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Based on the electromagnetic theory，the Manly-Rowe relations for nonlinear left-handed metamaterials are studied. Energy conversion process and spatial distribution of forward-propagating wave of fundamental frequency and backward-propagating second harmonic wave under phase-matching condition are investigated. That a surface of nonlinear left-handed metamaterials operates as an effective mirror which reflects the energy in the form of second harmonics is demonstrated. Numerical results of field intensity distribution of a finite thickness metamaterial slab is given. Finally，the importance of phase-matching condition to the investigation of nonlinear left-handed metamaterials is illustrated from the viewpoint of phase-mismatching. This work provides a basis for studying nonlinear left-handed metamaterials.
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Keywords:
- left-handed metamaterials /
- nonlinear effect /
- second harmonics /
- phase-matching condition
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