On the T-matrix for thermo-visco-elastic scattering

The T-matrix method with the Vector Spherical Wave Function (VSWF) expansions represents some difficulties for computing optical scattering of anisotropic particles. As the divergence of the electric field is nonzero in the anisotropic medium and the VSWFs do not satisfy the anisotropic wave equations one questioned whether the VSWFs are still a suitable basis in the anisotropic medium. We made a systematic and careful review on the vector basis functions and the VSWFs. We found that a field vector in Euclidean space can be decomposed to triplet vectors {L, M, N}, which as non-coplanar. Especially, the vector L is designed to represent non-zero divergence component of the vector solution, so that the VSWF basis is sufficiently general to represent the solutions of the anisotropic wave equation. The mathematical proof can be that when the anisotropic wave equations is solved in the Fourier space, the solution is expanded in the basis of the plan waves with angular spectrum amplitude distributions. The plane waves constitute an orthogonal and complete set for the anisotropic solutions. Furthermore, the plane waves are expanded into the VSWF basis. These two-step expansions are equivalent to the one-step direct expansion of the anisotropic solution to the VSWF basis. We used direct VSWF expansion, along with the point-matching method in the T-matrix, and applied the boundary condition to the normal components displacement field in order to compute the stress and the related forces and torques and to show the mechanism of the optical trap of the anisotropic nano-cylinders.

On the basis of the three-dimensional spherical vector wave functions in ferrite anisotropic media, and the fact that the first and second spherical vector wave functions in ferrite anisotropic media satisfy the same differential equations, the electromagnetic fields in homogeneous ferrite anisotropic media can be expressed as the addition of the first and second spherical vector wave functions in ferrite anisotropic media. Applying the continue boundary condition of the tangential component of electromagnetic fields in the interface between the ferrite anisotropic medium and free space, and the tangential electric field vanishing in the interface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in ferrite medium and the scattering fields in free space can be derived. The theoretical analysis and numerical result show that when the radius of a conducting sphere approaches zero, the present method can be reduced to that of the homogeneous ferrite anisotropic sphere. The present method can be applied to the analyses of related microwave devices, antennas and the character of radar targets.

A semi-analytical method is presented for the assessment of induced electromagnetic field inside a multilayer head model exposed to radiated field of an arbitrary source antenna. First the source antenna is simulated by a full-wave software in the absence of the head model to evaluate its radiating characteristics. Then, by sampling of the source radiated fields, its spherical vector wave function (SVWF) amplitudes are evaluated. The well-known translation addition theorem for spherical vector wave functions (SVWFs) is implemented to translate radiating field SVWFs to the local coordinates system of head model. Neglecting the reaction of model on source fields, using boundary conditions on the interfaces of adjacent layers, the unknown SVWF amplitudes of the fields inside each layer as well as those of the scattered field outside the head model are evaluated. Some numerical examples are presented for the verification of the proposed method. The acceptable consistency between the results obtained by the proposed method and full-wave simulations of the problem verifies the authenticity of the proposed method. In comparison to a full-wave numerical method, the proposed method provides an efficient repeatable simulation approach due to the independency of the source and head model analyses.

The translational addition theorem for the spherical vector wave functions (SVWFs) of the first kind is derived in an integral form by the use of the relations between the SVWFs and cylindrical vector wave functions. The integral representation provides a theoretical procedure for the calculation of the beam shape coefficients in the generalized Lorenz-Mie theory. The beam shape coefficients in the cylindrical or spheroidal coordinates, which correspond to an arbitrarily oriented infinite cylinder or spheroid, can be obtained conveniently by using the addition theorem for the SVWF under coordinate rotations and the expansions of the SVWF in terms of the cylindrical or spheroidal vector wave functions.

When a nanorod of typically d=100's nm diameter and h=1-3 micrometers length trapped in the optical tweezers, its orientation is along the trapping beam axis for h/d > 2 and is normal to beam axis for h/d < 2. We report the preliminary experimental observation that some anisotropic single crystal nanorod was stably trapped at a tiled angle to the beam axis. We explain the observation with the T-matrix calculation. In the anisotropic media, as the divergence of is non zero, the conventional vector spherical wave functions (VSWFs) do not individually satisfy the anisotropic vector wave equation. Some new bases, such as the modified VSWFS and qVSWF, have been proposed. Notice that the anisotropic nanorod is floating in the aquatic isotropic medium, we make the VSWF expansions of the incident and scattered fields in terms of, and the VSWF expansion of internal field in the anisotropic nanorod in terms of. Both expansions are therefore legitimate. The boundary condition was chosen as for the normal components of. The internal field is represented as a sum of a set of compoment VSWF expansions to gave better description with more expansion coefficients and to help the convergence of the T-matrix solver. Our calculation showed that when the optical axes of an anisotropic nanorod are not aligned to the nanorod axis, the nanorod may be trapped at a tilted angle position where the lateral torque is zero and its derivative is negative.

Based on spherical vector wave functions(SVWFs) in ferrite anisotropic medium, and the first, second spherical Bessel functions satisfying the same differential equation and recursive formula, the electromagnetic fields in two concentric ferrite anisotropic spheres, and free space can be expressed in terms of SVWFs in anisotropic ferrite medium, and isotropic medium. Applying the continue boundary conditions of electromagnetic fields in the interface of the ferrite anisotropic spherical shell, the coefficients of electromagnetic fields in terms of SVWFs in ferrite anisotropic medium in two concentric ferrite anisotropic spheres and scattering fields in free space are derived. Numerical results for the very general ferrite dielectric media are obtained and those in a special case are compared between the present method and the Method of Moments (MoM) speeded up with the Conjugate-Gradient Fast-Fourier-Transform (CG-FFT) approach. The present method can be probably used in antenna and radiowave propagation, etc.

On the basis of spherical vector wave functions in uniaxial anisotropic medium, and the first, second spherical vector wave functions in uniaxial anisotropic media satisfying the same differential equations, the electromagnetic fields in two concentric uniaxial anisotropic spheres can be expressed as the addition of the first and second spherical vector wave functions in uniaxial anisotropic medium. Numerical results between this paper with the isotropic Mie theory and Method of Moments accelerated with the Conjugate-Gradient Fast-Fourier-Transform (MoM-CG-FFT), a very agreement is found.

The first-order approximation description of Gaussian beam in the two parallel Cartesian coordinates was introduced. On the basis of Generalized Mie theory, adopting the relation between the spherical vector wave functions belonging to a rotating Cartesian coordinate system, the electromagnetic fields of Gaussian beam with spherical vector wave functions was deduced at any right coordinates system. Then taking advantage of the cylindrical vector wave functions given by Stratton, the relationship of the spherical vector wave functions expressed in cylindrical vector wave functions was deduced. Finally the electromagnetic fields of infinitely long cylinder was expanded by the cylindrical vector, and the approximate expression of the cylinder to the far zone scattered field was solved.

On the basis of spherical vector wave functions in uniaxial anisotropic left-handed materials (LHMs) and the first, second, third and fourth spherical vector wave functions in uniaxial anisotropic LHMs satisfy the same differential equation, the electromagnetic fields in uniaxial anisotropic LHMs can be expressed as an addition of the first and second spherical vector wave functions in uniaxial anisotropic LHMs. Applying the boundary conditions of electromagnetic fields in the interface between LHMs and free space, in the surface of conducting sphere, the expansion coefficients of electromagnetic field in uniaxial anisotropic LHMs and scattering field in free space can be derived, and then the radar section cross (RCS) of a plane wave scattering by a LHMs anisotropic uniaxial-coated conducting sphere. Some numerical results are given in this paper.

The far field scattering of single walled carbon nanotubes illuminated by a Gaussian beam

An analytical solution to the scattering of an off-axis Gaussian beam incident on an anisotropic coated sphere is proposed. Based on the local approximation of the off-axis beam shape coefficients, the field of the incident Gaussian beam is expanded using first spherical vector wave functions. By introducing the Fourier transform, the electromagnetic fields in the anisotropic layer are expressed as the addition of the first and the second spherical vector wave functions. The expansion coefficients are analytically derived by applying the continuous tangential boundary conditions to each interface among the internal isotropic dielectric or conducting sphere, the anisotropic shell, and the free space. The influence of the beam widths, the beam waist center positioning, and the size parameters of the spherical structure on the field distributions are analyzed. The applications of this theoretical development in the fields of biomedicine, target shielding, and anti-radar coating are numerically discussed. The accuracy of the theory is verified by comparing the numerical results reduced to the special cases of a plane wave incidence and the case of a homogeneous anisotropic sphere with results from a CST simulation and references.

It is well known that the generalized Lorenz-Mie theory (GLMT) is a rigorous analytical method for dealing with the interaction between light beams and spherical particles, which involves the description and reconstruction of the light beams with vector spherical wave functions (VSWFs). In this paper, a detailed study on the description and reconstruction of the typical structured light beams with VSWFs is reported. We first systematically derive the so-called beam shape coefficients (BSCs) of typical structured light beams, including the fundamental Gaussian beam, Hermite-Gaussian beam, Laguerre-Gaussian beam, Bessel beam, and Airy beam, with the aid of the angular spectrum decomposition method. Then based on the derived BSCs, we reconstruct these structured light beams using VSWFs and compare the results of the reconstructed beams with those of the original beams. Our results will be useful in the study of the interaction of typical structured light beams with spherical particles in the framework of GLMT.

The propagation of a pulsed elastic wave in the following geometry is considered. An elastic half-space has a surface layer of a different material and the layer furthermore contains a bounded 3-D inhomogeneity. The exciting source is an explosion, modelled as an isotropic pressure point source with Gaussian behaviour in time. The time-harmonic problem is solved using the null field approach (the T matrix method), and a frequency integral then gives the time-domain response. The main tools of the null field approach are integral representations containing the free space Green's dyadic, expansions in plane and spherical vector wave functions, and transformations between plane and spherical vector wave functions. It should be noted that the null field approach gives the solution to the full elastodynamic equations with, in principle, an arbitrarily high accuracy. Thus no ray approximations or the like are used. The main numerical limitation is that only low and intermediate frequencies, in the sense that the diameter of the inhomogeneity can only be a few wavelengths, can be considered. The numerical examples show synthetic seismograms consisting of data from 15 observation points at increasing distances from the source. The normal component of the velocity field is computed and the anomalous field due to the inhomogeneity is sometimes shown separately. The shape of the inhomogeneity, the location and depth of the source, and the material parameters are all varied to illustrate the relative importance of the various parameters. Several specific wave types can be identified in the seismograms: Rayleigh waves, direct and reflected P-waves, and head waves. (Less)

Fast superposition T-matrix solution for clusters with arbitrarily-shaped constituent particles

Estimation of wave source position is important technique for searching unknown noise source in EMI and EMC measurement. In this paper a new estimation technique for searching the position of wave source is proposed by using spherical vector wave function and point matching method. In our method a few virtual boundaries are placed on surrounding space encompassed the unknown wave source. Then, applying the boundary condition on the virtual boundaries, the unknown coefficients in the spherical vector wave function can be obtained. In order to verify the validity of this method, numerical experiments are carried out. As the result of them, position of unknown wave source can be estimated accurately by using our method.