Electromagnetic scattering by an infinite elliptic dielectric cylinder with small eccentricity using perturbative analysis

Tsogkas, Georgios D.; Roumeliotis, John A.; Savaidis, Stylianos P.

doi:10.1109/tap.2009.2024527

Cited by 14 publications

(20 citation statements)

References 27 publications

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“…(6) and (7) are not orthogonal [17], thus complicating the procedure by retaining the inner summation over index m. The primed Mathieu functions in Eq. (7) denote their derivative with respect to the radial coordinate ξ.…”

Section: E-wave Polarizationmentioning

confidence: 99%

“…Compared with the sets derived in [13,17] where expansions up to Oh 4 were used to retrieve the solution analytically, the present case is more challenging, since it retains the inner summation over index m, which originates from the expansion formulas from polar to elliptical coordinates, and moreover includes the nonorthogonal inner products around the elliptical interface, which separates the two dielectric media having different constitutive parameters. In the case of [13,17], the inner summation was absent, thus enabling a straightforward expansion of the quantities involved. In the present case, the inner summation over index m should be also expanded in powers of h, appropriately, and the resulting terms should be carefully combined to retrieve the solution.…”

Section: E-wave Polarizationmentioning

confidence: 99%

“…In the present case, the inner summation over index m should be also expanded in powers of h, appropriately, and the resulting terms should be carefully combined to retrieve the solution. After laborious calculations using Maclaurin series expansions for the Mathieu functions in a ims and c ims , as well as expansion coefficients and inner products from [17,18], and keeping terms up to Oh 4 , the even part of set (8) that includes the A i coefficients takes the form…”

Section: E-wave Polarizationmentioning

confidence: 99%

“…(10) can be found in Appendix A, while the closed-form expressions for b 0;2;4 of Eq. (11) are the same with the K e0;2;4 's in [17]. The form of Eqs.…”

Section: E-wave Polarizationmentioning

confidence: 99%

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Closed-form solution to the scattering by an infinite lossless or lossy elliptic cylinder coating a circular metallic core

2013

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An analytical, closed-form solution to the scattering problem from an infinite lossless or lossy elliptical cylinder coating a circular metal core is treated in this work. The problem is solved by expressing the electromagnetic field in both elliptical and circular wave functions, connected with one another by well-known expansion formulas. The procedure for solving the problem is cumbersome because of the nonexistence of orthogonality relations for Mathieu functions across the dielectric elliptical boundary. The solution obtained, which is free of Mathieu functions, is given in closed form, and it is valid for small values of the eccentricity h of the elliptical cylinder. Analytical expressions of the form S(h)=S(0)[1+g(2)h2+g(4)h4+O(h6] are obtained, permitting an immediate calculation for the scattering cross sections. The proposed method is an alternative one, for small h, to the standard exact numerical solution obtained after the truncation of the system matrices, composed after the satisfaction of the boundary conditions. Both polarizations are considered for normal incidence. The results are validated against the exact solution, and numerical results are given for various values of the parameters.

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Section: E-wave Polarizationmentioning

confidence: 99%

Section: E-wave Polarizationmentioning

confidence: 99%

Section: E-wave Polarizationmentioning

confidence: 99%

“…(10) can be found in Appendix A, while the closed-form expressions for b 0;2;4 of Eq. (11) are the same with the K e0;2;4 's in [17]. The form of Eqs.…”

Section: E-wave Polarizationmentioning

confidence: 99%

See 2 more Smart Citations

Closed-form solution to the scattering by an infinite lossless or lossy elliptic cylinder coating a circular metallic core

2013

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“…an elliptical dielectric cylinder [12] or the scattering by an elliptical dielectric cylinder having a circular metallic core [13]. Nonetheless, the scattering problems require a straightforward solution of nonhomogeneous matrix equations, unlike the waveguide problems where the roots of homogeneous matrix equations must be determined.…”

Section: Introductionmentioning

confidence: 99%

Efficient and Accurate Calculation of the Cutoff Wavenumbers of Coaxial Elliptical-Circular and Circular-Elliptical Metallic Waveguides

Kolezas

Zouros

Roumeliotis

2014

IEEE Trans. Microwave Theory Techn.

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In this paper, we propose an efficient method for the calculation of the cutoff wavenumbers of coaxial elliptical-circular and circular-elliptical metallic waveguides. The cutoff wavenumbers are obtained through closed-form expressions making the evaluation efficient, and moreover, very accurate even for large values of the eccentricity of the elliptical boundary. The resulting formulas are free of Mathieu functions, including only simple algebraic expressions with Bessel functions, and are valid for every different value of the indices and , corresponding to every higher order or mode. The validation of the method is performed by comparing to the general exact solution. The efficiency and accuracy of our method is presented by illustrative examples. Numerical results are given for the cutoff wavenumbers of various higher order modes.

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Bibliography

2013

Method of Moments for 2D Scattering Problems

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Electromagnetic scattering by an infinite elliptic dielectric cylinder with small eccentricity using perturbative analysis

Cited by 14 publications

References 27 publications

Closed-form solution to the scattering by an infinite lossless or lossy elliptic cylinder coating a circular metallic core

Closed-form solution to the scattering by an infinite lossless or lossy elliptic cylinder coating a circular metallic core

Efficient and Accurate Calculation of the Cutoff Wavenumbers of Coaxial Elliptical-Circular and Circular-Elliptical Metallic Waveguides

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