Calculation of the Free-Space Periodic Green's Function Using Equivalent Finite Array

Boutami, Salim; Fall, Mandiaye

doi:10.1109/tap.2012.2210179

Cited by 9 publications

(6 citation statements)

References 31 publications

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“…The asymptotic terms consist of quasistatic images due to the direct ray from the source to the observation point, and, if the source and the observation points are in the same layer, to the two rays reflected from adjacent interfaces. The extracted terms are then summed back, and correspond to homogeneous-medium Green's functions; their computation usually involves ad-hoc acceleration algorithms developed for the numerical analysis of periodic structures in free space [24]- [39]. In 1-D periodic structures, the general extraction is of the form…”

Section: B Kummer's Decompositionmentioning

confidence: 99%

“…The efficient computation of the Green's function g z,p is then of paramount importance for the effectiveness of the acceleration. Unfortunately, this cannot be accomplished through the Ewald method, as done for the point-source Green's functions (see (39) in the Appendix), due to the presence of the extra factor 1/jk z multiplying each term. In Section IV an original modified Ewald method is presented to overcome this problem.…”

Section: Vertical Potentialsmentioning

confidence: 99%

“…The computation of (19) can be accelerated through the Ewald method if the integrand g p is split into an Ewald spectral and an Ewald spatial series according to (39). The two series can then be integrated separately:…”

Section: E Integration Pathsmentioning

confidence: 99%

“…This approach reduces the computational domain to a single unit cell through the use of a 1-D periodic Green's function in layered media. Particular attention needs to be devoted both to the acceleration of slowly-converging series appearing in the periodic Green's functions [24]- [39], and to the overall speed up through a Green's function interpolation process [40]- [42]. Based on this approach, an accurate and efficient software tool (called here the Periodic Planar Simulator (PPS)) was developed for the analysis of planar periodic structures of arbitrary unit-cell configuration [12], [40], [43]).…”

Section: Introductionmentioning

confidence: 99%

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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: B Kummer's Decompositionmentioning

confidence: 99%

Section: Vertical Potentialsmentioning

confidence: 99%

Section: E Integration Pathsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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show abstract

“…Fortunately, the infinite series may be rewritten as a rapidly convergent series plus an asymptotic series which can be summed efficiently. Thus the infinite series in the periodic Green's function can be calculated efficiently [11][12][13][14][15][16].…”

Section: Forward Problemmentioning

confidence: 99%

Comparison of particle swarm optimization and self-adaptive dynamic differential evolution for the imaging of a periodic conductor

Cheng

Chiu

Chang

et al. 2014

JAE

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The application of two techniques to reconstruct the shape of a two-dimensional periodic perfect conductor from mimic the measurement data is presented. A periodic conducting cylinder of unknown periodic length and shape scatters the incident wave in half-space and the scattered field is recorded outside. After an integral formulation, the microwave imaging is recast as a nonlinear optimization problem; a cost functional is defined by the norm of a difference between the measured scattered electric fields and the calculated scattered fields for an estimated shape of a conductor. Thus, the shape of conductor can be obtained by minimizing the cost function. In order to solve this inverse scattering problem, transverse magnetic (TM) waves are incident upon the objects and two techniques are employed to solve these problems. The first is based on an particle swarm optimization (PSO) and the second is a self-adaptive dynamic differential evolution (SADDE). Both techniques have been tested in the case of simulated mimic the measurement data contaminated by additive white Gaussian noise. Numerical results indicate that the SADDE algorithm is better than the PSO in reconstructed accuracy and convergence speed.

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Dielectric objects reconstruction by combining subspace-based algorithm and randomly global optimization algorithm

Chiu

Yen

Lee

2017

Journal of Electromagnetic Waves and Applications

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Calculation of the Free-Space Periodic Green's Function Using Equivalent Finite Array

Cited by 9 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

Comparison of particle swarm optimization and self-adaptive dynamic differential evolution for the imaging of a periodic conductor

Dielectric objects reconstruction by combining subspace-based algorithm and randomly global optimization algorithm

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