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An infinite cylinder of arbitrary shape is embedded into a circular one, and the whole structure is illuminated by a plane wave. The electromagnetic scattering problem is solved rigorously under the condition that the materials of the two cylinders possess similar characteristics. The solution is based on a linear Taylor expansion of the scattering integral formula which can be useful in a variety of different configurations. For the specific structure, its own far field response is given in the form of a double series incorporating hypergeometric functions. The results are in good agreement with those obtained via eigenfunction expansion. Several numerical examples concerning various shape patterns are examined and discussed.

The electromagnetic scattering by arbitrary-shaped formations is a very intriguing issue examined by many researchers with obvious applicability to microwave and optic frequencies. In [

In [

In this work, we examine a two-dimensional structure comprised of two layers, the outer of which has a circular bound, while the inner one possesses an arbitrary one. We obtain rigorously the solution to the plane wave scattering from this complex rod via the scattering integral under the simplifying assumption that the materials the two regions are filled with, are similar. In particular, we take the first-order Taylor expansion of the scattering formula around the wavenumber of the external cell medium. The initial approximation of the total field is obtained as function of the incident one. The final result is expressed as an easily calculable double series whose terms incorporate hypergeometric functions. To validate the followed approach, we compare the results of the approximate method with the eigenfunction sums for a simple example that possesses analytic solution. To this end, various structures with cardioid-, astroid-, and egg-shaped bounds for the internal formation are studied, and their far field response is represented as function of the incidence angle. The behavior of the curves is observed, and discussed and certain conclusions connecting the inclusion shapes with the variations are drawn and justified.

We suppose the two-dimensional structure depicted in Figure

The physical configuration of the examined structure. A dielectric rod scatters the incident plane wave in the presence of an inclusion of arbitrary shape and similar texture.

One of the most useful formulas in electromagnetic theory is the scattering integral [

By considering the Taylor expansion of the function

The aforementioned analysis is a general purpose one as it can cover any two-dimensional problem. If one wishes to use it in studying the considered device, one can define the corresponding case-oriented quantities. Green’s function

Given the fact that the integral in (

The double integral over the cross section of the arbitrary scatterer is written in polar coordinates [

A set of computer programs has been developed to implement the proposed technique for a variety of internal formations. Prior to presenting the results, we should validate the aforementioned analysis when applied to a simple example possessing analytic solution. In particular, we consider a concentric circular core of radius

In Figure

The average percent error of the method in computing RCS, as function of the wavenumber ratio for various sizes of the concentric cylinder. Plot parameters are

In all the numerical simulations, we chose to examine the dependencies of the quantity defined as follows:

(a) The far field response along the horizontal direction, as function of the incidence angle for various cardioid shapes. (b) The polar plots of the corresponding cardioid shapes. Plot parameters are

In Figure

(a) The far field response along the horizontal direction, as function of the incidence angle for various astroid shapes. (b) The polar plots of the corresponding astroid shapes. Plot parameters are

In Figure

(a) The far field response along the horizontal direction, as function of the incidence angle for various egg shapes. (b) The polar plots of the corresponding egg shapes. Plot parameters: