A new technique for the derivation of closed-form electromagnetic Green's functions for unbounded planar layered media

Okhmatovski, Vladimir; Cangellaris, A.C.

doi:10.1109/tap.2002.800731

Cited by 65 publications

(60 citation statements)

References 22 publications

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“… , e.g., [9][10][11][12]. The spatial domain GFs are obtained as solutions of the following Sommerfeld integrals:…”

Section: Electric Field Integral Equationmentioning

confidence: 99%

“…The corresponding spatial domain term dominates the near field interaction ( For the microstrip analyzed here, these are the only components of interest, when z > 0 and z′ > 0. In the limit , these components may be obtained in closed form [9][10][11][12][13][14][15]. Let us introduce: In the spectral domain the quasidynamic GFs may be expressed in closed form as:…”

Section: Green's Functions Decomposition and Quasi-dynamic Termmentioning

confidence: 99%

“…The slow decaying nature of the integrands and the oscillatory nature of the Sommerfeld integrals make the numerical integration extremely slow and dramatically increases the computational cost of any numerical model based on integral formulation. For this reason, the efficient evaluation of the GFs has gained the attention of literature over the years, and still poses open questions, e.g., [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

Chiariello¹,

Maffucci²

2012

JEMAA

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Integral formulations are widely used for full-wave analysis of microstrip interconnects. A weak point of these formulations is the inclusion of the proper planar-layered Green's Functions (GFs), because of their computational cost. To overcome this problem, usually the GFs are decomposed into a quasi-dynamic term and a dynamic one. Under suitable approximations, the first may be given in closed form, whereas the second is approximated. Starting from a general criterion for this decomposition, in this paper we derive some simple criteria for using the closed-form quasi-dynamic GFs instead of the complete GFs, with reference to the problem of evaluating the full-wave current distribution along microstrips. These criteria are based on simple relations between frequency, line length, dielectric thickness and permittivity. The layered GFs have been embedded into a full-wave transmission line model and the results are first benchmarked with respect to a full-wave numerical 3D tool, then used to assess the proposed criteria.

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“… , e.g., [9][10][11][12]. The spatial domain GFs are obtained as solutions of the following Sommerfeld integrals:…”

Section: Electric Field Integral Equationmentioning

confidence: 99%

Section: Green's Functions Decomposition and Quasi-dynamic Termmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

Chiariello¹,

Maffucci²

2012

JEMAA

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“…It has been shown [10] that if the surface wave poles are not extracted prior to the exponential fitting, the DCIM approximation seems to deteriorate violently for moderate distances from the source. Another approach was proposed recently for evaluating the Green's functions of the potentials in planar stratified media [11], [12]. By solving the Helmholtz equation using the finitedifference (FD) method, this technique represents the spectraldomain Green's function in terms of a pole-residue form.…”

Section: Introductionmentioning

confidence: 99%

A Robust Method for the Computation of Green's Functions in Stratified Media

Polimeridis

Yioultsis

Tsiboukis

2007

IEEE Trans. Antennas Propagat.

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Abstract-Closed-form Green's functions for unbounded planar stratified media are derived in terms of cylindrical and spherical waves. The methodology is based on a two-level approximation of the spectral-domain representation of Green's functions. This robust, efficient, and fully numerical approach does not call for an analytical extraction of "problematic" behaviors, such as the quasi-static terms and the surface wave poles, prior to the spectrum fitting. Instead, the spatial-domain Green's functions derived in this paper provide an accurate description of both the near-field singularity in the vicinity of the source and the far-field dominant behavior of the surface waves.Index Terms-Closed-form Green's functions, discrete complex image method (DCIM), quasi-static terms, rational function fitting method (RFFM).

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“…Many theoretical and numerical advances have been published in the last decade [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]21]. From a practical point of view, the full vectorial analysis of this problem is very important in research areas such as Optical Communications, radio propagation in the Ionosphere, scattering in stratified and artificial materials, etc.…”

Section: Introductionmentioning

confidence: 99%

Rigorous Full Vectorial Analysis of Electromagnetic Wave Propagation in 1d

Rojas¹,

Alpuente²,

PiÃ±eiro³

et al. 2006

PIER

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Abstract-We propose a new approach to solve the problem of the propagation of electromagnetic waves in unidimensional media with an arbitrary variation of their dielectric permittivity. This method is deduced from the Maxwell equations with a minimum of approximations and allows a full vectorial description of both the electric and magnetic fields through the direct calculation of their Cartesian coordinates. The problem is then equivalent to the solution of a pair of uncoupled ordinary differential equations. We use a very intuitive, highly accurate, pseudospectral technique to solve these equations. This pseudospectral method is based in a combination of Fourier and polynomial expansions of the solution providing very good precision and excellent stability with a relatively low computational effort. We present a simple model of a photonic crystal as an example of application of this technique to real electromagnetic problems.

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A new technique for the derivation of closed-form electromagnetic Green's functions for unbounded planar layered media

Cited by 65 publications

References 22 publications

Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

A Robust Method for the Computation of Green's Functions in Stratified Media

Rigorous Full Vectorial Analysis of Electromagnetic Wave Propagation in 1d

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