Lateral electromagnetic waves along plane boundaries: A summarizing approach

Lateral electromagnetic waves along a plane boundary between homogeneous half-spaces are reviewed. The electromagnetic fields generated by vertical and horizontal electric dipoles near the boundary between air and the earth (salt or fresh water, soil, ice, etc.) are summarized in terms of a new unified theory of lateral-wave propagation. Complete theoretically determined fields are displayed and compared with measured fields at f = 601 MHz relative to the boundary between air and salt water (σ = 3.5 S/m, εr= 80). Near, intermediate, and asymptotic fields are related graphically to the new general theory and to the approximate and restricted formulas of Norton and Baños as well as to the Zenneck wave. Application is made to the specific problem of communication with submerged submarines by means of transmitters consisting of electrically short monopoles in air and horizontal traveling-wave antennas and directional arrays in sea water. The properties of the antennas are evaluated in the frequency range 10 ≤ f ≤ 30 kHz which is optimum for receiver depths near 10 m, and at f = 1 kHz which is optimum for depths up to 50 m. The effects of reflections from the ionosphere and of the earth's curvature are not included.     

The wave antenna for transmission and reception

The traveling-wave horizontal-wire antenna over the earth is analyzed in its original form with vertical ground connections (the Beverage antenna) and with these replaced by horizontal terminations. For transmission, the electromagnetic field of an antenna with optimum length is determined, both along the surface of the earth in air and in the earth, in an accurate but simple form that takes full account of the proximity of the earth (lake, sea) on the distribution of current. For reception, the induced currents in the antenna and in the load are determined for a field incident along the surface of the earth. The two types of termination are compared and their contributions shown to be small when the horizontal wire has a length near the optimum.     

Curves for ground wave propagation over mixed land and sea paths

Specific numerical results are presented for ground wave propagation over paths which are part sea and part land. The problem is idealized to the extent that the earth is a smooth spherical surface. The method is based on a previous formulation in terms of mutual impedance between two vertical electric dipoles on an inhomogeneous spherical earth. Amplitude and phase of the ground wave are given for various combinations of the following parameters: frequency 1000, 100, and 20 kc; land conductivities 100 and 10 mmhos/meter; and a sea conductivity of 4 mhos/meter. Most of the curves exhibit the well-known recovery effect which occurs beyond the coast line for propagation from land towards the sea.     

Electromagnetic field of a horizontal electric dipole buried in a medium covering one-dimensionally anisotropic medium

The electromagnetic fields of a horizontal electric dipole buried in a medium covering one-dimensionally anisotropic medium are studied. There are three media, one-dimensionally anisotropic medium covered with a dielectric under the air. The electromagnetic field components are complex because of the multiple reflections from the up and down boundaries. The electromagnetic field components between air and one-dimensionally anisotropic medium are given, the trapped surface waves and lateral waves along the dielectric-anisotropic medium boundary are computed. The results have some practical applications in the communication in sea or lake above one-dimensionally anisotropic earth or sediments.     

Radiation From a Vertical Electric Dipole in the Presence of a Three-Layered Region

We study in detail both the lateral wave and trapped surface wave generated by a vertical electric dipole over the air-dielectric boundary on a wide range medium such as sea and lake water and wet and dry earth. Graphs of the far-field pattern are shown and compared with the available results. Especially, when both the dipole point and the observation point are on the surface of dielectric-coated earth, the trapped surface wave is dominant.     

The horizontal-wire antenna over a dissipative half-space: Generalized formula and measurements

It is shown and verified by experiment that a horizontal resonant or traveling wave antenna placed in air close to a dense halfspace with the properties of lake or sea water or earth behaves like a terminated lossy transmission line. The terminal impedance is related to the radiation of the antenna into the air and the complex wavenumber and characteristic impedance are those of an infinitely long line. The complex wavenumber takes account of both dissipation in and radiation into the dense half-space.     

地下水平电偶极子在均匀球形地面产生的侧面波

讨论了位于地下的水平电偶极子在均匀球形地面上产生的侧面波（Lateral wave)。从位于球形地面场的垂直电偶极子和磁偶极子在地面上建立的电磁场出发，利用互易定理，获得了地下水平电偶极子在地面上和地面下产生的既方便于数值计算又具有足够精度的电磁场的解析表达式。计算结果表明，由于地球曲率的影响，沿球形地面传播的侧面波比沿平行地面传播的侧面波衰减的快，当收发地点的距离超过40km后，地球曲率对传播的影响就不能被忽视，对地下通信以及潜艇通信有一定指导意义。     

Optimization of radio communication in media with three layers

The electromagnetic radiation of an electric dipole in a medium with three layers is examined using dyadic Green's functions. The far zone field for problems of this nature is primarily determined from the lateral wave. It is shown that the excitation of this wave may be reinforced through a dipole inclination and an optimum position may be determined. The radio losses for typical forests were calculated for vertical and horizontal dipoles and for dipoles with an optimum inclination. The theoretical results are in good agreement with the available experimental data.     

浮标通信的仿真与设计

大容量浮标通信由于浮标体摇摆和多径的影响,其电波传播的可靠度通常不理想,而忽略工作频率的选择和天线工作形式的研究是浮标通信这种海面微波移动通信传输设计可靠度不高的一个重要原因。针对采用何种工作频段和天线工作方式有利于浮标通信电波传输,通过对几组不同工作频率在海面多径条件下相关通信距离的归一化合成场强理论特性进行仿真和测试,提出了采用1～2 GHz波段和垂直极化的浮标端全向天线和岸端定向天线工作方式更有利于浮标通信。     

Air to undersea communication with magnetic dipoles

Simplified expressions are derived for the electromagnetic fields produced by a vertical or horizontal magnetic dipole (loop antenna) located in air above the sea. The expressions hold over the quasi-near range in both media subject to certain mild restrictions. The solutions are obtained by first applying the boundary conditions to determine the magnetic Hertz potentialbar{pi}^{ast}in the form of Sommerfeld integrals, and then relating these to two auxiliary integralsU, Vand their derivatives, asymptotic series for which are obtained by extending the work of Baños and Wesley. The horizontal magnetic dipole (loop in the vertical plane) is found to be superior to the vertically-oriented dipole of the same size and excitation from the point of view of field strength induced in the sea at large distances from the source. A comparison with previously published results for the electric dipole shows the magnetic dipole to be better, provided the number of turns in the loop exceeds a certain minimum. An approximate analysis on the basis of equal powers also shows the magnetic dipole to be better except for points near the outer rim of the quasi-near range, where the two types of dipoles are equivalent.     

Currents induced in a wire cross by a plane wave incident at an angle

The currents induced in a thin-wire cross with equal mutually perpendicular arms by an incident plane electromagnetic wave are determined when the normal to the wave front is perpendicular to the horizontal wire and is at an anglethetawith respect to the vertical wire; the direction of the electric vector in the wave front is arbitrary. The analysis is formulated in general terms but explicit formulas are obtained only for the zero-order currents which are generally adequate to determine the scattered field of very thin wires. The relatively simple formulas consist of even and odd parts for both the vertical and horizontal wires; they include components due to mutual coupling as well as those excited directly by the incident field.     

HF Radio Wave Transmission over Sea Ice And Remote Sensing Possibilities

Ground wave propagation is analyzed for a path where sea water is covered by a uniform layer of sea ice. The source is taken to be a vertical electric dipole on or above the ice layer. The solution indicates that a trapped surface wave is significant at short ranges while, at longer ranges, the usual ground wave modes are dominant. The resulting interference pattern may produce rapid variations of the field at intermediate ranges. These characteristics, as well as the height dependence of the observed field strength, are strongly dependent on the thickness of the ice layer.     

Subsurface communication between dipoles in general media

In his book, Dipole Radiation in the Presence of a Conducting Half-Space, Baños analyzes the problem of communicating between two points in the ocean by means of infinitesimal dipoles. His general formulas involve complex integrals which are reduced to simple approximate expressions in special cases that correspond to limited ranges of the numerous parameters. A numerical study of the general problem for antennas in seawater was made by Siegel and King and compared with Baños' special cases. In this paper the numerical approach is extended to other than conducting half-spaces. The three cylindrical components of the electric field of a horizontal electric dipole in seawater, lake water, and dry earth have been computed and intercompared as functions of the frequency and of the distance between the source and the receiver. The applicability of Baños' special formulas is examined. The results are discussed in their bearing on the design of directive systems for lateral-wave and direct transmission.     

Very-low-frequency propagation below the bottom of the sea

Radio-wave propagation at very low frequencies (VLF) in the stratified rock below the bottom of the sea is studied. A reasonable assumption of extremely low electrical conductivity in the stratified rock is based upon available geological data. The surface wave traveling along the interface between this region of low conductivity and the highly conducting sea is compared with the vertically polarized ground wave found in VLF radio-wave propagation at the surface of the earth. When extremely low frequencies (ELF) are transmitted, the highly conducting layer found at greater depths below the bottom of the sea forms the lower surface of a spherical waveguide. This waveguide at ELF supports a propagation mode similar to the mode existing at VLF between the surface of the earth and the lower boundary of the ionosphere. The similarity in propagation mechanisms leads to the name "inverted ionosphere" (described by Wheeler [1]) for the underground region. The sea or relatively highly conducting soil at the surface of the earth is an almost impregnable shield against atmospheric noise and effects from sudden ionospheric disturbances or solar flares. In addition to providing a noise-free medium, the sea has the advantage that construction costs are much less than those of a VLF transmitter at the earth's surface. Presumably communication between shore installations and submarines on the floor of the ocean could be achieved with the inverse ionosphere. The power requirement for such communication with existing VLF transmitters at the earth's surface renders such transmission unattainable.     

Enhancing HF received fields with large planar and cylindrical ground screens

Users of extended range HF (3 to 30 MHz) radar and communication systems employing the ionosphere desire signal reception at incidence angles near-grazing to the local earth tangent. For vertical polarization, the vanishing received fields at low incidence angles over dielectric earth may be increased by using large ground screens. In this paper a ground-screen formulation based on scattering techniques is developed. The ground screen is viewed as a scatterer in free space, excited by a plane wave. A Fresnel image wave is added to establish the air-earth interface. Formulations are developed for the semi-infinite screen and for the circular-cylinder surface segment screen. The semi-infinite screen is representative in performance to a round screen of radius equal to the distance from the edge of the semi-infinite screen at which the field is computed or measured. For a ground screen on a hill the cylindrical segment is appropriate. Computations for a simulated earth were made and corroborated by experimental simulation with scale models. Improvements in field strength of 7 to 14 dB or more can be achieved with large screens over no screen. "Relatively small" tilted or raised flat screens, and cylindrical segment screens, can give improvements equal to very large flat screens on the earth.     

Image theory for electric dipoles above a conducting anisotropic earth

New image representations for vertical electric dipoles (VED) above an imperfectly conducting and axially anisotropic earth are developed. These include multidiscrete images at different depths below the air-earth interface and multipole image sources. It is shown that, in contrast with the available image representations in the literature, the developed ones predict the correct behavior of the fields in the far zone along the earth's surface. Extension to a layered earth's model is made. The theory is also extended to the horizontal electric dipole with similar conclusions to the case of the vertical dipole.     

多层媒质中谱域及空域格林函数的一般表达式

本文给出多层媒质中水平和垂直电、磁偶极子的谱域标量位和矢量位格林函数的一般表达式,并验证了其正确性。该表达式除了形式上比较简单,可以迅速提取准静态项和表面波项外,更重要的是便于向空域转化,利用离散镜象理论可以计算相应的以索末菲积分形式出现的空域格林函数。最后给出几个数值计算实例。     

Directive properties of antennas for transmission into a material half-space

The directive properties of antennas for transmission into a material half-space are investigated. In a practical situation, the antennas might be located in air with the directive transmission into the earth. The field of a general antenna over the half-space is expressed as a spectrum of plane waves. The integrals representing the field are evaluated asymptotically to obtain the "geometrical optics" field of the antenna, and this field is used to define quantities that describe the directive properties of the antenna (pattern function, gain, and directivity). Numerical results are presented for infinitesimal electric and magnetic horizontal dipole antennas in a dielectric half-space, region 1, with directive transmission into the adjacent dielectric half-space, region 2, and the ratio of permittivitiesepsilon_{2}/epsilon_{1}greater than one. The theory for the infinitesimal dipoles completely explains the directive properties previously obtained for the resonant circular-loop antenna over a material half-space. Measured field patterns and gains for dipole and loop antennas near an interface between air and fresh water are in good agreement with the theory.     

Far-field radiated from a vertical magnetic dipole in the sea with a rough upper surface

The problem of communication in the sea has been considered as propagation of radio waves in a three-layered medium (air, sea, and ground). With the aid of the perturbation calculus, this paper analyzes the influence exerted onto the electromagnetic field of arrangements radiating a pure transverse electric field in the sea. The sea height varies continuously with the distance from the transmitting end due to sea waves. Knowledge of the solution for the case of uniform sea height is presumed. The problem of the transition conditions at the upper boundary of the sea is solved in the imaging space of a Hankel transformation. Its reversal produces an integral presentation of the interfering field, which was previously quite difficult to evaluate. In this study, closed-form expressions for the far-field of a vertical magnetic dipole embedded below the sea surface are obtained by using a new technique to evaluate this integral with the aid of the complex image theory. The results obtained are compared with those mentioned elsewhere.     

Propagation of HF radio waves over sloping coastal land

The field of a TM wave at a reception point over sloping coastal land, farther than a wavelength from the sea, has been calculated for a transmitting element located infinitely far away over a flat sea. The field obtained is normalized to that of a wave approaching the water/land boundary from infinity. A transmitting element placed both at some elevation angle and on the surface of the sea has been considered. In both instances, simple formulas providing fast computation of the field have been obtained by employing the integral equation approach formulated in terms of the normalized surface impedance. It has been found that the sloping land to some extent compensates for power losses in the ground and may even enhance the power density of high-frequency waves coming from low elevation angles. The expressions obtained remain valid for flat ground in place of sea. In this instance, the permittivity and conductivity of the sea should simply be substituted by those of the ground