Hertzian dipole radiating over a lossy earth or sea: some early and late 20th-century controversies

This paper presents a contemporary solution to the problem of radiation from a vertical Hertzian dipole over a lossy earth. Sommerfeld's 1909 solution to the problem is re-examined. It is demonstrated that a change in sign in the square root of the numerical distance is mathematically not allowed. Thus, the sign error that has been claimed in the technical literature for more than 65 years is a myth. Recent work by King and Sandier is also examined. It is found that due to an incorrect asymptotic expansion of the complementary error function for the problem of a lossy earth or sea covered with a thin dielectric layer, a trapped surface wave was missed in their solution.     

垂直电偶极子在涂有介质层球形导电基底上的场

利用解析方法导出了垂直电偶极子在涂履有介质层的球形导电基底上产生的电磁场的解析表达式。所得结果表明，当介质层达到一定的厚度时，与文献[1]中的平面导电基底情况相类似，垂直电偶极子同样能够在球形介质层的表面激励起吸附表面波（Trapped surface wave)。文中对具有特殊地貌情况下和有冰层的海面上的通信有新的指导意义。     

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。     

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.     

求解埋入体电磁散射问题的矢量波函数展开法

本文利用矢量波函数展开法求解了任意激励原埋入体的电磁散射问题。通过导出圆柱和圆球矢量波函数的转换关系,使场量满足分界平面和数学球面边界条件,从而方便地利用矢量波函数展开求解了这一复杂边值问题。作为示例,本文计算了在平面波和偶极子激励下,埋入导体球和介质球的散射场。     

Transient electromagnetic fields of a vertical magnetic dipole on a two-layer earth

The transient fields of a vertical magnetic dipole on a two-layer earth model are expressed in analytical form using two different approaches. In the first, the fields in the time domain are obtained as the inverse Laplace transforms of derived full wave time-harmonic solutions, while in the second, the concept of natural frequencies of the stratified earth is utilized. Comparison with a previously obtained approximate solution reveals that the latter is the late time part of the present solution. Important features in the waveforms of the surface fields due to step and pulsed current excitations are demonstrated by a variety of numerical examples. These features provide diagnostic means of sensing the earth's stratification, overburden thickness, and the ratio of conductivities of the layers.     

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.     

水平电偶极子在负折射媒质半空间激励的场

讨论了水平电偶极子在由介电常数和磁导率都为负数的媒质和普通媒质构成的均匀半空间中激励的电磁场,并得出了远区场的解析表达式.理论分析和数值计算结果表明:位于普通介质中的水平电偶极子在普通媒质和负折射媒质分界面能够有效激励表面波.该表面渡是一种"慢波",沿分界面传播的波数小于波在两种均匀媒质中传播的波数.当两种介质均无损耗时,沿径向传播的幅度按波的几何扩散衰减.由于存在三种传播波数,表面波、侧面波、直达波和反射波共同作用形成的总场将发生复杂的干涉现象.     

ELF and VLF fields of a horizontal electric dipole

The waves in the spherical guide between the earth and ionosphere are excited by a horizontal electric dipole. The guide boundaries are characterized by surface impedances and the resulting waves are expressed as a superposition of TM and TE modes. The wavenumbers, excitation factors, height-gain functions, and height-dependent impedances are examined for both types of modes. A thin-shell approximation of the radial wave functions is shown to be adequate for phase velocity estimates; but other propagation parameters are of restricted validity in the VLF range where Airy integral approximations provide more reliable data. A horizontal electric dipole is shown to provide a nearly omnidirectional coverage of horizontal field components in the frequency range of the lower Schumann resonances. For an elevated source the horizontal fields are essentially omnidirectional also in the VLF range. Near fields are expressed as a summation of waveguide modes. The vertical field components vanish at the antipode, but the horizontal components remain of finite magnitude.     

Radiation from a vertical dipole in a warm plasma--Part II

A numerical evaluation of the integrals that constitute the formal solution of the problem of a vertical dipole, which is situated in a homogeneous, warm plasma half-space above a perfectly conducting plane, is considered. An asymptotic series expansion is obtained for these integrals by the double saddle point method of integration. The dominant terms of the solution in the far field are shown to consist of a surface wave, which arises from the residue of a pole, and a space wave, which is the leading term of the saddle point contribution. The space wave is identified as the geometrical ray approximation to the solution. It is demonstrated that the surface wave can propagate when the source frequency is either above or below the plasma frequency. The transfer of power from an incident acoustical (p) mode to a boundary-generated electromagnetic (e) mode, and from an incident e mode to a boundary-generatedpmode, is investigated at a plasma-conductor interface. It is evident in both situations that only a small percentage of the incident power is transformed into the boundary-generated mode. In the case of a vertical dipole, however, it is shown that, at source frequencies which are near to the plasma frequency, the power in the incidentpmode is much larger than that in theemode. Thus, the boundary-generatedemode, which is due to the incidentpmode, is as large as the reflectedemode due to an incidentemode. As a result of this effect, it is pointed out that one can represent the reflectedemode by two image sources.     

HF Ground Wave Propagation over Mixed Land, Sea, And Sea-Ice Paths

Ground wave propagation is analyzed for a two-section path on a spherical earth. Each section can be a two-layer medium which is characterized by a surface impedance. Specific calculations for a land-to-sea path indicate that the well-known recovery effect in amplitude and phase is more extreme at higher frequencies but is reduced for elevated observer heights. Calculations for a sea-to-sea ice path indicate a brief recovery because of the excitation of the trapped surface wave over sea ice. At greater distances from the boundary, the field may be seriously degraded due to the sea ice.     

VLF fields of a horizontal dipole below the polar anisotropic ionosphere

A study is made of VLF fields excited by a horizontal dipole in the waveguide formed between the ice-covered ground and the anisotropic ionosphere of Antarctica. Numerical results are presented which describe the excitation, propagation, and polarization of radiated energy for ionospheres typical during both summer (daylight) and winter (night) conditions in Antarctica. The polarization of fields observed at the ice surface is found to be a function of both azimuth and range. Ice layer characteristics have significant effects on received fields, especially those of the quasi-TM type. The possible excitation of a TM-type surface wave at the ice-air interface under special conditions is also discussed. Fields propagating with wave numbers corresponding to quasi-TE modal solutions are least attenuated in the waveguide. Summer ionospheres tend to increase modal attenuation rates. Results are applied to a real experimental situation in Antarctica involving a horizontal dipole source and trans-Antarctic propagation paths.     

Diffraction of a general surface wave mode by a surface reactance discontinuity

The scattering of a general hybrid surface wave mode at a reactance discontinuity, on a cylindrical surface waveguide, is considered both theoretically and experimentally. The theory leads to coupled Wiener-Hopf equations, which are solved approximately by assuming the hybrid modes to be mainly TE or TM. The theoretical expressions obtained are evaluated numerically for the symmetrical and dipole modes and compared with experimental results with which substantial agreement is obtained.     

Optimisation of the ground wave over a stratified earth

The ground-wave excitation of an electric dipole buried in a two-layer flat earth is considered. It is indicated that the optimum inclination of the dipole depends on both the thickness of the upper layer and the burial depth of the dipole.     

Theoretical gain of strained-layer semiconductor lasers in thelarge strain regime

The theoretical gain of strained-layer semiconductor lasers is analyzed in the large strain regime based on the density-matrix method, taking into account the modification of both the valence bands and the transition dipole moments. The wave functions for the valence-band states for an arbitrary wave vector at the Γ point in the presence of stain are derived from diagonalization of the strain Hamiltonian using the original wave functions obtained from the k-p method. These wave functions are then used to obtain the dipole moment matrix elements at the band edges, which are found to be independent of the wave vector     

Excitation of a grounded dielectric slab by a horizontal dipole

The structure consisting of a horizontal electric dipole above a grounded dielectric slab is examined, primarily from the standpoint of power distribution among the two power-carrying wave components, i.e., surface and space waves. It is shown that surface wave propagation is always in the form of two distinct modes characterized by the same cutoff properties. Also, surface wave excitation efficiency curves are given for a range of parameter variation.     

Locating a Buried Magnetic Dipole

Five measurements of the magnetic-field vector near the surface of the earth are shown to be sufficient to determine the orientation and location of a buried magnetic dipole. A discussion of field experiments which demonstrate the location concept is included.     

Characteristics of dielectric loaded and covered circular waveguide phased arrays

The use of dielectric materials for the hardening and matching of phased-array antennas in recent years has shown that a more complete understanding of the effects of these materials upon the array performance is necessary. The characteristics of fully loaded, plugged, and sheath covered circular waveguide phase arrays are analyzed and discussed. Numerical solutions of the boundary-value problem are verified by experimental and convergence tests. Particular emphasis is placed on the study of (forced) surface wave resonance effects. Three different cases for surface wave resonances were obtained. These include the case in which surface wave resonances are present in the absence of dielectrics, the case in which they are trapped by the presence of dielectric plugs, as well as the case in which waves are trapped by the presence of a dielectric sheath. The surface wave resonance due to the plug is shown to vanish for certain "bandpass" ranges of plug thickness which repeat periodically for a single trapped waveguide mode. On the other hand, the surface wave trapped in the sheath exhibits no "bandpass" characteristics. Instead, multiple surface wave resonances occur with increasing sheath thickness. Finally, the surface wave resonances observed here appear at isolated points in the scan plane.     

Coupling mechanism of two dipoles within a conductor-backed thindielectric slab above the earth

A coupling mechanism between two dipoles within a conductor-backed thin dielectric layer above the earth, suggested as subsurface interface CW radar transmitting and receiving antennas, is calculated by a saddle-point method. When the dielectric layer is thin enough to support a cutoff mode, the electric field at the point of receiving dipole due to a transmitting point dipole may be approximated by sum of contributions of branch points of TE mode and poles of TM mode. The branch points and poles contributions are interpreted as evanescent lateral-waves and leaky-waves, respectively. Comparison of numerical results and asymptotic results shows excellent agreement     

The differentiated on-surface poynting vector as a measure of radiation loss from wires

This article explores use of the on-surface Poynting vector to investigate the power flow at the surface of various thin wires, excited as antennas or scatterers. By differentiating the axial Poynting vector at the wire's surface, the rate of change of power flow in the current and charge along a perfectly electrically conducting (PEC) wire can be determined. The idea being explored is to see if a change in axial power flow can reveal anything about possible power loss due to radiation. The results from the differentiated Poynting vector are normalized with those obtained from an approach developed by the author called FARS (far-field analysis of radiation sources). Two antenna-excitation models are investigated for a straight-wire dipole: the usual tangential E-field model, and a two-wire transmission-line feed. Comparison of FARS and the differentiated Poynting vector results for a 10-wavelength dipole shows them to agree to within 10% relative to end peaks in the distribution of spatial radiation, except in the vicinity of the antenna's feed point. Both also show that radiation occurs not only near the feed point and ends of the antenna, but is distributed along its length, being associated with maxima of the current standing wave. Results presented for antennas such as a bent-wire dipole, circular and square loops, and for a straight-wire scatterer demonstrated the effects of shape and excitation on the distributed radiation