Abstract:
The diffraction of a uniform unit-amplitude E-polarized plane wave is considered in the case of its normal incidence on a strip periodic metal grating placed on the anisotropic hyrotropic ferromagnetic half-space boundary. The Dirichlet boundary conditions on the grating strips, the medium interface conjugation conditions, the Meixner condition that the energy is finite in any confined volume and the radiation condition are applied, and the boundary value diffraction problem in terms of Maxwell's (Helmholtz) equations is equivalently reduced to the dual system of functional equations with exponential kernel. The system is shown to be the Riemann-Hilbert problem in analytic function theory with the conjugation coefficient differing, in general, from ``-1" and dependent on the incident wave frequency. An analytical regularization procedure based on the Riemann-Hilbert boundary value problem solution with the following use of the Plemelle-Sokhotsky formulas is suggested, resulting in the system of linear algebraic equations of the second kind with a compact operator. For vthese systems, the truncation technique possibility has been shown. Calculation algorithms and simulation packages in terms of C++ language have been developed. As a result, the reflection coefficient performance has been studied over sufficiently wide ranges of frequency and constitutive and geometrical parameters of the electrodynamical systems of interest. The frequency bands of the reflection coefficient resonant behavior have been established and examined. A numerical analytical model of these resonances has been proposed.

Abstract:
In this paper two-dimensional problem of plane-wave diffraction by a "fractional strip" is studied. "Fractional strip" is introduced as a strip with fractional boundary conditions (FBC) involving fractional derivatives of the field components. FBC describe intermediate boundary between perfect electric conductor (PEC) and perfect magnetic conductor (PMC). It is shown that "fractional strip" has scattering properties similar to the well-known impedance strip. For one important case of fractional order equal to 0.5 the solution of the wave diffraction problem by a "fractional strip" can be found analytically. Detailed comparison analysis of the physical characteristics of the scattered fields for both fractional and impedance strips is presented. The relation between the fractional order and the value of impedance is derived. It is shown that in a wide range of input parameters the physical characteristics of the "fractional strip" are similar to the strip with pure imaginary impedance.

Abstract:
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined.

Abstract:
Tapered resistive strip realized by patterning the constant resistive strip is used to suppress edge scattering of a finite wedge. The suppression effect is simulated and evaluated by the reduction in mono-static RCS (Radar Cross Section). This reduction is compared with the one which loaded by the ideal tapered resistive strip. The result indicating that patterning a constant resistive strip to create a gradient in sheet resistance is feasible. To verify this method of fabricating tapered resistive strip, patterned resistive strip with a proper gradient in sheet resistance is conducted and loaded on the wedge target for test. The gradient in sheet resistance used for test is obtained from the optimization. Resistive strip with this sheet resistance gradient renders a promising effect of edge scattering suppression. The test result shows a reduction of 20dB for the geometric mean of mono-static RCS in the angular range of 45o. This value is close to the one of 23dB in simulation.

Abstract:
An original iterative method based on the conjugate gradient algorithm is developed in this paper to study electromagnetic scattering. The Generalized Equivalent Circuit (GEC) method is used to model the problem and then deduce an electromagnetic equation based on the impedance operator. For validation purposes, the developed method has been applied to various iris structures. Results computed using the new implementation of the conjugate gradient are similar to theoretical values. The field and current distribution are identical to the ones obtained with the moment method. Moreover, the memory resources required for storage are significantly reduced.

Abstract:
Medium and high energy absorptive parts contribute to dispersive expressions for D- wave scattering lengths, $a^0_2$ and $a^2_2$. For the model employed by Basdevant, Frogatt and Peterson we find the D- wave driving term contributions to the D- wave scattering lengths are $1.8\cdot 10^{-4}$ to $a^0_2$ and $0.4\cdot 10^{-4}$ to $a^2_2$, roughly $10\%$ and $30\%$ of their respective central experimental values. Inequivalent sets of sum rules are used as a compelling test of the consistency of the model for which crossing symmetry is not guaranteed. Results for the F- wave scattering length $a^1_3$ are presented, completing the recent Roy equation analysis of \pipi scattering in the range for $a^0_0$ favored by standard chiral perturbation theory.

Abstract:
Wave scattering is considered in a medium in which many small particles are embedded. Equations for the effective field in the medium are derived when the number of particles tends to infinity.

Abstract:
The mutual conversion of the TM and TE waves (m, n ≠ 0) in periodic and aperiodic (fractal-like) stratified waveguide structures composed of dense metal-strip gratings is studied. The stopbands and passbands conditions of Bloch waves, the reflection and transmission spectra of the periodic structure are examined versus the gratings parameters. Peculiarities of the wave localization, selfsimilarity and scalability of both reflected and transmitted spectra of the fractal-like structure are investigated. The appearance of additional peak multiplets in stopbands is revealed and a correlation of their properties with the parameter of grating filling is established.

Abstract:
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering coefficients and the far-field pattern is also derived. Furthermore, the sensitivity of the scattering coefficients with respect to changes in the permittivity and permeability distributions is investigated. In the linearized case, explicit formulas for reconstructing permittivity and permeability distributions from the scattering coefficients is proposed. They relate the exponentially ill-posed character of the inverse medium scattering problem at a fixed frequency to the exponential decay of the scattering coefficients. Moreover, they show the stability of the reconstruction from multifrequency measurements. This provides a new direction for solving inverse medium scattering problems.

Abstract:
We obtain in TM polarization an analytical expression of the scattering matrix of one infinitely conducting metallic lamellar grating with subwavelength slits. The theory is based on the Monomode Modal Method which consists in considering only one propagative mode in grating slits. Two expressions are exposed. The first one comes directly from the theory equations and the second one clearly reveals the Airy-like form of the scattering matrix terms. The theory is validated on a multi-grating object and the stability of the numerical results are shown at the same time. This work provides a basic and very efficient theoretical tool to calculate the diffraction by a stack of subwavelength metallic gratings.