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Progress In Electromagnetics Research B | ISSN: 1937-6472 |

Home > Vol. 87 > pp. 171-191
## GENERALIZED CURRENT GREEN'S FUNCTION FORMALISM FOR ELECTROMAGNETIC RADIATION BY COMPOSITE SYSTEMSBy S. Mikki
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.
2. Schelkunoff, S. A., "A mathematical theory of linear arrays," 3. Schelkunoff, S. A. and H. T. Friss, 4. Cho, K., 5. Keller, O., 6. Mikki, S. and A. Kishk, "A symmetry-based formalism for the electrodynamics of nanotubes," 7. Schwinger, J., et al., 8. Jackson, J., 9. Felsen, L., 10. Chew, W. C., 11. Jentschura, U., 12. Tai, C.-T., 13. Schelkunoff, S. A., "Theory of antennas of arbitrary size and shape," 14. Mikki, S. and Y. Antar, "On the fundamental relationship between the transmitting and receiving modes of general antenna systems: A new approach," 15. Mikki, S. and Y. Antar, "The antenna current Green’s function formalism — Part I," 16. Mikki, S. and Y. Antar, "The antenna current Green’s function formalism — Part II," 17. Mikki, S. and Y. Antar, "A rigorous approach to mutual coupling in general antenna systems through perturbation theory," 18. Henault, S., S. K. Podilchak, S. Mikki, and Y. Antar, "A methodology for mutual coupling estimation and compensation in antennas," 19. Alzahed, A., S. Mikki, and Y. Antar, "Design of nonlinear mutual coupling operator for antenna arrays using a novel ACGF-deep-learning technology," 20. Alzahed, A., S. Mikki, and Y. Antar, "Nonlinear mutual coupling compensation operator design using a novel electromagnetic machine learning paradigm," 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," 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," 23. Yang, S., Y. Kim, H. Jo, and N. Myung, "Alternative method for obtaining antenna current Green’s function based on infinitesimal dipole modeling," 24. Mikki, S. and Y. M. M. Antar, "Analysis of generic near-field interactions using the antenna current Green's function," 25. Hanoon, A. and S. Mikki, "Bandwidth-enhancement of digital communication systems employing narrowband antennas: A novel electromagnetic OFDM approach," 26. Mikki, S., A. Hanoon, J. Aulin, and Y. Antar, "The time-dependent ACGF with applications to M- ary digital communication systems," 27. Mikki, S., "The antenna spacetime system theory of wireless communications," 28. Kahn, D., 29. Agricola, I., 30. Mikki, S. and Y. M. Antar, "Analysis of electromagnetic interactions in antenna arrays using the antenna current Green's function method," 31. Kellogg, O. D., 32. Colton, D. and R. Kress, 33. Nedelec, J.-C., 34. Bladel, V. J., 35. Geyi, W., 36. Love, A. E. H., "The integration of the equations of propagation of electric waves," 37. Schelkunoff, S. A., "Some equivalence theorems of electromagnetics and their application to radiation problems," 38. Chew, W., M. S. Tong, and B. Hu, 39. Chew, W., J.-M. Jin, E. Michielssen, J. Song, and editors, 40. Kolundzija, B. M. and A. R. Djordjevic, 41. Warnick, K. and W. Chew, 42. Arvas, E., A. Rahhal Arabi, A. Sadigh, and S. M. Rao, "Scattering from multiple conducting and dielectric bodies of arbitrary shape," 43. Medgyesi-Mitschang, L. N., J. M. Putnam, and M. B. Gedera, "Generalized method of moments for three-dimensional penetrable scatterers," 44. Yla-Oijala, P., M. Taskinen, and J. Sarvas, "Surface integral equation method for general composite metallic and dielectric structures with junctions," 45. Appel, W., 46. Gelfand, I. and G. Shilov, 47. Zeidler, E., 48. Zeidler, E., 49. Hassani, S., 50. Gelfand, I. and G. Shilov, 51. Gelfand, I. and N. Vilenkin, "Generalized Functions: Volume 4," 52. Lee, J., 53. Schantz, H., 54. Mikki, S. and Y. Antar, "The antenna current Green's function as an alternative method to conventional full-wave analysis solvers: An outline," 55. Gibson, W. C., 56. Ramm, A., "Theoretical and practical aspects of singularity and eigenmode expansion methods," 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," 58. Alzahed, A. M., S. Mikki, Y. M. Antar, M. Clenet, and S. Jovic, "Characterization of a rectangular patch antenna using ACGF-SEM approach," 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," 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," 62. Alzahed, A., S. Mikki, and Y. Antar, "Electromagnetic machine learning for inverse modeling using the spatial singularity expansion method," 63. Mikki, S. and A. Kishk, "Theory and applications of in¯nitesimal dipole models for computational electromagnetics," 64. Mikki, S., S. Clauzier, and Y. Antar, "A correlation theory of antenna directivity with applications to superdirective arrays," 65. Dundas, B. I., 66. Godement, R., |

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