Electromagnetic plane wave diffraction by a cylindrical arc with edges: H-polarized case

Abstract

An accurate hybrid method (numerical-analytical method) for the diffraction of H-polarized electromagnetic plane wave by perfectly electric conducting cylindrical bodies containing edges and a longitudinal slit aperture is proposed. This method is the combination of the Method of Moment and semi-inversion method. The current density function is expressed as the Chebyshev polynomials forming a complete orthogonal set of basis functions. Then, the initial problem is reduced to a system of linear algebraic equations. After inversion, the unknown coefficients are obtained. Then, near and far-field distributions, radar cross-sections are obtained. The resonances are observed for different values of the aperture size, radius of the arc, and the results are compared with previous outcomes.

H‐polarized plane wave diffraction by a slotted cylinder with different surface impedances: Solution by the analytical—Numerical approach

“… The comparison of the total field $${H}_{z}$$ distributions with (a) Orthogonal Polynomials Method for perfect electric conducting (PEC) surface [15], (b) embedding formulae method [17], and the proposed method with ($${\xi }_{1}={\xi }_{2}=0.001$$) …”

“…The present study proposes an analytical‐numerical approach to solve the corresponding equations provided in Equations () and (); the current densities on the circular strip are expressed as the summation of the Gegenbauer polynomials $$({C}_{n}^{\nu +\frac{1}{2}})$$ with unknown coefficients and the weighting coefficient $${\left(1-{\eta }^{2}\right)}^{{\nu }_{i}}$$ to satisfy the edge condition as given in Equation (). It should be noted that the length of the arc is normalised by the change of variables as $$\eta =\frac{\varphi }{\theta }$$ , $$\varphi =\theta \eta $$ since the Gegenbauer polynomials are defined between [−1, 1] [13, 15]. $$${\mu }^{e}(\eta )={\left(1-{\eta }^{2}\right)}^{{\nu }_{1}}\sum\limits _{n=0}^{\infty }{x}_{n}{C}_{n}^{{\nu }_{1}+\frac{1}{2}}(\eta ),\,{\mu }^{m}(\eta )={\left(1-{\eta }^{2}\right)}^{{\nu }_{2}}\sum\limits _{n=0}^{\infty }{y}_{n}{C}_{n}^{{\nu }_{2}+\frac{1}{2}}(\eta ).$$$ where $${x}_{n}$$ and $${y}_{n}$$ are the constant unknown coefficients.…”

“…with unknown coefficients and the weighting coefficient ð1 − η 2 Þ ν i to satisfy the edge condition as given in Equation (7). It should be noted that the length of the arc is normalised by the change of variables as η ¼ φ θ , φ ¼ θη since the Gegenbauer polynomials are defined between [−1, 1] [13,15].…”

Electromagnetic scattering of H‐polarised cylindrical wave by a double‐sided impedance circular strip

“…Figure 3 provides the normalised near H-field distributions, and comparisons are made with both plane wave excitation and line source excitation of the circular strip with PEC surface, as referenced in Refs. [9,26], respectively. For PEC cases, the methodology of Refs.…”

“…For PEC cases, the methodology of Refs. [9,26] was employed to obtain Figure 3a,b. The observed deviation is less than 2%, indicating a reasonably close agreement between the results obtained in this study and those reported in the referenced works.…”