Closed-Form Green's Functions in Planar Layered Media for All Ranges and Materials

Alparslan, Aytac; Aksun, M.I.; Michalski, Krzysztof A.

doi:10.1109/tmtt.2010.2040354

Cited by 109 publications

(74 citation statements)

References 36 publications

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“…Since , (8) can be written in a following form: (9) Obviously, the optimal solution would come from the annihilation of the remainders of the linearly transformed sequence by imposing an appropriate ratio of the weights (10) In this point the WA method could be considered complete if the remainders were explicitly known, which is, unfortunately, not the case for the sequences of our interest. Instead, we use their asymptotic expansion (11) where are remainder estimates and are the associated coefficients, as given in [13]. Based on the asymptotic behavior of the spectral domain GFs (12) and using equidistant break points separated by asymptotic halfperiods of Bessel function, , as limits of partial integrals , the following analytical expression for the remainder estimates is obtained (13) for , where .…”

Section: A Partition-extrapolation Methods Involving Wa Techniquementioning

confidence: 99%

“…The numerous publications on this topic can be mainly categorized in two classes. In the first class, SIs are approximated by closed-form analytical formulas (see [4]- [11] among others). A typical example is provided by the "complex images" formulations.…”

Section: Introductionmentioning

confidence: 99%

“…But, there will be always some uncertainties about their range and precision. In a very recent paper dealing with closed-from GFs [11] it was pointed out the importance of alternative "safer" schemes that can be always used as benchmarks for testing purposes or for fine-tuning the coefficients of an analytical approximation. These alternative strategies are provided by a pure numerical evaluation of the SIs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Algorithms for Computing Sommerfeld Integral Tails

Golubovic

Polimeridis

Mosig

2012

IEEE Trans. Antennas Propagat.

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Abstract-Sommerfeld-integrals (SIs) are ubiquitous in the analysis of problems involving antennas and scatterers embedded in planar multilayered media. It is well known that the oscillating and slowly decaying nature of their integrands makes the numerical evaluation of the SI real-axis tail segment a very time consuming and computationally expensive task. Therefore, SI tails have to be specially treated. In this paper we compare two recently developed techniques for their efficient numerical evaluation. First, a partition-extrapolation method, in which the integration-then-summation procedure is combined with a new version of the weighted averages (WA) extrapolation technique, is summarized. The previous variants of WA technique are also discussed. Then, a review of double-exponential (DE) quadrature formulas for direct integration of the SI tails is presented. The efficient way of implementing the algorithms, their pros and cons, as well as comparisons of their performance are discussed in detail.

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Section: A Partition-extrapolation Methods Involving Wa Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Algorithms for Computing Sommerfeld Integral Tails

Golubovic

Polimeridis

Mosig

2012

IEEE Trans. Antennas Propagat.

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“…To effect these approximations, we employ the so-called discrete complex image method (DCIM), which has been used to approximate Green functions in layered media [21][22][23]. In the present case, we only need to perform three exponential fits…”

Section: Complex Image Approximationmentioning

confidence: 99%

Complex Image Method Analysis of a Plane Wave-Excited Subwavelength Circular Aperture in a Planar Screen

Michalski¹

2011

PIER B

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Abstract-A complex image method is presented for the analysis of a subwavelength circular aperture in a perfectly conducting screen of infinitesimal thickness illuminated by a plane wave. The method is based on the Bethe-Bouwkamp quasi static model of the aperture field and uses the spectral domain formulation as the point of departure. Closed-form expressions are obtained for the electromagnetic fields valid for all observation points. Sample numerical results demonstrate the accuracy and efficiency of the method for both normal and oblique illuminations, including an evanescent wave. In the latter case, the results show a circulating power flux and enhanced field confinement near the aperture.

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“…The direct application to layered structures has to face the problem of infinite interfaces. With the development of integration techniques for the evaluation of multilayer Green's functions [15,17], formulations on only the boundary of the scatterer are possible, and such a formulation has been successfully used with MMP [18]. For homogeneous exterior, there are a variety of local absorbing boundary conditions [8,9] which can be used with volume discretization methods such as FEM or the finite difference time domain method (FDTD).…”

Section: Introductionmentioning

confidence: 99%

Hp-Fem and PML Analysis of Plasmonic Particles in Layered Media

Wang¹,

Schmidt²,

Alparslan³

et al. 2013

PIER

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Abstract-In this paper, we introduce a high order finite element (FEM) implementation using perfectly matched layer (PML) for the scattering by plasmonic structures inside layered media. The PML is proven to be very accurate and efficient by a comparative analysis with a commercial FEM software and the Multiple Multipole Program (MMP). A convergence analysis using hp-adaptive refinement inside the PML layer shows that adaptive mesh refinement inside the PML layer is most efficient. Based on this convergence analysis an hpstrategy is proposed, which shows a remarkable error reduction for small additional computational costs.

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Closed-Form Green's Functions in Planar Layered Media for All Ranges and Materials

Cited by 109 publications

References 36 publications

Efficient Algorithms for Computing Sommerfeld Integral Tails

Efficient Algorithms for Computing Sommerfeld Integral Tails

Complex Image Method Analysis of a Plane Wave-Excited Subwavelength Circular Aperture in a Planar Screen

Hp-Fem and PML Analysis of Plasmonic Particles in Layered Media

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