This paper calls attention to some of the most important and easily recognizable forms of surface wave, pointing out that their essential common characteristic is the evanescent field structure over the wave front, as represented by equiphase planes. The problems of launching and supporting surface waves must, in general, be distinguished from one another and it does not necessarily follow that because a particular surface is capable of supporting a surface wave that a given aperture distribution of radiation, e.g. a vertical dipole, can excite such a wave. The paper concludes with a discussion of the behavior of surface waves and their applications.

http://ieeexplore.ieee.org/iel5/10933/4065481/04065500.pdf

Surface Waves

1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

Radio-wave transmission over the surface of the Earth is a subject of enquiry going back to the beginning of the century. In this review, an attempt is made to describe the ground-wave mechanism that is omni-present. We first call attention to the early analytical contributions of Zenneck and Sommerfeld, based on a flat-Earth model. The subsequent controversies, particularly with regard to the role of the Zenneck surface wave, are outlined. Further developments by other pioneers, such as van der Pol, Fock, Bremmer, Norton, and Millington, are reviewed, and an attempt is made to put these in a modern context. We also show that the trapped surface wave can be a significant contribution to the total ground-wave field, when the Earth boundary is sufficiently inductive. Mixed-path theory and confirming model tests by Ray King are described briefly, along with calculated propagation curves for twoand three-section paths. The bibliography includes references to related topics, such as tropospheric refraction and topographic influences.

The ancient and modern history of EM ground-wave propagation

In many cases, it is impractical or impossible to make antenna pattern measurements on a conventional far-field range; the distance to the radiating far field may be too long, it may be impractical to move the antenna from its operating environment to an antenna range, or the desired amount of pattern data may require too much time on a far-field range. For these and other reasons, it is often desirable or necessary to determine far-field antenna patterns from measurements made in the radiating near-field region; three basic techniques for accomplishing this have proven to be successful. In the first technique, the aperture phase and amplitude distributions are sampled by a scanning field probe, and then the measured distributions are transformed to the far field. In the second technique, a plane wave that is approximately uniform in amplitude is created by a feed and large reflector in the immediate vicinity of the test antenna. And in the third technique, the test antenna is focused within the radiating near-field region, patterns are measured at the reduced range, and then the antenna is refocused to infinity. Each of these techniques is discussed, and the various advantages and limitations of each technique are presented.

Determination of far-field antenna patterns from near-field measurements

The efficiency with which radial cylindrical surface waves may be launched by a circumferential slot is investigated theoretically and experimentally. The radius of the slot has been found to affect the launching efficiency very little. An optimum efficiency of about 68% is obtainable with a slot of 2cm radius above a 58-ohm reactive surface.

The launching of radial cylindrical surface waves by a circumferential slot

A critical examination is made of the somewhat loose and incomplete statement that a polar diagram is the Fourier transform of an aperture distribution. By aperture distribution it is necessary to understand, in the two-dimensional case, distribution across the aperture of the component along the aperture plane of the electromagnetic field in the plane of propagation. Furthermore, the concept of the polar diagram has to be replaced by that of an angular spectrum, except in the common case when the aperture may be considered more or less limited in width, and the field is being evaluated at a point whose distance from the aperture is large compared with the width of the aperture (and the wavelength). For example, it is convenient for some purposes to regard the problem of diffraction of a plane wave by a semi-infinite plane screen, with a straight edge, as a problem about an aperture distribution in the plane of the screen. This is a case for which the concept of a polar diagram is not in general applicable, and has to be replaced by that of an angular spectrum. The field at all points in front of a plane aperture of any distribution may be regarded as arising from an aggregate of plane waves travelling in various directions. The amplitude and phase of the waves, as a function of their direction of travel, constitutes an angular spectrum, and this angular spectrum, appropriately expressed, is, without approximation, the Fourier transform of the aperture distribution. If the aperture distribution is of such a nature that the concept of the polar diagram is applicable at sufficiently great distances, then the polar diagram is equal to the angular spectrum. But the angular spectrum is a concept that is always applicable, whereas the polar diagram is one that is liable to be invalid (for example, in the Sommerfeld theory of propagation over a plane, imperfectly reflecting earth).

The concept of an angular spectrum of plane waves and its relation to that of polar diagram and aperture distribution

A new way of visualizing the Sommerfeld theory of propagation over a flat, imperfectly reflecting earth is presented. The Sommerfeld theory arises because the ray theory of propagation from a source in the presence of a flat, imperfectly reflecting earth is only an approximation. The ray theory involves the assumption that the Fresnel reflection coefficient of the earth does not vary rapidly with angle of incidence, and this assumption is not satisfied for glancing incidence of vertically polarized waves on the earth's surface at broadcasting wavelengths. The main object of the new presentation is to facilitate the solution of problems involving propagation near the surface of the earth partly over land and partly over sea, but these applications are not included in the paper. It is convenient to think of a two-dimensional problem in which the transmitter is a line source parallel to the earth's surface, having a vertical polar diagram of circular shape. Such a source may be Fourier analysed into plane waves whose directions are distributed in a vertical plane of propagation perpendicular to the line source; the amplitudes of all the plane waves are the same and they are in the same phase at the source. When these waves are reflected from the earth they produce an angular spectrum of reflected waves, the amplitudes and phases of which are determined by the Fresnel reflection coefficient. This angular spectrum could be thought of as arising, in the absence of the earth, from an aperture distribution on the vertical plane through the primary line source. The aperture distribution that produces the angular spectrum of reflected waves in this way is the exact image of the primary source in the imperfectly reflecting earth, and is given by the Fourier transform of the Fresnel reflection coefficient. For a perfectly conducting earth this aperture distribution reduces to a line source identical with the primary source and located at the optical image line. The correction r

P.C. Clemmow

Papers

The concept of an angular spectrum of plane waves and its relation to that of polar diagram and aperture distribution

A relation between the Sommerfeld theory of radio propagation over a flat earth and the theory of diffraction at a straight edge