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.
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.