具有强非线性和旋电效应的有源微波媒质研究
|
摘要
本文结合Maxwell-Garnett等效媒质理论和人工媒质的有源构造方法,分别进行了具有强非线性和旋电效应的有源人工微波媒质研究。
自然媒质在微波频段通常只呈现极其微弱的非线性效应。对比类别丰富的空间光学非线性应用,微波频段的非线性应用通常局限于微波电路中实现。基于等效媒质理论,本文研究、设计和实现了具有强空间非线性电磁响应的有源人工微波媒质,在微瓦级空间微波照射下观测到了清晰的空间谐波产生和频谱调制等非线性效应,并从实验测量数据中有效地提取了上述人工微波媒质的等效非线性特征本构参数。在上述工作基础上,本文提出并实验演示了微波源的非线性空间成像和远场重构,得到了超过Abbe衍射极限(Abbe diffraction limit)的空间分辨率。
在Maxwell理论中,电磁波的传播满足互易原理,并在能量守恒的条件下遵循局部时间反演对称(Local time-reversal symmetry)。仅在外加偏置场的条件下,自然存在的少量回旋(Gyrotropic)媒质,如磁化等离子体和铁氧体,可以呈现微弱的非互易旋电或旋磁效应。本文创新地利用微波电路中常见的单向元件,提出了无需外加偏置磁场即可呈现强旋电效应的有源人工媒质构造方法。通过将有源元件的单向性转化为等效媒质的非互易电磁响应,物理实现了仅需直流电压偏置的人工旋电微波媒质,并采用逆问题优化算法提取了对应的等效特征本构参数。在进一步的实验研究中,本文清晰观测到了具有显著极化角度偏转的法拉第极化旋转效应,验证了电磁波在上述人工媒质传播中不对称的局部时间反演。
本文研究所得的两种人工微波媒质从原理上避免了相应的自然存在媒质在微波频段的性能局限,具有很好的潜在应用前景。
In this dissertation, assisted by Maxwell-Garnett effective medium theory and the construction approach with active elements, research on active metamaterials with strong microwave responses of nonlinearity and gyroelectricity were conducted.
At the microwave frequencies, natural media usually exhibit extremely weak nonlinear effects. Compared with diverse spatial nonlinear optical applications, nonlinear applications at microwave frequencies are usually limited to microwave circuits. Based on the effective medium theory, we designed and realized an active metamaterial with strong spatial nonlinear electromagnetic (EM) responses. Under the illumination of a micro-Watt spatial microwave, strong nonlinear EM responses, like spatial harmonic generation and spectrum modulation, were clearly observed. After that, the effective nonlinear constitutive parameters of the active metamaterial were successfully retrieved from measured data. Based on above research, we proposed and experimentally demonstrated the imaging of microwave sources. Spatial resolutions exceeding the Abbe diffraction limit were achieved.
In Maxwell's theory, EM waves propagating in most natural media satisfy the reciprocal theory. When energy conservation is satisfied, this propagation exhibits a local time-reversal symmetry. Few naturally occurring gyrotropic media, such as magnetized plasma and ferrite, behave relatively weak non-reciprocal, gyroelectric or gyromagnetic phenomena only when external bias magnetic fields are applied. In this dissertation, by innovatively introducing unidirectional devices commonly used in active microwave circuits, we proposed a construction method of the active metamaterial with strong gyroelectric effects in the absence of an external magnetic bias. By translating the property of a unidirectional active device into the non-reciprocal response of effective media, we realized a gyroelectric metamaterial that only depends on a DC-voltage bias. Effective constitutive parameters were retrieved by using an optimization algorithm. In further experiments, strong non-reciprocal Faraday rotations with large deflected polarization angles were observed, breaking the local time-reversal symmetry.
The obtained active metamaterials fundamentally avoided the inherent performance limits of the corresponding naturally occurring media at microwave frequencies, showing a wide range of potential applications in the future.
自然媒质在微波频段通常只呈现极其微弱的非线性效应。对比类别丰富的空间光学非线性应用,微波频段的非线性应用通常局限于微波电路中实现。基于等效媒质理论,本文研究、设计和实现了具有强空间非线性电磁响应的有源人工微波媒质,在微瓦级空间微波照射下观测到了清晰的空间谐波产生和频谱调制等非线性效应,并从实验测量数据中有效地提取了上述人工微波媒质的等效非线性特征本构参数。在上述工作基础上,本文提出并实验演示了微波源的非线性空间成像和远场重构,得到了超过Abbe衍射极限(Abbe diffraction limit)的空间分辨率。
在Maxwell理论中,电磁波的传播满足互易原理,并在能量守恒的条件下遵循局部时间反演对称(Local time-reversal symmetry)。仅在外加偏置场的条件下,自然存在的少量回旋(Gyrotropic)媒质,如磁化等离子体和铁氧体,可以呈现微弱的非互易旋电或旋磁效应。本文创新地利用微波电路中常见的单向元件,提出了无需外加偏置磁场即可呈现强旋电效应的有源人工媒质构造方法。通过将有源元件的单向性转化为等效媒质的非互易电磁响应,物理实现了仅需直流电压偏置的人工旋电微波媒质,并采用逆问题优化算法提取了对应的等效特征本构参数。在进一步的实验研究中,本文清晰观测到了具有显著极化角度偏转的法拉第极化旋转效应,验证了电磁波在上述人工媒质传播中不对称的局部时间反演。
本文研究所得的两种人工微波媒质从原理上避免了相应的自然存在媒质在微波频段的性能局限,具有很好的潜在应用前景。
In this dissertation, assisted by Maxwell-Garnett effective medium theory and the construction approach with active elements, research on active metamaterials with strong microwave responses of nonlinearity and gyroelectricity were conducted.
At the microwave frequencies, natural media usually exhibit extremely weak nonlinear effects. Compared with diverse spatial nonlinear optical applications, nonlinear applications at microwave frequencies are usually limited to microwave circuits. Based on the effective medium theory, we designed and realized an active metamaterial with strong spatial nonlinear electromagnetic (EM) responses. Under the illumination of a micro-Watt spatial microwave, strong nonlinear EM responses, like spatial harmonic generation and spectrum modulation, were clearly observed. After that, the effective nonlinear constitutive parameters of the active metamaterial were successfully retrieved from measured data. Based on above research, we proposed and experimentally demonstrated the imaging of microwave sources. Spatial resolutions exceeding the Abbe diffraction limit were achieved.
In Maxwell's theory, EM waves propagating in most natural media satisfy the reciprocal theory. When energy conservation is satisfied, this propagation exhibits a local time-reversal symmetry. Few naturally occurring gyrotropic media, such as magnetized plasma and ferrite, behave relatively weak non-reciprocal, gyroelectric or gyromagnetic phenomena only when external bias magnetic fields are applied. In this dissertation, by innovatively introducing unidirectional devices commonly used in active microwave circuits, we proposed a construction method of the active metamaterial with strong gyroelectric effects in the absence of an external magnetic bias. By translating the property of a unidirectional active device into the non-reciprocal response of effective media, we realized a gyroelectric metamaterial that only depends on a DC-voltage bias. Effective constitutive parameters were retrieved by using an optimization algorithm. In further experiments, strong non-reciprocal Faraday rotations with large deflected polarization angles were observed, breaking the local time-reversal symmetry.
The obtained active metamaterials fundamentally avoided the inherent performance limits of the corresponding naturally occurring media at microwave frequencies, showing a wide range of potential applications in the future.
引文
1. 夏征农 & 陈至立辞海.1116(上海辞书出版社：上海,2009).
2. Kong, J. A. Electromagnetic Wave Theory. (EMW:Cambridge,2008).
3. Maxwell Garnett, J. C. Colours in metal glasses and in metallic films. Phil. Trans. R. Soc. Lond. A 203,385-420 (1904).
4. Anantha Ramakrishna, S. & Grzegorczyk, T. M. Physics and applications of negative refractive index materials. (Taylor & Francis Group:Bellingham,2009).
5. Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic crystals-molding the flow of light. (Princeton University Press:Princeton,2008).
6. Munk, B. A. Frequency Selective Surfaces. (John Wiley & Sons:New York,2000).
7. Raether, H. Surface plasmon on smooth and rough surface and on gratings. (Springer-Verlag:Berlin,1988).
8. Notomi, M. Theory of light progagation in strongly modulated photonic crystal: refractionlike behavior in the vicinity of the photonic band gap. Physical Review B 62,10696-10705(2000).
9. Pendry, J. B. All-angle negative refraction without negative effective index. Physical Review B 65,201104 (2002).
10. Parimi, P. V., Lu, W. T., Vodo, P. & Sridhar, S. Imaging by flat lens using negative refraction. Nature 426,404 (2003).
11. Parimi, P. V. et al. Negative refraction and left-handed electromagnetism in microwave photonic crystals. Physical Review Letters 92,127401 (2004).
12. Veselago, V. G. The electrodynamics of substances with simultaneously negative values of epsilon and mu. Soviet Physics Uspekhi 10,509-514 (1968).
13. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292,77-79 (2001).
14. Pendry, J. B. Negative refraction makes a perfect lens. Physical review letters 85, 3966-3969 (2000).
15. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312,1780(2006).
16. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314,977-980 (2006).
17. Lucarini, V., Saarinen, J. J., Peiponen, K..-E. & Vartiainen, E. M. Kramers-Kronig Relations in Optical Materials Research. (Springer:New York,2004).
18. Cui, T. J., Smith, D. R. & Liu, R. Metamaterials-Theory design and applications. (Springer:New York,2010).
19. Lamb, H. On group-velocity. Proc. London Math. Soc.1,473-479 (1904).
20. Schuster, A. An introduction to the theory of optics. (Edward Arnold:London, 1904).
21. Pendry, J. B., Holden, A. J., Stewart, W. J. & Youngs, I. Extremely low frequency plasmons in metallic mesostructures. Physical review letters 76,4773-4776 (1996).
22. Pitarke, J. M. & Pendry, J. B. Effective electronic response of a system of metallic cylinders. Physical Review B 57,261-266 (1998).
23. Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Transactions on Microwave Theory and Techniques 47,2075-2084 (1999).
24. Smith, D. R., Padilla, W. J., Vier, D. C., Nernat-Nasser, S. C. & Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Physical Review Letters 84,4184-4187 (2000).
25. Huangfu, J. et al. Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns. Applied Physics Letters 84,1537 (2004).
26. Chen, H. et al. Metamaterial exhibiting left-handed properties over multiple frequency bands. Journal of Applied Physics 96,5338 (2004).
27. Wang, Z. et al. Very simple metallic subwavelength cell for constructing left-handed metamaterial. Applied Physics Letters 94,231905 (2009).
28. Peng, L. et al. Experimental Observation of Left-Handed Behavior in an Array of Standard Dielectric Resonators. Physical Review Letters 98,157403 (2007).
29. Smith, D. R., Schultz, S., Markos, P. & Soukoulis, C. M. Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Physical Review B 65,195104 (2002).
30. Koschny, T., Markos, P., Smith, D. R. & Soukoulis, C. M. Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. Physical Review E 68,065602 (2003).
31. Chen, X., Grzegorczyk, T. M., Wu, B.-I, Pacheco, J. & Kong, J. A. Robust method to retrieve the constitutive effective parameters of metamaterials. Physical review. E 70,016608(2004).
32. Smith, D. R., Vier, D. C., Koschny, T. & Soukoulis, C. M. Electromagnetic parameter retrieval from inhomogeneous metamaterials. Physical Review E 71, 036617(2005).
33. Chen, H. et al. Experimental retrieval of the effective parameters of metamaterials based on a waveguide method. Optics express 14,12944-12949 (2006).
34. Marques, R., Martel, J., Mesa, F. & Medina, F. Left-Handed-Media Simulation and Transmission of EM Waves in Subwavelength Split-Ring-Resonator-Loaded Metallic Waveguides. Physical Review Letters 89,183901 (2002).
35. Yuan, Y. et al. Backward coupling waveguide coupler using left-handed material. Applied Physics Letters 88,211903 (2006).
36. Grzegorczyk, T. M. & Kong, J. A. Experimental Realization of a One-Dimensional LHM-RHM Resonator. IEEE Transactions on Microwave Theory and Techniques 53,1522-1526(2005).
37. Antoniades, M. A., Member, S., Eleftheriades, G. V & Member, S. Compact Linear Lead/Lag Metamaterial Phase Shifters for Broadband Applications. IEEE Antennas and Wireless Propagation Letters 2,103-106 (2003).
38. Enoch, S., Tayeb, G., Sabouroux, P., Guerin, N. & Vincent, P. A Metamaterial for Directive Emission. Physical Review Letters 89,213902 (2002).
39. Fang, N., Lee, H., Sun, C. & Zhang, X. Sub-diffraction-limited optical imaging with a silver superlens. Science 308,534-537 (2005).
40. Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects. Science 315,1686 (2007).
41. Smith, D. R. & Schurig, D. Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors. Physical Review Letters 90,077405 (2003).
42. Smith, D. R., Kolinko, P. & Schurig, D. Negative refraction in indefinite media. Journal of the Optical Society of America B 21,1032-1043 (2004).
43. Grzegorczyk, T. M., Thomas, Z. M. & Kong, J. A. Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials. Applied Physics Letters 86, 251909(2005).
44. Jacob, Z., Alekseyev, L. V & Narimanov, E. Optical Hyperlens:Far-field imaging beyond the diffraction limit. Optics express 14,8247-8256 (2006).
45. Sivan, Y., Xiao, S., Chettiar, U. K., Kildishev, A. V & Shalaev, V. M. Frequency-domain simulations of a negative-index material with embedded gain. Optics express 17,24060-24074 (2009).
46. Wang, D. et al. Active left-handed material collaborated with microwave varactors. Applied Physics Letters 91,164101 (2007).
47. Shadrivov, I. V., Kozyrev, A. B., Van der Weide, D. W. & Kivshar, Y. S. Tunable transmission and harmonic generation in nonlinear metamaterials. Applied Physics Letters 93,161903(2008).
48. Linvillt, J. G. Transistor Negative-Impedance Converters. Proceedings of the I.R.E 1, 725-729(1953).
49. Jiang, T. et al. Gain-Assisted Metamaterial Embedded with Gain Elements. Microwave and Optical Technology Letters 52,92-95 (2009).
50. Anantha Ramakrishna, S. & Pendry, J. B. Removal of absorption and increase in resolution in a near-field lens via optical gain. Physical Review B 67,201101 (2003).
51. Kozyrev, A. B., Kim, H. & Van der Weide, D. W. Parametric amplification in left-handed transmission line media. Applied Physics Letters 88,264101 (2006).
52. Casares-miranda, F. P., Member, S., Camacho-penalosa, C., Caloz, C. & Member, S. High-Gain Active Composite Right/Left-Handed Leaky-Wave Antenna. IEEE Transactions on Antennas and Propagation 54,2292-2300 (2006).
53. Popa, B. & Cummer, S. A. An Architecture for Active Metamaterial Particles and Experimental Validation at RF. Microwave and Optical Technology Letters 49, 2574-2577 (2007).
54. Yuan, Y., Popa, B.-I. & Cummer, S. A. Zero loss magnetic metamaterials using powered active unit cells. Optics express 17,16135-16143 (2009).
55. Jiang, T., Chang, K., Si, L.-M., Ran, L. & Xin, H. Active Microwave Negative-Index Metamaterial Transmission Line with Gain. Physical Review Letters 107,205503 (2011).
56. Stockman, M. Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality. Physical Review Letters 98,177404 (2007).
57. Mackay, T. & Lakhtakia, A. Comment on "Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality". Physical Review Letters 99,189701(2007).
58. Kinsler, P. & McCall, M. Causality-Based Criteria for a Negative Refractive Index Must Be Used With Care. Physical Review Letters 101,167401 (2008).
59. Reynet, O. & Acher, O. Voltage controlled metamaterial. Applied Physics Letters 84, 1198(2004).
60. Gil, I. et al. Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies. Electronics Letters 40,1-2 (2004).
61. Pimenov, a., Loidl, A., Przyslupski, P. & Dabrowski, B. Negative Refraction in Ferromagnet-Superconductor Superlattices. Physical Review Letters 95,247009 (2005).
62. Chen, H., Wu, B.-I., Ran, L., Grzegorczyk, T. M. & Kong, J. A. Controllable left-handed metamaterial and its application to a steerable antenna. Applied Physics Letters 89,053509 (2006).
63. Zhao, Q. et al. Tunable negative refraction in nematic liquid crystals. Applied Physics Letters 89,221918 (2006).
64. Kang, L., Zhao, Q., Li, B., Zhou, J. & Zhu, H. Experimental verification of a tunable optical negative refraction in nematic liquid crystals. Applied Physics Letters 90, 181931 (2007).
65. Zhang, F. et al. Magnetically tunable left handed metamaterials by liquid crystal orientation. Optics express 17,4360-4366 (2009).
66. Zhang, F. et al. Voltage tunable short wire-pair type of metamaterial infiltrated by nematic liquid crystal. Applied Physics Letters 97,134103 (2010).
67. Chen, H. T. et al. Active terahertz metamaterial devices. Nature 444,597-600 (2006).
68. Degiron, A., Mock, J. J. & Smith, D. R. Modulating and tuning the response of metamaterials at the unit cell level. Optics express 15,10673-10680 (2007).
69. He, Y. et al. Tunable negative index metamaterial using yttrium iron garnet. Journal of Magnetism and Magnetic Materials 313,187-191 (2007).
70. Zhao, H. et al. Magnetotunable left-handed material consisting of yttrium iron garnet slab and metallic wires. Applied Physics Letters 91,131107 (2007).
71. Wang, D. et al. Experimental validation of negative refraction of metamaterial composed of single side paired S-ring resonators. Applied Physics Letters 90, 254103(2007).
72. Jiang, T. et al. Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. IEEE Transactions on Microwave Theory and Techniques 60,170-178 (2012).
73. Hrabar, S., Krois, I., Bonic, I. & Kiricenko, A. Dispersionless ENZ and MNZ metamaterials based on non-Foster elements. IEEE International Symposium on Antennas and Propagation (APSURSI) 1946-1949 (2011).
74. Saadat, S., Farahani, M. F., Mosallaei, H. & Afshari, E. Metamaterials Integrated with Active Electronic Circuits. IEEE APS International Symposium and USNC/URSI National Radio Science Meeting 02115, (2011).
75. Weldon, T. P., Miehle, K., Adams, R. S. & Daneshvar, K. A wideband microwave double-negative metamaterial with non-Foster loading. Proceedings of IEEE Southeast Con 1-5 (2012).
76. Hrabar, S., Krois, I., Bonic, I. & Kiricenko, A. Negative capacitor paves the way to ultra-broadband metamaterials. Applied Physics Letters 99,254103 (2011).
77. Sussman-fort, S. E., Member, S. & Rudish, R. M. Non-Foster Impedance Matching of Electrically-Small Antennas. IEEE Transactions on Antennas and Propagation 57, 2230-2241 (2009).
78. Mirzaei, H., Member, S. & Eleftheriades, G. V A Wideband Metamaterial-Inspired Compact Antenna Using Embedded Non-Foster Matching. IEEE International Symposium on Antennas and Propagation (APSURSI) 1950-1953 (2011).
79. Zhu, N., Member. S. & Ziolkowski, R. W. Active Metamaterial-Inspired Broad-Bandwidth, Efficient, Electrically Small Antennas. IEEE Antennas and Wireless Propagation Letters 10,1582-1585 (2011).
80. White, C. R., May, J. W. & Colburn, J. S. A variable negative-inductance integrated circuit at UHF frequencies. IEEE Microwave and Wireless Components Letters 22, 35-37(2012).
81. Ahmed, A. & Gordon, R. Single molecule directivity enhanced Raman scattering using nanoantennas. Nano letters 12,2625-2630 (2012).
82. Zharov, A.. Shadrivov, I. & Kivshar, Y. Nonlinear Properties of Left-Handed Metamaterials. Physical Review Letters 91,037401 (2003).
83. Lapine, M., Gorkunov, M. & Ringhofer, K. Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements. Physical Review E 67, 065601 (2003).
84. Gorkunov, M. & Lapine, M. Tuning of a nonlinear metamaterial band gap by an external magnetic field. Physical Review B 70,235109 (2004).
85. Klein, M. W., Enkrich, C., Wegener, M. & Linden, S. Second-harmonic generation from magnetic metamaterials. Science 313,502-504 (2006).
86. Shadrivov, I. V, Morrison, S. K. & Kivshar, Y. S. Tunable split-ring resonators for nonlinear negative-index metamaterials. Optics express 14,165112-165117 (2006).
87. Powell. D. a.. Shadrivov. I. V., Kivshar, Y. S. & Gorkunov, M. V. Self-tuning mechanisms of nonlinear split-ring resonators. Applied Physics Letters 91,144107 (2007).
88. Shadrivov, I. V, Kozyrev, A. B., Weide, D. W. van der & Kivshar, Y. S. Nonlinear magnetic metamaterials. Optics express 16,165112-165117 (2008).
89. Wang, Z. et al. Second-harmonic generation and spectrum modulation by an active nonlinear metamaterial. Applied Physics Letters 94,134102 (2009).
90. Rose, A. & Smith, D. R. Overcoming phase mismatch in nonlinear metamaterials. Optical Materials Express 1,1232-1243 (2011).
91. Rose, A., Huang, D. & Smith, D. Controlling the Second Harmonic in a Phase-Matched Negative-Index Metamaterial. Physical Review Letters 107,063902 (2011).
92. Zharov, A. A., Zharova, N. A., Shadrivov, I. V. & Kivshar, Y. S. Subwavelength imaging with opaque nonlinear left-handed lenses. Applied Physics Letters 87, 091104(2005).
93. Ciraci, C. & Centeno, E. Focusing of Second-Harmonic Signals with Nonlinear Metamaterial Lenses:A Biphotonic Microscopy Approach. Physical Review Letters 103,063901 (2009).
94. Wang, Z. et al. Harmonic Image Reconstruction Assisted by a Nonlinear Metamaterial Surface. Physical Review Letters 106,047402 (2011).
95. Lopez, M. a. et al. Nonlinear split-ring metamaterial slabs for magnetic resonance imaging. Applied Physics Letters 98,133508 (2011).
96. Tretyakov, S., Nefedov, I., Sihvola, A., Maslovski, S. & Simovski, C. Waves and energy in chiral nihility. Journal of Electromagnetic Waves and Applications 17, 695-706 (2003).
97. Pendry, J. B. A chiral route to negative refraction. Science 306,1353-1355 (2004).
98. Inoue, M., Arai, K., Fujii, T. & Abe, M. One-dimensional magnetophotonic crystals. Journal of Applied Physics 85,5768-5770 (1999).
99. Haldane, F. & Raghu, S. Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry. Physical Review Letters 100,013904(2008).
100. Wang, Z., Chong, Y., Joannopoulos, J. & Soljacic, M. Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal. Physical Review Letters 100, 013905(2008).
101. Yu, Z., Veronis, G., Wang, Z. & Fan, S. One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal. Physical Review Letters 100,023902 (2008).
102. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljacic, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772-775 (2009).
103. Wang, Z. et al Gyrotropic response in the absence of a bias field. Proceedings of the National Academy of Sciences of the United States of America (PNAS) 109, 13194-13197(2012).
104. Kodera, T., Sounas, D. L. & Caloz, C. Artificial Faraday rotation using a ring metamaterial structure without static magnetic field. Applied Physics Letters 99, 031114(2011).
105. Kodera, T., Sounas, D., Nguyen, H. V, Razavipour, H. & Caloz, C. Field Displacement in a Traveling-wave Ring Resonator Meta-structure. General Assembly and Scientific Symposium,2011 XXXth URS12,5-8 (2011).
106. Kodera, T., Sounas, D. L.& Caloz, C. Isolator utilizing artificial magnetic gyrotropy. Microwave Symposium Digest (MTT),2012 IEEE MTT-S International 1-3 (2012).
107. Kodera, T., Sounas, D. L. & Caloz, C. Nonreciprocal Magnetless CRLH Leaky-Wave Antenna Based on a Ring Metamaterial Structure. IEEE Antennas and Wireless Propagation Letters 10,1551-1554 (2011).
108. Yin, X., Feng, T., Liang, Z. & Li, J. Artificial Kerr-type medium using metamaterials. Optics express 20,295-298 (2012).
109. Popa, B.-1. & Cummer, S. Nonreciprocal active metamaterials. Physical Review B 85, 205101 (2012).
110. Jonscher. A. K. Dielectric relaxation in solids. (Chelsea Dielectrics Press:London, 1983).
111. Fox, M. Optical properties of solids. (Oxford University Press:New York,2001).
112. Makosz, J. J. & Urbanowicz, P. Relaxation and resonance absorption in dielectrics. Z Naturforsch 57a,119-125 (2002).
113. Lewin, L. The electrical constants of a material loaded with spherical particles. Journal of the Institution of Electrical Engineers 94,65-68 (1947).
114. Wang, D. et al. Measurement of negative permittivity and permeability from experimental transmission and reflection with effects of cell misalignment. Journal of Applied Physics 99,123114 (2006).
115. Boyd, R. W. Nonlinear Optics. (Academic:New York,2008).
116. Lipson, A., Lipson, S. G. & Lipson, H. Optical physics.340 (Cambridge University Press:Cambridge,2010).
117. Korovkin, N. V., Chechurin, V. L. & Hayakawa, M. Inverse problems in electric circuits and electromagnetics. (Springer:USA,2007).
118. Fox, A. G., Miller, S. E. & Weiss, M. T. Behavior and applications of ferrites in the microwave region. Bell System Technical Journal 34,5-104 (1955).
119. Zvezdin, A. K. & Kotov, V. A. Modern magnetooptics and magnetooptical materials. (Taylor & Francis Group:London,1997).
2. Kong, J. A. Electromagnetic Wave Theory. (EMW:Cambridge,2008).
3. Maxwell Garnett, J. C. Colours in metal glasses and in metallic films. Phil. Trans. R. Soc. Lond. A 203,385-420 (1904).
4. Anantha Ramakrishna, S. & Grzegorczyk, T. M. Physics and applications of negative refractive index materials. (Taylor & Francis Group:Bellingham,2009).
5. Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic crystals-molding the flow of light. (Princeton University Press:Princeton,2008).
6. Munk, B. A. Frequency Selective Surfaces. (John Wiley & Sons:New York,2000).
7. Raether, H. Surface plasmon on smooth and rough surface and on gratings. (Springer-Verlag:Berlin,1988).
8. Notomi, M. Theory of light progagation in strongly modulated photonic crystal: refractionlike behavior in the vicinity of the photonic band gap. Physical Review B 62,10696-10705(2000).
9. Pendry, J. B. All-angle negative refraction without negative effective index. Physical Review B 65,201104 (2002).
10. Parimi, P. V., Lu, W. T., Vodo, P. & Sridhar, S. Imaging by flat lens using negative refraction. Nature 426,404 (2003).
11. Parimi, P. V. et al. Negative refraction and left-handed electromagnetism in microwave photonic crystals. Physical Review Letters 92,127401 (2004).
12. Veselago, V. G. The electrodynamics of substances with simultaneously negative values of epsilon and mu. Soviet Physics Uspekhi 10,509-514 (1968).
13. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292,77-79 (2001).
14. Pendry, J. B. Negative refraction makes a perfect lens. Physical review letters 85, 3966-3969 (2000).
15. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312,1780(2006).
16. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314,977-980 (2006).
17. Lucarini, V., Saarinen, J. J., Peiponen, K..-E. & Vartiainen, E. M. Kramers-Kronig Relations in Optical Materials Research. (Springer:New York,2004).
18. Cui, T. J., Smith, D. R. & Liu, R. Metamaterials-Theory design and applications. (Springer:New York,2010).
19. Lamb, H. On group-velocity. Proc. London Math. Soc.1,473-479 (1904).
20. Schuster, A. An introduction to the theory of optics. (Edward Arnold:London, 1904).
21. Pendry, J. B., Holden, A. J., Stewart, W. J. & Youngs, I. Extremely low frequency plasmons in metallic mesostructures. Physical review letters 76,4773-4776 (1996).
22. Pitarke, J. M. & Pendry, J. B. Effective electronic response of a system of metallic cylinders. Physical Review B 57,261-266 (1998).
23. Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Transactions on Microwave Theory and Techniques 47,2075-2084 (1999).
24. Smith, D. R., Padilla, W. J., Vier, D. C., Nernat-Nasser, S. C. & Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Physical Review Letters 84,4184-4187 (2000).
25. Huangfu, J. et al. Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns. Applied Physics Letters 84,1537 (2004).
26. Chen, H. et al. Metamaterial exhibiting left-handed properties over multiple frequency bands. Journal of Applied Physics 96,5338 (2004).
27. Wang, Z. et al. Very simple metallic subwavelength cell for constructing left-handed metamaterial. Applied Physics Letters 94,231905 (2009).
28. Peng, L. et al. Experimental Observation of Left-Handed Behavior in an Array of Standard Dielectric Resonators. Physical Review Letters 98,157403 (2007).
29. Smith, D. R., Schultz, S., Markos, P. & Soukoulis, C. M. Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Physical Review B 65,195104 (2002).
30. Koschny, T., Markos, P., Smith, D. R. & Soukoulis, C. M. Resonant and antiresonant frequency dependence of the effective parameters of metamaterials. Physical Review E 68,065602 (2003).
31. Chen, X., Grzegorczyk, T. M., Wu, B.-I, Pacheco, J. & Kong, J. A. Robust method to retrieve the constitutive effective parameters of metamaterials. Physical review. E 70,016608(2004).
32. Smith, D. R., Vier, D. C., Koschny, T. & Soukoulis, C. M. Electromagnetic parameter retrieval from inhomogeneous metamaterials. Physical Review E 71, 036617(2005).
33. Chen, H. et al. Experimental retrieval of the effective parameters of metamaterials based on a waveguide method. Optics express 14,12944-12949 (2006).
34. Marques, R., Martel, J., Mesa, F. & Medina, F. Left-Handed-Media Simulation and Transmission of EM Waves in Subwavelength Split-Ring-Resonator-Loaded Metallic Waveguides. Physical Review Letters 89,183901 (2002).
35. Yuan, Y. et al. Backward coupling waveguide coupler using left-handed material. Applied Physics Letters 88,211903 (2006).
36. Grzegorczyk, T. M. & Kong, J. A. Experimental Realization of a One-Dimensional LHM-RHM Resonator. IEEE Transactions on Microwave Theory and Techniques 53,1522-1526(2005).
37. Antoniades, M. A., Member, S., Eleftheriades, G. V & Member, S. Compact Linear Lead/Lag Metamaterial Phase Shifters for Broadband Applications. IEEE Antennas and Wireless Propagation Letters 2,103-106 (2003).
38. Enoch, S., Tayeb, G., Sabouroux, P., Guerin, N. & Vincent, P. A Metamaterial for Directive Emission. Physical Review Letters 89,213902 (2002).
39. Fang, N., Lee, H., Sun, C. & Zhang, X. Sub-diffraction-limited optical imaging with a silver superlens. Science 308,534-537 (2005).
40. Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects. Science 315,1686 (2007).
41. Smith, D. R. & Schurig, D. Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors. Physical Review Letters 90,077405 (2003).
42. Smith, D. R., Kolinko, P. & Schurig, D. Negative refraction in indefinite media. Journal of the Optical Society of America B 21,1032-1043 (2004).
43. Grzegorczyk, T. M., Thomas, Z. M. & Kong, J. A. Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials. Applied Physics Letters 86, 251909(2005).
44. Jacob, Z., Alekseyev, L. V & Narimanov, E. Optical Hyperlens:Far-field imaging beyond the diffraction limit. Optics express 14,8247-8256 (2006).
45. Sivan, Y., Xiao, S., Chettiar, U. K., Kildishev, A. V & Shalaev, V. M. Frequency-domain simulations of a negative-index material with embedded gain. Optics express 17,24060-24074 (2009).
46. Wang, D. et al. Active left-handed material collaborated with microwave varactors. Applied Physics Letters 91,164101 (2007).
47. Shadrivov, I. V., Kozyrev, A. B., Van der Weide, D. W. & Kivshar, Y. S. Tunable transmission and harmonic generation in nonlinear metamaterials. Applied Physics Letters 93,161903(2008).
48. Linvillt, J. G. Transistor Negative-Impedance Converters. Proceedings of the I.R.E 1, 725-729(1953).
49. Jiang, T. et al. Gain-Assisted Metamaterial Embedded with Gain Elements. Microwave and Optical Technology Letters 52,92-95 (2009).
50. Anantha Ramakrishna, S. & Pendry, J. B. Removal of absorption and increase in resolution in a near-field lens via optical gain. Physical Review B 67,201101 (2003).
51. Kozyrev, A. B., Kim, H. & Van der Weide, D. W. Parametric amplification in left-handed transmission line media. Applied Physics Letters 88,264101 (2006).
52. Casares-miranda, F. P., Member, S., Camacho-penalosa, C., Caloz, C. & Member, S. High-Gain Active Composite Right/Left-Handed Leaky-Wave Antenna. IEEE Transactions on Antennas and Propagation 54,2292-2300 (2006).
53. Popa, B. & Cummer, S. A. An Architecture for Active Metamaterial Particles and Experimental Validation at RF. Microwave and Optical Technology Letters 49, 2574-2577 (2007).
54. Yuan, Y., Popa, B.-I. & Cummer, S. A. Zero loss magnetic metamaterials using powered active unit cells. Optics express 17,16135-16143 (2009).
55. Jiang, T., Chang, K., Si, L.-M., Ran, L. & Xin, H. Active Microwave Negative-Index Metamaterial Transmission Line with Gain. Physical Review Letters 107,205503 (2011).
56. Stockman, M. Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality. Physical Review Letters 98,177404 (2007).
57. Mackay, T. & Lakhtakia, A. Comment on "Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality". Physical Review Letters 99,189701(2007).
58. Kinsler, P. & McCall, M. Causality-Based Criteria for a Negative Refractive Index Must Be Used With Care. Physical Review Letters 101,167401 (2008).
59. Reynet, O. & Acher, O. Voltage controlled metamaterial. Applied Physics Letters 84, 1198(2004).
60. Gil, I. et al. Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies. Electronics Letters 40,1-2 (2004).
61. Pimenov, a., Loidl, A., Przyslupski, P. & Dabrowski, B. Negative Refraction in Ferromagnet-Superconductor Superlattices. Physical Review Letters 95,247009 (2005).
62. Chen, H., Wu, B.-I., Ran, L., Grzegorczyk, T. M. & Kong, J. A. Controllable left-handed metamaterial and its application to a steerable antenna. Applied Physics Letters 89,053509 (2006).
63. Zhao, Q. et al. Tunable negative refraction in nematic liquid crystals. Applied Physics Letters 89,221918 (2006).
64. Kang, L., Zhao, Q., Li, B., Zhou, J. & Zhu, H. Experimental verification of a tunable optical negative refraction in nematic liquid crystals. Applied Physics Letters 90, 181931 (2007).
65. Zhang, F. et al. Magnetically tunable left handed metamaterials by liquid crystal orientation. Optics express 17,4360-4366 (2009).
66. Zhang, F. et al. Voltage tunable short wire-pair type of metamaterial infiltrated by nematic liquid crystal. Applied Physics Letters 97,134103 (2010).
67. Chen, H. T. et al. Active terahertz metamaterial devices. Nature 444,597-600 (2006).
68. Degiron, A., Mock, J. J. & Smith, D. R. Modulating and tuning the response of metamaterials at the unit cell level. Optics express 15,10673-10680 (2007).
69. He, Y. et al. Tunable negative index metamaterial using yttrium iron garnet. Journal of Magnetism and Magnetic Materials 313,187-191 (2007).
70. Zhao, H. et al. Magnetotunable left-handed material consisting of yttrium iron garnet slab and metallic wires. Applied Physics Letters 91,131107 (2007).
71. Wang, D. et al. Experimental validation of negative refraction of metamaterial composed of single side paired S-ring resonators. Applied Physics Letters 90, 254103(2007).
72. Jiang, T. et al. Low-DC Voltage-Controlled Steering-Antenna Radome Utilizing Tunable Active Metamaterial. IEEE Transactions on Microwave Theory and Techniques 60,170-178 (2012).
73. Hrabar, S., Krois, I., Bonic, I. & Kiricenko, A. Dispersionless ENZ and MNZ metamaterials based on non-Foster elements. IEEE International Symposium on Antennas and Propagation (APSURSI) 1946-1949 (2011).
74. Saadat, S., Farahani, M. F., Mosallaei, H. & Afshari, E. Metamaterials Integrated with Active Electronic Circuits. IEEE APS International Symposium and USNC/URSI National Radio Science Meeting 02115, (2011).
75. Weldon, T. P., Miehle, K., Adams, R. S. & Daneshvar, K. A wideband microwave double-negative metamaterial with non-Foster loading. Proceedings of IEEE Southeast Con 1-5 (2012).
76. Hrabar, S., Krois, I., Bonic, I. & Kiricenko, A. Negative capacitor paves the way to ultra-broadband metamaterials. Applied Physics Letters 99,254103 (2011).
77. Sussman-fort, S. E., Member, S. & Rudish, R. M. Non-Foster Impedance Matching of Electrically-Small Antennas. IEEE Transactions on Antennas and Propagation 57, 2230-2241 (2009).
78. Mirzaei, H., Member, S. & Eleftheriades, G. V A Wideband Metamaterial-Inspired Compact Antenna Using Embedded Non-Foster Matching. IEEE International Symposium on Antennas and Propagation (APSURSI) 1950-1953 (2011).
79. Zhu, N., Member. S. & Ziolkowski, R. W. Active Metamaterial-Inspired Broad-Bandwidth, Efficient, Electrically Small Antennas. IEEE Antennas and Wireless Propagation Letters 10,1582-1585 (2011).
80. White, C. R., May, J. W. & Colburn, J. S. A variable negative-inductance integrated circuit at UHF frequencies. IEEE Microwave and Wireless Components Letters 22, 35-37(2012).
81. Ahmed, A. & Gordon, R. Single molecule directivity enhanced Raman scattering using nanoantennas. Nano letters 12,2625-2630 (2012).
82. Zharov, A.. Shadrivov, I. & Kivshar, Y. Nonlinear Properties of Left-Handed Metamaterials. Physical Review Letters 91,037401 (2003).
83. Lapine, M., Gorkunov, M. & Ringhofer, K. Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements. Physical Review E 67, 065601 (2003).
84. Gorkunov, M. & Lapine, M. Tuning of a nonlinear metamaterial band gap by an external magnetic field. Physical Review B 70,235109 (2004).
85. Klein, M. W., Enkrich, C., Wegener, M. & Linden, S. Second-harmonic generation from magnetic metamaterials. Science 313,502-504 (2006).
86. Shadrivov, I. V, Morrison, S. K. & Kivshar, Y. S. Tunable split-ring resonators for nonlinear negative-index metamaterials. Optics express 14,165112-165117 (2006).
87. Powell. D. a.. Shadrivov. I. V., Kivshar, Y. S. & Gorkunov, M. V. Self-tuning mechanisms of nonlinear split-ring resonators. Applied Physics Letters 91,144107 (2007).
88. Shadrivov, I. V, Kozyrev, A. B., Weide, D. W. van der & Kivshar, Y. S. Nonlinear magnetic metamaterials. Optics express 16,165112-165117 (2008).
89. Wang, Z. et al. Second-harmonic generation and spectrum modulation by an active nonlinear metamaterial. Applied Physics Letters 94,134102 (2009).
90. Rose, A. & Smith, D. R. Overcoming phase mismatch in nonlinear metamaterials. Optical Materials Express 1,1232-1243 (2011).
91. Rose, A., Huang, D. & Smith, D. Controlling the Second Harmonic in a Phase-Matched Negative-Index Metamaterial. Physical Review Letters 107,063902 (2011).
92. Zharov, A. A., Zharova, N. A., Shadrivov, I. V. & Kivshar, Y. S. Subwavelength imaging with opaque nonlinear left-handed lenses. Applied Physics Letters 87, 091104(2005).
93. Ciraci, C. & Centeno, E. Focusing of Second-Harmonic Signals with Nonlinear Metamaterial Lenses:A Biphotonic Microscopy Approach. Physical Review Letters 103,063901 (2009).
94. Wang, Z. et al. Harmonic Image Reconstruction Assisted by a Nonlinear Metamaterial Surface. Physical Review Letters 106,047402 (2011).
95. Lopez, M. a. et al. Nonlinear split-ring metamaterial slabs for magnetic resonance imaging. Applied Physics Letters 98,133508 (2011).
96. Tretyakov, S., Nefedov, I., Sihvola, A., Maslovski, S. & Simovski, C. Waves and energy in chiral nihility. Journal of Electromagnetic Waves and Applications 17, 695-706 (2003).
97. Pendry, J. B. A chiral route to negative refraction. Science 306,1353-1355 (2004).
98. Inoue, M., Arai, K., Fujii, T. & Abe, M. One-dimensional magnetophotonic crystals. Journal of Applied Physics 85,5768-5770 (1999).
99. Haldane, F. & Raghu, S. Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry. Physical Review Letters 100,013904(2008).
100. Wang, Z., Chong, Y., Joannopoulos, J. & Soljacic, M. Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal. Physical Review Letters 100, 013905(2008).
101. Yu, Z., Veronis, G., Wang, Z. & Fan, S. One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal. Physical Review Letters 100,023902 (2008).
102. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljacic, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772-775 (2009).
103. Wang, Z. et al Gyrotropic response in the absence of a bias field. Proceedings of the National Academy of Sciences of the United States of America (PNAS) 109, 13194-13197(2012).
104. Kodera, T., Sounas, D. L. & Caloz, C. Artificial Faraday rotation using a ring metamaterial structure without static magnetic field. Applied Physics Letters 99, 031114(2011).
105. Kodera, T., Sounas, D., Nguyen, H. V, Razavipour, H. & Caloz, C. Field Displacement in a Traveling-wave Ring Resonator Meta-structure. General Assembly and Scientific Symposium,2011 XXXth URS12,5-8 (2011).
106. Kodera, T., Sounas, D. L.& Caloz, C. Isolator utilizing artificial magnetic gyrotropy. Microwave Symposium Digest (MTT),2012 IEEE MTT-S International 1-3 (2012).
107. Kodera, T., Sounas, D. L. & Caloz, C. Nonreciprocal Magnetless CRLH Leaky-Wave Antenna Based on a Ring Metamaterial Structure. IEEE Antennas and Wireless Propagation Letters 10,1551-1554 (2011).
108. Yin, X., Feng, T., Liang, Z. & Li, J. Artificial Kerr-type medium using metamaterials. Optics express 20,295-298 (2012).
109. Popa, B.-1. & Cummer, S. Nonreciprocal active metamaterials. Physical Review B 85, 205101 (2012).
110. Jonscher. A. K. Dielectric relaxation in solids. (Chelsea Dielectrics Press:London, 1983).
111. Fox, M. Optical properties of solids. (Oxford University Press:New York,2001).
112. Makosz, J. J. & Urbanowicz, P. Relaxation and resonance absorption in dielectrics. Z Naturforsch 57a,119-125 (2002).
113. Lewin, L. The electrical constants of a material loaded with spherical particles. Journal of the Institution of Electrical Engineers 94,65-68 (1947).
114. Wang, D. et al. Measurement of negative permittivity and permeability from experimental transmission and reflection with effects of cell misalignment. Journal of Applied Physics 99,123114 (2006).
115. Boyd, R. W. Nonlinear Optics. (Academic:New York,2008).
116. Lipson, A., Lipson, S. G. & Lipson, H. Optical physics.340 (Cambridge University Press:Cambridge,2010).
117. Korovkin, N. V., Chechurin, V. L. & Hayakawa, M. Inverse problems in electric circuits and electromagnetics. (Springer:USA,2007).
118. Fox, A. G., Miller, S. E. & Weiss, M. T. Behavior and applications of ferrites in the microwave region. Bell System Technical Journal 34,5-104 (1955).
119. Zvezdin, A. K. & Kotov, V. A. Modern magnetooptics and magnetooptical materials. (Taylor & Francis Group:London,1997).