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GENERALIZED CURRENT GREEN'S FUNCTION FORMALISM FOR ELECTROMAGNETIC RADIATION BY COMPOSITE SYSTEMS

By S. Mikki

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Abstract:
We provide an explicit geometric generalisation of the antenna current Green's function (ACGF) formalism from the perfect electric conducting (PEC) to generic coupled N-body systems composed of arbitrarily shaped coupled PEC and dielectric objects, with the main emphasis on the mathematical foundations and the rigorous construction of the Green's function using distributional limits. Starting from mainly reciprocity, surface equivalence theorems, and other typical regularity conditions, we carefully construct the current Green's function by employing a combination of methods including Riemannian geometry, distribution theory, and functional analysis. The formalism outlined here for composite domains turns out to be more complicated than the PEC-only formulation due to the former's need to explicitly account for the coupling interaction between the magnetic and electric degrees of freedom. The approach is developed for extremely general systems, and use is made of Riemannian geometry to avoid working with specific or concrete configurations, hence retaining high generality in our final conclusions. While the ACGF tensor's matrix representations depend on the coordinate system on the manifolds supporting the electromagnetic boundary conditions, we focus here on providing coordinate-independent integral expressions for the induced current. With the ACGF it is possible to theoretically treat arbitrary N-body coupled PEC-dielectric configurations as space-frequency linear systems with an exact and rigorous response function being the current Green's function itself. While the derivation is very general, it still leaves open questions regarding whether the ACGF can be constructed for nonreciprocal systems or using volume integral equations.

Citation:
S. Mikki, "Generalized Current Green's Function Formalism for Electromagnetic Radiation by Composite Systems," Progress In Electromagnetics Research B, Vol. 87, 171-191, 2020.
doi:10.2528/PIERB20031801
http://www.jpier.org/pierb/pier.php?paper=20031801

References:
1. Mikki, S. and Y. Antar, ew Foundations for Applied Electromagnetics: The Spatial Structure of Fields, Artech House, London, 2016.

2. Schelkunoff, S. A., "A mathematical theory of linear arrays," The Bell System Technical Journal, Vol. 22, 1943.
doi:10.1002/j.1538-7305.1943.tb01306.x

3. Schelkunoff, S. A. and H. T. Friss, Antennas: Theory and Practice, Chapman & Hall, New York, London, 1952.

4. Cho, K., Optical Response of Nanostructures: Microscopic Nonlocal Theory, Springer, Berlin New York, 2003.
doi:10.1007/978-3-662-05175-7

5. Keller, O., Quantum Theory of Near-Field Electrodynamics, Springer, Berlin New York, 2011.
doi:10.1007/978-3-642-17410-0

6. Mikki, S. and A. Kishk, "A symmetry-based formalism for the electrodynamics of nanotubes," Progress In Electromagnetics Research, Vol. 86, 111-134, 2008.
doi:10.2528/PIER08081704

7. Schwinger, J., et al., Classical Electrodynamics, Perseus Books, Reading, Mass, 1998.

8. Jackson, J., Classical Electrodynamics, Wiley, New York, 1999.

9. Felsen, L., Radiation and Scattering of Waves, IEEE Press, Piscataway, NJ, 1994.

10. Chew, W. C., Waves and Fields in Inhomogeneous Media, Wiley-IEEE, 1999.

11. Jentschura, U., Advanced Classical Electrodynamics: Green Functions, Regularizations, Multipole Decompositions, World Scientific, New Jersey, 2017.

12. Tai, C.-T., Dyadic Green Functions in Electromagnetic Theory, IEEE Press, Piscataway, NJ, 1994.

13. Schelkunoff, S. A., "Theory of antennas of arbitrary size and shape," Proceedings of the IEEE, Vol. 72, No. 9, 1165-1190, Sep. 1984.

14. Mikki, S. and Y. Antar, "On the fundamental relationship between the transmitting and receiving modes of general antenna systems: A new approach," IEEE Antennas and Wireless Propagation Letters, Vol. 11, 232-235, 2012.

15. Mikki, S. and Y. Antar, "The antenna current Green’s function formalism — Part I," IEEE Transactions on Antennas and Propagation, Vol. 9, 4493-4504, Sep. 2013.

16. Mikki, S. and Y. Antar, "The antenna current Green’s function formalism — Part II," IEEE Transactions on Antennas and Propagation, Vol. 9, 4505-4519, Sep. 2013.

17. Mikki, S. and Y. Antar, "A rigorous approach to mutual coupling in general antenna systems through perturbation theory," IEEE Antennas and Wireless Communication Letters, Vol. 14, 115-118, 2015.

18. Henault, S., S. K. Podilchak, S. Mikki, and Y. Antar, "A methodology for mutual coupling estimation and compensation in antennas," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 3, 1119-1131, Mar. 2013.

19. Alzahed, A., S. Mikki, and Y. Antar, "Design of nonlinear mutual coupling operator for antenna arrays using a novel ACGF-deep-learning technology," International Union of Radio Science General Assembly & Scientific (URSI) Symposium, Montreal, 2017.

20. Alzahed, A., S. Mikki, and Y. Antar, "Nonlinear mutual coupling compensation operator design using a novel electromagnetic machine learning paradigm," IEEE Antennas and Wireless Propagation Letters, Vol. 18, No. 5, 861-865, 2019.

21. Kim, Y.-D., H.-J. Kim, K.-U. Bae, J.-H. Park, and N.-H. Myung, "A hybrid UTD-ACGF technique for DOA finding of receiving antenna array on complex environment," IEEE Transactions on Antennas and Propagation, Vol. 63, 11, 2015.

22. Kim, Y.-D., D.-W. Yi, S.-J. Yang, H. Chae, J.-W. Yu, and N.-H. Myung, "Beam pattern analysis of antenna array on complex platform using AEP method based on hybrid UTD-ACGF technique," IEEE Transactions on Antennas and Propagation, Vol. 65, 3, 2017.

23. Yang, S., Y. Kim, H. Jo, and N. Myung, "Alternative method for obtaining antenna current Green’s function based on infinitesimal dipole modeling," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 4, 2583-2590, Apr. 2019.

24. Mikki, S. and Y. M. M. Antar, "Analysis of generic near-field interactions using the antenna current Green's function," Progress In Electromagnetic Research C, Vol. 59, 1-9, 2015.

25. Hanoon, A. and S. Mikki, "Bandwidth-enhancement of digital communication systems employing narrowband antennas: A novel electromagnetic OFDM approach," 2017 IEEE International Symposium on Antennas and Propagation USNC/URSI National Radio Science Meeting, 527-528, Jul. 2017.

26. Mikki, S., A. Hanoon, J. Aulin, and Y. Antar, "The time-dependent ACGF with applications to M- ary digital communication systems," The 11th European Conference on Antennas and Propagation (EuCap 2017), 19-24, 2017.

27. Mikki, S., "The antenna spacetime system theory of wireless communications," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Apr. 2019.

28. Kahn, D., Introduction to Global Analysis, Dover Publications, Mineola, N.Y., 2007.

29. Agricola, I., Global Analysis: Di®erential Forms in Analysis, Geometry, and Physics, American Mathematical Society, Providence, R.I., 2002.

30. Mikki, S. and Y. M. Antar, "Analysis of electromagnetic interactions in antenna arrays using the antenna current Green's function method," Proceedings of IEEE APS-URSI International Symposium, 3-8, 2011.

31. Kellogg, O. D., Foundations of Potential Theory, Springer, Berlin, J., 1929.

32. Colton, D. and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Cham., 2019.

33. Nedelec, J.-C., Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems, Springer, New York, 2001.

34. Bladel, V. J., Electromagnetic Fields, Wiley-Intersience, IEEE, 2007.

35. Geyi, W., Foundations of Applied Electrodynamics, Wiley, Chichester, West Sussex Hoboken, N.J., 2010.

36. Love, A. E. H., "The integration of the equations of propagation of electric waves," Philosophical Transactions of the Royal Society of London, Series A, Containing Papers of a Mathematical or Physical Character, Vol. 197, 1-45, 1901.

37. Schelkunoff, S. A., "Some equivalence theorems of electromagnetics and their application to radiation problems," The Bell System Technical Journal, Vol. 15, No. 1, 92-112, Jan. 1936.

38. Chew, W., M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves, Morgan & Claypool Publishers, San Rafael, Calif., 2009.

39. Chew, W., J.-M. Jin, E. Michielssen, J. Song, and editors, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Boston, 2001.

40. Kolundzija, B. M. and A. R. Djordjevic, Electromagnetic Modeling of Composite Metallic and Dielectric Structures, Artech House, 2003.

41. Warnick, K. and W. Chew, Numerical Analysis for Electromagnetic Integral Equations, Artech House, Boston, 2008.

42. Arvas, E., A. Rahhal Arabi, A. Sadigh, and S. M. Rao, "Scattering from multiple conducting and dielectric bodies of arbitrary shape," IEEE Antennas and Propagation Magazine, Vol. 33, No. 2, 29-36, Apr. 1991.

43. Medgyesi-Mitschang, L. N., J. M. Putnam, and M. B. Gedera, "Generalized method of moments for three-dimensional penetrable scatterers," J. Opt. Soc. Am. A, Vol. 11, No. 4, 1383-1398, Apr. 1994.

44. Yla-Oijala, P., M. Taskinen, and J. Sarvas, "Surface integral equation method for general composite metallic and dielectric structures with junctions," Progress In Electromagnetics Research, Vol. 52, 81-108, 2005.

45. Appel, W., Mathematics for Physics and Physicists, Princeton University Press, Princeton, N.J., 2007.

46. Gelfand, I. and G. Shilov, Generalized Functions: Volume 1, American Mathematical Society AMS Chelsea Publishing, Providence, Rhode Island, 2016.

47. Zeidler, E., Quantum Field Theory I: Basics in Mathematics and Physics, Springer, 2009.

48. Zeidler, E., Quantum Field Theory II: Quantum Electrodynamics, Springer, 2006.

49. Hassani, S., Mathematical Physics: A Modern Introduction to Its Foundations, Springer, Cham., 2013.

50. Gelfand, I. and G. Shilov, Generalized Functions: Volume 2, American Mathematical Society AMS Chelsea Publishing, Providence, Rhode Island, 2016.

51. Gelfand, I. and N. Vilenkin, "Generalized Functions: Volume 4," Academic Press, New York London, 1964.

52. Lee, J., Introduction to Smooth Manifolds, Springer, New York London, 2012.

53. Schantz, H., The Art and Science of Ultrawideband Antennas, Artech House, Boston, 2015.

54. Mikki, S. and Y. Antar, "The antenna current Green's function as an alternative method to conventional full-wave analysis solvers: An outline," 2015 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 1-3, Aug. 2015.

55. Gibson, W. C., The Method of Moments in Electromagnetics, CRC Press, 2015.

56. Ramm, A., "Theoretical and practical aspects of singularity and eigenmode expansion methods," IEEE Transactions on Antennas and Propagation, Vol. 28, No. 6, 897-901, Nov. 1980.

57. Sarrazin, F., S. Mikki, Y. Antar, P. Pouliguen, and A. Sharaiha, "Study of dipole antennas' characteristic modes through the antenna current Green's function and the singularity expansion method," 2015 9th European Conference on Antennas and Propagation (EuCAP), 1-2, May 2015.

58. Alzahed, A. M., S. Mikki, Y. M. Antar, M. Clenet, and S. Jovic, "Characterization of a rectangular patch antenna using ACGF-SEM approach," 2016 IEEE Conference on Antenna Measurements & Applications (CAMA), 1-3, IEEE, 2016.

59. Alzahed, A. M., S. Mikki, Y. M. Antar, M. Clenet, and S. Jovic, "The ACGF-SEM approach to electromagnetic radiation with applications in radar and inverse modeling," Proc. Int. Union Radio Sci. General Assem. Sci. Symp. (URSI), 2017.

60. Alzahed, A., "Analysis of electromagnetic systems using the Antenna Current Green's function (ACGF) and machine learning,", Ph.D. Dissertation, Royal Military College of Canada, 2019.

61. Alzahed, A. M., S. M. Mikki, and Y. M. Antar, "Electromagnetic deep learning technology for radar target identification," 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, 579-580, IEEE, 2019.

62. Alzahed, A., S. Mikki, and Y. Antar, "Electromagnetic machine learning for inverse modeling using the spatial singularity expansion method," IEEE Journal on Multiscale and Multiphysics Computational Techniques, Vol. 5, 59-71, 2020.

63. Mikki, S. and A. Kishk, "Theory and applications of in¯nitesimal dipole models for computational electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 5, 1325-1337, May 2007.

64. Mikki, S., S. Clauzier, and Y. Antar, "A correlation theory of antenna directivity with applications to superdirective arrays," IEEE Antennas and Wireless Propagation Letters, Vol. 18, No. 5, 811-815, May 2019.

65. Dundas, B. I., Short Course in Di®erential Topology, Cambridge University Press, Cambridge, United Kingdom New York, NY, 2018.

66. Godement, R., Analysis III: Analytic and Di®erential Functions, Manifolds and Riemann Surfaces, Springer, Cham., 2015.


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