Nonlocal radiating systems are new functional structures composed of externally applied currents radiating in nonlocal material domains, for example hot plasma, optically active media, or nanoengineered spatially dispersive metamaterials. We here develope the requisite mathematical foundations of the subject needed for investigating how such new generation of radiating systems may be analyzed at a very general level (Part I), while radiation pattern constructions for applications are provided in Part II. A key feature in our approach is the adoption of a fully-fledged momentum space perspective, where the spacetime Fourier transform method is exploited to derive, analyze, and understand how externally-controlled currents embedded into nonlocal media radiate. In particular, we avoid working in the spatio-temporal domain popular in conventional local radiation theory. Instead, we focus on the basic but nontrivial problem of infinite generic (anisotropic or isotropic) homogeneous nonlocal domain excited by an external source and investigate this structure in depth by deriving the dyadic Green's functions of nonlocal media in momentum space. Afterwords, the radiated energy in the far-zone is estimated directly in the spectral domain using a generalized momentum space energy density concept after the use of a suitable power theorem. The derived expressions of the radiation power pattern of the source can be computed analytically provided that the medium dielectric functions and the dispersion relation data of the nonlocal metamaterial are available. Detailed examples and applications of the theory and its algorithm are given in Part II of the present paper.
2. Agranovich, V. and V. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, Springer Berlin HeidelbergImprint Springer, Berlin, Heidelberg, 1984.
3. Ginzburg, V. L., Theoretical Physics and Astrophysics, Pergamon Press, Oxford, New York, 1979.
4. Mikki, S. M. and A. A. Kishk, "Electromagnetic wave propagation in nonlocal media: Negative group velocity and beyond," Progress In Electromagnetics Research B, Vol. 14, 149-174, 2009.
5. Mikki, S. M. and Y. M. M. Antar, "On electromagnetic radiation in nonlocal environments: Steps toward a theory of near field engineering," 2015 9th European Conference on Antennas and Propagation (EuCAP), 1-5, Apr. 2015.
6. Mikki, S. M. and Y. M. M. Antar, New Foundations for Applied Electromagnetics: The Spatial Structure of Fields, Artech House, London, 2016.
7. Orlov, A., P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, "Engineered optical nonlocality in nanostructured metamaterials," Phys. Rev. B, Vol. 84, 045424, Jul. 2011.
8. Wells, B. M., A. V. Zayats, and V. A. Podolskiy, "Nonlocal optics of plasmonic nanowire metamaterials," Phys. Rev. B, Vol. 89, 035111, Jan. 2014.
9. Mikki, S. M. and A. A. Kishk, "Theory of optical scattering by carbon nanotubes," Microwave and Optical Technology Letters, Vol. 49, No. 10, 2360-2364, Jul. 2007.
10. Mikki, S. M. and A. A. Kishk, "Electromagnetic scattering by multi-wall carbon nanotubes," Progress In Electromagnetics Research B, Vol. 17, 49-67, 2009.
11. Mikki, S. M. and A. A. Kishk, "Effective medium theory for carbon nanotube composites and their potential applications as metamaterials," 2007 IEEE/MTT-S International Microwave Symposium, 1137-1140, Jun. 2007.
12. Mikki, S. M. and A. A. Kishk, "Mean-field electrodynamic theory of aligned carbon nanotube composites," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 5, 1412-1419, May 2009.
13. Mikki, S. M. and A. A. Kishk, "An efficient algorithm for the analysis and design of carbon nanotube photonic crystals," Progress In Electromagnetics Research C, Vol. 83, 83-96, 2018.
14. Enoch, S., G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett., Vol. 89, 213902, Nov. 2002.
15. Yuan, Y., L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A, Vol. 77, 053821, May 2008.
16. Dong, Z.-G., H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, "Modeling the directed transmission and reflection enhancements of the lasing surface plasmon amplification by stimulated emission of radiation in active metamaterials," Phys. Rev. B, Vol. 80, 235116, Dec. 2009.
17. Halterman, K., S. Feng, and V. C. Nguyen, "Controlled leaky wave radiation from anisotropic epsilon near zero metamaterials," Phys. Rev. B, Vol. 84, 075162, Aug. 2011.
18. Kort-Kamp, W. J. M., F. S. S. Rosa, F. A. Pinheiro, and C. Farina, "Spontaneous emission in the presence of a spherical plasmonic metamaterial," Phys. Rev. A, Vol. 87, 023837, Feb. 2013.
19. Schulz, K. M., H. Vu, S. Schwaiger, A. Rottler, T. Korn, D. Sonnenberg, T. Kipp, and S. Mendach, "Controlling the spontaneous emission rate of quantum wells in rolled-up hyperbolic metamaterials," Phys. Rev. Lett., Vol. 117, 085503, Aug. 2016.
20. Nyman, M., V. Kivijarvi, A. Shevchenko, and M. Kaivola, "Generation of light in spatially dispersive materials," Phys. Rev. A, Vol. 95, 043802, Apr. 2017.
21. Mikki, S. M., "Theory of electromagnetic radiation in nonlocal metamaterials — Part II: Applications," Progress In Electromagnetics Research, 2020 (accepted).
22. Ilinskii, Y. A. and L. Keldysh, Electromagnetic Response of Material Media, Springer Science+Business Media, New York, 1994.
23. Zeidler, E., Quantum Field Theory II: Quantum Electrodynamics, Springer, 2006.
24. Keller, O., Quantum Theory of Near-field Electrodynamics, Springer-Verlag Berlin Heidelberg, 2011.
25. Kerns, D., "Reviews and abstracts—Plane wave scattering-matrix theory of antennas and antenna --- antenna interactions," IEEE Antennas and Propagation Society Newsletter, Vol. 21, No. 1, 11-11, Feb. 1979.
26. Mikki, S. M. and Y. M. M. Antar, "A theory of antenna electromagnetic near field — Part I," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 12, 4691-4705, Dec. 2011.
27. Mikki, S. M. and Y. M. M. Antar, "A theory of antenna electromagnetic near field — Part II," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 12, 4706-4724, Dec. 2011.
28. Mikki, S. M. and Y. M. M. Antar, "A new technique for the analysis of energy coupling and exchange in general antenna systems," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 12, 5536-5547, Dec. 2015.
29. Sarkar, D., S. Mikki, K. V. Srivastava, and Y. M. M. Antar, "Dynamics of antenna reactive energy using time-domain IDM method," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 2, 1084-1093, Feb. 2019.
30. Mikki, S. M., D. Sarkar, and Y. M. M. Antar, "On localized antenna energy in electromagnetic radiation," Progress In Electromagnetics Research M, Vol. 79, 1-10, 2019.
31. Mikki, S. M., A. M. Alzahed, and Y. M. M. Antar, "Radiation energy of antenna fields: Critique and a solution through recoverable energy," 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), 1-4, Aug. 2017.
32. Mikki, S. M. and Y. M. M. Antar, "Critique of antenna fundamental limitations," 2010 URSI International Symposium on Electromagnetic Theory, 122-125, Aug. 2010.
33. Hansen, T. and A. Yaghjian, Plane-wave Theory of Time-domain Fields: Near-field Scanning Applications, IEEE Press, New York, 1999.
34. Felsen, L., Radiation and Scattering of Waves, IEEE Press, Piscataway, NJ, 1994.
35. Chew, W. C., Waves and Fields in Inhomogenous Media, Wiley-IEEE, 1999.
36. Novotny, L., Principles of Nano-Optics, Cambridge University Press, Cambridge, 2012.
37. Mikki, S. M. and Y. M. M. 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.
38. Mikki, S. M. and Y. M. M. Antar, "The antenna current Green's function formalism — Part I," IEEE Trans. Antennas Propagat., Vol. 9, 4493-4504, Sep. 2013.
39. Mikki, S. M. and Y. M. M. Antar, "The antenna current Green’s function formalism — Part II," IEEE Trans. Antennas Propagat., Vol. 9, 4505-4519, Sep. 2013.
40. Brillouin, L., Wave Propagation in Periodic Structures, Electric Filters and Crystal Lattices, Dover Publications, New York, 1953.
41. Mikki, S. M., "Exact derivation of the radiation law of antennas embedded into generic nonlocal metamaterials: A momentum-space approach," 2020 14th European Conference on Antennas and Propagation (EuCAP), 1-5, 2020.
42. Mikki, S. M., "Quantum antenna theory for secure wireless communications," 2020 14th European Conference on Antennas and Propagation (EuCAP), 1-4, 2020.
43. Mikki, S. M. and A. A. Kishk, "Nonlocal electromagnetic media: A paradigm for material engineering," Passive Microwave Components and Antennas, InTech, Apr. 2010.
44. Brillouin, L., "Origin of radiation resistance," Radioelectricite, Vol. 3, 147-152, 1922.
45. Landau, L. D., Electrodynamics of Continuous Media, Butterworth-Heinemann, Oxford, England, 1984.
46. Mikki, S. M. and Y. M. M. Antar, "Aspects of generalized electromagnetic energy exchange in antenna systems: A new approach to mutual coupling," EuCap 2015, 1-5, Apr. 2015.
47. Garrison, J. C. and R. Chiao, Quantum Optics, Oxford University Press, Oxford, 2014.
48. Cho, K., "Reconstruction of Macroscopic Maxwell Equations: A Single Susceptibility Theory," Springer, 2018.
49. Cho, K., Optical Response of Nanostructures: Microscopic Nonlocal Theory, Springer, Berlin, Germany, 2003.
50. Mikki, S. M. and A. A. Kishk, "Derivation of the carbon nanotube susceptibility tensor using lattice dynamics formalism," Progress In Electromagnetics Research B, Vol. 9, 1-26, 2008.
51. Mikki, S. M. and A. A. Kishk, "A symmetry-based formalism for the electrodynamics of nanotubes," Progress In Electromagnetics Research, Vol. 86, 111-134, 2008.
52. Mikki, S. M. and A. A. Kishk, "Exact derivation of the dyadic Green's functions of carbon nanotubes using microscopic theory," 2007 IEEE Antennas and Propagation Society International Symposium, 4332-4335, Jun. 2007.
53. Schwinger, J., et al., Classical Electrodynamics, Perseus Books, Reading, Mass, 1998.
54. Zeidler, E., "Quantum Field Theory I: Basics in Mathematics and Physics," Springer, 2009.
55. Godement, R., Analysis II: Differential and integral Calculus, Fourier Series, Holomorphic Functions, Springer-Verlag, Berlin, 2005.
56. Colton, D. and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory," Springer, 2019.
57. Fabrizio, M. and A. Morro, Electromagnetism of Continuous Media: Mathematical Modelling and Applications, Oxford University Press, Oxford, 2003.
58. Sitenko, A. G., Electromagnetic Fluctuations in Plasma, Academic Press, 1967.
59. Korner, T. W., Vectors, Pure and Applied: A General Introduction to Linear Algebra, Cambridge University Press, Cambridge, 2013.
60. Mikki, S. M. and A. A. Kishk, "Electromagnetic wave propagation in dispersive negative group velocity media," 2008 IEEE MTT-S International Microwave Symposium Digest, 205-208, Jun. 2008.
61. Toyozawa, Y., Optical Processes in Solids, Cambridge University Press, Cambridge, UK, 2003.
62. Altland, A. and B. Simmons, Condensed Matter Field Theory, Cambridge University Press, Leiden, 2010.
63. Melrose, D. B., Instabilities in Space and Laboratory Plasmas, Cambridge University Press, Cambridge, 1986.
64. Kulsrud, R. M., Plasma Physics for Astrophysics, Princeton University Press, Princeton, NJ, 2005.
65. Fleishman, G., Cosmic Electrodynamics: Electrodynamics and Magnetic Hydrodynamics of Cosmic Plasmas, Springer, London, 2013.
66. Peratt, A., Physics of the Plasma Universe, Springer-Verlag, New York, 2014.
67. Schelkunoff, S. A. and H. T. Friss, Antennas: Theory and Practice, Wiley, New York; Chapman & Hall, London, 1952.
68. Balanis, C. A., Antenna Theory: Analysis and Design, 4th Ed., Wiley, Inter-Science, 2015.
69. Geyi, W., Foundations of Applied Electrodynamics, Wiley, Chichester, West Sussex Hoboken, NJ, 2010.
70. Melrose, D. B. and R. C. McPhedran, Electromagnetic Processes in Dispersive Media: A Treatment Based on the Dielectric Tensor, Cambridge University Press, Cambridge, England, 1991.
71. Koks, D., Explorations in Mathematical Physics: The Concepts Behind an Elegant Language, Springer, New York, 2006.
72. Appel, W., Mathematics for Physics and Physicists, Princeton University Press, Princeton, NJ, 2007.
73. Papas, C., Theory of Electromagnetic Wave Propagation, Dover Publications, New York, 1988.