色散媒质的瞬态电磁特性研究
|
摘要
自然界中绝大部分物质属于色散媒质，研究和了解色散媒质的宽频特性对推动现代通信与信息技术、生物电子科学、材料科学和空间技术等领域的科技发展及应用具有非常重要的意义。而由于色散媒质特性的复杂性，其瞬态电磁特性研究作为电磁学领域的前沿研究课题之一，历来是电磁研究中的难题，至今尚未得到很好的解决。本文着重在数学模型建立和色散媒质瞬态电磁特性研究两方面进行研究工作：
首先，本文基于数字信号处理技术建立和完善新的适用于色散媒质瞬态电磁特性研究的时域有限差分法((FD)~2TD)，以提高其有效性和普适性。基于对数字滤波器频响特性和媒质色散特性相似性的考虑，提出了采用无限冲激响应滤波器(ⅡR)模拟色散媒质特性的新思路。在此基础上，结合数字信号处理给出了基于复介电常数的(FD)~2TD-PF法和基于电导率的(FD)~2TD-CF法。并对新算法的数值色散关系、稳定性条件和适用范围等进行深入研究。另外借助MATLAB数值软件包及其提供的数字信号处理工具，对新算法进行改进和完善。
第二，在(FD)~2TD法中引入离散时间系统的概念，建立了新的适用于任意色散媒质的吸收边界条件，并对其吸收效果及稳定性条件进行了研究。
第三，利用所建立的新数学模型与方法对色散媒质的瞬态电磁特性及其作用机理进行分析与研究。运用新的(FD)~2TD算法和
2001年上海大学博士学位论文
小波变换对色散媒质的瞬态电磁传播特性进行系统研究与分析，
尤其是分析与比较各类色散媒质电参量对瞬态电磁波传播特性
的影响。并且以典型色散媒质为例，对不同形状色散目标及多层
色散媒质柱体目标的时域散射特性进行数值模拟与分析.通过对
简化色散媒质模型进行时域散射测量，与数值结果进行对比。研
究表明色散媒质材质的影响在瞬态电磁波的传播及散射中具有
一致的反映，主要体现在物体瞬态电磁的后期响应;目标的几何
信息则主要体现在早期响应中。
最后，简要论述了目标识别的方法，讨论色散媒质的瞬态特
性研究对目标识别的意义和作用。为开拓瞬态电磁场应用的新方
法与新技术，特别是色散目标识别新技术，提供必要的理论基础
与依据。
It is of great importance to study the transient electromagnetic characteristics of dispersive media owing to its promotive effects in many fields of engineering interest. However, due to the complexity of the dispersive media, the study of the transient electromagnetic characteristics, the leading research in the electromagnetic field, remains one of the unsolved problems. In this paper attention is paid to the model theories of transient electromagnetic problems of dispersive media and the study of the transient electromagnetic characteristics.
Firstly, based on the digital signal processing, a new frequency-dependent finite-difference time-domain ((FD)2TD) method for arbitrary dispersive media is established and improved. The validity of the new numerical method is improved and the application is extended to dispersive media. The dispersion of media is modeled with the infinite-impulsive response filters (IIR). In this paper two (FD)2TD methods based on the permittivity or conductivity are proposed and their numerical dispersion, stability and applicability are also studied.
Secondly, based on the concepts of discrete system a new absorbing boundary condition for arbitrary dispersive media is derived. Its stability and efficiency are also studied.
Thirdly, the transient electromagnetic problems of dispersive media are simulated and studied with the new (FD)2TD method built
in this paper. The propagation and scattering characteristics of dispersive media are studied in-depth in time-domain. The (FD)2TD method and Wavlet transform are applied to analyze the transient propagation in dispersive media. The scattering of several objects with different shape and complex objects formed with multi-layer dispersive media are simulated. The simple experiment models for dispersive media are built and the measurement results are compared to the numerical solutions. It is shown that the media information is indicated in the late-time response of the transient response, while the geometry information is indicated in the early-time response.
Finally, the method of object identification including the significance of the research in this paper is discussed briefly. The research in this paper has laid a foundation for the object identification.
首先，本文基于数字信号处理技术建立和完善新的适用于色散媒质瞬态电磁特性研究的时域有限差分法((FD)~2TD)，以提高其有效性和普适性。基于对数字滤波器频响特性和媒质色散特性相似性的考虑，提出了采用无限冲激响应滤波器(ⅡR)模拟色散媒质特性的新思路。在此基础上，结合数字信号处理给出了基于复介电常数的(FD)~2TD-PF法和基于电导率的(FD)~2TD-CF法。并对新算法的数值色散关系、稳定性条件和适用范围等进行深入研究。另外借助MATLAB数值软件包及其提供的数字信号处理工具，对新算法进行改进和完善。
第二，在(FD)~2TD法中引入离散时间系统的概念，建立了新的适用于任意色散媒质的吸收边界条件，并对其吸收效果及稳定性条件进行了研究。
第三，利用所建立的新数学模型与方法对色散媒质的瞬态电磁特性及其作用机理进行分析与研究。运用新的(FD)~2TD算法和
2001年上海大学博士学位论文
小波变换对色散媒质的瞬态电磁传播特性进行系统研究与分析，
尤其是分析与比较各类色散媒质电参量对瞬态电磁波传播特性
的影响。并且以典型色散媒质为例，对不同形状色散目标及多层
色散媒质柱体目标的时域散射特性进行数值模拟与分析.通过对
简化色散媒质模型进行时域散射测量，与数值结果进行对比。研
究表明色散媒质材质的影响在瞬态电磁波的传播及散射中具有
一致的反映，主要体现在物体瞬态电磁的后期响应;目标的几何
信息则主要体现在早期响应中。
最后，简要论述了目标识别的方法，讨论色散媒质的瞬态特
性研究对目标识别的意义和作用。为开拓瞬态电磁场应用的新方
法与新技术，特别是色散目标识别新技术，提供必要的理论基础
与依据。
It is of great importance to study the transient electromagnetic characteristics of dispersive media owing to its promotive effects in many fields of engineering interest. However, due to the complexity of the dispersive media, the study of the transient electromagnetic characteristics, the leading research in the electromagnetic field, remains one of the unsolved problems. In this paper attention is paid to the model theories of transient electromagnetic problems of dispersive media and the study of the transient electromagnetic characteristics.
Firstly, based on the digital signal processing, a new frequency-dependent finite-difference time-domain ((FD)2TD) method for arbitrary dispersive media is established and improved. The validity of the new numerical method is improved and the application is extended to dispersive media. The dispersion of media is modeled with the infinite-impulsive response filters (IIR). In this paper two (FD)2TD methods based on the permittivity or conductivity are proposed and their numerical dispersion, stability and applicability are also studied.
Secondly, based on the concepts of discrete system a new absorbing boundary condition for arbitrary dispersive media is derived. Its stability and efficiency are also studied.
Thirdly, the transient electromagnetic problems of dispersive media are simulated and studied with the new (FD)2TD method built
in this paper. The propagation and scattering characteristics of dispersive media are studied in-depth in time-domain. The (FD)2TD method and Wavlet transform are applied to analyze the transient propagation in dispersive media. The scattering of several objects with different shape and complex objects formed with multi-layer dispersive media are simulated. The simple experiment models for dispersive media are built and the measurement results are compared to the numerical solutions. It is shown that the media information is indicated in the late-time response of the transient response, while the geometry information is indicated in the early-time response.
Finally, the method of object identification including the significance of the research in this paper is discussed briefly. The research in this paper has laid a foundation for the object identification.
引文
1 方俊鑫，殷之文．电介质物理学．北京：科学出版社，1989
2 陈季丹，刘子玉．电介质物理学．北京：机械工业出版社，1982
3 孟中岩等．电介质理论基础．北京：国防工业出版社，1980
4 Cole K.S., et al. Dispersion and absorption in dielectrics. J.Chem. Phys., 1941; 9:341-351
5 Wait J.R. Complex resistivity of the earth. In: Kong J.A. ed. Progress in Electromagnetic Research, New York: Elsevier, 1989
6 Gabriel S., et al. The dielectric properties of biological tissiues: Part 3—parametric models for the dielectric spectrum of tissues. Phys. Med. Biol., 1996; 41:2271-2293
7 Hurt W. P. Multiterm debye dispersion relations for permittivity of muscle, IEEE Trans. Biomed. Eng., 1985; 32:60-63
8 彭仲秋．瞬变电磁场．北京：高等教育出版社，1989
9 张文俊等．瞬变电磁波在色散媒质中的传播和散射．电子学报，1994；22：48-53
10 张文俊等．N 阶色散媒质的瞬态传播特性．上海大学学报，1995；1：533-541
11 张文俊等．N 阶色散媒质的瞬态散射特性．微波学报，1996；12：9-14
12 高本庆等．色散媒质中电磁场的时域有限差分算法．中国科学(A辑)，1994：24：538-545
13 Mrozowski M., et al. Parameterzation of media dispersive properties for FDTD. IEEE Trans. AP, 1997; ,15(9): 1438-1440
14 Kunz K.S., Luebbers R.J. The Finite Difference Time Domain Method for Electromagnetics, CRC Press. Inc., 1993:1-49
15 Taflove. Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrry structures. Wave Motion, 1988; 10(12): 547-582
16 Simons N.R.S., et al. Equivalence of propagation characteristics for the transmission line matrix and finite-difference time-domain methods in two dimensions. IEEE Trans, 1991; 39:354-356
17 Lee J.-E, et al. Time-domain finite-element methods. IEEE Trans. AP, 1997; 45(3): 430-441
18 Nikoskinen K.I. Time-domain study of half-space transmission problem with vertical and horizontal dipoles. IEEE. Trans. AP, 1993; 41(10): 1399-1407
19 Joseph R.M., et al. Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtoseeond electromagnetic pulses. Opt. Lett., 1991; 16:1412-1414
20 Goorjian P.L., et al. Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtoseeond electromagnetic solutions. Opt. Lett., 1992; 17:180-182
21 Walker S.P. Developments in time-domain integral equation modeling at imperial college. IEEE. AP Magazine, 1997; 39:7-19
22 Kragalott M., et al. Time-domain fields exterior to a two-dimensional FDTD space. IEEE. Trans. AP, 1997; 45(11): 1655-1663
23 张云华．电磁辐射与散射问题的传输线矩阵方法数值模拟研究．浙江大学博士论文
24 Cerri G., et al. Field penetration through slots into shielded enclosures:a time domain approach. IEEE. Trans. EMC, 1997; 39(4): 377-385
25 Lazzi G., et al. On modeling and personal dosimetry of cellular telephone helical antennas with the FDTD code. IEEE. Trans. AP, 1998; 46(4): 525-530
26 Chen H.-Y., et aL Analysis of electromagnetic radiation from a video output amplifier inside a monitor by using FDTD method. IEEE. Trans. EMC, 1997; 39(4): 394-397
27 Smith G.S., et al. A scale model for studying ground penetrating radars. IEEE. Trans. Geoscience and Remote Sensing, 1989; 27(4): 358-363
28 Shlager K.L., Schneider J.B. A selective survey of the finite-differencetime-domain literature. IEEE. AP.Mag., 1995; 37(8): 39-57
29 Luebbers R., Hunsberger E P., Kunz K. S., et al. A frequency-dependent finite-difference time-domain formulation for dispersive materials. IEEE Trans. EMC, 1990; 32:222-227
30 Luebbers R., et al. A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma. IEEE Trans. AP, 1991; 39: 29-34
31 Luebbers R., Hunsberger F.P FDTD for Nth-order dispersive media. IEEE Trans. AP, 1992; 40:1297-1301,
32 Luebbers R. J., et al. FDTD for Nth-order dispersive media. IEEE Trans. AP, 1992; 40(11): 1297-1301
33 Nickisch L.J., et al. Finite-difference time-domain solution of Maxwell's equations for the dispersive ionosphere. IEEE AP Magazine, 1992; 34(5): 33-39
34 Kashiwa T., et al. Transient analysis of magnetized plasma in three-dimensional space. IEEE. Trans. AP.., 1988; 36(8): 1096-1105
35 Tortes E, et al. Complete FDTD analysis of microwave heating processes in frequency-dependent and temperature-dependent media. IEEE Trans. MTT, 1997; 45(1): 108-117
36 Gandhi O.E, et al. A frequency-dependent finite-difference time-domain formulation for general dispersive media. 1993; 41(4): 658-665
37 Sullivan D.M., et al. Use of the finite-difference time-domain method in
calculation EM absorption in human tissues. IEEE Trans. Biomed. Eng., 1987; 34:148-157
38 Sullivan D.M., et al. Use of the finite-difference time-domain method in calculation EM absorption in man models. IEEE Trans. Biomed. Eng., 1988; 35:179-186
39 Sullivan D.M. A frequency-dependent FDTD method for biological applications. IEEE Trans. AP., 1991; 39(1): 29-34
40 Sullivan D.M. Frequency-dependent FDTD methods using z transforms. IEEE Trans. AP, 1992; 40(10): 1223-1230
41 Sullivan D.M. Z-transform theory and the FDTD method. IEEE. Trans. AP, 1996; 44(1): 28-34
42 Sullivan D.M. Mathmatical methods for treatment planning in deep regional hyperthermia. IEEE Trans. MTT, 1991; 39:864-872
43 Bui M. D., et al. propagation of transients in dispersive dielectric media. IEEE. Trans. MTT., 1991; 39(7): 1165-1172
44 胡广书．数字信号处理．北京：清华大学出版社，1997
45 Taflove, et al. The finite-difference time-domain method for numerical modeling of electromagnetic wave interactions. Electromagn., 1990; 10:105-126
46 Kunz K.S., et al. A three dimensional finite-difference solution of the external response of an aircraft to a complox transient EM environment: Part Ⅰ-Method and its implomentation. IEEE. Trans. EMC., 1978; 20(2):328-341
47 Wang Yuanxun, et al. Multimode parameter extraction for multiconductor transmission lines via single-pass FDTD and signal-processing techniques. IEEE Trans. MTT, 1998; 46(1): 89-95
48 Ko W.L., et al. A combination of FDTD and Prony's methods for analyzing microwave integrated circuits. IEEE Trans. MTT, 1991; 39(12): 2176-2181
49 Dawson J.E Representing ferrite absorbing tiles as frequency dependent boundaries in TLM. Electronics Lett., 1993; 29(9): 791-792
50 张志涌等．掌握和精通MATLAB．北京航空航天大学出版社，1997
51 Zhou J.Y., et al. Construction of the absorbing boundary conditions for the FDTD method with transfer functions. IEEE Trans.MTT, 1998; 46(11)
52 Blaschak J.G. A comparative study of absorbing boundary conditions. J. Computat. Phys., 1988; 77:109-139
53 Keller J.B., et al. Exact non-reflecting boundary conditions. J.Computat. Phys., 1989; 82:172-192
54 Lindma E.L. F ree space boundary conditions for the time dependent wave equation. J. Computa. Phys., 1988; 6(10): 427-475
55 Peng Jian, et al. A generalized reflection-free domain-truncation method: transparent absorbing boundary. IEEE Trans. AP, 1998; 46(7): 1015-1022
56 Tromp E.N.M., et al. Synthesis of absorbing boundary conditions for the FDTD method:numerical results. IEEE Trans. AP, 1995; (2): 213-215
57 Mur G. Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations. IEEE. Trans. EMC, 1981; 23(4): 377-382
58 Engquist B. Absorbing boundary conditions for the numerical simulation of wave. Math. Comput., 1977; 13(139): 629-651
59 Zhang X., Mei K.K. A super-absorbing boundary algorithm for numerical solving electromagnetic problems by time-domain finite difference method. IEEE Trans., MTT, 1988; 36(12): 1775-1787
60 Bi Zhiqiang, et al. A dicpersive boundary condition for microstrip component analysis using the FD-TD method. IEEE Trans. MTT, 1992; 40(4): 774-777
61 Moore T.G., et al. Theory and application of radiation boundary operators. IEEE Trans. MTT, 1988; 36:1797-1811
62 Higdon R.L. Absorbing boundary conditions for difference apporximations to the multi-dimensional wave equation. Math. Comput., 1986; 47(176): 437-459
63 Higdon R.L. Numerical absorbing boundary conditions for the wave equation. Math. Comput., 1987; 49(179): 65-90
64 Berenger J.P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys., 1994; 114(10): 185-200
65 Tang Jingwu, et al. Perfectly matched layer mesh terminations for nodal-based finite element methods in electromagnetics scattering. IEEE Trans. AP, 1998; 46(4): 507-516
66 Lau Y.C., et al. Extension of Berenger's PML boundary condition in matching lossy medium and evanescent waves. Electronics Letters, 1996; 32(11): 974-977
67 Wu J.Y., et al. A comparison of anisotropic PML to Berenger's PML and its application to the finite-element method for EM scattering. IEEE Trans. AP, 1997; 45(1): 40-50
68 Prescott D.T., et al. Reflection analysis of FDTD boundary conditions—part Ⅰ: time-space absorbing boundaries. IEEE Trans. MTT, 1997, 45(8): 1162-1177
69 Prescott D.T., et al. Reflection analysis of FDTD boundary conditions—part Ⅱ: Berenger's PML absorbing layers. IEEE Trans. MTT, 1997; 45(8): 1171-1178
70 Zhao P., et al. A new stable and very dispersive boundary condition for the FDTD method. IEEE Trans. MTT, 1993; 41:290-297
71 Ziolkowski R.W. Time-derivative Lorentz material model-based absorbing boundary condition. IEEE. Trans. AP, 1997; 45(10): 1530-1535
72 OppenheimA.V.,et al. 数字信号处理．北京：科学出版社，1980
73 Proakis J.G., et al. Digital Signal Processing, 2nd ed, New York:
Macmillan, 1992
74 Weedom W. H. A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media. IEEE. Trans. AP, 1997; 45(3): 401-409
75 Kumpel W., et al. Digital signal processing of time domain field simulation results using the system identification method. IEEE Trans. MTT, 1994; 42(4): 667-671
76 王长清．时域有限差分法原理．无线电电子汇刊，1988；10：38-48
77 王长清．FD-TD法计算机程序要领．无线电电子汇刊，1988；12：1-8
78 王长清．FD-TD法中的吸收边界条件．无线电电子汇刊，1988；11：49-57
79 王长清．FD-TD法在电磁工程中的应用．无线电电子汇刊，1998；1：9-18
80 Omick S.R., et al. A new finite-difference time-domain algorithm for the accurate modeling of wide-bank electromagnetic phenomena. IEEE. Trans. EMC, 1993; 35(2): 215-221
81 Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. AP, 1966; 14(5): 302-307
82 Taflove, et al. Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations. IEEE. Trans. MTT, 1975; 23(8): 623-630
83 Zhang Xiaolei, et al. Time-domain finite difference approach to the calculation of the frequency-dependent characteristics of microstrip discontnuities. IEEE Trans. MTT, 1988; 36(12): 1775-1787
84 Furse C.M., et al. Improvements to the finite-difference time-domain method for calculating the radar cross section of a perfectly conducting target. IEEE Trans. MTT, 1990; 38:919-927
85 Farias R.G., et al. The use of FDTD for the analysis of magnetoplasma channel waveguides. IEEE Trans. MTT., 1998; 46(4): 387-394
86 Gandhi O.P., et al. Electromagnetic absorption in the human head and neck for mobile telephones at 835 and 1900 MHz. IEEE Trans. MTT, 1996; 44(10): 1884-1897
87 Petropoulos P.G. Stability and phase error analysis of FD-TD in dispersive dielectrics. IEEE Trans. AP, 1994; 42(1): 62-69
88 Young J.L., et al. On the dispersion errors related to (FD)2TD type schemes. IEEE. Trans. MTT, 1995; 43(8): 1902-1909
89 Young J.L. Propagation in linear dispersive media:finite difference time domain methodologies. IEEE Trans. AP, 1995; 43:422-426
90 Young J.L. A full finite difference time domain implementation for radio wave propagation in a plasma. Radio Sci., 1994; 29:1513-1522
91 Hunsberger E, et al. Finite-difference time-domain analysis of gyrotropic media—Ⅰ: magnetized plasma. IEEE Trans. AP, 1992; 40(12): 1489-1495
92 Pontalti R., et al. A multi-relaxation (FD)2TD method for modeling dispersion in biological tissues. IEEE Trans. MTT, 1994; 42:526-528
93 Wang Tong, et al. FD-FDTD using DSP for arbitrary dispersive media. J. of Shanghai University, 2000; 4(3): 230-234
94 Nehrbass J.W., et al. Reducing the phase error for finite-difference methods without increasing the order. IEEE Trans. AP, 1998; 46(8): 1194-1201
95 Furse C.M., et al. The use of the frequency-dependent finite-difference time-domain method for induced current and SAR calculations for a heterogeneous model of the human body. IEEE. Trans. EMC, 1994; 36(2): 128-133
96 Yee K.S., et al. The finite-difference time-domain and finite-volume time-domain methods in solving maxwell's equations. IEEE Trans. AP, 1997; 45(3): 354-362
97 Ingle V.K., et al. Digital Signal Processing Using MATLAB. International Thomson Publishing Inc., 1996
98 L．科恩．时-频分析：理论与应用．西安交通大学出版社，1998
99 Carin L., et al. Wave-oriented signal processing of dispersive time-domain scattering data. IEEE. Trans. AP, 1997; 45(4): 592-599
100 Moghaddar, et al. Time-frequency distribution analysis of scattering from waveguide cavities. IEEE Trans. AP, 1993; 41:677-679
101 Carin L., et al. Dispersive modes in the time domain: analysis and time-frequency representation. IEEE Microwave Guided Wave Lett., 1994; 4:23-25
102 沈民奋，孙丽莎．现代随机信号与系统分析．北京：科学出版社，1998：247-282
103 Kim H., et al. Wavelet analysis of backscattering data from an open-ended waveguide cavity. IEEE Microwave Guided Wave Lett., 1992; 2:140-142
104 Kim H., et al. Wavelet analysis of radar echo from finite size targets. IEEE. Trans. AP, 1993; 41(3): 200-207
105 Daubechies. The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inform. Theory, 1990; 36:961-1005
106 Rothwell E.J., et al. An adaptive-window-width short time Fourier transform for visualization of radar target substructure resonances. IEEE Trans. AP, 1999:1393-1397
107 Taflove. Application of the finite-difference Time-domain method to sinusoidal steady-state electromagnetic penetration problems. IEEE. Trans. EMC, 1980; 22:191-202
108 Dmdo S.E, et al. FDTD formulation of an inverse scattering scheme for remote sensing of inhomgeneous lossy-layered media. J. Electromagnetic Waves and Applications, 1994; 8: 509-529
109 Teixeira F.L., et al. A general approach to extend Berenger's absorbing boundary condition to anistropic and dispersive media. IEEE Trans. AP, 1999:1386-1390
110 谢处方，邱文杰．天线原理与设计．西安：西北电讯工程学院出版社，1985
111 Collin R.E., Zucker F.J. Antenna Theory, Vol.1, Ch.8. New York: McGraw-Hill, 1969
112 胡继才．应用模糊数学．武汉测大出版社，1999
113 边肇祺．模式识别(二版)．清华大学出版社，2000
114 徐扬．模糊模式识别及其应用．西南交大出版社，1999
115 金亚秋．电磁散射信息与定量遥感．复旦大学出版社，2000
116 陈世福，陈兆乾．人工智能与知识工程．南京大学出版社，1997
2 陈季丹，刘子玉．电介质物理学．北京：机械工业出版社，1982
3 孟中岩等．电介质理论基础．北京：国防工业出版社，1980
4 Cole K.S., et al. Dispersion and absorption in dielectrics. J.Chem. Phys., 1941; 9:341-351
5 Wait J.R. Complex resistivity of the earth. In: Kong J.A. ed. Progress in Electromagnetic Research, New York: Elsevier, 1989
6 Gabriel S., et al. The dielectric properties of biological tissiues: Part 3—parametric models for the dielectric spectrum of tissues. Phys. Med. Biol., 1996; 41:2271-2293
7 Hurt W. P. Multiterm debye dispersion relations for permittivity of muscle, IEEE Trans. Biomed. Eng., 1985; 32:60-63
8 彭仲秋．瞬变电磁场．北京：高等教育出版社，1989
9 张文俊等．瞬变电磁波在色散媒质中的传播和散射．电子学报，1994；22：48-53
10 张文俊等．N 阶色散媒质的瞬态传播特性．上海大学学报，1995；1：533-541
11 张文俊等．N 阶色散媒质的瞬态散射特性．微波学报，1996；12：9-14
12 高本庆等．色散媒质中电磁场的时域有限差分算法．中国科学(A辑)，1994：24：538-545
13 Mrozowski M., et al. Parameterzation of media dispersive properties for FDTD. IEEE Trans. AP, 1997; ,15(9): 1438-1440
14 Kunz K.S., Luebbers R.J. The Finite Difference Time Domain Method for Electromagnetics, CRC Press. Inc., 1993:1-49
15 Taflove. Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrry structures. Wave Motion, 1988; 10(12): 547-582
16 Simons N.R.S., et al. Equivalence of propagation characteristics for the transmission line matrix and finite-difference time-domain methods in two dimensions. IEEE Trans, 1991; 39:354-356
17 Lee J.-E, et al. Time-domain finite-element methods. IEEE Trans. AP, 1997; 45(3): 430-441
18 Nikoskinen K.I. Time-domain study of half-space transmission problem with vertical and horizontal dipoles. IEEE. Trans. AP, 1993; 41(10): 1399-1407
19 Joseph R.M., et al. Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtoseeond electromagnetic pulses. Opt. Lett., 1991; 16:1412-1414
20 Goorjian P.L., et al. Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtoseeond electromagnetic solutions. Opt. Lett., 1992; 17:180-182
21 Walker S.P. Developments in time-domain integral equation modeling at imperial college. IEEE. AP Magazine, 1997; 39:7-19
22 Kragalott M., et al. Time-domain fields exterior to a two-dimensional FDTD space. IEEE. Trans. AP, 1997; 45(11): 1655-1663
23 张云华．电磁辐射与散射问题的传输线矩阵方法数值模拟研究．浙江大学博士论文
24 Cerri G., et al. Field penetration through slots into shielded enclosures:a time domain approach. IEEE. Trans. EMC, 1997; 39(4): 377-385
25 Lazzi G., et al. On modeling and personal dosimetry of cellular telephone helical antennas with the FDTD code. IEEE. Trans. AP, 1998; 46(4): 525-530
26 Chen H.-Y., et aL Analysis of electromagnetic radiation from a video output amplifier inside a monitor by using FDTD method. IEEE. Trans. EMC, 1997; 39(4): 394-397
27 Smith G.S., et al. A scale model for studying ground penetrating radars. IEEE. Trans. Geoscience and Remote Sensing, 1989; 27(4): 358-363
28 Shlager K.L., Schneider J.B. A selective survey of the finite-differencetime-domain literature. IEEE. AP.Mag., 1995; 37(8): 39-57
29 Luebbers R., Hunsberger E P., Kunz K. S., et al. A frequency-dependent finite-difference time-domain formulation for dispersive materials. IEEE Trans. EMC, 1990; 32:222-227
30 Luebbers R., et al. A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma. IEEE Trans. AP, 1991; 39: 29-34
31 Luebbers R., Hunsberger F.P FDTD for Nth-order dispersive media. IEEE Trans. AP, 1992; 40:1297-1301,
32 Luebbers R. J., et al. FDTD for Nth-order dispersive media. IEEE Trans. AP, 1992; 40(11): 1297-1301
33 Nickisch L.J., et al. Finite-difference time-domain solution of Maxwell's equations for the dispersive ionosphere. IEEE AP Magazine, 1992; 34(5): 33-39
34 Kashiwa T., et al. Transient analysis of magnetized plasma in three-dimensional space. IEEE. Trans. AP.., 1988; 36(8): 1096-1105
35 Tortes E, et al. Complete FDTD analysis of microwave heating processes in frequency-dependent and temperature-dependent media. IEEE Trans. MTT, 1997; 45(1): 108-117
36 Gandhi O.E, et al. A frequency-dependent finite-difference time-domain formulation for general dispersive media. 1993; 41(4): 658-665
37 Sullivan D.M., et al. Use of the finite-difference time-domain method in
calculation EM absorption in human tissues. IEEE Trans. Biomed. Eng., 1987; 34:148-157
38 Sullivan D.M., et al. Use of the finite-difference time-domain method in calculation EM absorption in man models. IEEE Trans. Biomed. Eng., 1988; 35:179-186
39 Sullivan D.M. A frequency-dependent FDTD method for biological applications. IEEE Trans. AP., 1991; 39(1): 29-34
40 Sullivan D.M. Frequency-dependent FDTD methods using z transforms. IEEE Trans. AP, 1992; 40(10): 1223-1230
41 Sullivan D.M. Z-transform theory and the FDTD method. IEEE. Trans. AP, 1996; 44(1): 28-34
42 Sullivan D.M. Mathmatical methods for treatment planning in deep regional hyperthermia. IEEE Trans. MTT, 1991; 39:864-872
43 Bui M. D., et al. propagation of transients in dispersive dielectric media. IEEE. Trans. MTT., 1991; 39(7): 1165-1172
44 胡广书．数字信号处理．北京：清华大学出版社，1997
45 Taflove, et al. The finite-difference time-domain method for numerical modeling of electromagnetic wave interactions. Electromagn., 1990; 10:105-126
46 Kunz K.S., et al. A three dimensional finite-difference solution of the external response of an aircraft to a complox transient EM environment: Part Ⅰ-Method and its implomentation. IEEE. Trans. EMC., 1978; 20(2):328-341
47 Wang Yuanxun, et al. Multimode parameter extraction for multiconductor transmission lines via single-pass FDTD and signal-processing techniques. IEEE Trans. MTT, 1998; 46(1): 89-95
48 Ko W.L., et al. A combination of FDTD and Prony's methods for analyzing microwave integrated circuits. IEEE Trans. MTT, 1991; 39(12): 2176-2181
49 Dawson J.E Representing ferrite absorbing tiles as frequency dependent boundaries in TLM. Electronics Lett., 1993; 29(9): 791-792
50 张志涌等．掌握和精通MATLAB．北京航空航天大学出版社，1997
51 Zhou J.Y., et al. Construction of the absorbing boundary conditions for the FDTD method with transfer functions. IEEE Trans.MTT, 1998; 46(11)
52 Blaschak J.G. A comparative study of absorbing boundary conditions. J. Computat. Phys., 1988; 77:109-139
53 Keller J.B., et al. Exact non-reflecting boundary conditions. J.Computat. Phys., 1989; 82:172-192
54 Lindma E.L. F ree space boundary conditions for the time dependent wave equation. J. Computa. Phys., 1988; 6(10): 427-475
55 Peng Jian, et al. A generalized reflection-free domain-truncation method: transparent absorbing boundary. IEEE Trans. AP, 1998; 46(7): 1015-1022
56 Tromp E.N.M., et al. Synthesis of absorbing boundary conditions for the FDTD method:numerical results. IEEE Trans. AP, 1995; (2): 213-215
57 Mur G. Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations. IEEE. Trans. EMC, 1981; 23(4): 377-382
58 Engquist B. Absorbing boundary conditions for the numerical simulation of wave. Math. Comput., 1977; 13(139): 629-651
59 Zhang X., Mei K.K. A super-absorbing boundary algorithm for numerical solving electromagnetic problems by time-domain finite difference method. IEEE Trans., MTT, 1988; 36(12): 1775-1787
60 Bi Zhiqiang, et al. A dicpersive boundary condition for microstrip component analysis using the FD-TD method. IEEE Trans. MTT, 1992; 40(4): 774-777
61 Moore T.G., et al. Theory and application of radiation boundary operators. IEEE Trans. MTT, 1988; 36:1797-1811
62 Higdon R.L. Absorbing boundary conditions for difference apporximations to the multi-dimensional wave equation. Math. Comput., 1986; 47(176): 437-459
63 Higdon R.L. Numerical absorbing boundary conditions for the wave equation. Math. Comput., 1987; 49(179): 65-90
64 Berenger J.P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys., 1994; 114(10): 185-200
65 Tang Jingwu, et al. Perfectly matched layer mesh terminations for nodal-based finite element methods in electromagnetics scattering. IEEE Trans. AP, 1998; 46(4): 507-516
66 Lau Y.C., et al. Extension of Berenger's PML boundary condition in matching lossy medium and evanescent waves. Electronics Letters, 1996; 32(11): 974-977
67 Wu J.Y., et al. A comparison of anisotropic PML to Berenger's PML and its application to the finite-element method for EM scattering. IEEE Trans. AP, 1997; 45(1): 40-50
68 Prescott D.T., et al. Reflection analysis of FDTD boundary conditions—part Ⅰ: time-space absorbing boundaries. IEEE Trans. MTT, 1997, 45(8): 1162-1177
69 Prescott D.T., et al. Reflection analysis of FDTD boundary conditions—part Ⅱ: Berenger's PML absorbing layers. IEEE Trans. MTT, 1997; 45(8): 1171-1178
70 Zhao P., et al. A new stable and very dispersive boundary condition for the FDTD method. IEEE Trans. MTT, 1993; 41:290-297
71 Ziolkowski R.W. Time-derivative Lorentz material model-based absorbing boundary condition. IEEE. Trans. AP, 1997; 45(10): 1530-1535
72 OppenheimA.V.,et al. 数字信号处理．北京：科学出版社，1980
73 Proakis J.G., et al. Digital Signal Processing, 2nd ed, New York:
Macmillan, 1992
74 Weedom W. H. A general method for FDTD modeling of wave propagation in arbitrary frequency-dispersive media. IEEE. Trans. AP, 1997; 45(3): 401-409
75 Kumpel W., et al. Digital signal processing of time domain field simulation results using the system identification method. IEEE Trans. MTT, 1994; 42(4): 667-671
76 王长清．时域有限差分法原理．无线电电子汇刊，1988；10：38-48
77 王长清．FD-TD法计算机程序要领．无线电电子汇刊，1988；12：1-8
78 王长清．FD-TD法中的吸收边界条件．无线电电子汇刊，1988；11：49-57
79 王长清．FD-TD法在电磁工程中的应用．无线电电子汇刊，1998；1：9-18
80 Omick S.R., et al. A new finite-difference time-domain algorithm for the accurate modeling of wide-bank electromagnetic phenomena. IEEE. Trans. EMC, 1993; 35(2): 215-221
81 Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. AP, 1966; 14(5): 302-307
82 Taflove, et al. Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations. IEEE. Trans. MTT, 1975; 23(8): 623-630
83 Zhang Xiaolei, et al. Time-domain finite difference approach to the calculation of the frequency-dependent characteristics of microstrip discontnuities. IEEE Trans. MTT, 1988; 36(12): 1775-1787
84 Furse C.M., et al. Improvements to the finite-difference time-domain method for calculating the radar cross section of a perfectly conducting target. IEEE Trans. MTT, 1990; 38:919-927
85 Farias R.G., et al. The use of FDTD for the analysis of magnetoplasma channel waveguides. IEEE Trans. MTT., 1998; 46(4): 387-394
86 Gandhi O.P., et al. Electromagnetic absorption in the human head and neck for mobile telephones at 835 and 1900 MHz. IEEE Trans. MTT, 1996; 44(10): 1884-1897
87 Petropoulos P.G. Stability and phase error analysis of FD-TD in dispersive dielectrics. IEEE Trans. AP, 1994; 42(1): 62-69
88 Young J.L., et al. On the dispersion errors related to (FD)2TD type schemes. IEEE. Trans. MTT, 1995; 43(8): 1902-1909
89 Young J.L. Propagation in linear dispersive media:finite difference time domain methodologies. IEEE Trans. AP, 1995; 43:422-426
90 Young J.L. A full finite difference time domain implementation for radio wave propagation in a plasma. Radio Sci., 1994; 29:1513-1522
91 Hunsberger E, et al. Finite-difference time-domain analysis of gyrotropic media—Ⅰ: magnetized plasma. IEEE Trans. AP, 1992; 40(12): 1489-1495
92 Pontalti R., et al. A multi-relaxation (FD)2TD method for modeling dispersion in biological tissues. IEEE Trans. MTT, 1994; 42:526-528
93 Wang Tong, et al. FD-FDTD using DSP for arbitrary dispersive media. J. of Shanghai University, 2000; 4(3): 230-234
94 Nehrbass J.W., et al. Reducing the phase error for finite-difference methods without increasing the order. IEEE Trans. AP, 1998; 46(8): 1194-1201
95 Furse C.M., et al. The use of the frequency-dependent finite-difference time-domain method for induced current and SAR calculations for a heterogeneous model of the human body. IEEE. Trans. EMC, 1994; 36(2): 128-133
96 Yee K.S., et al. The finite-difference time-domain and finite-volume time-domain methods in solving maxwell's equations. IEEE Trans. AP, 1997; 45(3): 354-362
97 Ingle V.K., et al. Digital Signal Processing Using MATLAB. International Thomson Publishing Inc., 1996
98 L．科恩．时-频分析：理论与应用．西安交通大学出版社，1998
99 Carin L., et al. Wave-oriented signal processing of dispersive time-domain scattering data. IEEE. Trans. AP, 1997; 45(4): 592-599
100 Moghaddar, et al. Time-frequency distribution analysis of scattering from waveguide cavities. IEEE Trans. AP, 1993; 41:677-679
101 Carin L., et al. Dispersive modes in the time domain: analysis and time-frequency representation. IEEE Microwave Guided Wave Lett., 1994; 4:23-25
102 沈民奋，孙丽莎．现代随机信号与系统分析．北京：科学出版社，1998：247-282
103 Kim H., et al. Wavelet analysis of backscattering data from an open-ended waveguide cavity. IEEE Microwave Guided Wave Lett., 1992; 2:140-142
104 Kim H., et al. Wavelet analysis of radar echo from finite size targets. IEEE. Trans. AP, 1993; 41(3): 200-207
105 Daubechies. The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inform. Theory, 1990; 36:961-1005
106 Rothwell E.J., et al. An adaptive-window-width short time Fourier transform for visualization of radar target substructure resonances. IEEE Trans. AP, 1999:1393-1397
107 Taflove. Application of the finite-difference Time-domain method to sinusoidal steady-state electromagnetic penetration problems. IEEE. Trans. EMC, 1980; 22:191-202
108 Dmdo S.E, et al. FDTD formulation of an inverse scattering scheme for remote sensing of inhomgeneous lossy-layered media. J. Electromagnetic Waves and Applications, 1994; 8: 509-529
109 Teixeira F.L., et al. A general approach to extend Berenger's absorbing boundary condition to anistropic and dispersive media. IEEE Trans. AP, 1999:1386-1390
110 谢处方，邱文杰．天线原理与设计．西安：西北电讯工程学院出版社，1985
111 Collin R.E., Zucker F.J. Antenna Theory, Vol.1, Ch.8. New York: McGraw-Hill, 1969
112 胡继才．应用模糊数学．武汉测大出版社，1999
113 边肇祺．模式识别(二版)．清华大学出版社，2000
114 徐扬．模糊模式识别及其应用．西南交大出版社，1999
115 金亚秋．电磁散射信息与定量遥感．复旦大学出版社，2000
116 陈世福，陈兆乾．人工智能与知识工程．南京大学出版社，1997