An Implementation of King’s Green Functions in Thin Wire Scattering Problems

Authors

  • Ömer Zor Electronics Engineering Department Uludağ University, Bursa, TR-16059, Turkey
  • Burak Polat Electrical and Electronics Engineering Department Trakya University, Edirne, TR-22030, Turkey

Keywords:

An Implementation of King’s Green Functions in Thin Wire Scattering Problems

Abstract

We investigate electromagnetic scattering from metallic thin wire structures located over planar and spherical lossy dielectric half-spaces by applying Green’s function formulation and method of moments in the resonance region and under “high contrast approximation” (HCA). For this purpose, in the calculations of the impedance matrix and the potential column of the moment system, we employ the Green functions of King valid for arbitrary range under HCA and the asymptotic (far field) Green functions for planar and spherical impedance surfaces delivered by Norton and Wait, respectively. For a verification of the developed codes, the current distributions obtained under plane wave illumination on the arms of a cross shaped thin wire structure are compared to the same results obtained by the commercial software SNEC™. Various illustrations for the scattered electrical field from a thin wire plate located over planar and spherical half-spaces are also presented.

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References

A. Sommerfeld, “Propagation ofWaves in

Wireless Telegraphy,” Ann. Phys., vol. 28, pp.

-736, 1909.

Y. R. Samii, R. Mittra and P. Parhami,

“Evaluation of SommerfeldIntegrals for Lossy

Half-Space Problems,” Electromagnetics, vol. 1,

no. 1, pp. 1-28, 1981.

R. W. P. King, “New Formulas for the

Electromagnetic Field of aVertical Electric

Dipole in a Dielectric or Conducting Half-Space

Near its Horizontal Interface,” J. Appl. Phys., vol.

, pp. 8476-8472, 1982 (Erratum:vol. 56, pp.

-66, 1984).

R. W. P. King, M. Owens, and T. T. Wu, Lateral

Electromagnetic Waves: Theory and Applications

to Communications, Geophysical Exploration,

and Remote Sensing, Springer Verlag, New York,

V. A. Houdzoumis, “Vertical Electric Dipole

Radiation Over a Sphere: Character of the Waves

that Propagate Through the Sphere,” J. Appl.

Phys., vol. 86, pp. 3939-3942, 1999.

V. A. Houdzoumis, “Two Modes of Wave

Propagation Manifested in Vertical Electric

Dipole Radiation Over a Sphere,” Radio Science,

vol. 35, no.1, pp. 19-29, 2000.

D. Margetis and T. T. Wu, “Exactly Calculable

Field Components of Electric Dipoles in Planar

Boundary,” J. Math. Phys., vol. 42 (2), pp. 713-

, 2001.

D. Margetis, “Radiation ofHorizontal Electric

Dipole on Large Dielectric Sphere,” J. Math.

Phys., vol. 43, pp. 3162-3201, 2002.

K. Li and S. O. Park, “Electromagnetic Field in

the Air Generated by a Horizontal Electric Dipole

Located in the Spherical Electrically Earth Coated

with a Dielectric Layer,” J. Electromagn. Waves

Applicat., vol. 17, no. 10, pp. 1399-1417, 2003.

W. Y. Pan and H. Q. Zhang, “Electromagnetic

Field of aVertical Electric Dipole on the

Spherical Conductor Covered with aDielectric

Layer,” Radio Sci., vol. 38, no. 3, p. 1061, 2003.

K. Li, S. O. Park, and H. Q. Zhang,

“Electromagnetic Field in thePresence of a

Three-Layered Spherical Region,” Progress in

Electromagnetics Research, vol. 45, pp. 103–121,

K. Li, S. O. Park, and H. Q. Zhang,

“Electromagnetic Field over theSpherical Earth

Coated with n-Layered Dielectric,” Radio

Science, vol. 39, 2004.

H. Q. Zhang, K. Li, and W. Y. Pan, “The

Electromagnetic Field of a Vertical Dipole on the

Dielectric-Coated Imperfect Conductor,” J. of

Electromag. Waves and Appl., vol. 18, no. 10, pp.

-1320, 2004.

K. Li and Y. L. Lu, “Electromagnetic Field from a

Horizontal Electric Dipole in theSpherical

Electrically Earth Covered with n-Layered

Dielectrics,” Progress In Electromagnetics

Research, vol. 54, pp. 221-244, 2005.

J. P. Mei and K. Li, “Electromagnetic Field from

a Horizontal Electric Dipole on the Surface of a

High Lossy Dielectric Coated with aUniaxial

Layer,” Progress in Electromagnetics Research,

vol. 73, pp. 71-91, 2007.

T. Fei, L. W. Li, T. S. Yeo, H. L. Wang, and Q.

Wu, “A Comparative Study of Radio Wave

Propagation Over the Earth Due to aVertical

Electric Dipole,” IEEE Trans. Antennas

Propagat., vol. 55, no. 10, pp. 2723-2732, 2007.

L. Liang and K. Li, “Radiation from aVertical

Electric Dipole in thePresence of aThree-

Layered Region,” IEEE Trans. Antennas

Propagat., vol. 55, no. 12, pp. 3469-3475, 2007.

J. H. Richmond, “A Wire-Grid Model for

Scattering by Conducting Bodies,” IEEE Trans.

Antennas Propagat., vol. AP-14, no. 6, pp. 782-

, 1966.

J. L. Lin, W. L. Curtis, and M. C. Vincent, “On

the Field Distribution of anAperture,” IEEE

Trans. Antennas Propagat., vol. AP-22, pp. 467-

, 1974.

K. S. H. Lee, L. Martin, and J. P. Castillo,

“Limitations of Wire-Grid Modeling of a Closed

Surface,” IEEE Trans. Electromag. Compat., vol.

, no. 3, pp. 123-129, 1976.

A. C. Ludwig, “Wire Grid Modeling of Surface,”

IEEE Trans. Antennas Propagat., vol. AP-14, no.

, pp. 1045-1048, 1987.

A. F. Peterson, “DifficultiesEncountered when

Attempting to Validate Thin Wire Formulations

for Linear Dipole Antennas,” Applied

Computational Electromagnetic Society (ACES)

Journal, vol. 4, no. 3, pp. 25-40, 1990.

T. H. Hubing and J.F. Kauffman, “Modeling

Electrically Small, Thin Surfaces with Wire

Grids,” Applied Computational Electromagnetic

Society (ACES) Journal, vol. 5, no. 1, pp. 19-24,

ACES JOURNAL, VOL. 26, NO. 12, DECEMBER 2011

J. T. Mayhan, “Characteristic Modes and Wire

Grid Modeling,” IEEE Trans. Antennas

Propagat., vol. 38, no. 4, pp. 457-469, 1990.

S. Kashyap, “Wire Grid and Surface Patch

Modelling for EMPInteraction,” IEEE and

Propagation Society International Symposium,

AP-S, 1990.

R. Paknys, “The Near Field of aWire Grid

Model,” IEEE Trans. Antennas Propagat., vol.

, no. 7, pp. 994-999, 1991.

R. Paknys and L.R. Raschkowan, “Moment

Method Surface Patch and Wire Grid Accuracy in

the Computation of Near Fields,” Applied

Computational Electromagnetic Society (ACES)

Journal, vol. 12, no. 3, pp. 16-25, 1997.

R. F. Harrington, “Moment Methods for Field

Problems,” Proc. of the IEEE, vol. 55, no. 2, pp.

-149, 1967.

T. K. Sarkar and R. F. Harrington, “Radar Cross

Sections of Conducting Bodies over a Lossy Half

Space,” Radio Science, vol. 15, no. 3, pp. 581-

, 1980.

G. J. Burke and A. J. Poggio, “Numerical

Electromagnetics Code (NEC)-Method of

Moments,” Lawrence Livermore Laboratory, Jan.

SuperNec, Poynting Software (Pty) Ltd., South

Africa. http://www.supernec.com/

T. T. Crow and T. H. Shumpert, “Electromagnetic

Scattering from Configurations of Thin Wire with

Multiple Junctions,” Interaction Note 99, 1972.

R. W. P. King and T. T. Wu, “Analysis of

Crossed Wires in aPlane-Wave Field,”

Interaction Note 216, 1975.

A. R. Bretones, A. S. Extrema, R. M. Gómes, and

J. F. Callejón, “About theStudy in the Time

Domain of Junctions Between Thin Wires,”

Applied Computational Electromagnetic Society

(ACES) Journal, vol. 6, no. 2, pp. 2-20, 1991.

K. A. Norton, “The Propagation of Radio Waves

over the Surface of theEarth and in theUpper

Atmosphere,” Proc. IRE, vol. 25, pp. 1203-1236,

T. S. M. Maclean and Z. Wu, Radiowave

Propagation over Ground, Chapman & Hall,

J. R. Wait, “Radiation from aVertical Antenna

over a Curved Stratified Ground,” J. Res. Natl.

Bur. Stand., vol. 56D, no. 4, pp. 237-244, 1956.

J. R. Wait, Electromagnetic Surface Waves, in

Advances in Radio Research, ed. J.A. Saxton, vol.

, Academic Press, New York, pp. 157-217, 1964.

B. Van Der Pol,“Theory of Reflection of the

Light from a Point Source by a Finite Conducting

Flat Mirror, with anApplication to

Radiotelegraphy,” Physica, vol. 2, pp.843-853,

H. Bremmer, Terrestrial Radio Waves, New

York, Elsevier, 1949.

J. Galejs, Terresterial Propagation of Long

Electromagnetic Waves, Pergamon Press, New

York, 1972.

V. A. Houdzoumis, “Scattering of

Electromagnetic Missiles-Part I; Vertical Electric

Dipole Radiation over Spherical Earth- Part II,”

Ph.D. Dissertation, Harvard Univ., 1994.

K. Furutsu, “On theTheory of Radio Wave

Propagation over Inhomogeneous Earth,” J. Res.

Natl. Bur. Stand., vol. 67D, no. 1, pp. 39-62,

K. Furutsu, “On theStatistical Theory of

Electromagnetic Waves in a Fluctuating Medium

(I),” J. Res. Natl. Bur. Stand., vol. 67D, no. 3, pp.

-323, 1963.

K. Furutsu, R. E. Wilkerson, and R. F. Hartmann,

“Some Numerical Results Based on the Theory

of Radio Wave Propagation over Inhomogeneous

Earth,” J. Res. Natl. Bur. Stand., vol. 68D, no. 7,

pp. 827-846, 1964.

K. Furutsu, “Calculated Curves for Groundwave

Propagation over Inhomogeneous Earth with

Pronounced Topographical Features,” J. Res.

Natl. Bur. Stand., vol. 69D, no. 7, pp. 1011-1025,

K. Furutsu and R. E. Wilkerson, “Optical

Approximation for Residue Series of Terminal

Gain in Radiowave Propagation over

Inhomogeneous Earth,” Proc. IEE, vol. 118, pp.

-1202, 1971.

K. Furutsu, “A Systematic Theory of Wave

Propagation over Irregular Terrain,” Radio

Science, vol. 17, no. 5, pp. 1037-1050, 1982.

B. Polat, “Ground Wave Attenuation Curves in

the Presence of Successive 2-D Islands,” Bulletin

of the Technical University of Istanbul (ARI), vol.

, no. 2, pp. 34-39, 2004.

M. K. Ochi, Ocean Waves – The Stochastic

Approach, Cambridge University Press, 1998.

G. Kinsman, Wind Waves: Their Generation and

Propagation on the Ocean Surface, Prentice Hall,

Englewood Cliffs, New Jersey, 1965.

O. M. Phillips, Dynamics of the Upper Ocean,

Cambridge University Press, New York, 1966.

W. J. Pierson and L. Moskowitz, “A Proposed

Spectral Form for Fully Developed Wind Seas

Based on theSimilarity Theory of S.A.

Kitaigorodski,” J. Geophys. Res., vol. 69, pp.

-5190, 1964.

D. E. Hasselmann, M. Dunckel, and J. A. Ewing,

“Directional Wave Spectra Observed during

ZOR, POLAT: AN IMPLEMENTATION OF KING’S GREEN FUNCTIONS IN THIN WIRE SCATTERING PROBLEMS

JONSWAP 1973,” J. Phys. Oceanogr., vol. 10,

pp. 1264-1280, 1980.

F. Berizzi and E. Dalle Mese, “Sea-Wave Fractal

Spectrum for SAR Remote Sensing,” IEE Proc.-

Radar, Sonar Navig., vol. 148, no. 2, pp. 56-66,

D. E. Barrick, “Theory of HF and VHF

Propagation Across the Rough Sea: 1, The

Effective Surface Impedance for a Slightly Rough

Highly Conducting Medium at Grazing

Impedance; 2, Application to HF and VHF

Propagation Above the Sea,” Radio Science, vol.

, no. 5, pp. 517-533, 1971.

M. M. Weiner, “Validation of theNumerical

Electromagnetics Code (NEC) for Antenna Wire

Elements in Pproximity to Earth,” Applied

Computational Electromagnetic Society (ACES)

Journal, vol. 8, no. 2, pp. 44-71, 1993.

D. B. Davidson and H. T. Mouton, “Validation of

and Limitations on the Use of NEC-4 for

Radiation from Antennas Buried within a

Homogeneous Half-Space,” Applied

Computational Electromagnetic Society (ACES)

Journal, vol. 13, no. 3, pp. 302–309, 1998.

R. W. P. King, “Electromagnetic Ground Wave

Field of Vertical Antennas for Communication at

to 30 MHz,” IEEE Trans. Electromag.

Compatibility, vol. 40, no. 4, pp. 337-342, 1998.

E. H. Newman, “Simple Examples of the Method

of Moments in Electromagnetics,” IEEE Trans.

Education., vol. 31, no. 3, pp. 193-200, 1988.

R. W. P. King and T. T. Wu, “The Propagation of

a Radar Pulse in Sea Water,” J. Appl. Phys., vol.

, no. 4, pp. 1581-1590, 1993 (Erratum: J. Appl.

Phys., vol. 77, no. 7, pp. 3586-3587, 1995.)

R. W. P. King, “The Propagation of a Gaussian

Pulse in Sea Water and its Application to Remote

Sensing,” IEEE Trans. Geoscience and Remote

Sensing, vol. 31, no. 3, pp. 595-605, 1993.

R. W. P. King, “Propagation of a Low Frequency

Rectangular Pulse in Sea Water,” Radio Science,

vol. 28, no. 3, pp. 299-307, 1993.

B. Polat, “Approximate Boundary Conditions on

Anisotropic Sheets,” Progress in

Electromagnetics Research-B, vol. 29, pp.355–

, 2011.

C. F. du Toitand D. B. Davidson, “Wiregrid:a

NEC2 Pre-Processor,” Applied Computational

Electromagnetic Society (ACES) Journal, vol. 10,

no. 1, pp. 31–39, 1995.

C. W. Trueman and S.J. Kubina, “Verifying

Wire-Grid Model Integrity with Program

CHECK,” Applied Computational

Electromagnetic Society ( ACES) Journal, vol. 5,

no. 2, pp. 17–42, 1990.

L. A. Oyekanmi and J. Watkins, “Selecting Wire

Radius for Grid/Mesh Models,” Applied

Computational Electromagnetic Society (ACES)

Journal, vol. 5, no. 2, pp. 43–57, 1990.

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Published

2022-05-02

How to Cite

[1]
Ömer . Zor and B. . Polat, “An Implementation of King’s Green Functions in Thin Wire Scattering Problems”, ACES Journal, vol. 26, no. 12, pp. 1024–1038, May 2022.

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