Computation of the one-dimensional free-space periodic Green's function for leaky waves using the Ewald method

Komanduri, Varada Rajan; Jackson, David R.; Capolino, Filippo; Wilton, Donald R.

doi:10.1109/iceaa.2012.6328809

Cited by 2 publications

(9 citation statements)

References 3 publications

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“…Note that the proper or improper nature of the terms is determined by the choice of the logarithmic branch cut of the exponential integral E q (·) [57]. The Green's function g E,p spectral can then be evaluated even if a finite number of harmonics is improper.…”

Section: Appendixmentioning

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: Appendixmentioning

confidence: 99%

“…Accordingly, the correct determination for the homogeneousmedium term G p ∞ , when added back in (3), has to be improper in both cases. The computation of the improper determination of G p ∞ can be performed as explained in [57].…”

Section: E Integration Pathsmentioning

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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“…4is slowly convergent, and it is even divergent for complex values of the wavenumber z k , and some technique must be adopted to allow analytic continuation of the GF into the complex z k plane. The GF representation adopted in this work makes use of Ewald's method for linear arrays, which, besides providing analytic continuation, it also provides series with Gaussian convergence and only a handful of terms are needed [32][33][34]. The dyadic form of the Ewald representation of the periodic GF evaluation used in this paper is provided in Appendix B.…”

Section: Simulation Modelmentioning

confidence: 99%

“…Modes 'Proper 1', 'Proper 2', 'Improper 1' and 'Improper 2' in Figs. 3 and 4 are computed using the method described in [33], where only m = 0 and −1 are considered, and adapted to the present case as in Appendix B. When the wavenumber dispersion curves change complex quadrant, they can be continued with dispersion curves computed with different m-values (see appendix B).…”

Section: Mode Analysismentioning

confidence: 99%

“…As a consequence, full characterization of the modes with complex wavenumber in the linear chain is provided, in terms of guidance/radiance, proper/improper, physical/nonphysical, and propagation direction conditions. In this paper, a new numerical procedure that uses the Ewald representation for the periodic dyadic GF for linear arrays has been introduced, based on previous scalar developments [32][33][34]. Our method is alternative to the one used in [18,20,21,26] based on polylogarithms, and future studies will be devoted to relate these two techniques.…”

Section: Introductionmentioning

confidence: 99%

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Complex bound and leaky modes in chains of plasmonic nanospheres

Campione¹,

Steshenko²,

Capolino³

2011

Opt. Express

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Bound and leaky modes with complex wavenumber in chains (linear arrays) of plasmonic nanospheres are characterized for both longitudinal and transverse polarization states (with respect to the array axis). The proposed method allows for the description of each mode evolution when varying frequency. As a consequence, full characterization of the guided modes with complex wavenumber is provided in terms of propagation direction, guidance or radiance, proper or improper, and physical or nonphysical conditions. Each nanosphere is modeled according to the single dipole approximation, and the metal permittivity is described by the Drude model. Modal wavenumbers are obtained by computing the complex zeroes of the homogeneous equation characterizing the field in the one dimensional periodic array. The required periodic Green's function is analytically continued into the complex wavenumber space by using the Ewald method. Furthermore, a parametric analysis of the mode wavenumbers is performed with respect to the geometrical parameters of the array.

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Computation of the one-dimensional free-space periodic Green's function for leaky waves using the Ewald method

Cited by 2 publications

References 3 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

Complex bound and leaky modes in chains of plasmonic nanospheres

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