基于缝隙耦合腔链异向传输线谐振器的研究
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摘要
异向介质是等效介电常数和等效磁导率同时为负数的人造介质,是物理学和电磁学领域的一个新兴的研究热点。异向介质具有许多异于普通介质的特殊性质,如负折射率、逆多普勒效应、逆切伦科夫辐射以及相速度与群速度的方向相反等等。目前,主要有两种方式实现微波异向介质:1.金属棒(ROD)和开路谐振环(SRR)的阵列结构;2.基于传输线的结构。一维的异向介质又被称为异向传输线,异向传输线是异向介质最可能被广泛应用的形式,现有被提出的异向介质的应用几乎都以异向传输线形式实现的。本论文分析了微波异向介质所具有的一些特殊电磁特性,着重分析了实现异向介质的两种方法,在此基础提出新的基于金属波导的异向介质传输线的结构,并对异向介质传输线的应用做了一些探讨。
本文根据经典电磁理论和电路理论,通过严格数学推导建立电磁波在异向传输线中的传输机理;并根据这一传输机理提出可以实现“异向传输线结构的传输线单元等效电路。通过在空间中加载金属周期结构等效出异向介质的传输线单元等效电路,从而设计出可工作在较高频率、有较大功率容量、低损耗的异向介质”,并通过仿真和试验证明结构的合理性,最后给出这种异向介质的设计方法。
首先对隙缝耦合腔链实现异向传输线进行了研究,提出了一种新的异向传输线实现方法。利用场论方法和有限元法的本征模式仿真对结构的色散特性进行了分析,证明所提出的结构存在左手通带,可以看成异向传输线。利用有限元法的驱动模式仿真对结构中电磁波的传播特性进行了分析。
然后设计出一种新型的谐振腔,该谐振腔的谐振条件与普通谐振腔不同,其两个端面的总相移不必是180°的正整数倍。这种谐振腔由异向传输线和右手传输线两种不同性质的传输线级联构成,它利用耦合腔链作为异向传输线实现负相移,同轴波导作为右手传输线实现正相移,使谐振腔两个端面的总相移为零,满足谐振腔的谐振条件。由于它与传统谐振腔谐振条件不同,理论证明这种谐振腔的长度可远远小于传统谐振腔,设计实例的仿真结果表明这种新型谐振腔的长度最短仅为传统谐振腔的1/ 7。
Metamaterial is one of the frontiers of Physics and Electromagnetism currently, which is a kind of artificial material with simultaneously negative permittivity and permeability. It has many special characters different from normal materials, such as negative refraction, inverse Doppler effect, inverse Cerenkov radiation, anti-paralled phase and group velocities, and so on. There are two methods to realize metamaterial at present: the first is (ROD) and split ring resonators (SRR) array and the other is based on transmission line. One dimension metamaterial is also called left-handed transmission line, which will be most probably used in microwave application because the most of proposed metamaterial are based on left-handed transmission line. In this paper, some special characters of metamaterial are analyzed and the realization of metamaterial are mainly focused on. Based on above analysis, a new type of left-handed transmission line based on waveguide is proposed, and then the application of it is discussed.
In this paper,according to classical EM filed theory and circuit theory, this project will establish the transmission mechanism for EM wave in left-handed material(LHM) by strictly mathematic deduction. Unit equivalent circuit of Transmission line for LHM can be proposed in accordance with the transmission mechanism.Working on realizing the unit equivalent circuit by loading metallic periodic structure in LHM with higher working frequency, power capacity as well as lower loss can be designed. The rationality of the new structure will be proved by means of simulation and experiment and the desinging method for the LHM will be given atlast.
At first, a novel realization of left-handed transmission line is presented; the proposed structure is based on resonant-slot coupled cavity chain. The dispersion characteristic of two different resonant-slot coupled cavity chain cells are studied in the way of field theory and FEM eigenmode simulation, a LH Passband . at last, a backward wave behavior is predicted and demonstrated unambiguously from driven modal simulation.
For more, a new of cavity resonators is presented according to the proposed left-handed transmission line。Resonant condition of this new cavity resonator is different from that of the traditional cavity resonators for its total phase shift need not be a positive integral multiple of 180°. The left-handed transmission line (LHTL) which can realize a negative phase shift is a resonant-slot coupled cavity chain, while the right-handed t ransmission line (RHTL) which realizes a positive phase shift is a coaxial waveguide , and resonant condition can be satisfied as long as the total phase shift keep zero. Because of it s larruping resonant condition , the theory and simulation prove the length of the cavity resonators can be much smaller than that of the traditional cavity resonator.
本文根据经典电磁理论和电路理论,通过严格数学推导建立电磁波在异向传输线中的传输机理;并根据这一传输机理提出可以实现“异向传输线结构的传输线单元等效电路。通过在空间中加载金属周期结构等效出异向介质的传输线单元等效电路,从而设计出可工作在较高频率、有较大功率容量、低损耗的异向介质”,并通过仿真和试验证明结构的合理性,最后给出这种异向介质的设计方法。
首先对隙缝耦合腔链实现异向传输线进行了研究,提出了一种新的异向传输线实现方法。利用场论方法和有限元法的本征模式仿真对结构的色散特性进行了分析,证明所提出的结构存在左手通带,可以看成异向传输线。利用有限元法的驱动模式仿真对结构中电磁波的传播特性进行了分析。
然后设计出一种新型的谐振腔,该谐振腔的谐振条件与普通谐振腔不同,其两个端面的总相移不必是180°的正整数倍。这种谐振腔由异向传输线和右手传输线两种不同性质的传输线级联构成,它利用耦合腔链作为异向传输线实现负相移,同轴波导作为右手传输线实现正相移,使谐振腔两个端面的总相移为零,满足谐振腔的谐振条件。由于它与传统谐振腔谐振条件不同,理论证明这种谐振腔的长度可远远小于传统谐振腔,设计实例的仿真结果表明这种新型谐振腔的长度最短仅为传统谐振腔的1/ 7。
Metamaterial is one of the frontiers of Physics and Electromagnetism currently, which is a kind of artificial material with simultaneously negative permittivity and permeability. It has many special characters different from normal materials, such as negative refraction, inverse Doppler effect, inverse Cerenkov radiation, anti-paralled phase and group velocities, and so on. There are two methods to realize metamaterial at present: the first is (ROD) and split ring resonators (SRR) array and the other is based on transmission line. One dimension metamaterial is also called left-handed transmission line, which will be most probably used in microwave application because the most of proposed metamaterial are based on left-handed transmission line. In this paper, some special characters of metamaterial are analyzed and the realization of metamaterial are mainly focused on. Based on above analysis, a new type of left-handed transmission line based on waveguide is proposed, and then the application of it is discussed.
In this paper,according to classical EM filed theory and circuit theory, this project will establish the transmission mechanism for EM wave in left-handed material(LHM) by strictly mathematic deduction. Unit equivalent circuit of Transmission line for LHM can be proposed in accordance with the transmission mechanism.Working on realizing the unit equivalent circuit by loading metallic periodic structure in LHM with higher working frequency, power capacity as well as lower loss can be designed. The rationality of the new structure will be proved by means of simulation and experiment and the desinging method for the LHM will be given atlast.
At first, a novel realization of left-handed transmission line is presented; the proposed structure is based on resonant-slot coupled cavity chain. The dispersion characteristic of two different resonant-slot coupled cavity chain cells are studied in the way of field theory and FEM eigenmode simulation, a LH Passband . at last, a backward wave behavior is predicted and demonstrated unambiguously from driven modal simulation.
For more, a new of cavity resonators is presented according to the proposed left-handed transmission line。Resonant condition of this new cavity resonator is different from that of the traditional cavity resonators for its total phase shift need not be a positive integral multiple of 180°. The left-handed transmission line (LHTL) which can realize a negative phase shift is a resonant-slot coupled cavity chain, while the right-handed t ransmission line (RHTL) which realizes a positive phase shift is a coaxial waveguide , and resonant condition can be satisfied as long as the total phase shift keep zero. Because of it s larruping resonant condition , the theory and simulation prove the length of the cavity resonators can be much smaller than that of the traditional cavity resonator.
引文
[1] Veselago V G. The Electrodynamics of Substances with Simultaneously Negative Values ofεandμ. Sov Phys Usp, 1968, 10(4): 509-514
[2] Pendry J B, Holden A J, Stewart W J, et al. Extremely Low Frequency Plasmons in Metallic Mesostructures. Physical Review Letters, 1996, 76(25): 4773-4776
[3] Pendry J B, Holden A J, Bobbins D J, et al. Low frequency plasmons in thin-wire structures. Journal of Physics: Condensed Matter, 1998, 10:4785-4809
[4] Pendry J B, Holden A J, Bobbins D J, et al. Magnetism from Conductors and Enhanced Nonlinear Phenomena. IEEE Transactions on Microwave Theory and Techniques, 1999, 47(11): 2075-2084
[5] Smith D R, Vier D C, Willie Padilla, et al. Loop-wire medium for investigating plasmons at microwave frequencies. Applied Physics Letters, 1999, 75(10): 1425-1427]
[6] Shelby R A, Smith D R, Schultz S. Experimental Verification of a Negative Index of Refraction. Science, 2001, 292(6): 77-79
[7]徐耿钊,张伟华,朱星.奇妙的左手物质.物理, 2004, 33(11): 801-807
[8] Weiland T, Schuhmann R, Greegor R B, et al. Ab initio numerical simulation of left-handed metamaterials: Comparison of calculations and experiments. Journal of Applied Physics, 2001, 90(10): 5419-5424
[9] Markos P, Soukoulis C M. Numerical studies of left-handed materials and arrays of split ring resonators. Physical Review E, 2002, 65: 036622-1- 036622-8
[10] Smith D R, Schultz S, Markos P, et al. Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Physical Review B, 2002, 65: 195104-1-195104-5
[11] Caloz C, Chang C C, Itoh T. Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations. Journal of Applied Physics, 2001, 90(11): 5483-5486
[12] Smith D R, Willie J Padilla, Vier D C, et al. Composite Medium with Simultaneously Negative Permeability and Permittivity. Physical Review Letters, 2000, 84(18): 4184-4187
[13] Ricardo Marques, Francisco Medina, Rafii-ElIdrissi. Role of bianisotropy in negative permeability and left-handed metamaterials. Physical Review B, 2002, 65: 144440-1-144440-6
[14] Valanju P M, Walser R M, Valanju A P. Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous. Physical Review Letters, 2002, 88(18): 187401-1-187401-4
[15] Garcia N, Nieto-Vesperinas M. Is there an experimental verification of a negative index of refraction yet. Optoelectronics Letters, 2002, 27(11): 885-887
[16]黄志洵.微波异常传播中的负折射问题.物理,2001,30(11):689-692
[17]黄志洵.超光速研究新进展.北京:国防工业出版社,2002,189-196
[18] Gennaro E D, Parimi P V, Lu W T, et al. Slow microwaves in left-handed materials. Physical Review B, 2005, 72: 033110-1-033110-4
[19] Kong J A. Electromagnetic wave interaction with stratified negative isotropic media. Progress In Electromagnetics Research, 2002, 35(4): 1-52
[20] Kong J A, Wu B I, Zhang Y. Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability. Applied Physics Letters, 2001, 80 (12): 2084-2086
[21]杰克逊J D.经典电动力学(朱培豫译).北京:人民教育出版社,1982,313-329
[22]龚中麟,徐承和.近代电磁理论.北京:北京大学出版社,1990,32-42
[23] Grbic A, Eleftheriades G V. Subwavelength Focusing Using a Negative-Refractive-Index Transmission Line Lens. IEEE Antennas and Wireless Propagation Letters, 2003, 2(1): 186-189
[24] Caloz C, Okabe H, Iwai T, et al. Transmission line approach of left-handed (LH) materials. USNC/URSI National Radio Science Meeting Digest, 2002, 41-45
[25] Eleftheriades G V, Iyer A K, Kremer P C. Planar Negative Refractive Index Media Using Periodically L-C Loaded Transmission Lines. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(12): 2072-2712
[26] L. Shaowei, Y. Pin, X. Jianhua, et al., Coaxial Waveguide Based Left-Handed Transmission Line, IEEE Microwave and Wireless Compon. Lett., 2007, 8: 568-570.
[27] J.Garcia-Garcia,F.Martin,F.Falcone,J.Bonache,I.Gil,T.Lopetegi,M.A.G.Laso,M.Sorolla,R. Marques.Spurious Passband Suppression in Microstrip Coupled Line Band Pass Filters by Means of Split Ring Resonators.IEEE Microwave and Wireless Components Letters.2004,14(9) :416~418
[28] M.A.AntoniadesG.V.Eleftheriades.A Broadband Wilkinson Balun Using Microstrip Metamaterial Lines.IEEE Antennas and Wireless Propagation Letters.2005,4(1):209~212
[29] L. Shaowei, Y. Pin, X. Jianhua, et al.,“Left-handed Transmission Line Based on Resonant-Slot Coupled Cavity Chain,”IEEE Microwave and Wireless Compon. Lett., 2007, 4:292-294.
[30] Antoniades M A, Eleftheriades G V. Compact linear lead/lag metamaterial phase shifters for broadband applications. IEEE Antennas and Wireless Propagation Letters, 2003, 2(1): 103-106
[31] Ricardo Marques, Francisco Medina, Rafii-ElIdrissi. Role of bianisotropy in negative permeability and left-handed metamaterials. Physical Review B, 2002, 65: 144440-1-144440-6
[32] Smith D R, Schultz S, Kroll N. Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity. Applied Physics Letters, 1994, 65(5): 645-647
[33] Sui Q, Li C, Lin L L, et al. Experimental Study ofλ/4 Monopole Antennas in a Left-Handed Meta-Material. Progress In Electromagnetics Research, 2005, 51(3): 281-293
[34] Grbic A, Eleftheriades G V. A backward-wave antenna based on negative refractive index L-C networks. IEEE International Symposium on Antennas and Propagation, 2002, 4(1): 340-343
[35] Huangfu Jiangtao, Ran Lixin, Chen Hongsheng, et al. Experimental confirmation of negative refractive index of a metamaterial composed of a ?-like metallic patterns. Applied Physics Letters, 2004, 84(9): 1537-1539
[36] Chen Hongsheng, Ran LiXin, Huangfu Jiangtao, et al. Left-handed materials composed of only S-shaped resonators. Physical Review E, 2004, 70: 057605-1-057605-4
[37] Collin R E. Foundations for Microwave Engineering, 2nd. New York: McGraw-Hill, 1992:552-556, 570.
[38] Pozar D M. Microwave Engineering, 2nd. New York: Wiley, 1998:424-427, 162.
[39] Decoopman T, Marteau A, Lheurette E, et al. Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology. IEEE Trans. Microw. Theory Tech., 2006, 54(4):1451-1457
[40] Salehi H, Mansour R R. A new realization of left-handed transmission lines employing a coaxial waveguide structure. IEEE MTT-S Int. Microwave Symp., Long Beach, CA, Jun. 2005:1941-1944
[41] Salehi H, Mansour R R. A new realization of left-handed transmission lines employing a coaxial waveguide structure. IEEE MTT-S Int. Microwave Symp., Long Beach, CA, Jun. 2005:1941-1944
[42] Kim H, Kozyrev A B, Karbassi A, et al.. Linear tunable phase shifter using a left-handed transmission line. IEEE Antennas Wireless Propag. Lett., 2005,15(5): 366-368.
[43] Caloz C, Sanada A, Itoh T. A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth. IEEE Trans. Microwave Theory Tech, 2004,52(3): 980-992
[44] Antoniades M A, Eleftheriades G V. A broadband wilkinson balun using microstrip metamaterial lines. IEEE Antennas Wireless Propag. Lett ., 2005,4(1): 209-212.
[45] Bevensee R M, Electromagnetic Slow Wave System, New York: Wiley, 1964. p207-212
[46] N .Engheta. An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability[J]. IEEE Antennas Wireless Propag. Lett., 2002, 1(1):10-13.
[47] Li Y, Ran L X, Chen H S, et al. Experimental Realization of a One-Dimensional LHM–RHM Resonator[J]. IEEE Trans. Microwave Theory Tech., 2005, 53(4):1522-1526.
[48] Allen, G. S Kino, On the Theory of Strongly Coupled Cavity Chains. IEEE Trans. Microwave Theory Tech., 1960, 8(3):362-372.
[49] M. A. Allen, G. S Kino,“On the Theory of Strongly Coupled Cavity Chains,”IEEE Trans. Microwave Theory Tech., vol. 8, no. 3, pp. 362-372, May 1960.
[50] E. L. Ginzton, microwave measurements, New York: McGraw-Hill, 1957, pp. 403.
[2] Pendry J B, Holden A J, Stewart W J, et al. Extremely Low Frequency Plasmons in Metallic Mesostructures. Physical Review Letters, 1996, 76(25): 4773-4776
[3] Pendry J B, Holden A J, Bobbins D J, et al. Low frequency plasmons in thin-wire structures. Journal of Physics: Condensed Matter, 1998, 10:4785-4809
[4] Pendry J B, Holden A J, Bobbins D J, et al. Magnetism from Conductors and Enhanced Nonlinear Phenomena. IEEE Transactions on Microwave Theory and Techniques, 1999, 47(11): 2075-2084
[5] Smith D R, Vier D C, Willie Padilla, et al. Loop-wire medium for investigating plasmons at microwave frequencies. Applied Physics Letters, 1999, 75(10): 1425-1427]
[6] Shelby R A, Smith D R, Schultz S. Experimental Verification of a Negative Index of Refraction. Science, 2001, 292(6): 77-79
[7]徐耿钊,张伟华,朱星.奇妙的左手物质.物理, 2004, 33(11): 801-807
[8] Weiland T, Schuhmann R, Greegor R B, et al. Ab initio numerical simulation of left-handed metamaterials: Comparison of calculations and experiments. Journal of Applied Physics, 2001, 90(10): 5419-5424
[9] Markos P, Soukoulis C M. Numerical studies of left-handed materials and arrays of split ring resonators. Physical Review E, 2002, 65: 036622-1- 036622-8
[10] Smith D R, Schultz S, Markos P, et al. Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Physical Review B, 2002, 65: 195104-1-195104-5
[11] Caloz C, Chang C C, Itoh T. Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations. Journal of Applied Physics, 2001, 90(11): 5483-5486
[12] Smith D R, Willie J Padilla, Vier D C, et al. Composite Medium with Simultaneously Negative Permeability and Permittivity. Physical Review Letters, 2000, 84(18): 4184-4187
[13] Ricardo Marques, Francisco Medina, Rafii-ElIdrissi. Role of bianisotropy in negative permeability and left-handed metamaterials. Physical Review B, 2002, 65: 144440-1-144440-6
[14] Valanju P M, Walser R M, Valanju A P. Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous. Physical Review Letters, 2002, 88(18): 187401-1-187401-4
[15] Garcia N, Nieto-Vesperinas M. Is there an experimental verification of a negative index of refraction yet. Optoelectronics Letters, 2002, 27(11): 885-887
[16]黄志洵.微波异常传播中的负折射问题.物理,2001,30(11):689-692
[17]黄志洵.超光速研究新进展.北京:国防工业出版社,2002,189-196
[18] Gennaro E D, Parimi P V, Lu W T, et al. Slow microwaves in left-handed materials. Physical Review B, 2005, 72: 033110-1-033110-4
[19] Kong J A. Electromagnetic wave interaction with stratified negative isotropic media. Progress In Electromagnetics Research, 2002, 35(4): 1-52
[20] Kong J A, Wu B I, Zhang Y. Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability. Applied Physics Letters, 2001, 80 (12): 2084-2086
[21]杰克逊J D.经典电动力学(朱培豫译).北京:人民教育出版社,1982,313-329
[22]龚中麟,徐承和.近代电磁理论.北京:北京大学出版社,1990,32-42
[23] Grbic A, Eleftheriades G V. Subwavelength Focusing Using a Negative-Refractive-Index Transmission Line Lens. IEEE Antennas and Wireless Propagation Letters, 2003, 2(1): 186-189
[24] Caloz C, Okabe H, Iwai T, et al. Transmission line approach of left-handed (LH) materials. USNC/URSI National Radio Science Meeting Digest, 2002, 41-45
[25] Eleftheriades G V, Iyer A K, Kremer P C. Planar Negative Refractive Index Media Using Periodically L-C Loaded Transmission Lines. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(12): 2072-2712
[26] L. Shaowei, Y. Pin, X. Jianhua, et al., Coaxial Waveguide Based Left-Handed Transmission Line, IEEE Microwave and Wireless Compon. Lett., 2007, 8: 568-570.
[27] J.Garcia-Garcia,F.Martin,F.Falcone,J.Bonache,I.Gil,T.Lopetegi,M.A.G.Laso,M.Sorolla,R. Marques.Spurious Passband Suppression in Microstrip Coupled Line Band Pass Filters by Means of Split Ring Resonators.IEEE Microwave and Wireless Components Letters.2004,14(9) :416~418
[28] M.A.AntoniadesG.V.Eleftheriades.A Broadband Wilkinson Balun Using Microstrip Metamaterial Lines.IEEE Antennas and Wireless Propagation Letters.2005,4(1):209~212
[29] L. Shaowei, Y. Pin, X. Jianhua, et al.,“Left-handed Transmission Line Based on Resonant-Slot Coupled Cavity Chain,”IEEE Microwave and Wireless Compon. Lett., 2007, 4:292-294.
[30] Antoniades M A, Eleftheriades G V. Compact linear lead/lag metamaterial phase shifters for broadband applications. IEEE Antennas and Wireless Propagation Letters, 2003, 2(1): 103-106
[31] Ricardo Marques, Francisco Medina, Rafii-ElIdrissi. Role of bianisotropy in negative permeability and left-handed metamaterials. Physical Review B, 2002, 65: 144440-1-144440-6
[32] Smith D R, Schultz S, Kroll N. Experimental and theoretical results for a two-dimensional metal photonic band-gap cavity. Applied Physics Letters, 1994, 65(5): 645-647
[33] Sui Q, Li C, Lin L L, et al. Experimental Study ofλ/4 Monopole Antennas in a Left-Handed Meta-Material. Progress In Electromagnetics Research, 2005, 51(3): 281-293
[34] Grbic A, Eleftheriades G V. A backward-wave antenna based on negative refractive index L-C networks. IEEE International Symposium on Antennas and Propagation, 2002, 4(1): 340-343
[35] Huangfu Jiangtao, Ran Lixin, Chen Hongsheng, et al. Experimental confirmation of negative refractive index of a metamaterial composed of a ?-like metallic patterns. Applied Physics Letters, 2004, 84(9): 1537-1539
[36] Chen Hongsheng, Ran LiXin, Huangfu Jiangtao, et al. Left-handed materials composed of only S-shaped resonators. Physical Review E, 2004, 70: 057605-1-057605-4
[37] Collin R E. Foundations for Microwave Engineering, 2nd. New York: McGraw-Hill, 1992:552-556, 570.
[38] Pozar D M. Microwave Engineering, 2nd. New York: Wiley, 1998:424-427, 162.
[39] Decoopman T, Marteau A, Lheurette E, et al. Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology. IEEE Trans. Microw. Theory Tech., 2006, 54(4):1451-1457
[40] Salehi H, Mansour R R. A new realization of left-handed transmission lines employing a coaxial waveguide structure. IEEE MTT-S Int. Microwave Symp., Long Beach, CA, Jun. 2005:1941-1944
[41] Salehi H, Mansour R R. A new realization of left-handed transmission lines employing a coaxial waveguide structure. IEEE MTT-S Int. Microwave Symp., Long Beach, CA, Jun. 2005:1941-1944
[42] Kim H, Kozyrev A B, Karbassi A, et al.. Linear tunable phase shifter using a left-handed transmission line. IEEE Antennas Wireless Propag. Lett., 2005,15(5): 366-368.
[43] Caloz C, Sanada A, Itoh T. A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth. IEEE Trans. Microwave Theory Tech, 2004,52(3): 980-992
[44] Antoniades M A, Eleftheriades G V. A broadband wilkinson balun using microstrip metamaterial lines. IEEE Antennas Wireless Propag. Lett ., 2005,4(1): 209-212.
[45] Bevensee R M, Electromagnetic Slow Wave System, New York: Wiley, 1964. p207-212
[46] N .Engheta. An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability[J]. IEEE Antennas Wireless Propag. Lett., 2002, 1(1):10-13.
[47] Li Y, Ran L X, Chen H S, et al. Experimental Realization of a One-Dimensional LHM–RHM Resonator[J]. IEEE Trans. Microwave Theory Tech., 2005, 53(4):1522-1526.
[48] Allen, G. S Kino, On the Theory of Strongly Coupled Cavity Chains. IEEE Trans. Microwave Theory Tech., 1960, 8(3):362-372.
[49] M. A. Allen, G. S Kino,“On the Theory of Strongly Coupled Cavity Chains,”IEEE Trans. Microwave Theory Tech., vol. 8, no. 3, pp. 362-372, May 1960.
[50] E. L. Ginzton, microwave measurements, New York: McGraw-Hill, 1957, pp. 403.