Derivation and Fast Computation of Dyadic Green's Functions of Magnetic Vector Potential for Unbounded Uniaxial Anisotropic Media

Authors

  • Jianliang Zhuo Institute of Electromagnetics and Acoustics, and Department of Electronic Science Xiamen University, Xiamen, Fujian-361008, China
  • Feng Han Institute of Electromagnetics and Acoustics, and Department of Electronic Science Xiamen University, Xiamen, Fujian-361008, China
  • Na Liu Institute of Electromagnetics and Acoustics, and Department of Electronic Science Xiamen University, Xiamen, Fujian-361008, China
  • Longfang Ye Institute of Electromagnetics and Acoustics, and Department of Electronic Science Xiamen University, Xiamen, Fujian-361008, China
  • Hai Liu Institute of Electromagnetics and Acoustics, and Department of Electronic Science Xiamen University, Xiamen, Fujian-361008, China
  • Qing Huo Liu Department of Electrical and Computer Engineering Duke University, Durham, NC-27705, USA

Keywords:

Dyadic Green's function, magnetic vector-potential, unbounded, uniaxial anisotropic media

Abstract

The dyadic Green's function of the magnetic vector-potential A (DGFA) for unbounded uniaxial anisotropic media is unavailable in literature but it is needed in numerical computation. The equation of the DGFA was directly derived from the Maxwell's equations. Through the Fourier transform and the inverse Fourier transform, the triple integral form of the DGFA in the spatial domain was obtained. And it was finally simplified to Sommerfeld integrals. In order to verify these formulas, we applied the singularity subtraction technique to evaluate the Sommerfeld integrals rapidly and compared the numerical results with the analytical solutions for degenerated cases for the isotropic unbounded media, as well as the simulated results from a commercial finite element software for uniaxial anisotropic unbounded media. Finally, the effect of the singularity subtraction method was discussed.

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References

M. J. Havrilla, “Scalar potential depolarizing dyad artifact for a uniaxial medium,” Progress In Electromagnetics Research, vol. 134, no. 1, pp. 151-168, 2013.

M. J. Havrilla, “Scalar potential formulation for a uniaxial inhomogeneous medium,” Radio Science Meeting (USNC-URSI NRSM), 2014.

W. S. Weiglhofer and S. O. Hansen, “Faraday chiral media revisited. I. Fields and sources,” IEEE Transactions on Antennas and Propagation, vol. 47, no. 5, pp. 807-814, 1999.

A. Y. Qing, “Electromagnetic inverse scattering of multiple perfectly conducting cylinders by differential evolution strategy with individuals in groups (GDES),” IEEE Transactions on Antennas and Propagation, vol. 52, no. 5, pp. 1223-1229, 2004.

L. P. Zha, R. S. Chen, and T. Su, “Fast EM scattering analysis for the hard targets in a layered medium by using the hierarchical vector basis functions,” Applied Computational Electromagnetics Society Journal, vol. 30, no. 11, pp. 1154- 1160, 2015.

J. L. Hu, Z. P. Wu, H. Mccann, L. E. Davis, and C. G. Xie, “Sequential quadratic programming method for solution of electromagnetic inverse problems,” IEEE Transactions on Antennas and Propagation, vol. 53, no. 8, pp. 2680-2687, 2005.

D. W. Winters, B. D. Van Veen, and S. C. Hagness, “A sparsity regularization approach to the electromagnetic inverse scattering problem,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 1, pp. 145-154, 2010.

X. M. Xu and Q. H. Liu, “The BCGS-FFT method for electromagnetic scattering from inhomogeneous objects in a planarly layered medium,” IEEE Antennas and Wireless Propagation Letters, vol. 1, no. 1, pp. 77-80, 2002.

F. H. Li, L. P. Song, and Q. H. Liu, “Threedimensional reconstruction of objects buried in layered media using born and distorted born iterative methods,” IEEE Antennas and Wireless Propagation Letters, vol. 1, no. 2, pp. 107-111, 2004.

M. Pastorino, M. Raffetto, and A. Randazzo, “Electromagnetic inverse scattering of axially moving cylindrical targets,” IEEE Transactions on Geoscience and Remote Sensing, vol. 53, no. 3, pp. 1452-1462, 2015.

J. G. Wang, Z. Q. Zhao, Z. P. Nie, and Q. H. Liu, “Electromagnetic inverse scattering series method for positioning three-dimensional targets in nearsurface two-layer medium with unknown dielectric properties,” IEEE Geoscience and Remote Sensing Letters, vol. 12, no. 2, pp. 299-303, 2015.

J. L. Xiong and W. C. Chew, “A newly developed formulation suitable for matrix manipulation of layered medium Green’s functions,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 3, pp. 868-875, 2010.

A. Yakovlev, S. Ortiz, et al., “Electric dyadic Green’s functions for modeling resonance and coupling effects in waveguide-based aperturecoupled patch arrays,” Applied Computational Electromagnetics Society Journal, vol. 17, no. 2, pp. 123-133, 2002.

P. M. Smith, “Dyadic Green’s functions for multilayer SAW substrates,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 48, no. 1, pp. 171-179, 1999.

G. W. Hanson, “Dyadic Green’s function for a multilayered planar medium-A dyadic eigenfunction approach,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 12, pp. 3350-3356, 2004.

E. Simsek and Q. H. Liu, “Fast computation of dyadic Green’s function for layered media and its application in interconnect simulations,” IEEE Transactions on Antennas and Propagation, vol. 3, no. 3, pp. 2783, 2004.

K. A. Michalski and J. R. Mosig, “Multilayered media Green’s functions in integral equation formulations,” IEEE Transactions on Antennas and Propagation, vol. 45, no. 3, pp. 508-519, 1997.

P. G. Cottis, C. N. Vazouras, and C. Spyrou, “Green’s function for an unbounded biaxial medium in cylindrical coordinates,” IEEE Transactions on Antennas and Propagation, vol. 47, no. 1, pp. 195-276 199, 1999.

P. G. Cottis and G. D. Kondylis, “Properties of the dyadic Green’s function for an unbounded anisotropic medium,” IEEE Transactions on Antennas and Propagation, vol. 43, no. 2, pp. 154- 279 161, 1995.

Y. Huang and J. K. Lee, “Dyadic green’s functions for unbounded and two-layered general anisotropic media,” Progress In Electromagnetics Research B, vol. 30, no. 30, pp. 27-46, 2011.

F. L. Mesa, R. Marques, and M. Horno, “A general algorithm for computing the bidimensional spectral Green’s dyad in multilayered complex bianisotropic media: The equivalent boundary method,” IEEE Transactions on Microwave Theory and Techniques, vol. 39, no. 9, pp. 1640-1649, 1991.

A. Eroglu, Y. H. Lee, and J. K. Lee, “Dyadic Green’s functions for multi-layered uniaxially anisotropic media with arbitrarily oriented optic axes,” IET Microwaves, Antennas, Propagation, vol. 5, no. 15, pp. 1779-1788, 2011.

P. P. Ding, C. W. Qiu, Z. Sad, and S. P. Yeo, “Rigorous derivation and fast solution of spatial domain Green’s functions for uniaxial anisotropic multilayers using modified fast Hankel transform method,” IEEE Transactions on Microwave Theory and Techniques, vol. 60, no. 2, pp. 205-217, 2012.

S. M. Ali and S. F. Mahoud, “Electromagnetic fields of buried sources in stratified anisotropic media,” IEEE Transactions on Antennas and Propagation, vol. 27, no. 5, pp. 671-678, 1979.

D. H. Werner, “An exact integration procedure for vector potentials of thin circular loop antennas,” IEEE Transactions on Antennas and Propagation, vol. 44, no. 8, pp. 157-165, 1996.

N. Georgieva, Z. Z. Chen, and P. Bhartia, “Analysis of transient electromagnetic fields based on the vector potential function,” IEEE Transactions on Magnetics, vol. 35, no. 3, pp. 1410-1413, 1999.

F. De. Flaviis, M. G. Noro, R. E. Diaz, G. Franceschetti, and N. G. Alexopoulos, “A timedomain vector potential formulation for the solution of electromagnetic problems,” IEEE Microwave and Guided Wave Letters, vol. 8, no. 9, pp. 310- 312, 1998.

Z. R. Yu, W. J. Zhang, and Q. H. Liu, “A mixedorder stabilized bi-conjugate gradient FFT method for magnetodielectric objects,” IEEE Transactions on Antennas and Propagation, vol. 62, no. 11, pp. 5647-5655, 2014.

Z. R. Yu, W. J. Zhang, and Q. H. Liu, “The mixedorder BCGS-FFT method for the scattering of threedimensional inhomogeneous anisotropic magnetodielectric objects,” IEEE Transactions on Antennas and Propagation, vol. 63, no. 12, pp. 5709-5717, 2015.

R. D. Nevels and J. Jeong, “Time domain coupled field dyadic Green function solution for Maxwell’s equations,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 8, pp. 2761-2764, 2008.

J. H. Moran and S. Gianzero, “Effects of formation anisotropy on resistivity-logging measurements,” Geophysics, vol. 44, no. 7, pp. 1266-1286, 1979.

A. Abubakar and T. M. Habashy, “A closed-form expression of the electromagnetic tensor Green’s functions for a homogeneous TI-anisotropic medium,” IEEE Geoscience and Remote Sensing Letters, vol. 3, no. 4, pp. 447-451, 2006.

E. Simsek, Q. H. Liu, and B. J. Wei, “Singularity subtraction for evaluation of Green’s functions for multilayer media,” IEEE Transactions on Microwave Theory and Techniques, vol. 54, no. 1, pp. 216-225, 2006.

W. C. Chew, “Vector potential electromagnetics with generalized gauge for inhomogeneous media: Formulation,” Progress in Electromagnetics Research, vol. 149, pp. 69-84, 2014.

A. Jeffrey and D. Zwillinger, Table of Integrals, Series, and Products. Elsevier, Burlington, 2007.

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Published

2021-07-30

How to Cite

[1]
Jianliang Zhuo, Feng Han, Na Liu, Longfang Ye, Hai Liu, and Qing Huo Liu, “Derivation and Fast Computation of Dyadic Green’s Functions of Magnetic Vector Potential for Unbounded Uniaxial Anisotropic Media”, ACES Journal, vol. 32, no. 10, pp. 862–871, Jul. 2021.

Issue

2017: Vol 32 Iss 10

Section

Articles