The Propagation of Radio Waves over the Surface of the Earth and in the Upper Atmosphere

Norton, Kenneth A.

doi:10.1109/jrproc.1937.228544

Cited by 346 publications

(157 citation statements)

References 10 publications

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“…Although the work by Sommerfeld set up the theoretical bases, further research was developed since the publication of his first paper on the subject [Sommerfeld, 1909] in order to investigate the application of the theory to several propagation and radiation problems of practical interest [Norton, 1937;Longman, 1956;Novikov and Makarov, 1961;Wait, 1964;Baños, 1966]. With the coming of numerical analysis techniques, an ever-growing attention was paid to the development of methods for the evaluation of both the Green functions and their integrals on the scattering geometries [Siegel and King, 1970;Bubenik, 1977;Mittra et al, 1979;Rahmat-Samii et al, 1981;Maclean and Wu, 1993;Chew, 2000a, 2000b].…”

Section: Introductionmentioning

confidence: 99%

Lightning return stroke current radiation in presence of a conducting ground: 1. Theory and numerical evaluation of the electromagnetic fields

2008

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[1] The general theory describing the electromagnetic field radiated by a lightning stroke over a conducting ground is presented in this paper. The derivation of the Green functions necessary to solve the problem is discussed in detail, and the determination of the expressions for the electromagnetic field components is carried out in a form that minimizes the final computational costs. A method for the numerical evaluation of the electromagnetic field is then proposed, and it is shown that it can be used starting from any ''engineering model'' representation for the lightning current distribution along the channel. Such method is based on a new efficient evaluation of the so-called Sommerfeld's integrals appearing in the electromagnetic field expressions, without resorting to any kind of approximated formulas for them. The numerical treatment of the Sommerfeld's integrals is characterized by a proper subdivision of the integration domain, the use of the Romberg technique and the determination of a suitable upper bound for the error due to the integral truncation. In the second part of this work it will be shown how the results provided by the developed theory can be used in order to assess the validity of the most common simplified approach for the calculation of the lightning radiation over a lossy ground plane.

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Section: Introductionmentioning

confidence: 99%

Lightning return stroke current radiation in presence of a conducting ground: 1. Theory and numerical evaluation of the electromagnetic fields

2008

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“…which is the form used by Norton [1937] for a homogeneous half-space, which, in the present context, corresponds to setting the coating thickness L equal to zero. In such a case the phase of the normalized surface impedance A is never less than -45 ø, in which case the phase angle of p is never negative.…”

Section: With Interest I Have Read King and Sandletmentioning

confidence: 99%

Comment on “The electromagnetic field of a vertical electric dipole in the presence of a three‐layered region” by Ronold W. P. King and Sheldon S. Sandler

Wait¹

1998

Radio Science

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It is pointed out that King and Sandler [1994] have overlooked that a trapped surface wave can be excited by the source for the case where the coating layer is a low-loss dielectric and the substrate is a highly con- To simplify the discussion, I will employ the notation familiar to the radio science community. The geometry of the model is the same as that shown in Figure 1 of KS, but I allow the vertical electric dipole to be in the air and located on the surface of the coating. The distance or range to the observer, also on the surface, is denoted by r. Following KS, the wave numbers for the air, coating, and substrate are k0, k l, and k2, respectively, and the adopted time factor is exp(-iwt).Restricting attention to the far field, defined by• Also where E 0 is the reference ideal ground wave field and is commonly known as the "inverse distance field" that varies as r-• exp (ikor) in the present context. In which is the form used by Norton [1937] for a homogeneous half-space, which, in the present context, corresponds to setting the coating thickness L equal to zero. In such a case the phase of the normalized surface impedance A is never less than -45 ø, in which case the phase angle of p is never negative. In the coated case, it is evident that the phase angle of A can be less than -45 ø, and, in fact, for a pure dielectric coating on a perfectly conducting 251

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“…The radiation of antennas at the interface of media has been the subject of numerous studies to date [1][2][3][4][5][6][7][8][9][10][11][12][13]. The scenario of interest is a classic problem in electromagnetics dating back to the work of Sommerfeld in 1909, investigating the radiation of a source above a lossy halfspace [1].…”

Section: Introductionmentioning

confidence: 99%

“…Other effects such as subsurface peaking was also explored by the same authors in [14]. Such studies have been intended for various applications such as Ground Penetrating Radar [15,16], antennas for communication above earth or under water [2,13], antennas on semiconductors [9] or above dielectrics for imaging [12], to only name a few.…”

Section: Introductionmentioning

confidence: 99%

Dipole Radiation Near Anisotropic Low-Permittivity Media

Memarian

Eleftheriades²

2013

PIER

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Abstract-We investigate radiation of a dipole at or below the interface of (an)isotropic Epsilon Near Zero (ENZ) media, akin to the classic problem of a dipole above a dielectric half-space. To this end, the radiation patterns of dipoles at the interface of air and a general anisotropic medium (or immersed inside the medium) are derived using the Lorentz reciprocity method. By using an ENZ half-space, air takes on the role of the denser medium. Thus we obtain shaped radiation patterns in air which were only previously attainable inside the dielectric half-space. We then follow the early work of Collin on anisotropic artificial dielectrics which readily enables the implementation of practical anisotropic ENZs by simply stacking sub-wavelength periodic bi-layers of metal and dielectric at optical frequencies. We show that when such a realistic anisotropic ENZ has a low longitudinal permittivity, the desired shaped radiation patterns are achieved in air. In such cases the radiation is also much stronger in air than in the ENZ media, as air is the denser medium. Moreover, we investigate the subtle differences of the dipolar patterns when the anisotropic ENZ dispersion is either elliptic or hyperbolic.

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The Propagation of Radio Waves over the Surface of the Earth and in the Upper Atmosphere

Cited by 346 publications

References 10 publications

Lightning return stroke current radiation in presence of a conducting ground: 1. Theory and numerical evaluation of the electromagnetic fields

Lightning return stroke current radiation in presence of a conducting ground: 1. Theory and numerical evaluation of the electromagnetic fields

Comment on “The electromagnetic field of a vertical electric dipole in the presence of a three‐layered region” by Ronold W. P. King and Sheldon S. Sandler

Dipole Radiation Near Anisotropic Low-Permittivity Media

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