Four-Wave Mixing in Metamaterials

Interaction of four counterpropagating waves in a cubic medium being “left” for the signal wave is considered in the constant-intensity approximation. Analytical expression for the signal wave intensity is derived for the general case of four-wave interaction in a metamaterial. The influence of different parameters on the signal wave amplification coefficient, efficiency of conversion into the signal wave, and the reflection coefficient of the mirror whose role is played by the metamaterial is analyzed. It has been obtained for the first time that the determining role in the backward signal wave amplification is played by the total length of the metamaterial and the intensities of all three forward waves. An analysis has shown that the optimal thickness of the metamaterial depends not only on the phase mismatch and the strong coherent pump field intensity, as in the constant-field approximation, but also on the intensity of the weak wave at the frequency ω₂. It has been demonstrated for the first time that the efficiency of frequency conversion in metamaterials depends on the total metamaterial length, input intensities of all four interacting waves, phase mismatch, and losses in the medium. It is established that the maxima of the reflection coefficient of the metamaterial depend on the total metamaterial length and the intensities of all three forward waves.