The Eigenfunctions and Exact Solutions of Discrete mKdV Hierarchy with Self-Consistent Sources via the Inverse Scattering Transform

Another form of the discrete mKdV hierarchy with self-consistent sources is given in the paper. The self-consistent sources are presented only by the eigenfunctions corresponding to the reduction of the Ablowitz-Ladik spectral problem. The exact soliton solutions are also derived by the inverse scattering transform.     

Light scattering by an erythrocyte based on discrete sources method: Shape and refractive index influence

An efficient method for the fast detection of properties of a single erythrocyte from its scattering characteristics is needed in practice. To develop such a method a detailed investigation of the light scattering properties of the erythrocyte and their dependence on its shape and refractive index is of great interest. In this paper the influence of the real erythrocyte's shape with deep concavities and refractive index on the scattering characteristics is analyzed based on an updated scheme of the discrete sources method. Realistic shape models of an erythrocyte, calculated from minima of membrane potential energy are considered. The numerical scheme of discrete sources method has been adjusted for shape profiles given numerically. An improved algorithm allows increasing of an accuracy of calculations.     

Scattering of E and H polarized waves from covered cylindrical structures

A modification of the method of discrete sources (MMDS) is applied for solving 2D scattering problems by metal (or dielectric) cylindrical structure covered with a dielectric layer. The scattering of E (or H) polarized incident plane and cylindrical wave was considered. The problems of accuracy, choosing auxiliary contours and impedance approximation in scattering problem are discussed.     

Analysis of spectral characteristics of scattering of evanescent waves

The spectral scattering characteristics of nanoscale particles exhibited in the field of evanescent waves are analyzed using the method of discrete sources. The effect of various parameters on the behavior of the scattering characteristics is studied. The material of the particles is shown to have the most substantial effect on the scattering cross section.     

Exact Solutions of Ablowitz-Ladik Hierarchy with Self-Consistent Sources Revisited and Reductions

In the paper, Ablowitz-Ladik hierarchy with new self-consistent sources is investigated. First the source in the hierarchy is described as φ_nφ_n+1, where φ_n is related to the Ablowitz-Ladik spectral problem, instead of the corresponding adjoint spectral problem. Then by means of the inverse scattering transform, the multi-soliton solutions for the hierarchy are obtained. Two reductions to the discrete mKdV and nonlinear Schrödinger hierarchies with self-consistent sources are considered by using the uniqueness of the Jost functions, as well as their N-soliton solutions.     

T-matrix method for biaxial anisotropic particles

Using the T-matrix approach electromagnetic scattering by a biaxial anisotropic non-axisymmetric particle is studied. Electromagnetic fields inside the scatterer are expressed by a system of quasi-spherical vector wave functions which are derived by use of inverse Fourier transform. Using this expansion a solution of the light scattering problem in the framework of the null-field method with discrete sources is obtained.Numerical scattering results for ellipsoids and cubes are presented. For validation the calculation results obtained are compared with results from other light scattering programs such as DDSCAT and ADDA.     

Discrete sources method for light scattering analysis from 3D asymmetrical features on a substrate

The discrete sources method is extended to analyze polarized light scattering by three-dimensional asymmetrical features on a plane penetrable substrate. The strict mathematical model and corresponding numerical scheme are described. Computer simulation results of non-spherical micro-particle scattering show that particle shape has a stronger effect on measured response for normal incident scanners.     

Scattering of evanescent waves by a sensor tip near a plane surface

The paper is devoted to the application of a rigorous approach for analyzing the evanescent wave scattering by sensor tip near a plane surface. On the basis of the discrete sources method a numerical schemes was developed and implemented in computer program. Numerical results related to the influence of the position of the sensor tip on the scattering characteristics are discussed.     

Analysis of the scattering properties of defects of layered substrates

The light scattering by defects of a layered substrate, such as foreign particles on a film and damages of the film itself, is analyzed. The analysis of the scattered light intensity is based on the generalization of the method of discrete sources. To identify defects of different kinds, it is proposed to use the integral scattering characteristics of polarized light.     

Light scattering by needle-type and disk-type particles

A powerful tool to analyze light scattering by 3D arbitrary-shaped homogeneous or inhomogeneous obstacles located in free space is based on volume integral equation. In this paper we apply a weak form of volume integral equation to simulate light scattering by needle- and disk-type particles such as straight and curved cylinders, cylindrical plate and hexagonal prism with high aspect ratio and low and high values of refractive indexes. For problems where discrete sources method could be applied, we calculated differential scattering cross-section using both methods and got excellent agreement in results.     

Analysis of the scattering properties of a nanometric insertion in a film on a substrate

The scattering characteristics of an insertion in a gold film deposited on a glass prism are analyzed using the method of discrete sources. The effect of extreme energy transmission through the film is revealed in the range of total internal reflection.     

Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method

The resonance properties of nanoshells are of great interest in nanosensing applications such as surface enhanced Raman scattering or biological sensing. In this paper the discrete sources method has been applied to analyze the spectrum of evanescent light scattering from a nanoshell particle deposited near a plane surface. Based on the rigorous theoretical model, which allows to take into account all features of the scattering problem as: medium with frequency dispersion, presence of the interface, the objective aperture and its location and core-shell asphericity, the scattering spectrum of nanoshells was calculated. The dependence of the local nanoshell spectral density behavior on its properties is discussed.     

On the modified discrete KP equation with self-consistent sources

The modified discrete KP equation is the Bäcklund transformation for the Hirota’s discrete KP equation or the Hirota-Miwa equation. We construct the modified discrete KP equation with self-consistent sources via source generation procedure and clarify the algebraic structure of the resulting coupled modified discrete KP system by presenting its discrete Gram-type determinant solutions. It is also shown that the commutativity between the source generation procedure and Bäcklund transformation is valid for the discrete KP equation. Finally, we demonstrate that the modified discrete KP equation with self-consistent sources yields the modified differential-difference KP equation with self-consistent sources through a continuum limit. The continuum limit of an explicit solution to the modified discrete KP equation with self-consistent sources also gives the explicit solution for the modified differential-difference KP equation with self-consistent sources.     

Different shape models for erythrocyte: Light scattering analysis based on the discrete sources method

In practical applications a precise and fast detection of the shape of a single erythrocyte from its scattering characteristics is needed. For this reason detailed investigations of light scattering properties of erythrocyte and their relation to shape is of great interest in recent years. In this paper we analyze light scattering behavior of different shape models of erythrocyte using the discrete sources method. For this we compare scattering results for oblate spheroid, disk-sphere, Cassini-based shape and a shape for a real strainless erythrocyte introduced by Skalak. Numerical results for the scattering indicatrix and the differential cross section by different shape models and its orientations are presented.     

Nonlinear susceptibilities of quantum dots

A new method for the analysis of light scattering by a nonspherical penetrable microparticle located on the substrate surface is developed. A computational algorithm is constructed on the basis of generalization of the method of discrete sources. The results of a numerical simulation are discussed.     

Investigation the spectral scattering characteristics of a nanohole in a film

Based on the method of discrete sources, an analysis is made of the spectral scattering characteristics of a nanohole in a metal film applied onto a glass prism. An effect of extremal electromagnetic energy leakage through the hole is discovered in the evanescent wave formation region.     

Cancellation of spurious arrivals in Green's function retrieval of multiple scattered waves

The Green's function for wave propagation can be extracted by cross-correlating field fluctuations excited on a closed surface that surrounds the employed receivers. This study treats an acoustic multiple scattering medium with discrete scatterers and shows that for a given source the cross-correlation of waves propagating along most combinations of scattering paths gives unphysical arrivals. Because theory predicts that the true Green's function is retrieved, such unphysical arrivals must cancel after integration over all sources. This cancellation occurs because the scattering amplitude of each scatterer satisfies the generalized optical theorem. The cross-correlation of scattered waves with themselves does not lead to the correct retrieval of scattered waves, because the cross-terms between the direct and scattered waves is essential.     

Analysis of light scattering in the evanescent waves area by a cylindrical nanohole in a noble-metal film

The discrete sources method has been extended to analyze the scattering behavior of a cylindrical nanohole in a noble-metal film deposited on a glass prism. The dependence of the transmitted intensity on the incident angle has been investigated. Extreme transmission of the incident plane wave has been detected in the evanescent waves area.     

Investigation of the resonance properties of nanodimensional rods by the method of discrete sources

Based on the method of discrete sources, a mathematical model for the analysis of the spectral characteristics of the scattering of nonradiative waves by nanodimensional rods arranged on the surface of a glass prism was constructed. It was shown that the spectral characteristics significantly depend on both the elongation of the rods and their orientation.