半空间环境下复杂旋转对称体电磁散射特性的分析
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摘要
利用轴对称性可以将电大的旋转对称体电磁问题转化为求解每个具有小规模矩阵方程的问题,即原问题的Fourier模式,从而可以大大提高计算效率,并且减少内存需求。本文发展了旋转对称体矩量法来快速有效地分析半空问环境下复杂旋转对称体的电磁散射特性。
本文研究了介质旋转对称体在半空间环境下的散射问题。首先通过麦克斯韦方程、辅助位函数、等效原理和边界条件建立了电、磁流的混合场积分方程(Poggio-Miller-Chang-Harrington-Wu,PMCHW);在外部等效积分中引入了并矢格林函数,它的计算是通过离散复镜像方法来实现的。然后再利用旋转对称性,将等效流(等效电流、磁流)展开为关于φ的傅立叶级数形式和关于,的分段函数形式。最后运用矩量法求得每个Fourier模式矩阵方程的解。因为各傅立叶模式之间存在正交性,可以分别计算单个独立模式下的等效流,再进行线性叠加,这样就大大减少了未知量个数和计算时间。
本文还进一步研究了含有均匀手征媒质的旋转对称目标在自由空间以及半空间环境下的电磁散射特性。利用了等效原理、边界条件和手征媒质中波的分解技术,在手征物体表面建立了关于等效电、磁流的PMCHW方程,然后运用矩量法同介质旋转对称体类似求解。最后给出了一些典型数值算例,表明了本文所发展的旋转对称体矩量法对分析含有手征媒质目标的电磁散射特性具有很好的准确性和很高的计算效率。
The usage of the axisymmetric property of the body of revolution(BoR) can translate an original electrically large BoR-problem into a series problems with small size of matrix equations,namely a Fourier mode of the original one,which can greatly improve the computational efficiency and reduce the memory requirements.In this thesis,the accurate and efficient analyses of electromagnetic scattering of complex BOR above half space has been realized by the development of method of moments for BOR.
This paper mainly researches electromagnetic scattering from dielectric bodies of revolution above a lossy half space.A set of Poggio-Miller-Chang-Harrington-Wu (PMCHW) are formulated via Maxwell's equations,potential functions,equivalent principle and the boundary conditions.Introducing the dyadic Green's functions of exterior equivalent integral equations are computed by the discrete complex image method.With the rotational symmetry,the unknown equivalent surface currents(electric currents and magnetic currents) can be expanded in Fourier series inφand sectional function in t.Finally,a solution of each Fourier model matrix equation is solved by the methods of moment.Because each mode is orthogonal to the others,the problem can be solved under each mode respectively and each solution is summed up subsequently.Thus it reduces greatly the sum of unknown variable and the calculational time.
The problem of electromagnetic scattering from homogeneous chiral BOR in free space and above a lossy half space is further studied in this thesis.A set of PMCHW for the unknown equivalent electric and magnetic currents on the chiral BOR's surface are formulated,it is based upon using equivalent principle,the boundary conditions and the technique of wave decomposition.The PMCHW is solved using the method of moments in a formulation as the problem of dielectric BOR.Finally,the accuracy and efficiency of the methods proposed in this thesis has been validated by some representative numerical results.
本文研究了介质旋转对称体在半空间环境下的散射问题。首先通过麦克斯韦方程、辅助位函数、等效原理和边界条件建立了电、磁流的混合场积分方程(Poggio-Miller-Chang-Harrington-Wu,PMCHW);在外部等效积分中引入了并矢格林函数,它的计算是通过离散复镜像方法来实现的。然后再利用旋转对称性,将等效流(等效电流、磁流)展开为关于φ的傅立叶级数形式和关于,的分段函数形式。最后运用矩量法求得每个Fourier模式矩阵方程的解。因为各傅立叶模式之间存在正交性,可以分别计算单个独立模式下的等效流,再进行线性叠加,这样就大大减少了未知量个数和计算时间。
本文还进一步研究了含有均匀手征媒质的旋转对称目标在自由空间以及半空间环境下的电磁散射特性。利用了等效原理、边界条件和手征媒质中波的分解技术,在手征物体表面建立了关于等效电、磁流的PMCHW方程,然后运用矩量法同介质旋转对称体类似求解。最后给出了一些典型数值算例,表明了本文所发展的旋转对称体矩量法对分析含有手征媒质目标的电磁散射特性具有很好的准确性和很高的计算效率。
The usage of the axisymmetric property of the body of revolution(BoR) can translate an original electrically large BoR-problem into a series problems with small size of matrix equations,namely a Fourier mode of the original one,which can greatly improve the computational efficiency and reduce the memory requirements.In this thesis,the accurate and efficient analyses of electromagnetic scattering of complex BOR above half space has been realized by the development of method of moments for BOR.
This paper mainly researches electromagnetic scattering from dielectric bodies of revolution above a lossy half space.A set of Poggio-Miller-Chang-Harrington-Wu (PMCHW) are formulated via Maxwell's equations,potential functions,equivalent principle and the boundary conditions.Introducing the dyadic Green's functions of exterior equivalent integral equations are computed by the discrete complex image method.With the rotational symmetry,the unknown equivalent surface currents(electric currents and magnetic currents) can be expanded in Fourier series inφand sectional function in t.Finally,a solution of each Fourier model matrix equation is solved by the methods of moment.Because each mode is orthogonal to the others,the problem can be solved under each mode respectively and each solution is summed up subsequently.Thus it reduces greatly the sum of unknown variable and the calculational time.
The problem of electromagnetic scattering from homogeneous chiral BOR in free space and above a lossy half space is further studied in this thesis.A set of PMCHW for the unknown equivalent electric and magnetic currents on the chiral BOR's surface are formulated,it is based upon using equivalent principle,the boundary conditions and the technique of wave decomposition.The PMCHW is solved using the method of moments in a formulation as the problem of dielectric BOR.Finally,the accuracy and efficiency of the methods proposed in this thesis has been validated by some representative numerical results.
引文
[1]盛新庆.计算电磁学要论[M].第一版.北京:科学出版社,2004.
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[4]Andreasen.M.G.,Scattering from bodies of revolution[J],IEEE Trans.On Antennas Propagation,13:303-310.
[5]J.R.Mautz and R.F.Harrington,Radiation and scattering from bodies of revolution[R],Appl.Sci.1969,20:405-435.
[6]J.R.Mautz and R.F.Harrington,H-field,E-field and combined-field solutions for conducting bodies of revolution[J],1978,32:157-164.
[7]J.R.Mautz and R.F.Harrington,Computer programs for H-field,E-field,and combined field solutions for bodies of revolution[R],Technical Report,TR-77-3.Syracuse University,Syracuse,NY 13244,1977.
[8]Y.Leviatan,A.Boag,and A.Boag,Generalized formulations for electromagne -tic scattering from perfectly conducting and homogeneous material bodies theory and numerical solution[J].IEEE Trans.Antennas Propagat.1988,36(12):1722-1734.
[9]D.B.Davidson and D.A.McNamara,Moment method formulation for asymmet -tic excited conducting bodies of revolution[J],Electronics Letters,1988,24(20):1280-1282.
[10]T.K.Wu and L.L.Tsai,Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,Radio Science,Sep-Oct.1977,vol.12,NO.5.
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[34]I.V.Lindell,and K.F.Lindman,The last Hertzian and a Harginger of electromagnetic chirallity[J].AP.Magazine,1992,34:24-30.
[35]M.Yuceer,J.R.Mautz,and E.Arvas,Method of moments solution for the radar cross section of a chiral body of revolution[J],IEEE Trans.Antennas Propagat.,Vol.53,No.3,pp.1163.1167,2005.
[36]X.D.Wang,D.H.Wemer and L.W.Li,Interaction of electromagnetic waves with 3-D arbitrarily shaped homogeneous chiral targets in the presence of a lossy half space[J].IEEE Trans.Antennas Propag.,vol.55,no.12,pp.3647-3655,Dec.2007.
[37]M.Yuceer,Electromagnetic scattering from an arbitrarily shaped chiral body of revolution[D],PHD,Syracuse University,Syracuse,New York 2003.
[38]K.A.Michalski et al,Analysis of electromagnetic scattering by conducting BOR's in layered media using the discrete complex image method[J],IEEE Antennas Propag.Symp.Dig.,Newport Beach,CA,1995.
[39]T.K.Sarkar,Odilon Pereira,Using the Matrix Pencil Method to Estimate the Parameters of a Sum of Complex Exponentials[J]IEEE Trans.Antennas Propagat.,Vol.37,No.1,pp.48-55,February 1995.
[40]R.Coccioli,G.Lombardi,G.Pelosi,A Finite Element-Boundary Integral analysis of electromagnetic scattering by a buried dielectric object[J],IEEE MTT-SIMOC Proceed- ing,pp.888-892,1995.
[41]郭辉萍,刘学观,殷红成等,手征材料涂覆导体目标电磁散射特性的PO分析[J],微波学报,2002,18(4):21-25.
[42]方剑,任朗,时域有限面积法解手征介质涂层导体柱的电磁散射[J],电子学报,2001,29(3):368-372.
[43]D.X.Wang,P.Y.Lau and R.S.Chen,Scattering by conducting bodies coated with bi-isotropic materials[J],IEEE Trans.Antennas Propag.,Vol.55,No.8,pp.2313-2319,2007.8.
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[2]J.R Mautz and R.F.Harrington,Generalized network parameters for bodies of revolution,Technical Report,TR-687.Syracuse University[R].Syracuse.NY 13244.1968.
[3]J.R.Mautz and R.F.Harrington,Radiation and scattering from bodies of revolution[C],Appl.Sci.Res,1969,20:405-435.
[4]Andreasen.M.G.,Scattering from bodies of revolution[J],IEEE Trans.On Antennas Propagation,13:303-310.
[5]J.R.Mautz and R.F.Harrington,Radiation and scattering from bodies of revolution[R],Appl.Sci.1969,20:405-435.
[6]J.R.Mautz and R.F.Harrington,H-field,E-field and combined-field solutions for conducting bodies of revolution[J],1978,32:157-164.
[7]J.R.Mautz and R.F.Harrington,Computer programs for H-field,E-field,and combined field solutions for bodies of revolution[R],Technical Report,TR-77-3.Syracuse University,Syracuse,NY 13244,1977.
[8]Y.Leviatan,A.Boag,and A.Boag,Generalized formulations for electromagne -tic scattering from perfectly conducting and homogeneous material bodies theory and numerical solution[J].IEEE Trans.Antennas Propagat.1988,36(12):1722-1734.
[9]D.B.Davidson and D.A.McNamara,Moment method formulation for asymmet -tic excited conducting bodies of revolution[J],Electronics Letters,1988,24(20):1280-1282.
[10]T.K.Wu and L.L.Tsai,Scattering from arbitrarily-shaped lossy dielectric bodies of revolution,Radio Science,Sep-Oct.1977,vol.12,NO.5.
[11]Shu-Kong Chang and Kenneth K.Mel,Generalized sommerfeld Integrals and Field Expansions in Two-Medium Half-Spaces[J],IEEE Trans.Antennas Propagat.,vol.AP-28,pp.504-512,JULY.1980.
[12]Shu-Kong Chang and Kenneth K.Mel,Generalized sommerfeld Integrals and Field Expansions in Two-Medium Half-Spaces[J],IEEE Trans.Antennas Propagat.,vol.AP-28,pp.504-512,JULY.1980.
[13]S.Vitebskiy and L.Carin,Moment-method modeling of short-pulse scattering from and the resonances of a wire buried inside a lossy,dispersive half space[J], IEEE Trans.Antennas Propagat,1995,43:1303-1312.
[14]K.A.MichaIski and D.Zheng,Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media,part Ⅰ and Ⅱ[J],IEEE Trans.Antennas and Propagat,.1990,38:335-352.
[15]N.Geng and L.Carin,Wide-Band Electromagnetic Scattering from a dielectric BOR buried in a layered lossy dispersive medium[J],IEEE Trans.Antennas Propag.,vol.47,pp.610-618,APRIL.1999.
[16]J.Q.He,Morn and Mlfma for scattering from dielectric target in layered med -ium environment[D],Ph.D.dissertation,Duke Uni.,2000.
[17]X.Wang,Y.-B.Gan and L.W.Li,Calculation of scattering from dielectric objects above half space[J],IEE Electronics Letters.4th March 2004.Vol.40,No.5.
[18]N.Geng,A.Sullivan,and L.Carin,Multi-level fast-multipole algorithm for scattering from conducting targets above or embedded in a lossy half space[J],IEEE Trans.Geosci.Remote Sensing,2000,38:1567-1579.
[19]刘金权.分层介质中目标体的电磁特性研究[D].南京:南京理工大学电子信息与光电技术学院,2008年.
[20]M.S.Kluskens and E.H.Newman,Scattering by a chiral cylinder of arbitrary cross section[J],IEEE Trans.Antennas Propag.,vol.38,no.9,pp.1448-1455,Sep.1990.
[21]M.A.A1-Kanhal and E.Arvas,Electromagnetic scattering from a chiral cylinder of arbitrary cross section[J],IEEE Trans.Antennas Propag.,vol.44,no.7,pp.1041- 1048,Jul.1996.
[22]D.Worasawate,J.R.Mautz and E.Arvas.Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body[J].IEEE Trans.Antennas Propag.,vol.51,no.5,pp.1077-1084,May.2003.
[23]X.Wang,Y.-B.Gan and L.W.Li,Calculation of scattering from dielectric objects above half space[J],IEE Electronics Letters.4th March 2004.Vol.40,No.5.
[24]J.J.Yang,Y.L.Chow,and D.G.Fang.Discrete complex images of a three-dimensional dipole above and within a lossy ground[J],IEE Proc,H,Aug.1991,138:319-326.
[25]M.I.Aksun.A robust approach for the derivation of closed-form Green's functions[J].IEEE Trans.Microwave Theory Tech.,1996,vol.44:651-658.
[26]张剑锋,旋转对称介质壳体的矩量法分析[D].南京:南京电子技术研究所,2004年。
[27]包伟.旋转对称体的电磁散射研究[D].南京:南京理工大学电子信息与光电技术学院,2007年.
[28]阳晓丽.旋转对称体散射特性的高效分析[D].南京:南京理工大学电子信息与光电技术学院,2008年.
[29]Robert A.Shore,and Arthur D.Yaghjian,A low order-singularity electric-field integral equation solvable with pulse basis functions and point matching[R],AFRL-SN-TR- 2005-2007,In-House Technique Report,2004.
[30]J.F.Shaeffer and L.N.Medgyesi-Mitschang,Radiation from wire antennas attached to bodies of revolution:The junction problem[J],IEEE Trans.Antennas Propagat,1981,AP-29:479-487。
[31]V.K.Varadan,A.Lakhtakia,and V.V.Varadan,Scattering by beaded helices:anisotropy and chirality[J],Wave-Mater.Interact.,vol.2,pp.153-160,Apr.1987.
[32]C.F.Bohren,Craig F,Light scattering by an optically active sphere[J],Chemical Physics Letters,Volume 29,Issue 3,pp.458-462,December 1974.
[33]R.G.Rojas,Integral equations for EM scattering by homogeneous/inhomogene -ous two-dimensional chiral bodies[J],Inst.Elect.Eng.Microw.,Antennas Propag.,Vol.141,No.5,pp.385-392,May 1994.
[34]I.V.Lindell,and K.F.Lindman,The last Hertzian and a Harginger of electromagnetic chirallity[J].AP.Magazine,1992,34:24-30.
[35]M.Yuceer,J.R.Mautz,and E.Arvas,Method of moments solution for the radar cross section of a chiral body of revolution[J],IEEE Trans.Antennas Propagat.,Vol.53,No.3,pp.1163.1167,2005.
[36]X.D.Wang,D.H.Wemer and L.W.Li,Interaction of electromagnetic waves with 3-D arbitrarily shaped homogeneous chiral targets in the presence of a lossy half space[J].IEEE Trans.Antennas Propag.,vol.55,no.12,pp.3647-3655,Dec.2007.
[37]M.Yuceer,Electromagnetic scattering from an arbitrarily shaped chiral body of revolution[D],PHD,Syracuse University,Syracuse,New York 2003.
[38]K.A.Michalski et al,Analysis of electromagnetic scattering by conducting BOR's in layered media using the discrete complex image method[J],IEEE Antennas Propag.Symp.Dig.,Newport Beach,CA,1995.
[39]T.K.Sarkar,Odilon Pereira,Using the Matrix Pencil Method to Estimate the Parameters of a Sum of Complex Exponentials[J]IEEE Trans.Antennas Propagat.,Vol.37,No.1,pp.48-55,February 1995.
[40]R.Coccioli,G.Lombardi,G.Pelosi,A Finite Element-Boundary Integral analysis of electromagnetic scattering by a buried dielectric object[J],IEEE MTT-SIMOC Proceed- ing,pp.888-892,1995.
[41]郭辉萍,刘学观,殷红成等,手征材料涂覆导体目标电磁散射特性的PO分析[J],微波学报,2002,18(4):21-25.
[42]方剑,任朗,时域有限面积法解手征介质涂层导体柱的电磁散射[J],电子学报,2001,29(3):368-372.
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