左手材料电磁特性与时域有限差分算法研究
|
摘要
左手材料是一种新型的人工电磁功能材料,它所具有的多种独特电磁特性使其在很多方面得到应用。本文讨论了左手材料在天线的定向辐射以及隐身衣结构方面的应用,推导出左手材料物理尺寸与其工作频率之间的关系,提出左手材料等效电路模型各元件参数以及组成左手材料的细导线棒和缺陷环尺寸参数计算的方法,设计出应用于手机频率的左手材料天线覆盖层,使天线实现定向辐射。
由于左手材料的制备过程比较复杂,需要首先利用电磁仿真算法对其进行仿真计算,对其电磁特性进行理论预测,因此本文利用时域有限差分算法对左手材料进行三维全波电磁仿真,推导出各向异性介质中的时域有限差分算法的差分表达式,并仿真验证三维隐身衣结构的电磁隐身效果。
由于左手材料是一种色散介质,而且其几何结构非常复杂,因此在利用时域有限差分算法对其进行仿真时,需要消耗大量的计算时间,为了在保证计算精度的前提下提高全波电磁仿真的效率,本文提出了针对色散介质的分段线性递归卷积弱条件稳定时域有限差分方法,该算法能够在节省大量的计算机资源的同时满足高精度的要求。
利用分段线性递归卷积弱条件稳定时域有限差分方法,本文又对微带天线衬底的色散特性进行了研究,对微带天线的衬底分别进行色散以及非色散两种形式的建模,分析衬底色散对天线性能的影响,讨论得出色散衬底模型下的回波损耗以及输入阻抗都比非色散模型的低,这对高频天线的设计具有指导作用。
总之,本文主要是利用时域有限差分算法对左手材料的电磁特性进行仿真,并在此过程中提出了适用于色散介质的高效精确的分段线性递归卷积弱条件稳定时域有限差分算法,具有一定的理论和实际意义。
Left-Handed materials is a new kind of artificial electromagnetic materials, it has a variety of unique electrical and magnetic properties to be applied in many areas, this paper discusses the left-handed materials in the directional radiation, and the application of metamaterial cloak. We conclude the relationship between the physical dimensions and the operating frequency in the design of Left-Handed materials, then study the calculation method of L, C parameter of Left-Handed materials equivalent circuit model, and design a left-handed materials cover which is suitable for mobile phone antenna, so that the antenna can achieve directional radiation.
As the preparation process of Left-Handed materials is relatively complex, and generally we use the electromagnetic simulation algorithm firstly to get the theoretical prediction of its electromagnetic properties, so we use Finite Difference Time Domain algorithm to get the full-wave electromagnetic simulation result. In this paper, we get the differential expression in the anisotropy media and simulate the three-dimensional metamaterial cloak.
Because the Left-Handed materials is a type of dispersive media, and its geometry is very complex, so when we need a lot of computing time and resource, in order to get the high accuracy and save the computational resource, we propose the Piecewise Linear Recursive Convolution Weakly Conditional Stability algorithm which can save a lot of computer resources while meeting the required precision.
Using the Piecewise Linear Recursive-Convolution Weakly Conditional Stability algorithm, we study the effect of dispersive substrate of microstrip antenna, then discuss the difference of return loss and input impendence between dispersive and nondispersive substrate model, and we find that the resonant frequency of dispersive model is slightly lower than nondispersive model, meanwhile, the input impendence for the dispersive substrate model is lower than the nondispersive model.
To summarize, we use Finite-Difference Time-Domain algorithm to simulate the Left-Handed materials electromagnetic properties in this paper, and in the process we propose the high accurate and efficient Piecewise-Linear-Recursive-Convolution Weakly-Conditional-Stability algorithm for dispersion medium.
由于左手材料的制备过程比较复杂,需要首先利用电磁仿真算法对其进行仿真计算,对其电磁特性进行理论预测,因此本文利用时域有限差分算法对左手材料进行三维全波电磁仿真,推导出各向异性介质中的时域有限差分算法的差分表达式,并仿真验证三维隐身衣结构的电磁隐身效果。
由于左手材料是一种色散介质,而且其几何结构非常复杂,因此在利用时域有限差分算法对其进行仿真时,需要消耗大量的计算时间,为了在保证计算精度的前提下提高全波电磁仿真的效率,本文提出了针对色散介质的分段线性递归卷积弱条件稳定时域有限差分方法,该算法能够在节省大量的计算机资源的同时满足高精度的要求。
利用分段线性递归卷积弱条件稳定时域有限差分方法,本文又对微带天线衬底的色散特性进行了研究,对微带天线的衬底分别进行色散以及非色散两种形式的建模,分析衬底色散对天线性能的影响,讨论得出色散衬底模型下的回波损耗以及输入阻抗都比非色散模型的低,这对高频天线的设计具有指导作用。
总之,本文主要是利用时域有限差分算法对左手材料的电磁特性进行仿真,并在此过程中提出了适用于色散介质的高效精确的分段线性递归卷积弱条件稳定时域有限差分算法,具有一定的理论和实际意义。
Left-Handed materials is a new kind of artificial electromagnetic materials, it has a variety of unique electrical and magnetic properties to be applied in many areas, this paper discusses the left-handed materials in the directional radiation, and the application of metamaterial cloak. We conclude the relationship between the physical dimensions and the operating frequency in the design of Left-Handed materials, then study the calculation method of L, C parameter of Left-Handed materials equivalent circuit model, and design a left-handed materials cover which is suitable for mobile phone antenna, so that the antenna can achieve directional radiation.
As the preparation process of Left-Handed materials is relatively complex, and generally we use the electromagnetic simulation algorithm firstly to get the theoretical prediction of its electromagnetic properties, so we use Finite Difference Time Domain algorithm to get the full-wave electromagnetic simulation result. In this paper, we get the differential expression in the anisotropy media and simulate the three-dimensional metamaterial cloak.
Because the Left-Handed materials is a type of dispersive media, and its geometry is very complex, so when we need a lot of computing time and resource, in order to get the high accuracy and save the computational resource, we propose the Piecewise Linear Recursive Convolution Weakly Conditional Stability algorithm which can save a lot of computer resources while meeting the required precision.
Using the Piecewise Linear Recursive-Convolution Weakly Conditional Stability algorithm, we study the effect of dispersive substrate of microstrip antenna, then discuss the difference of return loss and input impendence between dispersive and nondispersive substrate model, and we find that the resonant frequency of dispersive model is slightly lower than nondispersive model, meanwhile, the input impendence for the dispersive substrate model is lower than the nondispersive model.
To summarize, we use Finite-Difference Time-Domain algorithm to simulate the Left-Handed materials electromagnetic properties in this paper, and in the process we propose the high accurate and efficient Piecewise-Linear-Recursive-Convolution Weakly-Conditional-Stability algorithm for dispersion medium.
引文
[1]V. G Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of Permittivity and Permeability," Soviet Physics Uspekhi, no.4, pp.509-514, Jan., Feb. 1968.
[2]J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructure," Phys. Rev. Lett., vol.76, no.25, pp.4773-4776, June 1996.
[3]J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low Frequency Plasmons in Thin-Wire Structures," J. Phys. Condens. Matter, vol.10, pp.4785-4809,1998.
[4]J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Micro. Theory. Tech., vol.47, no.11, pp. 2075-1084, Nov.1999.
[5]D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, "Direct Calculation of Permeability and Permittivity for a Left-Handed Metamaterial," App. Phys. Lett., vol.77, no.14, pp.2246-2248, Oct.2000.
[6]R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science, vol.292, pp.77-79, April 2001.
[7]D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, "Determination of Effective-Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients," Physical Review B, vol.65, pp.195104:1-5, April 2002.
[8]D. R. Smith, D. Schurig, J. B. Pendry, "Negative Refraction of Modulated Electromagnetic Waves," Applied Physics Letters, vol.81, pp.2713-2715,2002.
[9]R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz, "Microwave Transmission through a Two-Dimensional, Isotropic, Left-Handed Metamaterial," Applied Physics Letters. vol.78, pp.489-491,2001.
[10]J. B. Pendry, D. Schurig, D. R. Smith, "Controlling Electromagnetic Fields," Science, vol. 312,no.5781, pp.1780-1782, June 2006.
[11]D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science, vol.314. no.
5801, pp.977-980, Nov.2006.
[12]S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, "Full-wave Simulations of Electromagnetic Cloaking Structures," Phys. Rev. E, vol.74, pp.036621:1-5, Sept.2006.
[13]W. S. Cai, U. K. Chettiar, A. V. Kildishev and V. M. Shalaev, "Optical Cloaking with Metamaterials," Nature Photonics, vol.1, pp.224-229, Apr.2007.
[14]H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y Jiang, H. R. Ma, and C. T. Chan, "Extending the Bandwidth of Electromagnetic Cloaks," Phys. Rev. B, vol.76, pp.241104:1-4, Dec.2007.
[15]S. Enoch, "A Metamaterial for Directive Emission," Phys. Rev. Lett, vol.89, pp.213902: 1-4, Nov.2002.
[16]J. Hu, C. S. Yan, Q. C. Lin, "A New Patch Antenna with Metamaterial Cover," Journal of Zhejiang University, vol.7, pp.89-94. Jan.2006.
[17]D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett., vol.85, no.14, pp.2933-2936, Oct.2000.
[18]R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave Transmission through A Two-Dimensional, Isotropic, Left-Handed Metamaterial," App. Phys. Lett., vol. 78, no.4, pp.489-491, Jan.2001.
[19]M. Garcia, and M. Nieto-Vesperinas, "Left-Handed Materials Do Not Make A Perfect Lens," Phys. Rev. Lett., vol.88, no.20, pp.207403:1-4, Jan.2002.
[20]J. B. Pendry, "A Chiral Route to Negative Refraction," Science, pp.1353-1355,2004.
[21]D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Physical Review Letters, vol. 84, pp.4184-4187. May.2000.
[22]Nader Engheta, "Circuits with Light at Nanoscales:Optical Nanocircuits Inspired by Metamaterials," Science, vol.317, pp.1968-1702. Sept.2007.
[23]A. Alu, A. Salandrino, and N. Engheta, "Negative Effective Permeability and Left-Handed Materials at Optical Frequencies," http://arxiv.org/pdf/condmat/0412263.
[24]N. Engheta, A. Salandrino, and A. Alu, "Circuit Elements at Optical Frequencies: Nano-Inductors, Nano-Capacitors and Nano-Resistors," Physical Review Letters, vol.95, 095504, August 26,2005.
[25]"Filling the THz Gap," Science, vol.320. Jun.2008.
[26]R. F. Harrington, "Time-Harmonic Electromagnetic Fields," IEEE Press,2001.
[27]C. A. Balanis, "Advanced Engineering Electromagnetics," IEEE Press,1989.
[28]C. Caloz, T. Itoh, "Electromagnetic Metamaterials:Transmission Line Theory and Microwave Applications," JohnWiley& Sons Publication,2006.
[29]R. J. Doviak, D. S. Zrnic, and R. J. Doviak, "Doppler Radar and Weather Observations," Second Edition, Academic Press,1993.
[30]J. A. Kong, "Electromagnetic Wave Theory, Second Edition," John Wiley& Sons,1990.
[31]J. L, T. M. Grzegorczyk, Y. Zhang, J. Pacheo, B. I. Wu, J. A. Kong, and M. Chen, "Cerenkov Radiation in Materials with Negative Permittivity and Permeability," Optics Express, vol.11, no.7, pp.723-734, April 2003.
[32]C. Caloz and T. Itoh, "Array Factor Approach of Leaky-Wave Antennas and Application to 1D/2D Composite Right/Left-Handed (CRLH) Structures "IEEE Microwave Wireless Compon. Lett., vol.14, no.6, pp.274-276, June 2004.
[33]R. F. Harrington, "Matrix Methods for Field Problems," Proceedings of the IEEE, vol.55, no.2, Feb.1967.
[34]M. J. Turner, R. W. Clough, H. C. Martin, L. J. Topp, "Stiffness and Deflection Analysis of Complex Structures,"J. Aero. Sci,1956.
[35]R. W. Clough, "The Finite Element Method in Plane Stress Analysis," Conference on Electronic Computation (2nd:1960:Pittsburgh).
[36]K. S. Yee, "Numerical Solution of Initial-Boundary Value Problems Involving Maxwell's Equation in Isotropic Media," IEEE Trans. Antennas Propagat., vol. AP-14, no.5, pp. 302-307,1966.
[37]A. Talfove, "Computational Electrodynamics," Artech House, Norwood, MA,1995.
[38]Talfove, "Advances in computational electromagnetic:the FDTD method," Artech House, Norwood, MA,1998.
[39]Bayliss, E. Turkel, "Radiation Boundary Conditions for Wave-Like Equations," Communications on Pure and Applied Mathematics, vol.33, Issue 6, Pages 707-725.
[40]G Mur, "Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Trans. On Electromag. Compat., vol. EMC-23, no.4, Nov 1981.
[41]Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, "A Transmitting Boundary for Transient Wave Analyzes," Scientia Sinica, vol.27, no.10, pp.1063-1076, Oct.1984.
[42]J. P. Berenger, "Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J. Comp. Phys., vol.114, pp.185-200, Oct.1994.
[43]Z. S. Sacks, D. M. Kingsland, and R. Lee, "A Perfectly Matched Anisotropic Absorber for Use as Absorbing Boundary condition," IEEE Trans. Antennas and Propagation, Dec.1995, vol.43, pp.1460-1463.
[44]J. D. Moerloose and M. Stuchly, "Behavior of Berenger's ABC for Evanescent Waves," IEEE Micorwave Guided Wave Lett, vol.5, pp.344-346, Oct 1995.
[45]A. D. Boardman and K. Marinov, "Radiation Enhancement and Radiation Supepression by a Left-Handed Metamaterial," Microwave and Optical Technology Letter, vol.48, no.12, pp. 2512-2516, Dec.2006.
[46]Q. Cheng and T. J. Cui, "Electromagnetic Properties of A Left-Handed Medium Slab Excited by Three-Dimensional Electric Dipoles," Phys Lett A, vol.345, pp.439-447.2005.
[47]I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Second-Harmonic Generation in Nonlinear Left-Handed Metamaterials," J Opt SocAm B, vol.23, pp.529-534,2006.
[48]A. Ourir, A. de Lustrac, and J.-M. Lourtioz, "Optimization of Metamaterial Based Subwavelength Cavities for Ultracompact Directive Antennas," Microwave and Optical Technology Letter, vol.48, no.12, pp.2573-2577, Dec 2006.
[49]D. Sievenpiper, "High Impedance Electromagnetic Surfaces," Ph. D. Thesis, University of California, Los Angeles,1999.
[50]L. Zhou, H. Li, Y. Qin, Z. Wei, and C. T. Chan, "Directive Emissions from Subwavelength Metamaterial-Based Cavities," ApplPhys Lett., vol.86,2005.
[51]A. P. Feresidis, G Goussetis, S. Wang, and J. C, "Vardaxoglou, Artificial Magnetic Conductor Surfaces and Their Application to Low-Profile Highgain Planar Antennas," IEEE Trans Antennas Propag., vol.53 pp.209-215.2005.
[52]S. Enoch, G Tayeb, P. Sabouroux, N. Guerin, and R. Vincent, "A Metamaterial for Directive Emission,"Phys Rev Lett., vol.89, pp.213902:1-4. Nov.2002.
[53]A. Ourir, A. de Lustrac, and J. M. Lourtioz, "All-Metamaterial-BasedSub-Wavelength Cavities for Ultra Thin Directive Antennas," Appl Phys Lett., vol.88, pp.084103:1-3, Jan. 2006.
[54]Zhongyan Sheng, and Vasundara V. Varadan, "Tuning the Effective Properties of Metamaterials by Changing the Substrate Properties," Jour. App. Phys., vol.101, pp.014909: 1-7.2007.
[55]Caloz and T. Itoh, "Novel Microwave Devices and Structures Based on The Transmission Line Approach of Metamaterials," IEEE Trans. Microwave Theory Tech., vol.1, pp. 195-198, June 2003.
[56]A. Sanada, C. Caloz and T. Itoh, "Characteristics of the Composite Right/Left-Handed Transmission Lines," IEEE Microwave Wireless Compon. Lett., vol.14, no.2, pp.68-70, Feb.2004.
[57]L. B. Felsen and N. Marcuvitz, "Radiation and Scattering of Waves," Reissue Edition, Ieee/Oup Series on Electronic Wave Theory,1996.
[58]Kittel, "Introduction to Solid State Physics," Eighth Edition, Wiley,2005.
[59]S. Ramo, J. R. Whinnery, and T. Van Duzer, "Fields and Waves in Communication Electronics," Third Edition, John Wiley& Sons,1994.
[60]M. D. Pozar, "Microwave Engineering," Third Edition, John Wiley& Sons,2004.
[61]R. E. Collin, "Foundations for Microwave Engineering," Second Edition, McGraw-Hill, 1992.
[62]Caloz, H. Okabe, T. Iwai, and T. Itoh, "Transmission Line Approach of Left-Handed (LH) Materials," USNC/URSI National Radio Science Meeting, San Antonio, TX, vol.1, pp.39, June 2002.
[63]Caloz and T. Itoh, "Transmission Line Approach of Left-Handed (LH) Structures and Microstrip Realization of A Low-Loss Broadband LH Filter," IEEE Trans. Antennas Propagat., vol.52, no.5, May 2004.
[64]Caloz, A. Sanada, and T. Itoh, "Microwave Applications of Transmission-Line Based Negative Refractive Index Structures," Proc. of Asia-Pacific Microwave Conf., Seoul, Korea, vol.3, pp.1708-1713, Nov.2003.
[65]A. Lai, C. Caloz and T. Itoh, "Transmission Line Based Metamaterials and Their Microwave Applications," Microwave Mag., vol.5, no.3, pp.34-50, Sept.2004.
[66]Cubukcu, K. Aydin, and E. Ozbay, "Subwavelength Resolution in a Two-Dimensional
Photonic-Crystal-Based Superlens," Physical Review Letter, vol.91, no.20, pp.207401: 1-4, Nov.2003.
[67]Ertugrul Cubukcu, Koray Aydin, Ekmel Ozbay, Stavroula Foteinopoulou, Costas M. Soukoulis, "Electromagnetic Waves:Negative Refraction by Photonic Crystals," Nature, vol. 423, pp.604-605, Jun.2003.
[68]Stefan Linden, Christian Enkrich, Martin Wegener, Jiangfeng Zhou, Thomas Koschny, Costas M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science, vol. 306. no.5700, pp.1351-1353, November 2004.
[69]Yen TJ, Padilla WJ, Fang N, Vier DC, Smith DR, Pendry JB, Basov DN, "Terahertz Magnetic Response from Artificial Materials," Science, vol.303, no.5663.2004.
[70]S. D. Gedney, "An Anisotropic Perfectly Matched Layer Absorbing Media for the Truncation of FDTD Lattices," IEEE Trans. Antennas Propagat, vol. AP-44, no.12, pp. 1630-1639, Dec.1996.
[71]L. Teixeira, W. C. Chew, M. Straka, "Finite-Difference Time-Domain Simulation of Ground Penetrating Radar on Dispersive, Inhomogeneous, and Cinductive Soils," IEEE Trans. Geoscience Remote Sensing, vol.36, no.6, pp.1928-1937, Nov.1998.
[72]A. P. Gandhi, B. Q. Gao, and J. Y. Chen, "A Frequency-Dependent Finite-difference Time-domain Formulation for General Dispersive Media," IEEE Trans. Microwave Theory Tech., vol.41, no.4, pp.658-665, Apr.1992.
[73]T. Kashiiva, Y. Ohtomo, and I. Fukai, "A Finite-difference Time-domain Formulation for Transient Propagation in Dispersive Media Associated with Cole-Cole's Circular ARC law," Microwave. Opt. Tech. Lett., vol.3, no.12, pp.416-419, Dec 1990.
[74]R. M. Joseph, S. C. Hagnes, and A. Taflove, "Direct Time Integration of Maxwell's Equation in Linear Dispersive Media with Absorption for Scatttering and Propagation of Femtosecond Electromagnetic Pulse," Opt. Lett., vol.16, no.18, pp.1412-1414, Sept 1991.
[75]M. Sullivan, "Frequency-Dependent FDTD Method Using Z Transform," IEEE Trans. Antennas Propagat., vol.40, no.10, pp.1223-1230, Oct 1992.
[76]D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method, New York, IEEE Press, pp.1-35,2000.
[77]R. J. Luebbers, F. P. Huusberger, K. S. Kunz, R. B. Standler, and M. Schneider, "A
Frequency-Dependent Finite-Difference Time-Domain Formulation for Dispersive Materials," IEEE Trans. Electromagn. Compat., vol.32, pp.222-227, Aug.1990.
[78]D. F. Kelley, and Raymond J. Luebbers, "Piecewise Linear Recursive Convolution for Dispersive Media Using FDTD," IEEE Trans. Antennas Propagat., vol.44, no.6, Jun.1996.
[79]A. Taflove, "Computational Electrodynamics," Norwood, MA, Artech House,1995.
[80]Zheng, Z. Chen, and J. Zhang, "A Finite-Difference Time-Domain Method without the Courant Stability Conditions," IEEEMicrow. Guided Wave Lett., vol.9, no.11, pp.441-443, Nov.1999.
[81]Yuan C and Chen Z, "A Three-Dimensional Unconditionally Stable ADI-FDTD Method in the Cylindrical Coordinate System," IEEE Trans Microwave Theory Tech., vol.50, pp. 2401-2405,2002.
[82]Chen HL, Chen B, Yi Y, et al, "Unconditionally Stable ADI-BOR-FDTD Algorithm for the Analysis of Rotationally Symmetric Geometries," IEEE Microwave Wire Comp Lett., vol.17, no.4, pp.304-306,2007.
[83]Zheng HX, "ADI-FDTD Formulation for General Dispersive Media," Antennas Propagat Intel Symp. IEEE, pp.1723-1726,2006.
[84]Wang SM, Chen J, and Ruchhoeft P, "An ADI-FDTD Method for Periodic Structures," IEEE Trans Antennas Propagat., vol.53, no.7, pp.2343-2346,2005.
[85]Zhao AP, "A Novel Implementation for Two-Dimensional Unconditionally Stable FDTD Method," Microwave Opt TechnolLett, vol.38, no.6, pp.457-462,2003.
[86]Sun G and Trueman CW, "Approximate Crank-Nicolson Schemes for the 2-D Finite-Difference Time Domain Method for TEz Waves," IEEE Trans Antennas Propagat., vol.52, no.11, pp.2963-2972,2004.
[87]Sun G and Trueman CW, "Unconditionally-Stable FDTD Method Based on Crank-Nicolson Scheme for Solving Three-Dimensional Maxwell Equations," Electron Lett., vol.40, no.10, pp.589-590,2004.
[88]Sun G and Trueman CW, "Efficient Implementations of the Crank-Nicolson Scheme for the Finite-Difference Time-Domain Method," IEEE Trans. Microwave Theory Tech., vol.54, no. 5, pp.2275-2284,2006.
[89]Yang Y, Chen RS, and Yung EKN, "The Uncondionally Stable Crank-Nicolson FDTD Method for Tthree-Dimensional Maxwell's Equations," Microwave Opt Technol Lett., vol. 48, no.8, pp.1619-1622,2006.
[90]A. Alighanbari, C. D. Sarris, "A High-Order MRTD Technique with Laguerre-Polynomial-Based Time-Integration," IEEE AP-S Symposium on Antennas and Propagation, July 2005.
[91]J. Chen and J. Wang, "A Novel WCS-FDTD Method with Weakly Conditional Stability," IEEE Trans. Electromagn. Compat., vol.49, no.2, pp.419-426, May 2007.
[92]Deseham Ps, G A., "Microstrip Microwave Antenas." 3rd USFA SymPosium on Antennas, 1953.
[93]Howell, J. Q, "Microstrip Antenas." IEEEAP-SInt. Symp. Digest,1972.
[94]Z. H. Qian and R. S. Chen, "FDTD Analysis of Microstrip Patch Antenna Covered by Plasma Sheath," Progress In Electromagnetics Research, PIER 52,173-183,2005.
[95]W. Xu, L.-W. Li, H.-Y. Yao, T.-S. Yeo and Q. Wu, "Left-Handed Material Effects on Wave's Modes and Resonant Frequencies:Field Waveguide Structures and Substrate-Loaded Patch Antennas," Journal of Electromagnetic Waves and Applications, vol.19, no. 15, pp.2033-2047, October,2005.
[96]K. P. Prokopidis and T. D. Tsiboukis, "The Effect of Dispersion on the Operation of Square Microstrip Antennas," IEEE Trans. Magnetics, vol.42, no.4. Apr.2006.
[97]X. Zhang, J. Fang, K. K. Mei, and Y. Liu, "Calculations of the Dispersive Characteristics of Microstrips by the Time-Domain Finite-Different Different Method," IEEE Trans. Microwave Theory Tech., vol.36, pp.263-267, Feb.1988.
[98]X. Zhang and K. K. Mei, "Time Domain Finite Difference Approach to the Calculation of the Frequency Dependent Characteristics of Microstrip Discontinuities," IEEE Trans. Microwave Theory Tech., vol.36, pp.1775-1787, Dec.1988.
[99]Liang, Y. Liu, and K. K. Mei, "Full-Wave Analysis of Coplanar Waveguide and Slotline Using the Time-Domain Finite-Difference Method," IEEE Trans. Microwave Theory Tech., vol.37, pp.1949-1957, Dec.1989.
[100]D. M. Sheen, S. M. Ali, M. D. Abouzahra, and J. A. Kong, "Application of the Three-Dimensional Finite-Difference Time-Domain Method to the Analysis of Planar Microstrip Circuits," IEEE Trans. Microwave Theory Tech., vol.38, pp.849-857, July 1990.
[101]J. Litva, Z. Bi, K. Wu, R. Fralich, and C. Wu, "Full-Wave Analysis of an Assortment of Printed Antenna Structures Using the FD-TD Method," 1991IEEEAP-SInt. Symp. Dig., pp. 410-413, June 1991.
[102]Mur, "Absorbing Boundary Conditions for the Finitr-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Trans. Electromagn Compat, vol. emc-23, no.4, Nov 1981.
[103]Z. Bi, K. Wu, C. Wu, and J. Litva, "A Dispersive Boundary Condition for Microstrip Component Analysis Using The FD-TD Method," IEEE Trans. Microwave Theory Tech., vol.40, no.4, Apr.1992.
[104]K. P. Prokopidis and T. D. Tsiboukis, "The Effect of Dispersion on the Operation of Square Microstrip Antennas," IEEE Trans. Magnetics, vol.42, no.4. Apr.2006.
[105]DesehamPs, G A., "Microstrip Microwave Antenas," 3rd USFA SymPosium on Antennas, 1953.
[106]Howell, J. Q, "Microstrip Antena" IEEE APS Int. Symp. Digest,1972.
[107]Z. H. Qian and R. S. Chen, "FDTD Analysis of Microstrip Patch Antenna Covered by Plasma Sheath," Progress In Electromagnetics Research, PIER 52,173-183,2005.
[108]W. Xu, L.-W. Li, H.-Y. Yao, T.-S. Yeo and Q. Wu, "Left-Handed Material Effects on Wave's Modes and Resonant Frequencies:Field Waveguide Structures and Substrate-Loaded Patch Antennas," Journal of Electromagnetic Waves and Applications, vol.19, no. 15, pp.2033-2047, October,2005.
[109]K. P. Prokopidis and T. D. Tsiboukis, "The Effect of Dispersion on the Operation of Square Microstrip Antennas," IEEE Trans. Magnetics, vol.42, no.4. Apr.2006.
[110]X. Zhang, J. Fang, K. K. Mei, and Y. Liu, "Calculations of the Dispersive Characteristics of Microstrips by the Time-DomainFinite-Different Different Method," IEEE Trans. Microwave Theory Tech., vol.36, pp.263-267, Feb.1988.
[111]X. Zhang and K. K. Mei, "Time Domain Finite Difference Approach to the Calculation of the Frequency Dependent Characteristics of Microstrip Discontinuities," IEEE Trans. Microwave Theory Tech., vol.36, pp.1775-1787, Dec.1988.
[112]Liang, Y. Liu, and K. K. Mei, "Full-Wave Analysis of Coplanar Waveguide and Slotline Using the Time-Domain Finite-Difference Method," IEEE Trans. Microwave Theory Tech., vol.37, pp.1949-1957, Dec.1989.
[113]D. M. Sheen, S. M. Ali, M. D. Abouzahra, and J. A. Kong, "Application of the Three-Dimensional Finite-Difference Time-Domain Method to The Analysis of Planar Microstrip Circuits," IEEE Trans. Microwave Theory Tech., vol.38, pp.849-857, July 1990.
[114]Litva, Z. Bi, K. Wu, R. Fralich, and C. Wu, "Full-Wave Analysis of an Assortment of Printed Antenna Structures Using the FD-TD Method," 1991 IEEE AP-S Int. Symp. Dig., June 1991, pp.410-413.
[115]Mur, "Absorbing Boundary Conditions for the Finitr-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Trans. Electromagn Compat., vol. emc-23, no.4, Nov 1981.
[116]Z. Bi, K. Wu, C. Wu, and J. Litva, "A Dispersive Boundary Condition for Microstrip Component Analysis Using The FD-TD Method," IEEE Trans. Microwave Theory Tech., vol.40, no.4, Apr.1992.
[117]P. Prokopidis and T. D. Tsiboukis, "The Effect of Dispersion on the Operation of Square Microstrip Antennas," IEEE Trans. Magnetics, vol.42, no.4. Apr.2006.
[2]J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructure," Phys. Rev. Lett., vol.76, no.25, pp.4773-4776, June 1996.
[3]J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low Frequency Plasmons in Thin-Wire Structures," J. Phys. Condens. Matter, vol.10, pp.4785-4809,1998.
[4]J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Micro. Theory. Tech., vol.47, no.11, pp. 2075-1084, Nov.1999.
[5]D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, "Direct Calculation of Permeability and Permittivity for a Left-Handed Metamaterial," App. Phys. Lett., vol.77, no.14, pp.2246-2248, Oct.2000.
[6]R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science, vol.292, pp.77-79, April 2001.
[7]D. R. Smith, S. Schultz, P. Markos, C. M. Soukoulis, "Determination of Effective-Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients," Physical Review B, vol.65, pp.195104:1-5, April 2002.
[8]D. R. Smith, D. Schurig, J. B. Pendry, "Negative Refraction of Modulated Electromagnetic Waves," Applied Physics Letters, vol.81, pp.2713-2715,2002.
[9]R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz, "Microwave Transmission through a Two-Dimensional, Isotropic, Left-Handed Metamaterial," Applied Physics Letters. vol.78, pp.489-491,2001.
[10]J. B. Pendry, D. Schurig, D. R. Smith, "Controlling Electromagnetic Fields," Science, vol. 312,no.5781, pp.1780-1782, June 2006.
[11]D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science, vol.314. no.
5801, pp.977-980, Nov.2006.
[12]S. A. Cummer, B. I. Popa, D. Schurig, and D. R. Smith, "Full-wave Simulations of Electromagnetic Cloaking Structures," Phys. Rev. E, vol.74, pp.036621:1-5, Sept.2006.
[13]W. S. Cai, U. K. Chettiar, A. V. Kildishev and V. M. Shalaev, "Optical Cloaking with Metamaterials," Nature Photonics, vol.1, pp.224-229, Apr.2007.
[14]H. Y. Chen, Z. X. Liang, P. J. Yao, X. Y Jiang, H. R. Ma, and C. T. Chan, "Extending the Bandwidth of Electromagnetic Cloaks," Phys. Rev. B, vol.76, pp.241104:1-4, Dec.2007.
[15]S. Enoch, "A Metamaterial for Directive Emission," Phys. Rev. Lett, vol.89, pp.213902: 1-4, Nov.2002.
[16]J. Hu, C. S. Yan, Q. C. Lin, "A New Patch Antenna with Metamaterial Cover," Journal of Zhejiang University, vol.7, pp.89-94. Jan.2006.
[17]D. R. Smith and N. Kroll, "Negative Refractive Index in Left-Handed Materials," Phys. Rev. Lett., vol.85, no.14, pp.2933-2936, Oct.2000.
[18]R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave Transmission through A Two-Dimensional, Isotropic, Left-Handed Metamaterial," App. Phys. Lett., vol. 78, no.4, pp.489-491, Jan.2001.
[19]M. Garcia, and M. Nieto-Vesperinas, "Left-Handed Materials Do Not Make A Perfect Lens," Phys. Rev. Lett., vol.88, no.20, pp.207403:1-4, Jan.2002.
[20]J. B. Pendry, "A Chiral Route to Negative Refraction," Science, pp.1353-1355,2004.
[21]D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Physical Review Letters, vol. 84, pp.4184-4187. May.2000.
[22]Nader Engheta, "Circuits with Light at Nanoscales:Optical Nanocircuits Inspired by Metamaterials," Science, vol.317, pp.1968-1702. Sept.2007.
[23]A. Alu, A. Salandrino, and N. Engheta, "Negative Effective Permeability and Left-Handed Materials at Optical Frequencies," http://arxiv.org/pdf/condmat/0412263.
[24]N. Engheta, A. Salandrino, and A. Alu, "Circuit Elements at Optical Frequencies: Nano-Inductors, Nano-Capacitors and Nano-Resistors," Physical Review Letters, vol.95, 095504, August 26,2005.
[25]"Filling the THz Gap," Science, vol.320. Jun.2008.
[26]R. F. Harrington, "Time-Harmonic Electromagnetic Fields," IEEE Press,2001.
[27]C. A. Balanis, "Advanced Engineering Electromagnetics," IEEE Press,1989.
[28]C. Caloz, T. Itoh, "Electromagnetic Metamaterials:Transmission Line Theory and Microwave Applications," JohnWiley& Sons Publication,2006.
[29]R. J. Doviak, D. S. Zrnic, and R. J. Doviak, "Doppler Radar and Weather Observations," Second Edition, Academic Press,1993.
[30]J. A. Kong, "Electromagnetic Wave Theory, Second Edition," John Wiley& Sons,1990.
[31]J. L, T. M. Grzegorczyk, Y. Zhang, J. Pacheo, B. I. Wu, J. A. Kong, and M. Chen, "Cerenkov Radiation in Materials with Negative Permittivity and Permeability," Optics Express, vol.11, no.7, pp.723-734, April 2003.
[32]C. Caloz and T. Itoh, "Array Factor Approach of Leaky-Wave Antennas and Application to 1D/2D Composite Right/Left-Handed (CRLH) Structures "IEEE Microwave Wireless Compon. Lett., vol.14, no.6, pp.274-276, June 2004.
[33]R. F. Harrington, "Matrix Methods for Field Problems," Proceedings of the IEEE, vol.55, no.2, Feb.1967.
[34]M. J. Turner, R. W. Clough, H. C. Martin, L. J. Topp, "Stiffness and Deflection Analysis of Complex Structures,"J. Aero. Sci,1956.
[35]R. W. Clough, "The Finite Element Method in Plane Stress Analysis," Conference on Electronic Computation (2nd:1960:Pittsburgh).
[36]K. S. Yee, "Numerical Solution of Initial-Boundary Value Problems Involving Maxwell's Equation in Isotropic Media," IEEE Trans. Antennas Propagat., vol. AP-14, no.5, pp. 302-307,1966.
[37]A. Talfove, "Computational Electrodynamics," Artech House, Norwood, MA,1995.
[38]Talfove, "Advances in computational electromagnetic:the FDTD method," Artech House, Norwood, MA,1998.
[39]Bayliss, E. Turkel, "Radiation Boundary Conditions for Wave-Like Equations," Communications on Pure and Applied Mathematics, vol.33, Issue 6, Pages 707-725.
[40]G Mur, "Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Trans. On Electromag. Compat., vol. EMC-23, no.4, Nov 1981.
[41]Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, "A Transmitting Boundary for Transient Wave Analyzes," Scientia Sinica, vol.27, no.10, pp.1063-1076, Oct.1984.
[42]J. P. Berenger, "Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J. Comp. Phys., vol.114, pp.185-200, Oct.1994.
[43]Z. S. Sacks, D. M. Kingsland, and R. Lee, "A Perfectly Matched Anisotropic Absorber for Use as Absorbing Boundary condition," IEEE Trans. Antennas and Propagation, Dec.1995, vol.43, pp.1460-1463.
[44]J. D. Moerloose and M. Stuchly, "Behavior of Berenger's ABC for Evanescent Waves," IEEE Micorwave Guided Wave Lett, vol.5, pp.344-346, Oct 1995.
[45]A. D. Boardman and K. Marinov, "Radiation Enhancement and Radiation Supepression by a Left-Handed Metamaterial," Microwave and Optical Technology Letter, vol.48, no.12, pp. 2512-2516, Dec.2006.
[46]Q. Cheng and T. J. Cui, "Electromagnetic Properties of A Left-Handed Medium Slab Excited by Three-Dimensional Electric Dipoles," Phys Lett A, vol.345, pp.439-447.2005.
[47]I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Second-Harmonic Generation in Nonlinear Left-Handed Metamaterials," J Opt SocAm B, vol.23, pp.529-534,2006.
[48]A. Ourir, A. de Lustrac, and J.-M. Lourtioz, "Optimization of Metamaterial Based Subwavelength Cavities for Ultracompact Directive Antennas," Microwave and Optical Technology Letter, vol.48, no.12, pp.2573-2577, Dec 2006.
[49]D. Sievenpiper, "High Impedance Electromagnetic Surfaces," Ph. D. Thesis, University of California, Los Angeles,1999.
[50]L. Zhou, H. Li, Y. Qin, Z. Wei, and C. T. Chan, "Directive Emissions from Subwavelength Metamaterial-Based Cavities," ApplPhys Lett., vol.86,2005.
[51]A. P. Feresidis, G Goussetis, S. Wang, and J. C, "Vardaxoglou, Artificial Magnetic Conductor Surfaces and Their Application to Low-Profile Highgain Planar Antennas," IEEE Trans Antennas Propag., vol.53 pp.209-215.2005.
[52]S. Enoch, G Tayeb, P. Sabouroux, N. Guerin, and R. Vincent, "A Metamaterial for Directive Emission,"Phys Rev Lett., vol.89, pp.213902:1-4. Nov.2002.
[53]A. Ourir, A. de Lustrac, and J. M. Lourtioz, "All-Metamaterial-BasedSub-Wavelength Cavities for Ultra Thin Directive Antennas," Appl Phys Lett., vol.88, pp.084103:1-3, Jan. 2006.
[54]Zhongyan Sheng, and Vasundara V. Varadan, "Tuning the Effective Properties of Metamaterials by Changing the Substrate Properties," Jour. App. Phys., vol.101, pp.014909: 1-7.2007.
[55]Caloz and T. Itoh, "Novel Microwave Devices and Structures Based on The Transmission Line Approach of Metamaterials," IEEE Trans. Microwave Theory Tech., vol.1, pp. 195-198, June 2003.
[56]A. Sanada, C. Caloz and T. Itoh, "Characteristics of the Composite Right/Left-Handed Transmission Lines," IEEE Microwave Wireless Compon. Lett., vol.14, no.2, pp.68-70, Feb.2004.
[57]L. B. Felsen and N. Marcuvitz, "Radiation and Scattering of Waves," Reissue Edition, Ieee/Oup Series on Electronic Wave Theory,1996.
[58]Kittel, "Introduction to Solid State Physics," Eighth Edition, Wiley,2005.
[59]S. Ramo, J. R. Whinnery, and T. Van Duzer, "Fields and Waves in Communication Electronics," Third Edition, John Wiley& Sons,1994.
[60]M. D. Pozar, "Microwave Engineering," Third Edition, John Wiley& Sons,2004.
[61]R. E. Collin, "Foundations for Microwave Engineering," Second Edition, McGraw-Hill, 1992.
[62]Caloz, H. Okabe, T. Iwai, and T. Itoh, "Transmission Line Approach of Left-Handed (LH) Materials," USNC/URSI National Radio Science Meeting, San Antonio, TX, vol.1, pp.39, June 2002.
[63]Caloz and T. Itoh, "Transmission Line Approach of Left-Handed (LH) Structures and Microstrip Realization of A Low-Loss Broadband LH Filter," IEEE Trans. Antennas Propagat., vol.52, no.5, May 2004.
[64]Caloz, A. Sanada, and T. Itoh, "Microwave Applications of Transmission-Line Based Negative Refractive Index Structures," Proc. of Asia-Pacific Microwave Conf., Seoul, Korea, vol.3, pp.1708-1713, Nov.2003.
[65]A. Lai, C. Caloz and T. Itoh, "Transmission Line Based Metamaterials and Their Microwave Applications," Microwave Mag., vol.5, no.3, pp.34-50, Sept.2004.
[66]Cubukcu, K. Aydin, and E. Ozbay, "Subwavelength Resolution in a Two-Dimensional
Photonic-Crystal-Based Superlens," Physical Review Letter, vol.91, no.20, pp.207401: 1-4, Nov.2003.
[67]Ertugrul Cubukcu, Koray Aydin, Ekmel Ozbay, Stavroula Foteinopoulou, Costas M. Soukoulis, "Electromagnetic Waves:Negative Refraction by Photonic Crystals," Nature, vol. 423, pp.604-605, Jun.2003.
[68]Stefan Linden, Christian Enkrich, Martin Wegener, Jiangfeng Zhou, Thomas Koschny, Costas M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science, vol. 306. no.5700, pp.1351-1353, November 2004.
[69]Yen TJ, Padilla WJ, Fang N, Vier DC, Smith DR, Pendry JB, Basov DN, "Terahertz Magnetic Response from Artificial Materials," Science, vol.303, no.5663.2004.
[70]S. D. Gedney, "An Anisotropic Perfectly Matched Layer Absorbing Media for the Truncation of FDTD Lattices," IEEE Trans. Antennas Propagat, vol. AP-44, no.12, pp. 1630-1639, Dec.1996.
[71]L. Teixeira, W. C. Chew, M. Straka, "Finite-Difference Time-Domain Simulation of Ground Penetrating Radar on Dispersive, Inhomogeneous, and Cinductive Soils," IEEE Trans. Geoscience Remote Sensing, vol.36, no.6, pp.1928-1937, Nov.1998.
[72]A. P. Gandhi, B. Q. Gao, and J. Y. Chen, "A Frequency-Dependent Finite-difference Time-domain Formulation for General Dispersive Media," IEEE Trans. Microwave Theory Tech., vol.41, no.4, pp.658-665, Apr.1992.
[73]T. Kashiiva, Y. Ohtomo, and I. Fukai, "A Finite-difference Time-domain Formulation for Transient Propagation in Dispersive Media Associated with Cole-Cole's Circular ARC law," Microwave. Opt. Tech. Lett., vol.3, no.12, pp.416-419, Dec 1990.
[74]R. M. Joseph, S. C. Hagnes, and A. Taflove, "Direct Time Integration of Maxwell's Equation in Linear Dispersive Media with Absorption for Scatttering and Propagation of Femtosecond Electromagnetic Pulse," Opt. Lett., vol.16, no.18, pp.1412-1414, Sept 1991.
[75]M. Sullivan, "Frequency-Dependent FDTD Method Using Z Transform," IEEE Trans. Antennas Propagat., vol.40, no.10, pp.1223-1230, Oct 1992.
[76]D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method, New York, IEEE Press, pp.1-35,2000.
[77]R. J. Luebbers, F. P. Huusberger, K. S. Kunz, R. B. Standler, and M. Schneider, "A
Frequency-Dependent Finite-Difference Time-Domain Formulation for Dispersive Materials," IEEE Trans. Electromagn. Compat., vol.32, pp.222-227, Aug.1990.
[78]D. F. Kelley, and Raymond J. Luebbers, "Piecewise Linear Recursive Convolution for Dispersive Media Using FDTD," IEEE Trans. Antennas Propagat., vol.44, no.6, Jun.1996.
[79]A. Taflove, "Computational Electrodynamics," Norwood, MA, Artech House,1995.
[80]Zheng, Z. Chen, and J. Zhang, "A Finite-Difference Time-Domain Method without the Courant Stability Conditions," IEEEMicrow. Guided Wave Lett., vol.9, no.11, pp.441-443, Nov.1999.
[81]Yuan C and Chen Z, "A Three-Dimensional Unconditionally Stable ADI-FDTD Method in the Cylindrical Coordinate System," IEEE Trans Microwave Theory Tech., vol.50, pp. 2401-2405,2002.
[82]Chen HL, Chen B, Yi Y, et al, "Unconditionally Stable ADI-BOR-FDTD Algorithm for the Analysis of Rotationally Symmetric Geometries," IEEE Microwave Wire Comp Lett., vol.17, no.4, pp.304-306,2007.
[83]Zheng HX, "ADI-FDTD Formulation for General Dispersive Media," Antennas Propagat Intel Symp. IEEE, pp.1723-1726,2006.
[84]Wang SM, Chen J, and Ruchhoeft P, "An ADI-FDTD Method for Periodic Structures," IEEE Trans Antennas Propagat., vol.53, no.7, pp.2343-2346,2005.
[85]Zhao AP, "A Novel Implementation for Two-Dimensional Unconditionally Stable FDTD Method," Microwave Opt TechnolLett, vol.38, no.6, pp.457-462,2003.
[86]Sun G and Trueman CW, "Approximate Crank-Nicolson Schemes for the 2-D Finite-Difference Time Domain Method for TEz Waves," IEEE Trans Antennas Propagat., vol.52, no.11, pp.2963-2972,2004.
[87]Sun G and Trueman CW, "Unconditionally-Stable FDTD Method Based on Crank-Nicolson Scheme for Solving Three-Dimensional Maxwell Equations," Electron Lett., vol.40, no.10, pp.589-590,2004.
[88]Sun G and Trueman CW, "Efficient Implementations of the Crank-Nicolson Scheme for the Finite-Difference Time-Domain Method," IEEE Trans. Microwave Theory Tech., vol.54, no. 5, pp.2275-2284,2006.
[89]Yang Y, Chen RS, and Yung EKN, "The Uncondionally Stable Crank-Nicolson FDTD Method for Tthree-Dimensional Maxwell's Equations," Microwave Opt Technol Lett., vol. 48, no.8, pp.1619-1622,2006.
[90]A. Alighanbari, C. D. Sarris, "A High-Order MRTD Technique with Laguerre-Polynomial-Based Time-Integration," IEEE AP-S Symposium on Antennas and Propagation, July 2005.
[91]J. Chen and J. Wang, "A Novel WCS-FDTD Method with Weakly Conditional Stability," IEEE Trans. Electromagn. Compat., vol.49, no.2, pp.419-426, May 2007.
[92]Deseham Ps, G A., "Microstrip Microwave Antenas." 3rd USFA SymPosium on Antennas, 1953.
[93]Howell, J. Q, "Microstrip Antenas." IEEEAP-SInt. Symp. Digest,1972.
[94]Z. H. Qian and R. S. Chen, "FDTD Analysis of Microstrip Patch Antenna Covered by Plasma Sheath," Progress In Electromagnetics Research, PIER 52,173-183,2005.
[95]W. Xu, L.-W. Li, H.-Y. Yao, T.-S. Yeo and Q. Wu, "Left-Handed Material Effects on Wave's Modes and Resonant Frequencies:Field Waveguide Structures and Substrate-Loaded Patch Antennas," Journal of Electromagnetic Waves and Applications, vol.19, no. 15, pp.2033-2047, October,2005.
[96]K. P. Prokopidis and T. D. Tsiboukis, "The Effect of Dispersion on the Operation of Square Microstrip Antennas," IEEE Trans. Magnetics, vol.42, no.4. Apr.2006.
[97]X. Zhang, J. Fang, K. K. Mei, and Y. Liu, "Calculations of the Dispersive Characteristics of Microstrips by the Time-Domain Finite-Different Different Method," IEEE Trans. Microwave Theory Tech., vol.36, pp.263-267, Feb.1988.
[98]X. Zhang and K. K. Mei, "Time Domain Finite Difference Approach to the Calculation of the Frequency Dependent Characteristics of Microstrip Discontinuities," IEEE Trans. Microwave Theory Tech., vol.36, pp.1775-1787, Dec.1988.
[99]Liang, Y. Liu, and K. K. Mei, "Full-Wave Analysis of Coplanar Waveguide and Slotline Using the Time-Domain Finite-Difference Method," IEEE Trans. Microwave Theory Tech., vol.37, pp.1949-1957, Dec.1989.
[100]D. M. Sheen, S. M. Ali, M. D. Abouzahra, and J. A. Kong, "Application of the Three-Dimensional Finite-Difference Time-Domain Method to the Analysis of Planar Microstrip Circuits," IEEE Trans. Microwave Theory Tech., vol.38, pp.849-857, July 1990.
[101]J. Litva, Z. Bi, K. Wu, R. Fralich, and C. Wu, "Full-Wave Analysis of an Assortment of Printed Antenna Structures Using the FD-TD Method," 1991IEEEAP-SInt. Symp. Dig., pp. 410-413, June 1991.
[102]Mur, "Absorbing Boundary Conditions for the Finitr-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Trans. Electromagn Compat, vol. emc-23, no.4, Nov 1981.
[103]Z. Bi, K. Wu, C. Wu, and J. Litva, "A Dispersive Boundary Condition for Microstrip Component Analysis Using The FD-TD Method," IEEE Trans. Microwave Theory Tech., vol.40, no.4, Apr.1992.
[104]K. P. Prokopidis and T. D. Tsiboukis, "The Effect of Dispersion on the Operation of Square Microstrip Antennas," IEEE Trans. Magnetics, vol.42, no.4. Apr.2006.
[105]DesehamPs, G A., "Microstrip Microwave Antenas," 3rd USFA SymPosium on Antennas, 1953.
[106]Howell, J. Q, "Microstrip Antena" IEEE APS Int. Symp. Digest,1972.
[107]Z. H. Qian and R. S. Chen, "FDTD Analysis of Microstrip Patch Antenna Covered by Plasma Sheath," Progress In Electromagnetics Research, PIER 52,173-183,2005.
[108]W. Xu, L.-W. Li, H.-Y. Yao, T.-S. Yeo and Q. Wu, "Left-Handed Material Effects on Wave's Modes and Resonant Frequencies:Field Waveguide Structures and Substrate-Loaded Patch Antennas," Journal of Electromagnetic Waves and Applications, vol.19, no. 15, pp.2033-2047, October,2005.
[109]K. P. Prokopidis and T. D. Tsiboukis, "The Effect of Dispersion on the Operation of Square Microstrip Antennas," IEEE Trans. Magnetics, vol.42, no.4. Apr.2006.
[110]X. Zhang, J. Fang, K. K. Mei, and Y. Liu, "Calculations of the Dispersive Characteristics of Microstrips by the Time-DomainFinite-Different Different Method," IEEE Trans. Microwave Theory Tech., vol.36, pp.263-267, Feb.1988.
[111]X. Zhang and K. K. Mei, "Time Domain Finite Difference Approach to the Calculation of the Frequency Dependent Characteristics of Microstrip Discontinuities," IEEE Trans. Microwave Theory Tech., vol.36, pp.1775-1787, Dec.1988.
[112]Liang, Y. Liu, and K. K. Mei, "Full-Wave Analysis of Coplanar Waveguide and Slotline Using the Time-Domain Finite-Difference Method," IEEE Trans. Microwave Theory Tech., vol.37, pp.1949-1957, Dec.1989.
[113]D. M. Sheen, S. M. Ali, M. D. Abouzahra, and J. A. Kong, "Application of the Three-Dimensional Finite-Difference Time-Domain Method to The Analysis of Planar Microstrip Circuits," IEEE Trans. Microwave Theory Tech., vol.38, pp.849-857, July 1990.
[114]Litva, Z. Bi, K. Wu, R. Fralich, and C. Wu, "Full-Wave Analysis of an Assortment of Printed Antenna Structures Using the FD-TD Method," 1991 IEEE AP-S Int. Symp. Dig., June 1991, pp.410-413.
[115]Mur, "Absorbing Boundary Conditions for the Finitr-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Trans. Electromagn Compat., vol. emc-23, no.4, Nov 1981.
[116]Z. Bi, K. Wu, C. Wu, and J. Litva, "A Dispersive Boundary Condition for Microstrip Component Analysis Using The FD-TD Method," IEEE Trans. Microwave Theory Tech., vol.40, no.4, Apr.1992.
[117]P. Prokopidis and T. D. Tsiboukis, "The Effect of Dispersion on the Operation of Square Microstrip Antennas," IEEE Trans. Magnetics, vol.42, no.4. Apr.2006.