Vol. 70
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2007-02-04
Counter-Propagating Energy-Flows in Nonlinear Left-Handed Metamaterials
By
Progress In Electromagnetics Research, Vol. 70, 257-267, 2007
Abstract
A peculiarity of counter-propagating energy-flows in nonlinear left-handed metamaterials (LHMs) is investigated for the case when the frequency of fundamental wave is in the negativeindex range and second-harmonic wave is in the positive-index range. Based on the electromagnetic theory,the comparisons of Manly-Rowe relations for nonlinear materials and process of secondharmonic generation under phase-matching condition in LHMs and RHMs are shown separately. That a surface of nonlinear left-handed metamaterials operates as an effective mirror which reflects the energy in form of second harmonics is demonstrated. Numerical results of fundamental and second-harmonic field intensity distributions are in agreement with theoretical results.
Citation
Liang Chen Wei Ding Xiao-Jie Dang Chang-Hong Liang , "Counter-Propagating Energy-Flows in Nonlinear Left-Handed Metamaterials," Progress In Electromagnetics Research, Vol. 70, 257-267, 2007.
doi:10.2528/PIER07012502
http://www.jpier.org/PIER/pier.php?paper=07012502
References

1. Veselago, V. G., "The electrodynamics of substances with simultaneously negative values of ε and µ," Soviet Physics USPEKI, Vol. 10, No. 4, 509-514, 1968.
doi:10.1070/PU1968v010n04ABEH003699

2. Pendry, J. B., "Negativ e refraction makes a perfect lens," Physical Review Letters, Vol. 85, No. 18, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966

3. Smith, D. R. and N. Kroll, "Negativ e refraction index in lefthanded materials," Physical Review Letters, Vol. 85, No. 14, 2933-2936, 2000.
doi:10.1103/PhysRevLett.85.2933

4. Kong, J. A., "Electromagnetic wave interaction with stratified negative isotropic media," Progress In Electromagnetics Research, Vol. 35, 1-52, 2002.
doi:10.2528/PIER01082101

5. Liang, L., B. Li, S.-H. Liu, and C.-H. Liang, "A study of using the double negative structure to enhance the gain of rectangular waveguide antenna arrays," Progress In Electromagnetics Research, Vol. 65, 275-286, 2006.
doi:10.2528/PIER06103102

6. Li, B., B. Wu, and C.-H. Liang, "Study on high gain circular waveguide array antenna with metamaterial structure," Progress In Electromagnetics Research, Vol. 60, 207-219, 2006.
doi:10.2528/PIER05121101

7. Zharov, A. A., I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Physical Review Letters, Vol. 91, No. 3, 03740121-03740124, 2003.
doi:10.1103/PhysRevLett.91.037401

8. Shadrivov, I. V., A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, "Nonlinear left-handed metamaterials," Radio Science, Vol. 40, 2005.
doi:10.1029/2004RS003191

9. Zharov, A. A., N. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Applied Physics Letters, Vol. 87, 2005.
doi:10.1063/1.2034114

10. Shadrivov, I. V., A. A. Zharov, and Yu. S. Kivshar, "Secondharmonic generation in nonlinear left-handed metamaterials," Optical Society of America, Vol. 23, No. 3, 529-534, 2006.
doi:10.1364/JOSAB.23.000529

11. Manley, J. M. and H. E. Rowe, General energy relations in nonlinear reactances, Proc.IRE, Vol. 47, No. 12, 2115-2116, 1959.