沿涂敷介质层的导电基底传播的表面波与侧面波
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摘要
本论文从哈佛大学的Ronold W.P.King和美国东北大学的Sheldon S.
Sandler同亚利桑那州大学的James R.Wait之间的学术争论问题出发，对垂
直和水平电偶极子分别在涂敷有介质层的导电基底上激励的电磁场问题进行了
深入研究，包括理想导电基底和非理想导电基底两种情况。现将作者在研究中
所做的主要工作以及主要成果如下：
首先对垂直电偶极子在涂敷介质层的理想导电基底上所激励的电磁场进行
了研究，在继承前人的研究结果上，深入分析了电磁场各分量积分表达式的特
征和性质，根据复变函数理论和贝塞尔函数的特点，推导出了电磁场各分量的
方便于数值计算的完整解析表达式，解决了King和Sandler与Wait之间所争论
的学术问题。
本文结果说明，King和Sandler的研究结果中，确实如Wait所言，遗漏
了一项吸附表面波（Trapped surface wave）。但是本论文得到的吸附表面波，并不
是Wait在评论中所说的的表面波，而是由场分量的被积函数中所含有的极点
的留数项产生的，而Wait却认为应该能够从F(p)函数中分离出一项以ρ~(-1/2)规律
衰减的传播波数为k_o表面波。
本论文给出了表面波的传播波数与介质层的关系。表明从极点留数上得到
的表面波，其传播波数和Wait所言不同，既不是空气中的k_o也不是介质中的k_l，
而是介于k_o和k_l之间，除主要与工作频率和介质层的厚度有关外还与介质层的
介电常数和导电率有关，由被积函数所满足的极点方程决定。只是其扩散衰减
规律和Wait所言相同，也是ρ~(-1/2)。
作者的结果还说明，被积函数的极点个数与介质层的厚度和介质层的波数
k_l的乘积有关，当介质层的参数满足（k_l取其实部，以下
相同）条件时，被积函数将有n个极点，也就是说吸附表面波将会有n个传播模
式，而Wait的分析是单模式。
本论文得到的侧面波，扩展了King和Sandler结果的适用范围，没有对覆
盖在导电基底上的介质层的厚度加以任何限制，而ing和Sandier的研究是将
介质层的厚度限制在片尸X1或者久1＜0石条件下。
作者在上述研究基础上，又进行了更深一步的研究．分别对垂直电偶极子
在涂敷介质层的非理想导电基底上激励的电磁场、水平电偶极子在涂敷介质层
的理想导电基底上激励的电磁场和位于覆盖有介质层的非理想导电基底中的水
平电偶极子在导电基底一侧激励的电磁场进行了深入研究，分别得到了这几种
情况下电磁场各场分量完整的解析表达式。
作者的研究结果还表明，在一般情况下，水平电偶极子激励出的电型表面
波和磁型表面波的传播被数是不相同的，其中的电型表面波与垂直电偶极子激
励的规律相类似，而磁型表面波只有当介质层满足J厅一庸1＞o．5。条件时才能
被激励，并且在满足…－0．5）＜Jki－片 l＜n＋0．5江条件下磁型表面波将会有 n
个传播模式。
被积函数的极点方程都是超越方程，作者提出了一种新的求解这些极点超
越方程的简便方法。
本论文给出了吸附表面波的传播波数在几种情况下的变化规律，并进行了
大量的数值计算，从计算结果中可以看出明确的物理意义。
The exact analysis expressions of the electromagnetic fields generated by a
vertical or a horizontal electric dipole in the air over or on a perfect or an imperfect
conductor coated with a dielectric layer have been obtained in this thesis. And the
electromagnetic fields generated by a horizontal electric dipole in the imperfect
conductor have been discussed too. The author抯 studies is inspired from the academic
arguments of Ronold W. P. King of Harvard University, Sheldon S. Sandier of the U.
S. A. Northeastern University and James R. Wait of the University of Arizona in the
field of radio-wave propagation. The main contributions of author抯 work are as
follows:
Firstly, The electromagnetic fields of a vertical electric dipole on a perfect
conductor coated with a dielectric layer have been discussed. The properties and the
characters of integral expressions of the electromagnetic field components are through
analyzed. And according to the theory of complex function and the characters of the
Bessel functions, the exact analysis expressions of the electromagnetic fields in the air
on a perfect conductor coated with a dielectric layer have been derived. It is easily to
evaluating the values of each filed components by these formulas. The debating
problem between K&S (R. W. P. King and S. S. Sandier) and Wait is resolved by the
author抯 studies.
The author抯 conclusion also shows that K&S 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 conducting half-space in their paper
But the conclusion of this thesis is that the trapped surface wave is derived from the
residues of the poles of the integrands of the field components, and is not derived
from the F(p) function. However Wait claims that the trapped surface wave is derived
from the F(p) function, and will vary with ji? over a major distance range and its
wave number is same as the wave number /c0 in the air.
The relations between the wave number of the surface wave and the parameters
of the dielectric are given in this thesis. The amplitude of the trapped surface wave in
this thesis attenuate as p~?2 along the surface of dielectric, coincide with that of
comments of Wait. The propagation wave number of trapped surface wave in this
thesis is different to that in the comments of Wait, and it is neither the wave number ~
in the air nor the wave number k1 in the dielectric layer, but it is a value between k0
and k~ Furthermore, it correlates with the frequency f~ the permittivity e~., the
III
?
conductivity a and the thickness of the dielectric layer, and it is determined by the
poles equation of integrand of these formulas.
The conclusions of the author show that the number of poles of the integrand
depends on the thickness of the dielectric layer and the wave number k1 in the
dielectric. When in this condition as (n ?l)r < ?k~ 1
these integrands, therefore, there are n modes of trapped surface wave in this case.
In addition, the lateral wave obtained in this thesis spread the result of K&S. The
thickness of the coating layer is not limited in this thesis, and the coating thickness is
limited as k1212 ? or k1 / <0.6 in their paper
Sandler同亚利桑那州大学的James R.Wait之间的学术争论问题出发，对垂
直和水平电偶极子分别在涂敷有介质层的导电基底上激励的电磁场问题进行了
深入研究，包括理想导电基底和非理想导电基底两种情况。现将作者在研究中
所做的主要工作以及主要成果如下：
首先对垂直电偶极子在涂敷介质层的理想导电基底上所激励的电磁场进行
了研究，在继承前人的研究结果上，深入分析了电磁场各分量积分表达式的特
征和性质，根据复变函数理论和贝塞尔函数的特点，推导出了电磁场各分量的
方便于数值计算的完整解析表达式，解决了King和Sandler与Wait之间所争论
的学术问题。
本文结果说明，King和Sandler的研究结果中，确实如Wait所言，遗漏
了一项吸附表面波（Trapped surface wave）。但是本论文得到的吸附表面波，并不
是Wait在评论中所说的的表面波，而是由场分量的被积函数中所含有的极点
的留数项产生的，而Wait却认为应该能够从F(p)函数中分离出一项以ρ~(-1/2)规律
衰减的传播波数为k_o表面波。
本论文给出了表面波的传播波数与介质层的关系。表明从极点留数上得到
的表面波，其传播波数和Wait所言不同，既不是空气中的k_o也不是介质中的k_l，
而是介于k_o和k_l之间，除主要与工作频率和介质层的厚度有关外还与介质层的
介电常数和导电率有关，由被积函数所满足的极点方程决定。只是其扩散衰减
规律和Wait所言相同，也是ρ~(-1/2)。
作者的结果还说明，被积函数的极点个数与介质层的厚度和介质层的波数
k_l的乘积有关，当介质层的参数满足（k_l取其实部，以下
相同）条件时，被积函数将有n个极点，也就是说吸附表面波将会有n个传播模
式，而Wait的分析是单模式。
本论文得到的侧面波，扩展了King和Sandler结果的适用范围，没有对覆
盖在导电基底上的介质层的厚度加以任何限制，而ing和Sandier的研究是将
介质层的厚度限制在片尸X1或者久1＜0石条件下。
作者在上述研究基础上，又进行了更深一步的研究．分别对垂直电偶极子
在涂敷介质层的非理想导电基底上激励的电磁场、水平电偶极子在涂敷介质层
的理想导电基底上激励的电磁场和位于覆盖有介质层的非理想导电基底中的水
平电偶极子在导电基底一侧激励的电磁场进行了深入研究，分别得到了这几种
情况下电磁场各场分量完整的解析表达式。
作者的研究结果还表明，在一般情况下，水平电偶极子激励出的电型表面
波和磁型表面波的传播被数是不相同的，其中的电型表面波与垂直电偶极子激
励的规律相类似，而磁型表面波只有当介质层满足J厅一庸1＞o．5。条件时才能
被激励，并且在满足…－0．5）＜Jki－片 l＜n＋0．5江条件下磁型表面波将会有 n
个传播模式。
被积函数的极点方程都是超越方程，作者提出了一种新的求解这些极点超
越方程的简便方法。
本论文给出了吸附表面波的传播波数在几种情况下的变化规律，并进行了
大量的数值计算，从计算结果中可以看出明确的物理意义。
The exact analysis expressions of the electromagnetic fields generated by a
vertical or a horizontal electric dipole in the air over or on a perfect or an imperfect
conductor coated with a dielectric layer have been obtained in this thesis. And the
electromagnetic fields generated by a horizontal electric dipole in the imperfect
conductor have been discussed too. The author抯 studies is inspired from the academic
arguments of Ronold W. P. King of Harvard University, Sheldon S. Sandier of the U.
S. A. Northeastern University and James R. Wait of the University of Arizona in the
field of radio-wave propagation. The main contributions of author抯 work are as
follows:
Firstly, The electromagnetic fields of a vertical electric dipole on a perfect
conductor coated with a dielectric layer have been discussed. The properties and the
characters of integral expressions of the electromagnetic field components are through
analyzed. And according to the theory of complex function and the characters of the
Bessel functions, the exact analysis expressions of the electromagnetic fields in the air
on a perfect conductor coated with a dielectric layer have been derived. It is easily to
evaluating the values of each filed components by these formulas. The debating
problem between K&S (R. W. P. King and S. S. Sandier) and Wait is resolved by the
author抯 studies.
The author抯 conclusion also shows that K&S 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 conducting half-space in their paper
But the conclusion of this thesis is that the trapped surface wave is derived from the
residues of the poles of the integrands of the field components, and is not derived
from the F(p) function. However Wait claims that the trapped surface wave is derived
from the F(p) function, and will vary with ji? over a major distance range and its
wave number is same as the wave number /c0 in the air.
The relations between the wave number of the surface wave and the parameters
of the dielectric are given in this thesis. The amplitude of the trapped surface wave in
this thesis attenuate as p~?2 along the surface of dielectric, coincide with that of
comments of Wait. The propagation wave number of trapped surface wave in this
thesis is different to that in the comments of Wait, and it is neither the wave number ~
in the air nor the wave number k1 in the dielectric layer, but it is a value between k0
and k~ Furthermore, it correlates with the frequency f~ the permittivity e~., the
III
?
conductivity a and the thickness of the dielectric layer, and it is determined by the
poles equation of integrand of these formulas.
The conclusions of the author show that the number of poles of the integrand
depends on the thickness of the dielectric layer and the wave number k1 in the
dielectric. When in this condition as (n ?l)r < ?k~ 1
these integrands, therefore, there are n modes of trapped surface wave in this case.
In addition, the lateral wave obtained in this thesis spread the result of K&S. The
thickness of the coating layer is not limited in this thesis, and the coating thickness is
limited as k1212 ? or k1 / <0.6 in their paper
引文
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[2] R. W. P. King, S. S. Sandier: Reply. Radio Science, (1998) , Vol.33, No.2, pp.255-256．
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(1982) , Vol.17, pp.532~538; Correction, (1984) , Vol.19, p.1422．
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[77] Ronold W. P. King, Margaret Owens, Tai Tsun Wu: Lateral Electromagnetic Waves. Springer-Verlag New York, (1992) , Chap.3, pp.51~87．
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[57] R. W. P. King, B. H. Sandier, L. C. Shen: A comprehensive study of subsurface propagation from horizontal electric dipoles. IEEE Trans. Geosci. Remote sensing, (1980) , Vol.GE-18, pp.225-233．
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[59] R. W. P. King, T. T. Wu, L. C. Shen: The horizontal wire antenna over a conducting or dielectric half-space: Current and admittance. Radio Sci. (1974) , Vol.9, pp.701-709．
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for lossy half-space problems. Electromagnetic (1981) , Vol.1, pp. 1-28．
[62] K. A. Norton: The calculations of ground-wave field intensity over a finitely conducting spherical earth. Proc. IRE , (1941) ,Vol.29, pp.623-639．
[63] B. Van der Pol: Propagation of electromagnetic waves over the plane earth. Ann. Phys. (Leipzip), (1930) , Vol.6, pp.273-295．
[64] B. Van der Pol: On discontinuous electromagnetic waves and the occurrence of a surface wave. IRE Trans. Antennas Propag. (1956) , AP-4, pp.288-293．
[65] J. R.: Wait The electromagnetic fileds of a horizontal dipole in the presence of a conducting half-space. Can. J. Phys. (1961) , Vol.39, pp.1017-1027．
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[68] J. R. Wait, D. A. Hill: Electromagnetic interaction between a conducting cylinder and a solenoid in relative motion. Journal of Applied physics, (1979) , Vol.50, pp.511 5-5119．
[69] A. Sommerfeld: In dia differential und integralgleichungen der meckanik und physik, Vol.11． P. Frank, R. v. Mises (eds.). Braunschweig, Germany: F. Vieweg and Son, (1935) , pp.932 and 933．
[70] J. R. Wait: Electromagnetic response of an anisotropic conducting cylinder to an external source. Radio Sci. (1978) , Vol.13, pp.798-792．
[71] J. R. Wait, R. L. Cardner: Electromagnetic testing of cylindrically layered conductors. IEEE Transactions, (1979) , Vol.IM-28, pp. 159-161．
[72] T. T. Wu, R. W. P. King: Lateral waves: A new formula and interference patterns. Radio Sci. (1982) , Vol.17, pp.521-531．
[73] J. R. Wait: Theories for radio ground wave transmission over a multisection path. Radio Science, (1980) , Vol.15, pp. 107-208．
[74] T. T. Wu, R. W. P. King: Lateral waves: New formula for E1φ and E1Z. Radio Sci.
(1982) , Vol.17, pp.532~538; Correction, (1984) , Vol.19, p.1422．
[75] T. T. Wu, R. W. P. King: Lateral electromagnetic pulses generated by a vertocal dipole on the boundary between two dielectrics. J. Appl. Phys. (1987) , Vol.62, pp.4345-4355．
[76] T. T. Wu, L. C. Shen, R. W. P. King: The dipole antenna with eccentric coating in a relatively medium. IEEE Trans. (1975) , Vol.AP-23, pp.57~62．
[77] Ronold W. P. King, Margaret Owens, Tai Tsun Wu: Lateral Electromagnetic Waves. Springer-Verlag New York, (1992) , Chap.3, pp.51~87．
[78] Ronold W. P. King, Margaret Owens, Tai Tsun Wu: Lateral Electromagnetic Waves. Springer-Verlag New York, (1992) , Chap.5, pp. 144-169,.
[79] H. Q. Zhang, W. Y. Pan: Electromagnetic field of a vertical electric dipole on a perfect conductor coated with a dielectric layer. Radio Sci. (In 2001, Aecepeted as RS2348) .
[80] 张红旗，潘威炎，沈凯先：．“水平电偶极子在涂敷介质层的导电基底上激起 的电磁场”．《电波科学学报》，(2001) ，Vol．16，No．3．
[81] 张红旗，潘威炎，沈凯先：．“位于覆盖介质层的导电基底中的水平电偶极子 激起的电磁场”．《电波科学学报》，(已经录用)。
[82] 刘鹏程： 《工程电磁场简明手册》，高等教育出版社(1989) ，pp．275～276。
[83] 熊皓等：《无线电波传播》，电子工业出版社，(2000) ，pp．341-344。
[84] 南京工学院数学教研组：《特殊函数简明教程》第二版，高等教育出版社， (1982) 。
[85] 钟玉泉：《复变函数论》，高等教育出版社，(1979) 。
[86] 郭敦仁：《数学物理方法》，人民教育出版社，(1965) 。