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Interactions between collective multi-layered cells and an off-axis high-order Bessel beam (HOBB) are investigated. The generalized Lorenz-Mie theory is applied to derive the expansion of HOBB. Based on the additional theorem, multiple scattering of collective multi-layered nanoparticles is obtained by considering the tangential continuous boundary conditions. The present theory and codes are proven to be effective by comparing with the simulations obtained from the computer simulation technology (CST) software. Numerical results concerning the effects of beam order, beam conical angle, spherical layer number, core radius and outer layer radius, outer layer refractive index and the spherical number on the scattering of various types of aggregated multi-layered particles are displayed in detail, which may provide critical support for analytically understanding the optical scattering characteristics of aggregated multi-layered biological cells of complex shapes and may find important applications in manipulating multi-layered biological structures.

Analytical solutions to the scattering of a uniform uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel vortex beam (HOBVB) are investigated. Using the vector wave theory, the expansion coefficients of the incident HOBVB in terms of the spherical vector wave functions (SVWFs) are obtained. According to the orthogonality of the associated Legendre function and exponential function, more concise expressions of the expansion coefficients are derived. It can reinterpret the incident HOBVB faster compared with the expansion coefficients of double integral forms. The internal fields of a uniform uniaxial anisotropic sphere are proposed in the integrating form of the SVWFs by introducing the Fourier transform. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by a zero-order Bessel beam, Gaussian beam, and HOBVB are exhibited. Influences of the topological charge, conical angle, and particle size parameters on the angle distributions of the radar cross section are analyzed in detail. The scattering and extinction efficiencies varied with the particle radius, conical angle, permeability, and dielectric anisotropy are also discussed. The results provide insights into the scattering and light–matter interactions and may find important applications in optical propagation and optical micromanipulation of biological and anisotropic complex particles.

A solution to the problem of Gaussian beam scattering by a circular perfect electric conductor coated with eccentrically anisotropic media is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with Taylor's series. The transmitted field in the anisotropically coated region is expressed as an infinite summation of Eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The addition theorem for cylindrical functions is applied to transfer from the local coordinates to the global ones. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting a similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the eccentric geometry comes to the concentric one.

We examined optical trapping force (TF) exerted on non-uniform chiral stratified spheres by a high-order Bessel beam (HOBB). Present theories were proven to be valid by comparison with the existing reference. Numerical simulations considering the effects of various parameters on TF are displayed in detail. The results show that different chirality distributions in stratified chiral sphere will affect significantly the trapping characteristics, and a stable three-dimensional capture can be realized only by selecting the appropriate parameters of incident beam and particles. The theoretical investigations may provide an analytical method to help understand the interaction of light with more complex stratified chiral cells and thus become an encouraging approach to better design an optical manipulation system.

Based on the generalized multi-particle Mie equation (GMM) and Electromagnetic Momentum (EM) theory, the lateral binding force (BF) exerted on multilayered spheres induced by an arbitrary polarized high-order Bessel beam (HOBB) is investigated with particular emphasis on the half-conical angle of the wave number components and the order (or topological charge) of the beam. The illuminating HOBB with arbitrary polarization angle is described in terms of beam shape coefficients (BSCs) within the framework of generalized Lorenz-Mie theories (GLMT). Utilizing the addition theorem of the spherical vector wave functions (SVWFs), the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the multilayered spheres is considered. Numerical results concerning the influences of different parameters of the incident Bessel beam and of the binding body on the lateral BF are displayed in detail. The observed dependence of the separation of optically bound particles on the incidence of HOBB is in agreement with earlier theoretical prediction. Accurate investigation of BF induced by HOBB exerted on multilayered spheres could provide key support for further research on optical binding between more complex multilayered biological cells, which plays an important role in using optical manipulation on stratified particle self-assembly.

Due to atmospheric absorption, the signal attenuation must be considered when designing communication links in the terahertz (THz) band. The equivalent height described in International Telecommunication Union Recommendation (Rec. ITU)-R P.676 can be used to evaluate the signal attenuation over satellite links by meteorological parameters of the Earth's surface, which are relatively convenient to obtain. Since both temperature and water vapour content can greatly influence the absorption of THz waves and have temporal and spatial variability, the equivalent height should be a combined value representing the influences of temperature, water vapour, and pressure. However, only pressure is considered in the ITU-R P.676 model. As a result, it will cause inaccuracies for different regions and seasons. In this study, a modified model of the equivalent height with temperature and water vapour near the Earth's surface is proposed. Compared with the forward equivalent heights, the equivalent heights based on both models are evaluated. Analyses of the window frequencies are performed, and improved results are achieved with the modified model, especially for mid- and high-latitude winter profiles. The accuracy of the modified model for other profiles is also analysed and the results indicate its suitability.

A solution to the problem of Gaussian beam scattering by an anisotropically coated circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with a Tayor’s series. The transmitted field in the anisotropically coated region is expressed as a infinite summation of eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting the similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.

Two-dimensional scattering of a Gaussian beam by a homogeneous gyrotropic circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression with Taylor's series. The transmitted field in the homogeneous gyrotropic cylinder is expressed in terms of the series of wave functions based on the integral equation. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions of continuous tangential electric and magnetic fields. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.

In this study, a method to choose the maximum calculation height and the maximum propagation angle of the split-step troposcatter wide-angle parabolic equation (TWAPE) method is presented. The method is implemented with the height and the scatter angle of the troposcatter common volume. The performance of this method is then demonstrated with a few examples which rely heavily on the choosing of the maximum calculation height and the maximum propagation angle. These examples include the comparison of calculated results of TWAPE for choosing different maximum calculated height and maximum propagation angle at frequencies of 3 and 1 GHz, path lengths of 300 and 500 km, respectively. Finally, the seasonal variation mechanism of the troposcatter propagation loss is discussed based on the seasonal variation of the refractive-index structure parameter.

Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addition theorem of SVWFs, interactive and total scattering coefficients are derived through the continuous boundary conditions on which the interaction of the particles is considered. The accuracy of the theory and codes are verified by comparing results with those obtained for arbitrary plane wave incidence by CST simulation, and for ZOBB incidence by a numerical method. The effects of angle of incidence, pseudo-polarization angle, half-conical angle, beam center position, and permittivity tensor elements on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres, such as a linear chain, a 4×4×4 cube-shaped array, and other periodical structures consisting of massive spheres, are numerically analyzed. Selected results on the properties of typical particles such as TiO2, SiO2, or other particle lattices are calculated. This investigation could provide an effective test for further research on the scattering characteristics of an aggregate of anisotropic spheres by a high-order Bessel vortex beam. The results have important application in optical tweezers and particle manipulation.

The composite electromagnetic scattering problem from the randomly rough sea surface and an object nearby is effectively analyzed by the Extended Propagation-Inside-Layer Expansion (EPILE) combined with the Forward-Backward method (FBM) scheme. The formulation of the composite scattering is given, the efficiency and accuracy of the adoptive algorithm are verified, and several scattering characteristics under various parameters are numerically analyzed.

Based on the practical situation of nondestructive examination, an improved analysis of the scattering properties of multiple-defect particles for an optical surface is shown. Using finite difference time domain method, the generalized perfectly matched layer can work very well against the half-space problem of optical surface and defect particles. Boundary-connecting condition is reduced by three-wave method. Reciprocity theorem is applied to near-far field extrapolation. Results are compared with those obtained using CST Microwave Studio software, and both are found to match each other very well, thereby proving the reliability of the proposed method. Angle distributions of double particles with different positions are shown. Some selected calculations on the effects of sphere number and sphere separation distance are described. As the most important factor, the position factor is numerically analyzed in detail. Theory and model are valuable in examining inspect optical or wafer surface.

Based on the generalized multi-particle Mie theory and the Fourier transformation approach, light scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes illuminated by a zero-order Bessel beam (ZOBB) is investigated. The size and configuration of the particles are arbitrary. The expansion expressions of the ZOBB are given in terms of the spherical vector wave functions (SVWFs) and the expansion coefficients are derived. Utilizing the vector addition theorem of the SVWFs, the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. The effects of the conical angle, beam centre position, sphere separation distance, and anisotropic parameters on the far-region field distributions are numerically analyzed in detail. Some results are compared with those results for a Gaussian beam incidence. Selected results of bispheres consisting of typical medium such as TiO2, SiO2, Silicon, water are exhibited. This investigation could provide an effective test for further research on the scattering characteristic of an aggregate of anisotropic spheres by a high-order Bessel vortex beam and radiation forces, which are important in optical tweezers and particle manipulation applications.

In order to estimate where the electromagnetic radiation associated with the seismic activity comes from, the propagation characteristics of the SLF/ELF electromagnetic waves on the ground should also be studied. The radiation source may also be modeled as a horizontal magnetic dipole (HMD), and it is precisely calculated by using a speeding numerical convergence algorithm. A theoretical calculation of the VLF/SLF electric wave propagating among the Earth-ionosphere cavity generally utilizes the full wave method to solve the model equation. The field in the cavity is comprehended as the sum of each wave mode. However, this method is very complex, and unsuitable to the ELF frequency band. To solve the problems under the non-ideal electric conductor condition, we have further developed Barrick's method. The approach we employ below subtracts and adds appropriate identical terms to the original exact series. The subtraction accelerates significantly its numerical convergence. The added terms sum to simple closed-form expressions. The spherical harmonic series expressions of electromagnetic fields excited by SLF/ELF HMD in non-ideal Earth-ionosphere cavity have been derived. The speed of our algorithm is faster twenty eight times than it of calculating directly the sum of the series. If it calculates directly the sum of the series, it needs 1,200 series items and takes 17 min, while it needs only 300 series items and takes 0.6 min. Moreover, under the ideal electric conductor condition, we have verified the correct of our algorithm that the result coincides with that of Barrick's method. Schumann resonance is also verified.

The problem of scattering by an anisotropic-coated nonconfocal conducting elliptic cylinder is investigated. In order to solve the boundary condition on the surface of the conducting cylinder, the transmitted field in the homogeneous anisotropic shell is described in the local coordinates. The addition theorem of Mathieu functions is used to transfer from the local coordinates to the global ones. Only the transverse magnetic case is presented. The result is in agreement with that available, as expected when the coated elliptic cylinder degenerates to a coated circular one.

Based on the Generalized Lorenz–Mie Theory (GLMT) and generalized multiparticle Miesolution (GMM), scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes and arbitrary configuration from a Gaussian beam is investigated. By introducing the Fourier transformation, the electromagnetic fields in the uniaxial anisotropic spheres are expanded in terms of the spherical vector wave functions (SVWFs). The interactive scattering coefficients and the expansion coefficients of the internal fields are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. The influences of the beam waist widths, beam center position, and spheres separation distance on scattering characteristics of uniaxial anisotropic bispheres located in a Gaussian beam are numerically analyzed in detail.

The angle distribution of the spheroid particle upon optical surface is discussed in this paper. Taking the advantage of the Bobbert-Vlieger (BV) theorem, the scattering model between optical surface and spheroid particles is established. The scattering process is analyzed and the scattering coefficients are derived by using of the vector spherical harmonic function. The differential scattering cross section (DSCS) of a spheroid particle upon the optical surface is calculated which is compared with the Discrete Sources Method (DSM) proved the validity of the method and the influences of the incident angle and scattering angle on the DSCS are analyzed numerically in details. The results show that the influence of the incident angle on the scattering intensity is less at the smaller scattering angle, which can be concluded that the influence of the incident angle is more serious to the back scattering .The polarization effect and back scattering effect become weaker and weaker with the increase of the incident angle, which provide strong theoretical foundation to the nondestructive detector engineer.

Based on the altitude-dependent model of the ITU-R slant atmospheric turbulence structure constant model, we present scintillation index calculations for a Gaussian Schell-model (GSM) beam under all irradiance fluctuation conditions. The longitudinal and radial components of the scintillation index are treated separately. Our results correctly reduce to the result of the horizontal path with atmospheric structure constant fixed, and simplify to a fully coherent beam with source coherence parameter ζs representing unit. The numerical conclusions indicate that within specific source and parameter ranges, the GSM beam is capable of offering less scintillation than the full coherent Gaussian beam. Before the maximum value of the scintillation, the scintillation index of the GSM beam will decrease with increased altitude. However, the off axis radial scintillation index will vanish when the Rytov variance is infinity.

Evaporation duct is a manifest phenomenon that can afiect microwave propagation seriously with low elevation angles near the sea surface. As an important parameter to describe the characteristic of the evaporation duct, duct height can be estimated from radar sea echo using a technique called as \refractivity from clutter". In this study, we proposed a novel approach to estimating the evaporation duct height. The signal power received by a ground- based GPS receiver is used when the GPS satellites rise or set at the local horizon over the sea. A forward propagation model and genetic algorithm are adopted to implement this method. The performance is evaluated via numerical simulation for inferring evaporation duct with difierent height. The results showed that the proposed method is well efiective, especially for the conditions with higher evaporation duct height.

Generally, the profile of many surfaces in the nature are of random and rough property, such as, the sea surface, the soil surface, etc., and different scattering characteristics will appear when they are incidented by the electromagnetic wave, which are of considerable value for the domain of remote sensing, radar exploration, etc.. A more complicated case is the composite scattering from the rough sea or soil surface and the target, which have been proved to have special importance about the target recognition. Many important research have been made for both the single rough surface scattering and the target-rough surface composite scattering. For the specific exponential spectrum rough soil surface including environmental factors and target composite electromagnetic scattering issue, the pre-sutdy basing on an efficient hybrid and numerical strategy, i.e., the Propagation-Inside-Layer-Expansion combing with the iterative technique is made by us. The composite sense was modeled. The coupling scattering integral equation was buit. The coupling mechanisms by using the metioned hybrid scheme were formulized. Comparing with the traditional numerical method, the efficiency and accuracy for this method aiming at this specific composite case were analyzed. Furthermore, by using this scheme, several scattering results under many different parameter, such as different target size, different target position, different soil roughness, different soil moisture, different soil temperature, etc., were obtained. The multiple and corresponding relationship between the typical coherent and incoherent scattering characteristics and the coupling interactions from target and rough soil surface are discussed and concluded. This pre-study will make considerable sense to the areas of remote sensing related the actual land and the buried target detection, etc..

Some computational electromagnetic strategies for surface with different scale of roughness combined with different physical or environmental factors are discussed in this presentation. For the relatively small scale roughness surface electromagnetic problem, the Small Perturbation Method and its higher order computational methods are compared. For the relative big scale roughness surface, the Kirchhoff Approximation and its higher order or modified method are listed and discussed. For the surface with both small and big scale roughness, due to the limitation of small argument expansion and tangential plane approximation, either the Small Perturbation Method and its higher order solving scheme or the Kirchhoff Approximation and its higher order or modified substitute will be invalid, the Two Scale Method that conquers the disadvantage of the above-mentioned schemes should be adopted, and its modified strategy will further improve the precision in the big angle region. Besides, some physical or environmental factors, such as the heat (temperature), moisture, wind, etc., that affect the electromagnetic characteristics of natural rough surface are also discussed. These studies will make sense to many fields, especially, the electromagnetics, remote sensing, optics, oceanography, radar surveillance, material science, etc.

Some studies of the influences from typical scene (target, rough surface) parameters on the target and rough surface composite electromagnetic scattering characteristics are carrying out. The target and rough surface with specific type and spectrum cases are considered. The composite scattering integral equations are built. The numerical hybrid strategies, such as the Propagation-Inside-Layer-Expansion (PILE) combined with the Forward-Backward Method (FBM) scheme, etc., are applied. The influence from different target parameters, such as, size, depth, etc., to the coupling inductions is investigated. The influence from different rough surface parameters, such as rms height, correlation length etc., to the composite scattering is implemented. The experiential and prediction models between typical scattering phenomenon and coupling interaction mechansium under different parameters can be built and analyzed. The presented studies will make considerable sense to the fields of electromagnetics, remote sensing, optics, radar surveillance, target recognition, material science, etc‥

The decomposition of the multivariate Non-Gaussian PDF in the sum of a Gaussian PDF instead of the Gram-Charlier series is investigated. Four parameters need to be found by minimizing the integrated square of the difference between Cox-Munk function and its approximation. The backscattering radar cross section (RCS) of the surface is calculated by the Kirchhoff approximation (KA) under different value of k using the formula of decomposition of the Non-Gaussian. The condition of KA satisfying electromagnetic scattering scale from Gaussian and Non-Gaussian surfaces is taken into account by computing the backscattering coefficients in HH and VV polarity.

Optical waveguide phased arrays have highlighted advantages than other electro-optical material optical arrays in scanning angle, response speed etc. For diffraction fields of uniform waveguide have strong side-lobes, which have influence on scanning performance of phased arrays. So side-lobes compression is one of the main issues for optical waveguide phased array device development. Based on photoelectric effect, the relations of voltage and phase are analysised. Phase-only array beam control using a Genetic Algorithm, an efficiency-optimized scheme, for uniform optical waveguide array with process errors is proposed. Phase distributions are arranged as randomly increasing distributions and random distributions. The results show phase-only optical waveguide arrays control, without the reconstruction of devices, has fine side-lobes compression effects with -9.89[dB] side-lobes intensity ratio. So the performance of scanning beams gets well improved.

Based on the extended Huygens-Fresnel principle, scintillation of a partially coherent Gaussian Schell-model (GSM) beam propagation in weakly slant atmospheric turbulence is studied. The expression of aperture-averaging factor of the system receiver is derived. We analyzed the aperture-averaged scintillation index numerically. A comparison of the aperture-averaged scintillation of the beam propagation in slant path with that of the beam propagation in horizontal path is made. Results obtained show using partially coherent beams and considering aperture-averaging effect can decrease the scintillation and improve the optical communication system performance.

Based on the derivatives between the fundamental and higher-order Hermite Gaussian beam and the Davis’s one-order approximation of slowly varying function, a general expression of the higher-order Hermite Gaussian beam are presented. Scattering characteristics of higher-order off-axis Hermite Gaussian is investigated. Some selected calculations on the effects of the beam waist width and the beam waist center positioning are described.

A model of laser fuse echo simulation based on radiometry is developed. Process of target/beam interaction is determined by target surface optical scattering properties, which can be characterized by bidirectional reflectivity distribution function (BRDF). Signal features of the near-zone echo wave scattered from complex target are analyzed. The results may provide reference for algorithm design of laser proximity fuse. The simulator has been successfully applied in semi-physical simulation of the fuse.

Scattering characteristic of complex target from the solar irradiance and sky-ground background radiance plays an important role in both theoretical researches and practical engineering. The solar irradiance and sky-ground background radiance and scattering property are discussed in this paper. BRDF (Bidirectional Reflectance Distributional Function) relates incident irradiance with scattering radiance while LRCS (Laser Radar Cross Section) shows the scattering characteristic of complex target. By using KA (Kirchhoff Approximation) method, we calculate the LCRS of facet of target and then get BRDF of each facet. Then all the visible faces are added up. Due to the complexity of the atmosphere model, MODTRAN is used to calculate the solar irradiance and background radiance. Finally, to give an example, a model airplane is taken for instance. The results indicate the effectiveness of the method we proposed.

Based on the equivalent dielectric model, the permittivity of the soil and simple plants which are assumed to satisfy exponential rough surface model is calculated. The electromagnetic scattering coefficients for the two types of rough surfaces are investigated by the Integral Equation Method (IEM) with the changing dielectric constant. The detailed analysis and discussions are made. And the results obtained are in good agreement with the experimental results.

As the classic analytical methods cannot calculate the electromagnetic scattering characteristics at Low Grazing Angle (LGA), a novel numerical method is presented by utilizing the Radar Cross Section (RCS) of the low grazing two-dimensional PM sea spectrum based on the triangles-based Physical Optics (PO) method in this paper. The calculated RCS is compared with the numerical calculation method of different targets and frequencies of incident wave. The results show that PO method is more accurate, especially under LGA condition, and it has a better agreement with the results calculated by commercial software FEKO.

Based on the single-scatter model of the Non-Line-of-Sight(NLOS), we analyze the effect of the geometric parameter of the transceiver on path loss, such as the receiver field of view(FOV), the transmitter apex angle and so on. And path loss in different visibility and weather conditions are simulated. The simulation results show that increasing the receiver FOV, or reducing the transmitter apex angle or the receiver apex angle can reduce path loss. And visibility and weather have an important effect on path loss.

Laser light scattering is a powerful tool for its noncontract nature and its convenience to nondestructive examination in the semiconductor industry. Taking the advantage of the scattering matrixes, the models of particulate contaminants on the wafer and subsurface defects are established, respectively. And the bidirectional reflectance distribution functions are derived. The results show that when the Rayleigh particle is on the wafer, the variation of BRDFpp is smooth without gulch for a definite incident angle. However, there is a gulch with the increment of scattering angle and the position of gulch is reduced with the increment of incident angle. When the Rayleigh particle is below the wafer, with an identical incident angle, there is a gulch with the variation of scattering azimuth angle. In addition, BRDFpp becomes larger and larger with the incident angle of p polarization light increment. The conclusions provide theoretical basis for quality evaluation and identify the information of contaminants detected in the semiconductor industry.

Dynamic speckles appear when a cylinder rotating with a constant angular velocity is irradiated by a Gaussian light beam. The statistical property of dynamic speckles in far-field diffraction is acquired when the irradiated area is larger than the cylinder surface. The normalized space-time cross-correlation of dynamic speckle intensity fluctuations is obtained with different cylinder radii in different incidence conditions. The results show that the correlation is improved when the cylinder radius and rotating speed decrease. When the cylinder rotates at a constant speed, the peak value of cross-correlation function descends gradually as the distance between the two observation points increases, whereas the peak position increases. In the case of approximate point irradiation, the spatial correlation length is almost unchanged and the correlation time extends obviously as the cylinder radius increases.

This paper introduced some significant applications of aurora images, listed the main factors of choosing wavelet basis in image compression coding and analyzed the influence of aurora image compression effect caused by different wavelet basis were experimentally. The results of two kinds of significant wavelet transform algorithms EZW and SPIHT were analyzed, compared and also experimentally improved.

In this paper, we propose an aurora classification method using a multi-level feature representation aimed to capture both global and local texture information, and to reduce the feature space dimension substantially. First-order and second-order statistics are computed for an input image and its low-frequency scaled images at three lower levels obtained using wavelet decomposition. The features include gray level distribution, co-occurrence matrix features, and run-length matrix features. A support vector machine (SVM) classifier was trained and tested on a Chinese Arctic Yellow River Station dayside aurora image dataset. Classification performance was evaluated and compared with those of k-nearest neighbor (KNN) classifiers and back-propagation neural networks (BPNN). To explore the possibility of using a smaller feature space, we used a Minimum-Redundancy Max-Relevance feature selection strategy. The result shows that there is only indistinct performance decrease by reducing the feature vector from a total of 88 to the most discriminatory 38 features. This proves that our multi-level feature representation is very robust.

A solution to the two-dimensional scattering properties of a conducting elliptic cylinder coated with a homogeneous anisotropic elliptical shell is obtained. The conducting elliptic cylinder and the shell have the same eccentricity. The transmitted and scattered fields of the anisotropic shell are expressed as Mathieu functions in elliptic coordinates. The unknown coefficients of the scattered and transmitted fields are solved with the aid of the boundary conditions and the Galerkin's method. Only the transverse magnetic (TM) polarization is presented and the transverse electric (TE) polarization can be obtained in the same way. Some numerical results are presented and discussed. As expected the result is in agreement with that available when the coated elliptic cylinder degenerates to a coated circular one.

Under the condition of ionosphere heating in the low region, the theoretical incoherent scatter model with the non-Maxwellian distribution in collisional plasma is presented, and the measured data in polar winter ionospheric modification experiments carried out in January 2008 at Tromso are analyzed. The obvious electron temperature enhancement can be seen in this experiment, and the maximum percentage is up to 168.9%. The non-Maxwellian index is also given, and the heating electric field is deduced from the index, which has important meaning for numerical simulation of the artificial ionospheric modification.

Based on the altitude-dependent model of ITU-R slant atmospheric turbulence structure constant, the log-amplitude variance of laser beam propagation on the slant path through turbulent atmosphere is obtained with transmitter and receiver parameters and can be degenerated to the result of the horizontal path with atmospheric structure constant as a flxed value. These expressions are convenient tools for beam-wave analysis. Finally, we apply the ITU-R turbulence structure constant model to calculate collimated, divergent and convergent beam log-amplitude variance. The numerical conclusions indicate the log-amplitude variance of laser beam propagation on slant path is generally smaller than those on horizontal path.