Abstract: Based on the nonlinear electromagnetic theory, general coupled-mode equations for difference-frequency coupling in nonlinear left-handed metamaterials(LHM) are studied. The co-directed energy conversion process and spatial distribution of the signal wave and difference-frequency wave under the phase-matching condition are investigated. It is shown that through a finite LHM slab, more output power of the signal wave and difference-frequency wave than through an RHM slab with the same thickness can be obtained. For this peculiar property, the nonlinear LHM may be utilized to design novel compact RF/microwave amplifiers. And through parameters adjustment of the material to control left-handed or right-handed properties, compact microwave amplifiers of the tunable output direction may be realized.

Key words: left-handed metamaterials, nonlinear effect, difference-frequency coupling, phase-matching condition