and near-surface field, and absorption and extinction efficiency factors are numerically calculated. Also, the effects of the beam order, scaling parameter, and polarization are mainly discussed. Numerical results represent that the intensity distribution of incident field, scattering field and near-surface field is intensely sensitive to the scaling parameters and the beam order. For the incident field, the bigger the order, the smaller the bending angle, and the closer the focus is to the source. By contrast, for the scattering and total field, the bigger the order, the larger the bending angle, and the farther the focus is to the source. Such results have potential applications in the imaging around steep corners and particle manipulation applications with minimal obstruction by particles. [ABSTRACT FROM AUTHOR]

• Evanescent wave scattering by a particle above a plane surface is obtained. • The projection method is applied to the scattering problem. • The normalized DSCS and SCS for the scattering problem are calculated. An exact semi-analytical solution to a scattering problem of evanescent wave incident on a particle is obtained. The evanescent wave is generated by total reflection as an electromagnetic plane wave propagates from an optically denser medium to an optically thinner one. The scattered fields by and internal fields within the particle are expanded in terms of spherical vector wave functions, and an integral representation of spherical vector wave functions over cylindrical ones is used to compute the reflection of the scattered fields on the interface between the optically denser and thinner media. By applying the boundary conditions and projection technique, the unknown expansion coefficients of the scattered fields are determined. The scattering cross sections are evaluated, and the scattering characteristics are analyzed briefly. [ABSTRACT FROM AUTHOR]

In our manuscript, we are reporting the translation criteria of scattering from Perfect Electric Conductor (PEC) sphere along three-dimensional axes using semianalytical approach. The presented scattering model is based on a generalized Lorenz-Mie theory framework and ensemble with the vector translation Addition Theorem (AT) for the Vector Spherical Harmonics (VSH). Applying extended Mie theory on a sphere leads to a set of an unknown coefficients by the use of translation AT. In the literature, there are many authors reporting different sets of the vector translation coefficients, of which we mention those calculated by Stein, Cruzan and, Mackowski in particular. We have selected the Cruzan formulation of the vector translation coefficients for its structure based on the Wigner 3-j function. As an illustration, we want to present numerical examples than simulations. of total scattered field PEC sphere using vector translation AT. We used advanced computational tools and approaches for mathematical modeling of an observation. During our numerical test, we have deeply investigated generic truncation criteria in scattered electric field using translation AT. However, we have been obtained numerical validation by using computational approach. [ABSTRACT FROM AUTHOR]

• Optical force on a sphere of arbitrary size illuminated by an Airy lightsheet is investigated using GLMT. • The BSCs of the Airy light-sheet are calculated using ASDM and VSWFs. • The negative longitudinal optical force is particularly emphasized. • The two kinds of polarizations (TE and TM) of Airy light-sheet are discussed. • The influences of the transverse scale parameter ω 0 and attenuation parameter γ of the Airy light-sheet are discussed. Based on the generalized Lorenz–Mie theory (GLMT) and the angular spectrum decomposition method (ASDM), we calculate the optical radiation force exerted on a lossless dielectric sphere of arbitrary size illuminated by an Airy light-sheet. The beam shape coefficients (BSCs) of the Airy light-sheet are calculated using the vector angular spectrum decomposition and vector spherical wave functions methods. The optical radiation force acting on the spherical particle is obtained by the integral of Maxwell's stress tensor. The transverse (F y) and longitudinal (F z) forces are numerically computed. Two kinds of polarization (TE and TM) are considered for the Airy light-sheet, and the negative longitudinal optical (pulling) force is particularly emphasized. The influence of the transverse scale parameter w 0 and attenuation parameter γ of the Airy light-sheet on the force is discussed. The results of the present theory are verified using the dipole approximation method in which the gradient force has been also computed for a Rayleigh sphere. The numerical results show that when the transverse scale parameter w 0 and attenuation parameter γ increase, the transverse and longitudinal forces decrease. Furthermore, the force caustic (i.e., maximum) shifts to the direction of y < 0 as the transverse scale parameter w 0 increases. As the dimensionless size parameter of the sphere ka increases (where k is the wavenumber and a is the radius), the resonance peaks of the optical forces become larger. The results of this paper are of practical significance for the development of Airy light-sheet based optical manipulation technologies. [ABSTRACT FROM AUTHOR]

• Gaussian beam scattering by a sphere embedded in an infinitely long circular cylinder is presented. • The projection method is applied to the scattering problem. • Total scattered field and normalized field intensity distribution are calculated. An analytical method of analyzing the electromagnetic scattering of a Gaussian beam by an infinitely long circular cylinder with a spherical inclusion is presented. The fields within different regions are expanded in terms of appropriate cylindrical or spherical vector wave functions. By applying the integral representation of spherical vector wave functions over cylindrical ones, boundary conditions and projection procedure, the unknown expansion coefficients are determined. For a localized beam model, numerical results of the total scattered field and normalized field intensity distribution are shown, and the scattering properties are discussed briefly. [ABSTRACT FROM AUTHOR]

• The lateral binding force exerted on chiral bi-sphere induced by a high-order Bessel beam with arbitrary polarization states is studied analytically. • The accuracy of the theory and codes is verified. • Numerical effects of various parameters and different properties are numerically analyzed in detail. Even more so in hindsight of these parameters with respect to optical binding clearly shows that in what case optical binding exists as a fine balance between those parameters. The generalized multi-particle Mie equation (GMM) and electromagnetic momentum (EM) theory are applied to investigate the stability and dynamics of chiral nanoparticles in lateral optical binding induced by a high-order Bessel beam (HOBB). Such non-diffracting light suppressed the influence of the axial intensity profile of the illuminating beams on the self-organization process which then depended critically upon the inter-particles interactions. The illuminating HOBB is described in terms of beam shape coefficients (BSCs) within the framework of generalized Lorenz–Mie theories (GLMT). Utilizing the addition theorem of the vector spherical wave functions (VSWFs), the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the chiral nanoparticles is considered. The observed lateral binding force (BF) dependence of the separation of optically bound particles on the incidence of HOBB is in agreement with earlier theoretical prediction when the chiral spheres degenerate into isotropic spheres. We discuss the influence of the different parameters of the incident Bessel beam and of the chiral body on lateral BF in detail. Linearly and circularly polarized incident Bessel beams are considered, and the corresponding lateral BFs are compared and analyzed. The polarizations of incident HOBB considerably influence the lateral BF of chiral nanoparticles. In binding chiral nanoparticles, the polarization of incident beams should be chosen in accordance with the chirality. This finding may provide a recipe to understand the light interaction with multiple chiral particles of arbitrary shapes with the aid of the analytical approach. It could be a promising avenue in controlling the optical micromanipulation on chiral structures self-arrangement. [ABSTRACT FROM AUTHOR]

• Non-orthogonal spherical Bessel functions may be used in the framework of generalized Lorenz-Mie theory. • This implies the existence of an infinite number of quadratures for evaluating the beam shape coefficients (BSCs). • This infinite number of quadratures nevertheless implies the uniqueness of BSCs, i.e. the uniqueness of the decomposition of EM fields over VSWFs. When dealing with light scattering theories such as the T-matrix methods for structured laser beams, e.g. Generalized Lorenz-Mie Theory (GLMT) or the Extended Boundary Condition Method (EBCM), EM fields are expanded over a set of Vector Spherical Wave Functions (VSWFs) involving spherical Bessel functions, with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). Although spherical Bessel functions are orthogonal over the range (− ∞ , + ∞) , the GLMT may be expressed using a non-orthogonal set of spherical Bessel functions defined over (0 , + ∞) , allowing one to generate an infinite number of quadratures for evaluating the BSCs. This paper points out the difference between orthogonal and non-orthogonal spherical Bessel functions, establishes the infinite number of quadratures and discusses its properties. [ABSTRACT FROM AUTHOR]

This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, Sκ3 (κ > 0) and Hk3 (κ < 0), to the standard spherical waves in E3. The curvature κ is considered as a parameter and for any κ we show how the radial Schrödinger equation can be transformed into a κ-dependent Gauss hypergeometric equation that can be considered as a κ-deformation of the (spherical) Bessel equation. The specific properties of the spherical waves in the spherical case are studied with great detail. These have a discrete spectrum and their wave functions, which are related with families of orthogonal polynomials (both κ-dependent and κ-independent), and are explicitly obtained. [ABSTRACT FROM AUTHOR]