The possibility of compensating absorption in negative-index metatamterials (NIMs) doped by resonant nonlinear-optical centers is shown. The role of quantum interference and extraordinary properties of four-wave parametric amplification of counter-propagating electromagnetic waves in NIMs are discussed.c 2018 Optical Society of America OCIS codes: 1904410, 270.1670. Negative refractive index metamaterials (NIMs) present a novel class of materials that promise a revolutionary breakthrough in electromagnetics (for review, see, e.g., [1]). Nonlinear optics in such materials remains so far a less developed branch of optics. The possibility of nonlinear electromagnetic responses in such materials attributed to the asymmetry of the voltage-current characteristics of their building blocks was predicted in [2,3]. Recent experimental demonstrations of the exciting opportunities to craft nonlinear optical materials with characteristics exceeding those in natural crystals are reported in [4]. Unique nonlinear-optical (NLO) propagation effects associated with three-wave (χ (2) ) coupling in NIMs, as compared with their well known counterparts in natural materials, were revealed in [5][6][7][8]. The striking changes in the optical bistability in a layered structure including a NIM layer were shown in [9]. A review of the corresponding theoretical approaches is given in [10]. The most detrimental obstacle toward applications of NIMs is strong absorption that is inherent to this class of materials. The possibility to overcome such obstacles based on three-wave optical parametric amplification (OPA) in NIMs was shown in [7,8]. A great deal of technical problems must be solved, however, in order to match the frequency domains of negative index (NI), strong NLO response and the phase-matching to realize such feasibility. Herewith, we propose and explore an alternative approach associated with resonant four-wave mixing (FWM) nonlinearities χ (3) embedded in NIMs and tailored through quantum control. The possibility of compensating losses and manipulating transparency, refractive index and nonlinear response of the NIM sample with control laser(s) is shown.The basic idea of the proposed approach is as follows. A slab of NIM is doped by four-level nonlinear centers [ Fig. 1(a)] so that the frequency ω 4 falls in the NI domain, whereas all the other frequencies are in the the positive index domain. Below, we show the feasibility to produce the transparency and amplification for the signal wave at ω 4 controlled by two lasers at ω 1 and ω 3 . These three fields also generate an idler at ω 2 = ω 3 + ω 1 − ω 4 , which experiences either ordinary, population-inversion, or Raman amplification provided by the driving field at ω 1 and controlled by another driving field at ω 3 . The amplified idler contributes back to ω 4 = ω 3 + ω 1 − ω 2 through FWM which leads to strongly enhanced OPA. We assume that the wave vectors of all waves, k j , are . ω 4 is signal frequency, ω 2 is idler, and ω 1 and ω 3 are control fields. n(ω 4 ) < 0.co-di...

Manipulative resonant nonlinear optics: nonlinear interference effects and quantum control of nonlinearity, dispersion, transparency and inversionless amplification in an extended strongly-absorbing inhomogeneously-broadened medium Specific features of nonlinear interference processes at quantum transitions in near-and fullyresonant optically-dense Doppler-broadened medium are studied. The feasibility of overcoming of the fundamental limitation on a velocity-interval of resonantly coupled molecules imposed by the Doppler effect is shown based on quantum coherence. This increases the efficiency of nonlinearoptical processes in atomic and molecular gases that possess the most narrow and strongest resonances. The possibility of all-optical switching of the medium to opaque or, alternatively, to absolutely transparent, or even to strongly-amplifying states is explored, which is controlled by a small variation of two driving radiations. The required intensities of the control fields are shown to be typical for cw lasers. These effects are associated with four-wave mixing accompanied by Stokes gain and by their interference in fully-and near-resonant optically-dense far-from-degenerate double-Lambda medium. Optimum conditions for inversionless amplification of short-wavelength radiation above the oscillation threshold at the expense of the longer-wavelength control fields, as well as for Raman gain of the generated idle infrared radiation, are investigated. The outcomes are illustrated with numerical simulations applied to sodium dimer vapor. Similar schemes can be realized in doped solids and in fiber optics.

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