The scattering of an incident plane wave from an array of parallel circular dielectric and/or conducting cylinders is derived rigorously using a boundary value approach. Both transverse electric (TE) and transverse magnetic (TM) polarized incident plane waves are considered. The validity and accuracy of the method are verified by comparing the numerical results with those based on other available methods. The advantage of the proposed analysis is the simplicity and efficiency in computation. The modeling of two-dimensional objects of arbitrary cross section and composite material is outlined and sample numerical results are presented to illustrate the versatility of the method. >

Modeling of cylindrical objects by circular dielectric and conducting cylinders

A new method for the analysis of the diffraction of a plane wave impinging on a perfectly conducting circular cylinder in front of a generally reflecting surface is presented. The surface is characterized by its complex reflection coefficient, enabling us to treat a wide class of reflecting surfaces. The presence of the surface is taken into account by means of a suitable expansion of the reflected field in terms of cylindrical functions. The method gives the solution of the scattering problem in both the near and the far field regardless of the polarization state of the incident field. Numerical examples for dielectric interfaces are presented, and comparisons are made with results presented in the literature.

/pdf/plane-wave-scattering-by-a-perfectly-conducting-circular-5015ixeyt1.pdf

Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach

The scattering of an electromagnetic plane wave from an arbitrary configuration of parallel circular cylinders is investigated using four different techniques. The cylinders are made of perfectly conducting or homogeneous dielectric material. These techniques are a boundary value type of solution, an iterative scattering procedure, a hybrid approach based on a combination of exact and method of moments solution, and a high-frequency asymptotic approximation. The analysis is given in detail for the transverse magnetic (TM) polarization, and that for the transverse electric (TE) polarization is outlined. Numerical results are provided to show the major differences between these techniques and the validity of using circular cylinders in modeling composite two-dimensional scatterers.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/94RS00327%4010.1002/%28ISSN%291944-799X.FFISM1

A comparative study of two-dimensional multiple scattering techniques

We study numerically the effect of periodicity on the plasmon-assisted scattering and absorption of visible light by infinite and finite gratings of circular silver nanowires. The infinite grating is a convenient object of analysis because of the possibility to reduce the scattering problem to one period. We use the well-established method of partial separation of variables however make an important improvement by casting the resulting matrix equation to the Fredholm second-kind type, which guarantees convergence. If the silver wires have sub-wavelength radii, then two types of resonances co-exist and may lead to enhanced reflection and absorption: the plasmon-type and the grating-type. Each type is caused by different complex poles of the field function. The low-Q plasmon poles cluster near the wavelength where dielectric function equals -1. The grating-type poles make multiplets located in close proximity of Rayleigh wavelengths, tending to them if the wires get thinner. They have high Q-factors and, if excited, display intensive near-field patterns. A similar interplay between the two types of resonances takes place for finite gratings of silver wires, the sharpness of the grating-type peak getting greater for longer gratings. By tuning carefully the grating period, one can bring together two resonances and enhance the resonant scattering of light per wire by several times.

Periodicity-induced effects in the scattering and absorption of light by infinite and finite gratings of circular silver nanowires.

An analytical solution is presented for the electromagnetic scattering from a perfect electromagnetic conducting circular cylinder, embedded in the dielectric half-space. The solution utilizes the spectral (plane wave) representations of the fields and accounts for all the multiple interactions between the buried circular cylinder and the dielectric interface separating the two half spaces.

https://www.jpier.org/PIER/pier78/03.07081601.A.Naqvi.pdf

Electromagnetic scattering from a perfect electromagnetic conductor cylinder buried in a dielectric half-space

The scattering pattern and back-scattering cross-section, due to an E-polarized plane wave incident on N circular parallel conducting cylinders in an arbitrary configuration, is computed by the boundary-value method. The results compare favourably for thin cylinders with an approximate solution based on an extension of the Karp–Russek technique for large separation between any two adjacent cylinders relative to the larger diameter. The results indicate that for broadside incidence and fixed radii and separation of an equi-spaced linear array of cylinders, the maximum back-scattering cross-section increases monotonically with an increasing number of cylinders. On the other hand, for normal incidence and fixed radii, the peak of the maximum back-scattering cross-section occurs at the same separation between the cylinders for any number of cylinders.

Scattering by N parallel conducting circular cylinders

An exact treatment using the boundary-value method for solving the problem of scattering of a line-source field or a plane wave by a perfectly conducting elliptic cylinder coated with a confocal di...

Electromagnetic scattering from a dielectric-coated elliptic cylinder

The scattering properties of a dielectric-coated nonconfocal conducting elliptic cylinder are investigated. The theoretical treatment of such a problem is based on the boundary value solution, which is an exact treatment of the problem. Only the transverse magnetic (TM) case is considered, although the transverse electric (TE) case can be treated in the same way. It is shown that this solution is much more general than all previous solutions because it can handle a variety of scattering geometries. Numerical results are presented in graphical form for the echo width pattern of various geometries. >

Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric

The radiation properties of axial slots on a conducting elliptic cylinder coated by a dielectric are investigated. The dielectric coating has an elliptical outer trajectory which is not confocal with the conducting slotted elliptic cylinder. A dual infinite-series solution based on the boundary-value method is obtained with the aid of the addition theorem of Mathieu functions. Both TM and TE cases are considered. The dual infinite series involved in the solution are then truncated to generate numerical results. The accuracy of the calculations is checked by comparison with published data. Other interesting results for different geometries are then illustrated.

Radiation by axial slots on a dielectric-coated nonconfocal conducting elliptic cylinder

The inverse black body radiation, which is the problem of determining the area-temperature distribution of a black body from its measured radiated power spectrum, was recently solved by Bojarski. His solution employs the inverse Laplace transform to reconstruct the area-coldness distribution from an integral equation based on Planck's law. Our solution is similar but restricted to microwave frequencies and employs the Rayleigh-Jeans approximation to yield the corresponding portion of the area-coldness distribution using the inverse Laplace transform but avoiding the iterative procedure of Bojarski.

Hassan A. Ragheb

Papers

Scattering by N parallel conducting circular cylinders

Electromagnetic scattering from a dielectric-coated elliptic cylinder

Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric

Radiation by axial slots on a dielectric-coated nonconfocal conducting elliptic cylinder

Inverse black body radiation at microwave frequencies