基于新型积分方程的三维介质目标的电磁散射特性分析
|
摘要
复杂目标电磁散射的高效求解对于雷达系统设计与雷达目标识别具有十分重要的意义。如何准确、快速地分析三维复杂目标的电磁特性,长期以来一直是计算电磁学领域的研究重点。
以矩量法(MOM)为基础的快速多极子方法(FMM)和多层快速多极子(MLFMA)的提出和实现,克服了经典高频方法的局限,使复杂电大尺寸目标的电磁散射特性分析成为可能。然而这些方法都是建立在均匀空间模型的基础上,即没有考虑周围环境因素的影响,所以在考虑目标体处于半空间环境下更有实际意义。本文的研究工作正是基于上述的工程应用背景下展开的,将目前较为成熟的均匀空间电磁场求解的各种算法扩展到半空间背景中,不但对半空间格林函数的表达和求解进行了研究,还考虑了各种环境因素对目标辐射特性或目标散射特性的影响,使目标与环境一体化高效建模成为可能。其次,本文对传统积分方程(PMCHWT)进行了改进,深入研究了一种新型的积分方程(JMCFIE),得到了具有良好性态的阻抗矩阵,从而加速了对半空间三维目标电磁特性数值计算的速度。同时Müller方程的应用,有效的解决了低频崩溃问题,一系列算例证明了此方法的可靠性。在此基础上,本文还对手征媒质的电磁特性进行了研究,一些数值计算结果的给出,验证了此方法的正确性与有效性,使其具有一定的实际意义和工程应用价值。
To realize efficient solution of electromagnetic(EM) scattering from complex target has very practical value for the design of radar system and identify of radar target. The electromagnetic scattering of 3 D complex targets has attracted much more attention in engineering applications.Recently,intensive investigations have been done to find fast and accurate numerical methods to solve such problems.
The FMM and MLFMA are applied to analyze the electromagnetic scattering and radiation of electrical-large targets which overcomes the limitation of conventional high frequency method.But those methods are all based on free space that leads to neglect some important factors.So it will have more significance that considering objects modeled in half-space.Based on these engineering application background,the research work realize a simple extension the free space algorithms to the half-space cases.The work not only investigates the expression and solution of half-space green's function, but also considers lots of different environment factors which can affect electromagnetic scattering and radiation of targets.In addition,a new integral function named JMCFIE is presented which improves the conventional PMCHWT integral function.The new integral function can essentially improve characteristic of impedance matrix and accelerate iterative converging.At the same time,the Müller function is applied for overcoming the low frequency breakdown.The JMCFIE integral function is implemented in analyzing the electromagnetic characteristic of chiral object.The numerical examples show the accuracy and efficiency of the methods proposed in the dissertation.
以矩量法(MOM)为基础的快速多极子方法(FMM)和多层快速多极子(MLFMA)的提出和实现,克服了经典高频方法的局限,使复杂电大尺寸目标的电磁散射特性分析成为可能。然而这些方法都是建立在均匀空间模型的基础上,即没有考虑周围环境因素的影响,所以在考虑目标体处于半空间环境下更有实际意义。本文的研究工作正是基于上述的工程应用背景下展开的,将目前较为成熟的均匀空间电磁场求解的各种算法扩展到半空间背景中,不但对半空间格林函数的表达和求解进行了研究,还考虑了各种环境因素对目标辐射特性或目标散射特性的影响,使目标与环境一体化高效建模成为可能。其次,本文对传统积分方程(PMCHWT)进行了改进,深入研究了一种新型的积分方程(JMCFIE),得到了具有良好性态的阻抗矩阵,从而加速了对半空间三维目标电磁特性数值计算的速度。同时Müller方程的应用,有效的解决了低频崩溃问题,一系列算例证明了此方法的可靠性。在此基础上,本文还对手征媒质的电磁特性进行了研究,一些数值计算结果的给出,验证了此方法的正确性与有效性,使其具有一定的实际意义和工程应用价值。
To realize efficient solution of electromagnetic(EM) scattering from complex target has very practical value for the design of radar system and identify of radar target. The electromagnetic scattering of 3 D complex targets has attracted much more attention in engineering applications.Recently,intensive investigations have been done to find fast and accurate numerical methods to solve such problems.
The FMM and MLFMA are applied to analyze the electromagnetic scattering and radiation of electrical-large targets which overcomes the limitation of conventional high frequency method.But those methods are all based on free space that leads to neglect some important factors.So it will have more significance that considering objects modeled in half-space.Based on these engineering application background,the research work realize a simple extension the free space algorithms to the half-space cases.The work not only investigates the expression and solution of half-space green's function, but also considers lots of different environment factors which can affect electromagnetic scattering and radiation of targets.In addition,a new integral function named JMCFIE is presented which improves the conventional PMCHWT integral function.The new integral function can essentially improve characteristic of impedance matrix and accelerate iterative converging.At the same time,the Müller function is applied for overcoming the low frequency breakdown.The JMCFIE integral function is implemented in analyzing the electromagnetic characteristic of chiral object.The numerical examples show the accuracy and efficiency of the methods proposed in the dissertation.
引文
[1]R.F.Harrington,Time-harmonic electromagnetic fields.McGraw-Hill Book Company,Newyork,1961.
[2]R.F.Harrington.Field Computation by Moment Methods.Krieger Publishing Company,Malabar,Florida,1983.
[3]李世智.电磁散射与辐射问题的矩量法.电子工业出版社.1985.
[4]Johnson,J.H.Wang.Generalized Moment Methods In electromagnetic Formulation and Computer Solution of Integral Equations.John Wiley&Sons,Inc,1991.
[5]A.W.Glisson,D.R.Wilton.Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces.IEEE Trans.on Antennas Propagat,vol.AP-28,pp.593-603,No.5,September 1980.
[6]S.M.Rao,D.R.Wilton,A.W.Glisson.Electromagnetic Scattering by Surfaces of Arbitrary Shape.IEEE Transactions on Antennas and Propagation AP-30,No.3,pp.409-419,May 1982.
[7]J.M.Song,W.C.Chew.Moment method solution using parametric geometry.Journal of Electromagnetic Waves and Applications,vol.9,No.112,pp.71-83,1995.
[8]Ronald Coifman,Vladimir Rokhlin,and Stephen Wandzura.The fast multipole method for the wave equation:a pedestrian prescription.IEEE Antennas and Propagation Magazine,vol.35,No.3,pp.7-12,1993.
[9]J.M.Song,W.C.Chew.Fast multipole method solution using parametric geometry.Microwave and Optical Technology Letters,vol.7,No.16,pp.760-765,1994.
[10]J.M.Song,C.C.Lu.,W.C.Chew.Multilevel fast multipole algorithm for Electromagnetic scattering by large complex objects.IEEE Transaction on Antennas Propagation,vol.45,No.10,pp.1488-1493,1997.
[11]J.M.Song,C.C.Lu,W.C.Chew and S.W.Lee.Introduction to Fast Illinois Solver Code(FISC).IEEE Antennas propagation symposium,pp.48-51,1997.
[12]J.M.Song,C.C.Lu,W.C.Chew,S.W.Lee.Fast Illinois solver code(FISC).IEEE Transactions on Antennas and Propagation,vol.40,No.3,pp.27-34,1998.
[13]J.M.Song,W.C.Chew.Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering.Microwave and Optical Tech.Lett.,10(10):pp.14-19,1995.
[14]金建铭著,王建国译,葛德彪校.电磁场有限元方法.西安:西安电子科技大学出版社,1991年.
[15]J.M.Song,W.C.Chew.Fast multipole method solution of three dimensional integral equations.IEEE Antennas Propagation Symposium,pp.1528-1531,1995.
[16]C.C.Lu,W.C.Chew.Fast algorithm for solving hybrid integral equations.IEE proceedings-H,vol.140,No.5,pp.455-460,1993.
[17]T.建,兰康,彭仲秋.有耗半空间天线问题中的广义索末菲积分.电子学报,1995年03期,23(3):104-107
[18]冯宁宁,方大纲.分层介质电、磁流场、位谱域并矢格林函数的统一形式.电波科学学报,1998.4.,13(4):335-340
[19]龙毅,方大纲等.微带印刷天线辐射与散射的全波分析方法.电波科学学报,1995,10(1.2):9196
[20]熊兵,侯晓华,张进民.有耗矩形微带贴片雷达截面的全波分析.西安电子科技大学学报(自然科学版),2002年4月,29(2):257-260
[21]李江,傅君眉.平面分层介质结构的空间域格林函数近似解.微波学报,1999.9.,15(3):221-226
[22]K.A.Michalski.Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media,part Ⅰ:Theory.IEEE Trans.on Antennas Propagation,vol.38,No.3,March 1990.
[23]K.A.Michalski.Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media.part Ⅱ:Implementation and Results for Contiguous Half-Space.IEEE Trans.on Antennas Propagation,vol.38,No.3,March 1990.
[24]徐利明,聂在平.半空间格林函数的角谱平面高效计算.电波科学学报2005,19(3):263-268.
[25]邹军,袁建生,马信山.计算分层大地媒质中格林函数的模拟镜像方法.华东电力大学学报,2002,29(2):13-15
[26]Sommerfeld.Partial differential equations.Academic Press,1949,pp:246-267.
[27]Jing yang Chen,Ahmed A.Kishk,and Allen W.Glisson.Application of a new MPIE formulation to the analysis of a dielectric resonator embedded in a multilayered medium coupled to a microstrip circuit.IEEE Transactions on Microwave Theory and Techniques,vol.49,no.2,Feb.2001
[28]R.C.Hsieh,J.T.Kuo.Fast full_wave analysis of planar microstrip circuit elements in stratified media.IEEE Trans.Microwave Theory Tech,1998,46(9):1292-1297
[29] T.J.Cui et.al. Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects. IEEE Geosci. Remote Sensing, 1999,37(3):887-900
[30] D.Gottieb et.al, edited by E.M.Murman and S.S.Arbarbanel,. Recovering point wise values of discontinuous data within spectral accuracy, In Progress and Supercomputing in Computational Fluid Dynamics. Birkhauser, Boston, 1985:357
[31] Y.L.Chow, J.J.Yang, D.G.Fang. A Closed-form spatial Green's function for the thick microstrip substrate. IEEE microwave Theory Tech., 1991, 39(3) pp: 588-592
[32] M.Siegel and R.W.P.King. Radiation from half-space. IEEE Trans Antennas Propagat., vol.linear antennas in a issipative AP-19, no.4, pp.477-485,July.1971.
[33] R.M.Sorbello, R.W.P.King etal. The horizontal-wire antenna over a dissipative half-space: Generalized formula and measurements. IEEE Trans. Antennas Propagat vol.AP-25,no.6,pp.850-854,Nov. 1977.
[34] C.A.Harrison, C.M.Butler. An Experimental Study of a Cylindrical Antenna in Two Half-spaces. IEEE Trans.Antennas Propagat. vol.AP-32(4),pp.387-390, Apr. 1984.
[35] C.M.Butler, X.B.Xu, and A.W.Glisson. Current induced on a conducting cylinder located near the planar interface between two semiinfinite half-space. IEEE Trans. Geosci. Remote Sensing,pt.2, vol.38, pp.357-365, Jan.2000.
[36] B.A.Baertlein, J.R.Wait, and D.G.Dudley. Scattering by a conducting strip over a lossy half-space. Radio Sci.,vol.24,pp.485-497,1987.
[37] E.Marx. Scattering by an arbitrary cylinder at a plane interface:Broadside incidence. IEEE Trans. Antennas Propagat.,vol.37,pp.l823-1828,May.l989.
[38] H.S.Chang and K.K.Mei. Scattering of electromagnetic waves by buried and partly buried bodies of revolution. IEEE Trans. Geosci. Remote Sensing, vol.23, pp.592-596, July 1985.
[39] J.R.Mosig, F.Gardiol. General integral equation formulation for microstrip antennas and scatterers. Inst. Elect. Eng. Proc, pt.H,vol.132, pp.424-432, Dec. 1985.
[40] K.A.Michalski. On the scalar potential of a point charge associated with a time-harmonic dipole in a layered medium. IEEE Trans. Antennas Propagat., vol.AP-35, pp. 1299-1301,Nov. 1987.
[41] Vitebskiy S, Carin L. Moment method modeling of short-pulse scatering from and the resonances of a wire buried in side a lossy dispersive half-space. IEEE trans Antennas Propagat., 43(11):pp.1303—1312,1995.
[42] S.Vitebskiy, K.Sturgess, and L.Carin. Short-pulse plane-wave scatering from buried perfectly conducting bodies of revolution. IEEE Trans. Antennas Propagat., vol.44, pp.143-151,Feb. 1996.
[43] L.Carin, N.Geng, M.McClure, J.Sichina. and L.Nguyen. Ultra wide-band synthetic-aperture radar for mine-field detection. IEEE Antennas Propagat., Mag.,vol.41,pp.18-33,Feb.1999.
[44] N.G eng and L.Carin. Wide band electromagnetic scattering form adielectric BOR buried in a layered, dispersive medium. IEEE Trans. Antennas Propagat, vol.47, pp.610-619, Apr. 1999.
[45] N.Geng, A.Sullivan, and L.Carin. Fast multipole method for scatering from an arbitrary PEC target above or buried in a lossy half space. IEEE Trans.Antennas Propagat, vol.49, pp.740-748,May 2001.
[46] N.Geng, A.Sullivan, and L.Carin. Fast multiple method for scatering from 3D PEC target situated in a half space environment. Microwave Opt .Technol.Let, vol.21, pp.399-405,June 1999.
[47] N.Geng, A.Sullivan, and L.Carin. Multilevel fastmultipole algorithm for Scattering from conducting targets above or embedded in a lossy half space. IEEE Trans Geosci.Remote Sensing, vol.38, pp.1567-1579,July 2000.
[48] J.Q.He, A.Sullivan, and L.Carin. Multilevel fast multipole algorithm for three -dimensional dielectric targets in the vicinity of a lossy half space. Microwave pt.Tech.Let.,vol.29 ,no.2,pp. 100-104,April 20,2001.
[49] Z.Liu, J.He ,Y.Xie, A.Sullivan, and L.Carin. Multi-level fast multipole algorithm for general targets on a half-space interface. IEEE Trans Antennas Propagat.,vol.51 pp.1877-1882,Aug,2003.
[50] Yi jun Yu, Tie jun Yu, L.Carin. Three-Dimensional Inverse Scatering of a Delectric Target Embedded in a Lossy Half-Space. IEEE Trans Geosci.Remote Sens., vol.42, pp.957-973,May 2000.
[51] X.Q. Sheng and J.-M Jin et. al. Solution of Combined-Field Integral Equation Using Multilevel Fast Multipole Algorithm for Scattering by Homogeneous Bodies. IEEE Trans. Antennas Propagat., 1998(46): 1718-1726
[52] J. M.Song and W.C.Chew. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering. Microwave and Optical Tech. Lett., 1995 (10): 14-19
[53] A. Helaly and H.M.Fahmy. Combined-field integral equation. Electronics Letters. 1993(29): 1678-1679
[54] J.R. Mautz and R.F.Harrington. H-field, E-field, and combined-field solutions for conducting body of revolution. AEU, 1978(32): 157-164
[55] Mautz,J.R.,and R.F.Harrington,Electromagnetic scattering from a homogeneous material bodies of revolution,Arch.EIektron.Uebertraeg.,33,71-80
[56] Pasi Yla-Oijala and Matti Taskinen. Application of Combined Field Integral Equation for Electromagnetic Scattering by Dielectric and Composite Objects. IEEE Trans. Antennas Propag., vol. 53, no. 3, March 2005.
[57] P. Yla-Oijala, M. Taskinen, and S. Jarvenpaa. Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods. Radio Sci., vol. 40, no. 6, Nov. 2005.
[58] K. A. Michalski and J. R Mosig. Multilayered media Green's functions in integral equation formulations. IEEE Trans. Antennas Propag., vol. 45, no. 5, 1997.
[59] G.A.E.Vandenbosch and A.R.Vande Capelle. Mix-potential integral expression formulation of the electric field in a stratified dielectric medium-Application to the case of a probe current source. IEEE Trans. Antennas Propag., vol. 40, no. 7, 1992, 806-817
[60] 盛新庆．计算电磁学要沦．第一版,北京：科学出版社,2004．
[61] D.R.Wilton and A.W.Glisson. On improving the electric field integral equation at low frequencies. 1981 Spring URSI Radio Science Meeting Digest, Los Angels, CA, June 1981:24
[62] Pasi Yla-Oijala and Matti Taskinen. Well-Conditioned Muller formulation for electromagnetic scattering by dielectric objects. IEEE Trans. Antennas Propag., vol. 53, no. 10, Oct.2005
[63] C. Muller. Foundations of the Mathematical Theory of Electromagnetic Waves. Berlin, Germany: Springer, 1969.
[64] Xiande Wang, Douglas H. Werner, Le-Wei Li, and Yeow-Beng Gan. Interaction of Electromagnetic Waves With 3-D Arbitrarily Shaped Homogeneous Chiral Targets in the Presence of a Lossy Half Space. IEEE Trans. Antennas Propag., vol. 55, no. 12, December 2007
[65] V. K. Varadan, V. V. Varadan, and A. Lakhtakia. On the possibility of designing anti-reflection coatings using chiral materials. J. Wave-Material Interaction, vol. 2, no. 1, pp. 71-81, 1987.
[66] H.Cory and I.Rosenhouse. Minimization of reflection coefficient at feed of radome-covered reflector antenna by chiral device. Electron Lett., vol. 27, no. 25, pp. 2345-2347, Dec. 1991.
[67] N.Engheta and P.Pelet. Reduction of surface waves in chirostrip antennas. Electron Lett., vol. 27, no. 1, pp. 5-7, Jan. 1991.
[68] D. M. Pozar. Microstrip antennas and arrays on chiral substrates. IEEE Trans. Antennas Propag., vol. 40, no. 10, pp. 1260-1263, Oct. 1992.
[69]X.Wang,Y.B.Gan,and L.W.Li.Scattering of an arbitrarily shaped 3D chiral object above half-space.IEEE Int.Symp.AntennasPropag.USNC/URSI National Radio Sci.Meet.,Monterey,CA,Jun.20-26,2004,pp.4192-4195.
[70]V.Lindell,A.H.Sihvola,S.A.Tretyakov,and A.J.Viitanen.Electromagnetic Waves in Chiral and Bi-Isotropic Media.Boston,MA:Artech House,1994.
[71]P.Yla-Oijala,M.Taskinen,and S.Jarvenpaa.Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods.Radio Sci.,vol.40,no.6,Nov.2005.
[72]Yaxun Liu,Le-Wei Li,Tat-Soon Yeo and Mook-Seng Leong.Application of DCIM to MPIE-MoM Analysis of 3-D PEC Objects in Multilayered Media.IEEE Trans.Antennas Propag.,vol.50,no.2,Feb.2002.
[2]R.F.Harrington.Field Computation by Moment Methods.Krieger Publishing Company,Malabar,Florida,1983.
[3]李世智.电磁散射与辐射问题的矩量法.电子工业出版社.1985.
[4]Johnson,J.H.Wang.Generalized Moment Methods In electromagnetic Formulation and Computer Solution of Integral Equations.John Wiley&Sons,Inc,1991.
[5]A.W.Glisson,D.R.Wilton.Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces.IEEE Trans.on Antennas Propagat,vol.AP-28,pp.593-603,No.5,September 1980.
[6]S.M.Rao,D.R.Wilton,A.W.Glisson.Electromagnetic Scattering by Surfaces of Arbitrary Shape.IEEE Transactions on Antennas and Propagation AP-30,No.3,pp.409-419,May 1982.
[7]J.M.Song,W.C.Chew.Moment method solution using parametric geometry.Journal of Electromagnetic Waves and Applications,vol.9,No.112,pp.71-83,1995.
[8]Ronald Coifman,Vladimir Rokhlin,and Stephen Wandzura.The fast multipole method for the wave equation:a pedestrian prescription.IEEE Antennas and Propagation Magazine,vol.35,No.3,pp.7-12,1993.
[9]J.M.Song,W.C.Chew.Fast multipole method solution using parametric geometry.Microwave and Optical Technology Letters,vol.7,No.16,pp.760-765,1994.
[10]J.M.Song,C.C.Lu.,W.C.Chew.Multilevel fast multipole algorithm for Electromagnetic scattering by large complex objects.IEEE Transaction on Antennas Propagation,vol.45,No.10,pp.1488-1493,1997.
[11]J.M.Song,C.C.Lu,W.C.Chew and S.W.Lee.Introduction to Fast Illinois Solver Code(FISC).IEEE Antennas propagation symposium,pp.48-51,1997.
[12]J.M.Song,C.C.Lu,W.C.Chew,S.W.Lee.Fast Illinois solver code(FISC).IEEE Transactions on Antennas and Propagation,vol.40,No.3,pp.27-34,1998.
[13]J.M.Song,W.C.Chew.Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering.Microwave and Optical Tech.Lett.,10(10):pp.14-19,1995.
[14]金建铭著,王建国译,葛德彪校.电磁场有限元方法.西安:西安电子科技大学出版社,1991年.
[15]J.M.Song,W.C.Chew.Fast multipole method solution of three dimensional integral equations.IEEE Antennas Propagation Symposium,pp.1528-1531,1995.
[16]C.C.Lu,W.C.Chew.Fast algorithm for solving hybrid integral equations.IEE proceedings-H,vol.140,No.5,pp.455-460,1993.
[17]T.建,兰康,彭仲秋.有耗半空间天线问题中的广义索末菲积分.电子学报,1995年03期,23(3):104-107
[18]冯宁宁,方大纲.分层介质电、磁流场、位谱域并矢格林函数的统一形式.电波科学学报,1998.4.,13(4):335-340
[19]龙毅,方大纲等.微带印刷天线辐射与散射的全波分析方法.电波科学学报,1995,10(1.2):9196
[20]熊兵,侯晓华,张进民.有耗矩形微带贴片雷达截面的全波分析.西安电子科技大学学报(自然科学版),2002年4月,29(2):257-260
[21]李江,傅君眉.平面分层介质结构的空间域格林函数近似解.微波学报,1999.9.,15(3):221-226
[22]K.A.Michalski.Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media,part Ⅰ:Theory.IEEE Trans.on Antennas Propagation,vol.38,No.3,March 1990.
[23]K.A.Michalski.Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media.part Ⅱ:Implementation and Results for Contiguous Half-Space.IEEE Trans.on Antennas Propagation,vol.38,No.3,March 1990.
[24]徐利明,聂在平.半空间格林函数的角谱平面高效计算.电波科学学报2005,19(3):263-268.
[25]邹军,袁建生,马信山.计算分层大地媒质中格林函数的模拟镜像方法.华东电力大学学报,2002,29(2):13-15
[26]Sommerfeld.Partial differential equations.Academic Press,1949,pp:246-267.
[27]Jing yang Chen,Ahmed A.Kishk,and Allen W.Glisson.Application of a new MPIE formulation to the analysis of a dielectric resonator embedded in a multilayered medium coupled to a microstrip circuit.IEEE Transactions on Microwave Theory and Techniques,vol.49,no.2,Feb.2001
[28]R.C.Hsieh,J.T.Kuo.Fast full_wave analysis of planar microstrip circuit elements in stratified media.IEEE Trans.Microwave Theory Tech,1998,46(9):1292-1297
[29] T.J.Cui et.al. Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects. IEEE Geosci. Remote Sensing, 1999,37(3):887-900
[30] D.Gottieb et.al, edited by E.M.Murman and S.S.Arbarbanel,. Recovering point wise values of discontinuous data within spectral accuracy, In Progress and Supercomputing in Computational Fluid Dynamics. Birkhauser, Boston, 1985:357
[31] Y.L.Chow, J.J.Yang, D.G.Fang. A Closed-form spatial Green's function for the thick microstrip substrate. IEEE microwave Theory Tech., 1991, 39(3) pp: 588-592
[32] M.Siegel and R.W.P.King. Radiation from half-space. IEEE Trans Antennas Propagat., vol.linear antennas in a issipative AP-19, no.4, pp.477-485,July.1971.
[33] R.M.Sorbello, R.W.P.King etal. The horizontal-wire antenna over a dissipative half-space: Generalized formula and measurements. IEEE Trans. Antennas Propagat vol.AP-25,no.6,pp.850-854,Nov. 1977.
[34] C.A.Harrison, C.M.Butler. An Experimental Study of a Cylindrical Antenna in Two Half-spaces. IEEE Trans.Antennas Propagat. vol.AP-32(4),pp.387-390, Apr. 1984.
[35] C.M.Butler, X.B.Xu, and A.W.Glisson. Current induced on a conducting cylinder located near the planar interface between two semiinfinite half-space. IEEE Trans. Geosci. Remote Sensing,pt.2, vol.38, pp.357-365, Jan.2000.
[36] B.A.Baertlein, J.R.Wait, and D.G.Dudley. Scattering by a conducting strip over a lossy half-space. Radio Sci.,vol.24,pp.485-497,1987.
[37] E.Marx. Scattering by an arbitrary cylinder at a plane interface:Broadside incidence. IEEE Trans. Antennas Propagat.,vol.37,pp.l823-1828,May.l989.
[38] H.S.Chang and K.K.Mei. Scattering of electromagnetic waves by buried and partly buried bodies of revolution. IEEE Trans. Geosci. Remote Sensing, vol.23, pp.592-596, July 1985.
[39] J.R.Mosig, F.Gardiol. General integral equation formulation for microstrip antennas and scatterers. Inst. Elect. Eng. Proc, pt.H,vol.132, pp.424-432, Dec. 1985.
[40] K.A.Michalski. On the scalar potential of a point charge associated with a time-harmonic dipole in a layered medium. IEEE Trans. Antennas Propagat., vol.AP-35, pp. 1299-1301,Nov. 1987.
[41] Vitebskiy S, Carin L. Moment method modeling of short-pulse scatering from and the resonances of a wire buried in side a lossy dispersive half-space. IEEE trans Antennas Propagat., 43(11):pp.1303—1312,1995.
[42] S.Vitebskiy, K.Sturgess, and L.Carin. Short-pulse plane-wave scatering from buried perfectly conducting bodies of revolution. IEEE Trans. Antennas Propagat., vol.44, pp.143-151,Feb. 1996.
[43] L.Carin, N.Geng, M.McClure, J.Sichina. and L.Nguyen. Ultra wide-band synthetic-aperture radar for mine-field detection. IEEE Antennas Propagat., Mag.,vol.41,pp.18-33,Feb.1999.
[44] N.G eng and L.Carin. Wide band electromagnetic scattering form adielectric BOR buried in a layered, dispersive medium. IEEE Trans. Antennas Propagat, vol.47, pp.610-619, Apr. 1999.
[45] N.Geng, A.Sullivan, and L.Carin. Fast multipole method for scatering from an arbitrary PEC target above or buried in a lossy half space. IEEE Trans.Antennas Propagat, vol.49, pp.740-748,May 2001.
[46] N.Geng, A.Sullivan, and L.Carin. Fast multiple method for scatering from 3D PEC target situated in a half space environment. Microwave Opt .Technol.Let, vol.21, pp.399-405,June 1999.
[47] N.Geng, A.Sullivan, and L.Carin. Multilevel fastmultipole algorithm for Scattering from conducting targets above or embedded in a lossy half space. IEEE Trans Geosci.Remote Sensing, vol.38, pp.1567-1579,July 2000.
[48] J.Q.He, A.Sullivan, and L.Carin. Multilevel fast multipole algorithm for three -dimensional dielectric targets in the vicinity of a lossy half space. Microwave pt.Tech.Let.,vol.29 ,no.2,pp. 100-104,April 20,2001.
[49] Z.Liu, J.He ,Y.Xie, A.Sullivan, and L.Carin. Multi-level fast multipole algorithm for general targets on a half-space interface. IEEE Trans Antennas Propagat.,vol.51 pp.1877-1882,Aug,2003.
[50] Yi jun Yu, Tie jun Yu, L.Carin. Three-Dimensional Inverse Scatering of a Delectric Target Embedded in a Lossy Half-Space. IEEE Trans Geosci.Remote Sens., vol.42, pp.957-973,May 2000.
[51] X.Q. Sheng and J.-M Jin et. al. Solution of Combined-Field Integral Equation Using Multilevel Fast Multipole Algorithm for Scattering by Homogeneous Bodies. IEEE Trans. Antennas Propagat., 1998(46): 1718-1726
[52] J. M.Song and W.C.Chew. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering. Microwave and Optical Tech. Lett., 1995 (10): 14-19
[53] A. Helaly and H.M.Fahmy. Combined-field integral equation. Electronics Letters. 1993(29): 1678-1679
[54] J.R. Mautz and R.F.Harrington. H-field, E-field, and combined-field solutions for conducting body of revolution. AEU, 1978(32): 157-164
[55] Mautz,J.R.,and R.F.Harrington,Electromagnetic scattering from a homogeneous material bodies of revolution,Arch.EIektron.Uebertraeg.,33,71-80
[56] Pasi Yla-Oijala and Matti Taskinen. Application of Combined Field Integral Equation for Electromagnetic Scattering by Dielectric and Composite Objects. IEEE Trans. Antennas Propag., vol. 53, no. 3, March 2005.
[57] P. Yla-Oijala, M. Taskinen, and S. Jarvenpaa. Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods. Radio Sci., vol. 40, no. 6, Nov. 2005.
[58] K. A. Michalski and J. R Mosig. Multilayered media Green's functions in integral equation formulations. IEEE Trans. Antennas Propag., vol. 45, no. 5, 1997.
[59] G.A.E.Vandenbosch and A.R.Vande Capelle. Mix-potential integral expression formulation of the electric field in a stratified dielectric medium-Application to the case of a probe current source. IEEE Trans. Antennas Propag., vol. 40, no. 7, 1992, 806-817
[60] 盛新庆．计算电磁学要沦．第一版,北京：科学出版社,2004．
[61] D.R.Wilton and A.W.Glisson. On improving the electric field integral equation at low frequencies. 1981 Spring URSI Radio Science Meeting Digest, Los Angels, CA, June 1981:24
[62] Pasi Yla-Oijala and Matti Taskinen. Well-Conditioned Muller formulation for electromagnetic scattering by dielectric objects. IEEE Trans. Antennas Propag., vol. 53, no. 10, Oct.2005
[63] C. Muller. Foundations of the Mathematical Theory of Electromagnetic Waves. Berlin, Germany: Springer, 1969.
[64] Xiande Wang, Douglas H. Werner, Le-Wei Li, and Yeow-Beng Gan. Interaction of Electromagnetic Waves With 3-D Arbitrarily Shaped Homogeneous Chiral Targets in the Presence of a Lossy Half Space. IEEE Trans. Antennas Propag., vol. 55, no. 12, December 2007
[65] V. K. Varadan, V. V. Varadan, and A. Lakhtakia. On the possibility of designing anti-reflection coatings using chiral materials. J. Wave-Material Interaction, vol. 2, no. 1, pp. 71-81, 1987.
[66] H.Cory and I.Rosenhouse. Minimization of reflection coefficient at feed of radome-covered reflector antenna by chiral device. Electron Lett., vol. 27, no. 25, pp. 2345-2347, Dec. 1991.
[67] N.Engheta and P.Pelet. Reduction of surface waves in chirostrip antennas. Electron Lett., vol. 27, no. 1, pp. 5-7, Jan. 1991.
[68] D. M. Pozar. Microstrip antennas and arrays on chiral substrates. IEEE Trans. Antennas Propag., vol. 40, no. 10, pp. 1260-1263, Oct. 1992.
[69]X.Wang,Y.B.Gan,and L.W.Li.Scattering of an arbitrarily shaped 3D chiral object above half-space.IEEE Int.Symp.AntennasPropag.USNC/URSI National Radio Sci.Meet.,Monterey,CA,Jun.20-26,2004,pp.4192-4195.
[70]V.Lindell,A.H.Sihvola,S.A.Tretyakov,and A.J.Viitanen.Electromagnetic Waves in Chiral and Bi-Isotropic Media.Boston,MA:Artech House,1994.
[71]P.Yla-Oijala,M.Taskinen,and S.Jarvenpaa.Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods.Radio Sci.,vol.40,no.6,Nov.2005.
[72]Yaxun Liu,Le-Wei Li,Tat-Soon Yeo and Mook-Seng Leong.Application of DCIM to MPIE-MoM Analysis of 3-D PEC Objects in Multilayered Media.IEEE Trans.Antennas Propag.,vol.50,no.2,Feb.2002.