复合基函数与广义传输矩阵在导体与介质电磁散射问题中的研究与应用
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摘要
电磁散射的数值计算方法的改进一直是计算电磁学界的主要研究方向,为了能够高效的分析电大尺寸或大规模阵列的散射问题,需要在传统方法上有效的提取物体的散射特征,进而使用较少的信息量求解物体的散射场,达到提高分析效率的要求。本文针对大规模导体阵列的散射问题,提出了基于传统矩量法的复合基函数(SBF)分析方法,它能够通过建立物体单元的解空间并从中提取有效的散射特征,进而在大规模阵列散射问题中通过少数的SBF表示每个散射单元的散射特征,建立的线性方程组比起传统矩量法未知数大大减少,有效提高了数值计算的效率。
同时,针对非均匀介质(包括手征介质与双各向异性介质)散射问题,本文给出了基于SWG基函数的矩量法数值求解过程。传统矩量法建立在体网格划分上,通过SWG基函数建立的矩阵方程组的未知数非常多,不利于大规模散射问题的数值计算。本文提出建立介质体的广义传输矩阵(GTM),将介质体的散射特征从介质体内部转化至表面上来,只需通过基于面网格划分的广义传输矩阵唯一表示介质体的散射特征,该介质体在表面外的散射场即可通过GTM得到有效的求解。在介质阵列散射问题中,只需分别计算并调用每个介质体单元的GTM,利用各个单元GTM之间的关系建立广义面积分方程(GSIE)进而求解散射场。GSIE的系统规模能够在矩量法的基础上大大减小,在GSIE的基础上再次应用SBF,可以进一步压缩系统未知数,从而使计算机的内存与CPU能够适应以往难以处理的大规模介质体的电磁散射求解问题。
To improve the numerical methods on electromagnetic scattering problems is always the research hotspot in computational electromagnetics. To efficiently analyze the scattering of large-scale structures, it is significant to extract the scattering characteristics of the scatterer effectively and use reduced information to achieve the accurate results. This paper proposes the method of synthetic basis functions (SBF), which is based on the conventional method of moments (MoM). The SBF method can establish the scattering solution space of every scatterer, and extract scattering characteristics from the space as SBFs. In large-scale conductor array scattering problems, the SBF linear system has much less number of unknowns than the conventional MoM, thus leading to higher efficiency in numerical computation.
In scattering of dielectric, including chiral and bianisotropic bodies, this paper discusses the conventional MoM in detail, in which the linear system is based on the volume mesh and SWG basis functions and usually has too many unknowns to solve. We propose to generate the generalized transition matrix (GTM) of the dielectric bodies by equaling the volume scattering characteristics of the scatterer onto its surface, and using the GTM on surface to calculate the far field scattering fields. In dielectric array scattering problem, it is effective to generate the GTM of every scattering unit, and establish the generalized surface integral equations (GSIE) based on GTMs of all units. The linear system is much smaller than the conventional MoM. And by introducing the SBF onto the GSIE system, the number of unknowns can be reduced further, thus make the computer memory and CPU possible to deal with the large-scale dielectric structures which can hardly be analyzed by conventional methods.
同时,针对非均匀介质(包括手征介质与双各向异性介质)散射问题,本文给出了基于SWG基函数的矩量法数值求解过程。传统矩量法建立在体网格划分上,通过SWG基函数建立的矩阵方程组的未知数非常多,不利于大规模散射问题的数值计算。本文提出建立介质体的广义传输矩阵(GTM),将介质体的散射特征从介质体内部转化至表面上来,只需通过基于面网格划分的广义传输矩阵唯一表示介质体的散射特征,该介质体在表面外的散射场即可通过GTM得到有效的求解。在介质阵列散射问题中,只需分别计算并调用每个介质体单元的GTM,利用各个单元GTM之间的关系建立广义面积分方程(GSIE)进而求解散射场。GSIE的系统规模能够在矩量法的基础上大大减小,在GSIE的基础上再次应用SBF,可以进一步压缩系统未知数,从而使计算机的内存与CPU能够适应以往难以处理的大规模介质体的电磁散射求解问题。
To improve the numerical methods on electromagnetic scattering problems is always the research hotspot in computational electromagnetics. To efficiently analyze the scattering of large-scale structures, it is significant to extract the scattering characteristics of the scatterer effectively and use reduced information to achieve the accurate results. This paper proposes the method of synthetic basis functions (SBF), which is based on the conventional method of moments (MoM). The SBF method can establish the scattering solution space of every scatterer, and extract scattering characteristics from the space as SBFs. In large-scale conductor array scattering problems, the SBF linear system has much less number of unknowns than the conventional MoM, thus leading to higher efficiency in numerical computation.
In scattering of dielectric, including chiral and bianisotropic bodies, this paper discusses the conventional MoM in detail, in which the linear system is based on the volume mesh and SWG basis functions and usually has too many unknowns to solve. We propose to generate the generalized transition matrix (GTM) of the dielectric bodies by equaling the volume scattering characteristics of the scatterer onto its surface, and using the GTM on surface to calculate the far field scattering fields. In dielectric array scattering problem, it is effective to generate the GTM of every scattering unit, and establish the generalized surface integral equations (GSIE) based on GTMs of all units. The linear system is much smaller than the conventional MoM. And by introducing the SBF onto the GSIE system, the number of unknowns can be reduced further, thus make the computer memory and CPU possible to deal with the large-scale dielectric structures which can hardly be analyzed by conventional methods.
引文
[1] M. I. Aksun, Ayta? Alparslan, and E. P. Karabulut,“Determining the Effective Constitutive Parameters of Finite Periodic Structures: Photonic Crystals and Metamaterials,”IEEE Trans. Microw. Theory Tech., vol. 56, no. 6, pp. 1423-1434, Jun. 2008.
[2] Thomas X. Wu, Dwight L. Jaggard,“Scattering of Chiral Periodic Structure,”IEEE Trans. Antennas Propagat., vol. 52, no. 7, pp. 1859-1870, Jul. 2004.
[3] G. Pelosi, A. Cocchi, and S. Selleri,“Electromagnetic Scattering from Infinite PeriodicStructures with a Localized Impurity,”IEEE Trans. Antennas Propagat., vol. 49, no. 5, pp. 697-702, May 2001.
[4] J. A. Stratton, Electromagnetic Theory, New York: McGraw-Hill, 1941
[5] R. F. Harrington, Field Computation by Moment Methods. New York: Macmilan, 1968.王尔杰译.计算电磁场的矩量法.北京:国防工业出版社, 1981.
[6] J. H. Richmond,“Scattering by a dielectric cylinder of arbitrary cross section shape,”IEEE Trans. Antennas Propagat., vol. AP-13, no. 3, pp. 334-341, 1965.
[7] Johnson J. H. Wang, Generalized Moment Methods in Electromagnetics: Formulation and Computer Solution of Integral Equations, New York: John Wiley, 1991.
[8] S. M. Rao, D. R. Wilton, and A. W. Glisson,“Electromagnetic Scattering by surfaces of arbitrary shape,”IEEE Trans. Antennas Propagat., vol. AP-30, no. 3, pp. 409-418, May 1982.
[9] D. H. Schaubert, D. R. Wilton and A. W. Glisson,“A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,”IEEE Trans. Antennas Propagat., vol. AP-32, no. 1, pp. 77-85, January 1984.
[10] You-Lin Geng, Xin-Bao Wu, and Bo-Ran Guan,“Electromagnetic Scattering from an Anisotropic Uniaxial-coated Conducting Sphere,”Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26.
[11]鲍健.任意形状双各向同性旋转体的电磁散射问题[学位论文].香港:香港城市大学. 2007
[12] You-Lin Geng and Sailing He,“Spherical vector wave functions solution to scattering of a plane wave by a spherical shell of uniaxial anisotropic left-handed material,”Microwave and Optical Technology Letters, vol. 50, no. 8, August 2008.
[13] R. G. Kouyoumjian,“Asymptotic high-frequency methods,”in Proc. IEEE, vol. 63, pp. 864-876, Aug. 1965.
[14] P. H. Pathak, N. Wang, W. D. Burnside and R. G. Kouyoumjian,“A uniform GTD solution for the radiation from sources on a convec surface,”IEEE Trans. Antennas Propagat., vol. 29, pp. 609-621, July 1981.
[15] P. Ya. Ufimtsev,“Elementary edge waves and the physical theory of diffraction,”Electromagn., vol. 11, pp. 125-160, Apr.-June 1991.
[16] R. Coifman, V. Rokhlin, and S. Wandzura,“The fast multipole method for the wave equation: A pedestrian prescription,”IEEE Antennas Propagat. Mag., vol. 35, no. 3, pp. 7–12, Jun. 1993.
[17] J. M. Song and W. C. Chew,“Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering,”Microwave Opt. Tech. Lett., vol. 10, no. 1, pp. 14–19, Sept. 1995.
[18] V. V. S. Prakash and R. Mittra,“Characteristic basis function method: A new technique for efficent solution of method of moments matrix quations,”Microwave Opt. Technol. Lett., vol. 36, pp. 95–100, Jan. 2003.
[19] J. Yeo, V. V. S. Prakash, and R. Mittra,“Efficient analysis of a class of microstrip antennas using the characteristic basis fucntion method (CBFM),”Microwave Opt. Technol. Lett., vol. 39, pp. 456–464, Dec. 2003.
[20] J. Yeo and R. Mittra,“Numerically efficient analysis of microstrip antennas using the characteristic basis function method (CBFM),”in Proc.IEEE AP-S Int. Symp., Columbus, OH, June 2003.
[21] L. Xu, Z. Nie, and J. Hu,“Investigation on Solving Electromagnetic Scattering by Characteristic Basis Function Method,”International Conference on Computational Electromagnetics, 2004.
[22] C. Delgado, R. Mittra, and F. Cátedra,“Accurate Representation of the Edge Behavior of Current When Using PO-Derived Characteristic Basis Functions,”IEEE Antenna and Wireless Propagation Letters, vol. 7, pp. 43-45, 2008.
[23] W. B. Lu, T. J. Cui, Z. G. Qian, X. X. Yin, and W. Hong,“Accurate Analysis of Large-Scale Periodic Structures Using an Efficient Sub-Entire-Domain Basis Function Method,”IEEE Trans. Antennas Propagat., vol. 52, no. 11, pp. 3078-3085, Nov. 2004.
[24] W. B. Lu, T. J. Cui, and H. Zhao,“Acceleration of Fast Multipole Method for Large-Scale Periodic Structures With Finite Sizes Using Sub-Entire-Domain Basis Functions,”IEEE Trans. Antennas Propagat., vol. 55, no. 2, pp. 414-421, Feb. 2007.
[25] L. Matekovits, G. Vecchi, G. Dassano, and M. Orefice,“Synthetic function analysis of large printed structures: The solution space sampling approach,”in Proc. IEEE AP-S Int. Symp., Boston, MA, pp. 568–571. July 2001.
[26] P. Focardi, A. Freni, S. Maci, and G. Vecchi,“Efficient analysis of arrays of rectangular corrugated horns: The synthetic aperture function approach,”IEEE Trans. Antennas Propag., vol. AP-53, no. 2, pp. 601–607, Feb. 2005.
[27] L. Matekovits, V. A. Laza, G. Vecchi,“Analysis of Large Complex Structures With the Synthetic-Functions Approach,”IEEE Trans. Antennas Propagat., vol. 55, no. 9, pp. 2509-2521, Sep. 2007.
[28] Gaobiao Xiao, Junfa Mao, and Bin Yuan,“Generalized transition matrix for arbitrarily shaped scatterers or scatterer groups,”IEEE Trans. Antennas Propagat., vol. 56, no. 12, pp. 3723-3732, December 2008.
[29] Gaobiao Xiao, Junfa Mao and Bin Yuan,“A generalized surface integral equation formulation for analysis of complex electromagnetic systems,”IEEE Trans. Antennas Propagat., vol. 57, no. 3, pp. 701-710, March 2009.
[30]黎滨洪,金荣洪,张佩玉,电磁场与波,上海:上海交通大学出版社. 1996.
[31]盛新庆,计算电磁学要论,第二版,合肥:中国科学技术大学出版社. 2008.
[32]杨儒贵,电磁定理和原理及其应用,成都:西南交通大学出版社. 2000
[33] Jin Au Kong著,吴季等译,电磁波理论,北京:电子工业出版社. 2003.
[34]何国瑜,卢才成等,电磁散射的计算与测量,北京:北京航空航天大学出版社. 2006.
[35]金建铭,电磁场有限元方法,西安:西安电子科技大学出版社. 2004.
[36] R. E. Hodges and Y. Rahmat-Smaii,“The evaluation of MFIE integrals with the use of vector triangle basis functions,”Microwave Opt. Tech. Lett., vol. 14, pp. 9-14, Jan. 1997.
[37]王勖成,邵敏,有限单元法基本原理和数值方法,北京:清华大学出版社. 1997.
[38] D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak and C. M. Butler,“Potential integrals for uniform and linear source distributions on polygonal andpolyhedral domains,”IEEE. Trans. Antennas Propagat., vol. AP-32, no. 3, pp. 276-281, March 1984.
[39] O. M. Bucci and G. Franceschetti,“On the degrees of freedom of scattered fields,”IEEE Trans. Antennas Propag., vol. AP-37, no. 7, pp. 918–926, July 1989.
[40] Moamer Hasanovic,“Electromagnetic scattering from an arbitrarily shaped three-dimensional inhomogeneous chiral body,”[Dissertation], Syracuse University, 2006.
[41] M. Hasanovic, Mei Chong, J. R. Mautz, and E. Arvas,“Scattering from 3-D inhomogeneous chiral bodies of arbitrary shape by the method of moments,”IEEE Trans. Antennas Propagat., vol. 55, no. 6, pp. 1817-1825, June 2007.
[42] R. D. Graglia,“On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,”IEEE Trans. Antennas Propagat., vol. 41, pp. 1448-1455, Oct. 1993.
[43] C. Mei, M. Hasanovic, J. K. Lee, and E. Arvas,“Electromagnetic scattering from an arbitrarily shaped three-dimensional inhomogeneous bianisotropic body,”PIERS Online, vol. 3, no. 5, pp. 680-684, 2007.
[44] G. Kobidze, and B. Shanker,“Integral equation based analysis of scattering from 3-D inhomogeneous anisotropic bodies,”IEEE Trans. Antennas Propagat., vol. 52, no. 10, pp. 2650-2658, Oct. 2004.
[45] L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves-Theories and Applications. New York: Wiley, 2000.
[46]戴振铎,电磁理论中的并矢格林函数,武汉:武汉大学出版社. 2005.
[47] M. F. R. Cooray, I. R. Ciric,“Wave scattering by a chiral spheroid,”Journal of the Optical Society of American A: Optics, Image Science and Vision, Vol. 10, No. 6, pp. 1197-1203, June 1993.
[48] Yu. A. Ryzhov, V. V. Tamoikin, Radiation and Propagation of Electromagnetic Waves In Randomly Inhomogeneous Media. New York: Consultants Bureau. 1973.
[49] You Lin Geng, Xin Bao Wu, Le Wei Li, Bo Ran Guan,“Mie scattering by a uniaxial anisotropic sphere,”Physical Review, E70, 056609, 2004.
[2] Thomas X. Wu, Dwight L. Jaggard,“Scattering of Chiral Periodic Structure,”IEEE Trans. Antennas Propagat., vol. 52, no. 7, pp. 1859-1870, Jul. 2004.
[3] G. Pelosi, A. Cocchi, and S. Selleri,“Electromagnetic Scattering from Infinite PeriodicStructures with a Localized Impurity,”IEEE Trans. Antennas Propagat., vol. 49, no. 5, pp. 697-702, May 2001.
[4] J. A. Stratton, Electromagnetic Theory, New York: McGraw-Hill, 1941
[5] R. F. Harrington, Field Computation by Moment Methods. New York: Macmilan, 1968.王尔杰译.计算电磁场的矩量法.北京:国防工业出版社, 1981.
[6] J. H. Richmond,“Scattering by a dielectric cylinder of arbitrary cross section shape,”IEEE Trans. Antennas Propagat., vol. AP-13, no. 3, pp. 334-341, 1965.
[7] Johnson J. H. Wang, Generalized Moment Methods in Electromagnetics: Formulation and Computer Solution of Integral Equations, New York: John Wiley, 1991.
[8] S. M. Rao, D. R. Wilton, and A. W. Glisson,“Electromagnetic Scattering by surfaces of arbitrary shape,”IEEE Trans. Antennas Propagat., vol. AP-30, no. 3, pp. 409-418, May 1982.
[9] D. H. Schaubert, D. R. Wilton and A. W. Glisson,“A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies,”IEEE Trans. Antennas Propagat., vol. AP-32, no. 1, pp. 77-85, January 1984.
[10] You-Lin Geng, Xin-Bao Wu, and Bo-Ran Guan,“Electromagnetic Scattering from an Anisotropic Uniaxial-coated Conducting Sphere,”Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26.
[11]鲍健.任意形状双各向同性旋转体的电磁散射问题[学位论文].香港:香港城市大学. 2007
[12] You-Lin Geng and Sailing He,“Spherical vector wave functions solution to scattering of a plane wave by a spherical shell of uniaxial anisotropic left-handed material,”Microwave and Optical Technology Letters, vol. 50, no. 8, August 2008.
[13] R. G. Kouyoumjian,“Asymptotic high-frequency methods,”in Proc. IEEE, vol. 63, pp. 864-876, Aug. 1965.
[14] P. H. Pathak, N. Wang, W. D. Burnside and R. G. Kouyoumjian,“A uniform GTD solution for the radiation from sources on a convec surface,”IEEE Trans. Antennas Propagat., vol. 29, pp. 609-621, July 1981.
[15] P. Ya. Ufimtsev,“Elementary edge waves and the physical theory of diffraction,”Electromagn., vol. 11, pp. 125-160, Apr.-June 1991.
[16] R. Coifman, V. Rokhlin, and S. Wandzura,“The fast multipole method for the wave equation: A pedestrian prescription,”IEEE Antennas Propagat. Mag., vol. 35, no. 3, pp. 7–12, Jun. 1993.
[17] J. M. Song and W. C. Chew,“Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering,”Microwave Opt. Tech. Lett., vol. 10, no. 1, pp. 14–19, Sept. 1995.
[18] V. V. S. Prakash and R. Mittra,“Characteristic basis function method: A new technique for efficent solution of method of moments matrix quations,”Microwave Opt. Technol. Lett., vol. 36, pp. 95–100, Jan. 2003.
[19] J. Yeo, V. V. S. Prakash, and R. Mittra,“Efficient analysis of a class of microstrip antennas using the characteristic basis fucntion method (CBFM),”Microwave Opt. Technol. Lett., vol. 39, pp. 456–464, Dec. 2003.
[20] J. Yeo and R. Mittra,“Numerically efficient analysis of microstrip antennas using the characteristic basis function method (CBFM),”in Proc.IEEE AP-S Int. Symp., Columbus, OH, June 2003.
[21] L. Xu, Z. Nie, and J. Hu,“Investigation on Solving Electromagnetic Scattering by Characteristic Basis Function Method,”International Conference on Computational Electromagnetics, 2004.
[22] C. Delgado, R. Mittra, and F. Cátedra,“Accurate Representation of the Edge Behavior of Current When Using PO-Derived Characteristic Basis Functions,”IEEE Antenna and Wireless Propagation Letters, vol. 7, pp. 43-45, 2008.
[23] W. B. Lu, T. J. Cui, Z. G. Qian, X. X. Yin, and W. Hong,“Accurate Analysis of Large-Scale Periodic Structures Using an Efficient Sub-Entire-Domain Basis Function Method,”IEEE Trans. Antennas Propagat., vol. 52, no. 11, pp. 3078-3085, Nov. 2004.
[24] W. B. Lu, T. J. Cui, and H. Zhao,“Acceleration of Fast Multipole Method for Large-Scale Periodic Structures With Finite Sizes Using Sub-Entire-Domain Basis Functions,”IEEE Trans. Antennas Propagat., vol. 55, no. 2, pp. 414-421, Feb. 2007.
[25] L. Matekovits, G. Vecchi, G. Dassano, and M. Orefice,“Synthetic function analysis of large printed structures: The solution space sampling approach,”in Proc. IEEE AP-S Int. Symp., Boston, MA, pp. 568–571. July 2001.
[26] P. Focardi, A. Freni, S. Maci, and G. Vecchi,“Efficient analysis of arrays of rectangular corrugated horns: The synthetic aperture function approach,”IEEE Trans. Antennas Propag., vol. AP-53, no. 2, pp. 601–607, Feb. 2005.
[27] L. Matekovits, V. A. Laza, G. Vecchi,“Analysis of Large Complex Structures With the Synthetic-Functions Approach,”IEEE Trans. Antennas Propagat., vol. 55, no. 9, pp. 2509-2521, Sep. 2007.
[28] Gaobiao Xiao, Junfa Mao, and Bin Yuan,“Generalized transition matrix for arbitrarily shaped scatterers or scatterer groups,”IEEE Trans. Antennas Propagat., vol. 56, no. 12, pp. 3723-3732, December 2008.
[29] Gaobiao Xiao, Junfa Mao and Bin Yuan,“A generalized surface integral equation formulation for analysis of complex electromagnetic systems,”IEEE Trans. Antennas Propagat., vol. 57, no. 3, pp. 701-710, March 2009.
[30]黎滨洪,金荣洪,张佩玉,电磁场与波,上海:上海交通大学出版社. 1996.
[31]盛新庆,计算电磁学要论,第二版,合肥:中国科学技术大学出版社. 2008.
[32]杨儒贵,电磁定理和原理及其应用,成都:西南交通大学出版社. 2000
[33] Jin Au Kong著,吴季等译,电磁波理论,北京:电子工业出版社. 2003.
[34]何国瑜,卢才成等,电磁散射的计算与测量,北京:北京航空航天大学出版社. 2006.
[35]金建铭,电磁场有限元方法,西安:西安电子科技大学出版社. 2004.
[36] R. E. Hodges and Y. Rahmat-Smaii,“The evaluation of MFIE integrals with the use of vector triangle basis functions,”Microwave Opt. Tech. Lett., vol. 14, pp. 9-14, Jan. 1997.
[37]王勖成,邵敏,有限单元法基本原理和数值方法,北京:清华大学出版社. 1997.
[38] D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak and C. M. Butler,“Potential integrals for uniform and linear source distributions on polygonal andpolyhedral domains,”IEEE. Trans. Antennas Propagat., vol. AP-32, no. 3, pp. 276-281, March 1984.
[39] O. M. Bucci and G. Franceschetti,“On the degrees of freedom of scattered fields,”IEEE Trans. Antennas Propag., vol. AP-37, no. 7, pp. 918–926, July 1989.
[40] Moamer Hasanovic,“Electromagnetic scattering from an arbitrarily shaped three-dimensional inhomogeneous chiral body,”[Dissertation], Syracuse University, 2006.
[41] M. Hasanovic, Mei Chong, J. R. Mautz, and E. Arvas,“Scattering from 3-D inhomogeneous chiral bodies of arbitrary shape by the method of moments,”IEEE Trans. Antennas Propagat., vol. 55, no. 6, pp. 1817-1825, June 2007.
[42] R. D. Graglia,“On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,”IEEE Trans. Antennas Propagat., vol. 41, pp. 1448-1455, Oct. 1993.
[43] C. Mei, M. Hasanovic, J. K. Lee, and E. Arvas,“Electromagnetic scattering from an arbitrarily shaped three-dimensional inhomogeneous bianisotropic body,”PIERS Online, vol. 3, no. 5, pp. 680-684, 2007.
[44] G. Kobidze, and B. Shanker,“Integral equation based analysis of scattering from 3-D inhomogeneous anisotropic bodies,”IEEE Trans. Antennas Propagat., vol. 52, no. 10, pp. 2650-2658, Oct. 2004.
[45] L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves-Theories and Applications. New York: Wiley, 2000.
[46]戴振铎,电磁理论中的并矢格林函数,武汉:武汉大学出版社. 2005.
[47] M. F. R. Cooray, I. R. Ciric,“Wave scattering by a chiral spheroid,”Journal of the Optical Society of American A: Optics, Image Science and Vision, Vol. 10, No. 6, pp. 1197-1203, June 1993.
[48] Yu. A. Ryzhov, V. V. Tamoikin, Radiation and Propagation of Electromagnetic Waves In Randomly Inhomogeneous Media. New York: Consultants Bureau. 1973.
[49] You Lin Geng, Xin Bao Wu, Le Wei Li, Bo Ran Guan,“Mie scattering by a uniaxial anisotropic sphere,”Physical Review, E70, 056609, 2004.