球形分层媒质中并矢格林函数的求解Ⅰ:并矢格林函数的推导
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摘要
首先,在球坐标系下,通过德拜位函数得到均匀各向同性介质中矢量波动方程的解。然后,分析了内、外向波的单界面和多层界面的反射和透射,得到了相应的反射系数和透射系数以及广义反射系数和透射系数。接着,推导了δ源在球形分层介质中的不同位置产生的德拜位。最后,根据得到的德拜位,用球坐标系下的矢量波函数表达出场点在不同位置时的电并矢格林函数和磁并矢格林函数。
Firstly,the solutions of vector wave equation in isotropic medium are obtained by the Debye potential functions under the spherical coordinates. Then,the reflection and transmission process of in-coming and out-going waves in single layer and in spherically multilayered media are analyzed,and the corresponding reflection coefficients,transmission coefficients,the generalized reflection coefficients and generalized transmission coefficients are gained. Next,the Debye functions produced by δ source at different places in spherically multilayered media are achieved. Finally,the electric type of dyadic Green's functions and the magnetic type of dyadic Green's functions are expressed by the vector wave functions under the spherical coordinates based on the Debye potential functions obtained.
Firstly,the solutions of vector wave equation in isotropic medium are obtained by the Debye potential functions under the spherical coordinates. Then,the reflection and transmission process of in-coming and out-going waves in single layer and in spherically multilayered media are analyzed,and the corresponding reflection coefficients,transmission coefficients,the generalized reflection coefficients and generalized transmission coefficients are gained. Next,the Debye functions produced by δ source at different places in spherically multilayered media are achieved. Finally,the electric type of dyadic Green's functions and the magnetic type of dyadic Green's functions are expressed by the vector wave functions under the spherical coordinates based on the Debye potential functions obtained.
引文
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[2]Kishk A A.Analysis of spherical annular microstrip antennas[J].IEEE Transactions on Antennas and Propagation,1993,41(3):338-343
[3]Lima A,Descardeci J,Giarola A.Circular microstrip antenna on a spherical surface[J].Microwave and Optical Technology Letters,1992,5(3):221-224
[4]胡梦中,尹成友,宋铮,等.圆柱分层介质中格林函数的完整求解Ⅰ:场型格林函数[J].微波学报,2009,25(3):1-6Hu M Z,Yin C Y,Song Z,et al.Full solving Green’s function for cylindrically media Part I:Green’s function of electric and magnetic fields[J].Journal of Microwaves,2009,25(3):1-6
[5]胡梦中,尹成友,宋铮,等圆柱分层介质中格林函数的完整求解Ⅱ:混合位格林函数[J].微波学报,2009,25(4):11-15Hu M Z,Yin C Y,Song Z,et al.Full solving Green’s function for cylindrically media PartⅡ:mixed potential Green’s function[J].Journal of Microwave,2009,25(4):11-15
[6]戴振铎,鲁述.电磁理论中的并矢格林函数[M].武汉:武汉大学出版社,2005Dai Z D,Lu S.Dyadic Green’s Functions in Electromagnetic Fields[M].Wuhan:Wuhan University Press,2005
[7]Li L W,Kooi P S,Leong M S,et al.Electromagnetic dyadic Green’s function in spherically multilayered media[J].IEEE Transactions on Microwave Theory and Techniques.1994,42(12):2302-2310
[8]Zvonimir S,Niksa B,Juraj B.Analysis of rectangular microstrip patch antennas on spherical structures[J].Microwave and Optical Technology Letters,2003,36(4):276-280
[9]Chew W C.Waves and Fields in Inhomogeneous Media[M].New York:Van Nostrand,1990
[10]王一平.工程电动力学(修订版)[M].西安:西安电子科技大学出版社.2007Wang Y P.Electrodynamics for Engineering(revised edition)[M].Xi'an:Xidian University Press,2007
[11]Harrington R F.Time-Harmonic Electromagnetic Fields[M].IEEE Press,2001