Controlling light with light at the nanoscale: Backward-wave optical parametric amplification and generation in negative-index metamaterials

The authors report the possibility to produce the transparency and amplification for negative index signal controlled by another positive index strong laser beams and their extraordinary properties based on the coherent energy transfer from the control field to the signal through a TWM OPA of the signal. The option of independent engineering of resonantly enhanced frequency-nondegenerate four-wave mixing nonlinearity through the embedded four-level centers is also discussed and compared. The transparency is shown to exhibit unusual resonance behavior as a function of intensity of the control field and the negative index metamaterials (NIM) slab thickness which occurs due to the backwardness of the light waves in NIMs. Basically, such resonances are narrow and the sample remains opaque anywhere beyond the resonance field´s and the samples´ parameters. Phase-matching of the contrapropagating waves also presents a technical challenge. The feasibility to remove such limitations was shown, so that the transparency and the amplification of the NIMs slab at the signal frequency can be made robust and achievable through a wide range of the control field intensity and the NIM slab thickness. The possibility to eliminate the negative role of the phase-mismatch on the tailored transparency of the slab is also shown. The possibility of creation of microscopic mirrorless backward-wave optical parametric oscillator generating contradirected beams of entangled right- and left-handed photons is proposed and supported by numerical estimates.