An Efficient Approach for the Computation of 2-D Green's Functions With 1-D and 2-D Periodicities in Homogeneous Media

Fructos, A.L.; Boix, Rafael R.; Mesa, Francisco; Medina, F.

doi:10.1109/tap.2008.2007281

Cited by 28 publications

(29 citation statements)

References 31 publications

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“…In particular, the case of 1-D periodic vertical mixed potentials has been investigated in [47] and [49], where acceleration procedures, based on Kummer's decompositions for the extraction of suitable asymptotic terms from the spectral series in conjunction with higher-order spectral Kummer-Poisson methods [36] and ε-and ̺-algorithms [28], [33], have been implemented.…”

Section: Introductionmentioning

confidence: 99%

Efficient Computation of 1-D Periodic Layered Mixed Potentials for the Analysis of Leaky-Wave Antennas With Vertical Elements

Valerio

Paulotto²,

Baccarelli

et al. 2015

IEEE Trans. Antennas Propagat.

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An efficient mixed-potential integral equation formulation is proposed for the analysis of one-dimensional (1-D) periodic leaky-wave antennas (LWAs) based on planar stratified configurations with inclusions of arbitrarily oriented metallic or dielectric perturbations. Both the transverse and vertical components of the mixed-potential Green's functions due to a 1-D phased array of dipoles in a layered medium are computed through suitable homogeneous-medium asymptotic extractions from the standard spectral series of Floquet harmonics. An original acceleration procedure is applied for the computation of the vertical potentials, whose extracted terms can be expressed as potentials from a 1-D phased array of half-line sources in a homogeneous medium. Their numerical calculation requires a suitable modification of the Ewald method, thus resulting in new modified spectral and spatial series, having Gaussian convergence even in the case of complex modes and improper harmonics. Numerical comparisons for the 1-D periodic potentials, both in the case of bounded and unbounded (e.g., leaky) harmonics, validate the efficiency and accuracy of the proposed acceleration technique. The method is illustrated and verified by determining the dispersion behavior of both bound and leaky modes for several LWA test cases.

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Section: Introductionmentioning

confidence: 99%

Efficient Computation of 1-D Periodic Layered Mixed Potentials for the Analysis of Leaky-Wave Antennas With Vertical Elements

Valerio

Paulotto²,

Baccarelli

et al. 2015

IEEE Trans. Antennas Propagat.

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“…The expression (12) is in fact obtained, where (13) is a homogeneous-medium spectral Green's function, and the series of the extracted terms is (14) corresponding to a spectral series of line sources, where each harmonic is multiplied by the extra term . This series is again poorly converging if , i.e., at an interface between slabs.…”

Section: Extractions For the Green's Functionsmentioning

confidence: 99%

“…This series is again poorly converging if , i.e., at an interface between slabs. As shown in the next section, an effective acceleration can nevertheless be obtained with a simple integral identity relating (14) and the standard line-source periodic Green's function (1).…”

Section: Extractions For the Green's Functionsmentioning

confidence: 99%

Acceleration of Mixed Potentials From Vertical Currents in Layered Media for 2-D Structures With 1-D Periodicity

Valerio

Wilton²,

Jackson³

et al. 2012

IEEE Trans. Antennas Propagat.

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An original acceleration procedure is proposed for the efficient calculation of the vertical components of the dyadic and scalar mixed-potential layered-media periodic Green's functions. The extraction of suitable asymptotic terms, i.e., quasi-static images, is performed in order to speed up the convergence of the relevant spectral series. This procedure, well known for planar Green's functions, is here generalized to treat the off-diagonal dyadic components and the corrective scalar potential arising from the vertical currents. The extracted terms are homogeneous-medium Green's functions due to a periodic phased array of half-plane currents, computed through a modified Ewald method, leading to a pair of Gaussian-convergent series. The highly improved convergence rate of the relevant series is shown, and the reduction of the computation time is numerically tested and discussed. The algorithm is implemented in EIGER, an open-source code based on the method of moments; several periodic structures are analyzed and fully validated through numerical comparisons. The proposed formulation has been proven very efficient, accurate, and stable

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“…Analysis of electromagnetic wave scattering by periodic structures with using the method of moments for a number of practical applications [1]- [5] requires efficient calculation of appropriate Green's functions. At present, there exist several approaches to solution of that problem [4]- [10].…”

Section: Introductionmentioning

confidence: 99%

A modification of the kummer's method for efficient computation of the 2-D Green's functions for 1-D periodic structures

Skobelev¹

2011

2011 XXXth URSI General Assembly and Scientific Symposium

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A new modification of the Kummer's method of Mth order for 2≤M≤6 is proposed for efficient computation of the 2-D Green's function for 1-D periodic structures in homogeneous media. The modification consists in transformation of the auxiliary series constructed of asymptotic terms of the original spectral series into a new series which, unlike the previous one, allows its summation in closed form. The new representation of the Green's functions consists of a rapidly converging difference series whose terms decay as q -(M+1) , as well a new rigorous expression for the sum of the transformed auxiliary series.

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An Efficient Approach for the Computation of 2-D Green's Functions With 1-D and 2-D Periodicities in Homogeneous Media

Cited by 28 publications

References 31 publications

Efficient Computation of 1-D Periodic Layered Mixed Potentials for the Analysis of Leaky-Wave Antennas With Vertical Elements

Efficient Computation of 1-D Periodic Layered Mixed Potentials for the Analysis of Leaky-Wave Antennas With Vertical Elements

Acceleration of Mixed Potentials From Vertical Currents in Layered Media for 2-D Structures With 1-D Periodicity

A modification of the kummer's method for efficient computation of the 2-D Green's functions for 1-D periodic structures

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