Four-wave mixing, quantum control, and compensating losses in doped negative-index photonic metamaterials

Abstract

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...

Experimental determination of the quadratic nonlinear magnetic susceptibility of a varactor-loaded split ring resonator metamaterial

“…Near resonance, many MM elements, such as split ring resonators ͑SRRs͒, exhibit a significant concentration of the electric field within the capacitive regions, potentially enhancing the nonlinear properties of materials integrated into those regions. 1 Many nonlinear phenomena such as wave-mixing, 2 bistability, 3 and parametric generation 4 have been predicted in such MMs but implementations are still scarce. 5,6 At radio or microwave frequencies, the nonlinear material can be substituted by nonlinear electronic components.…”

Metamaterials: transforming theory into reality

“…Some known sources of loss originate from surface roughness, quantum size and chemical interface effects, the resonant nature of their magnetic response, or the fundamental loss properties of metals. Therefore, several methods have been proposed to reduce or compensate the losses in metamaterials, including incorporation of gain media into the metamaterial design [14][15][16] and optical-parametric amplification [17][18][19][20][21][22][23] discussed in Section 3. Significant, even complete compensation of absorption losses and even lasing was predicted theoretically and demonstrated experimentally in various plasmonic systems [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

“…Metamaterials necessitate the reconsideration of many well-known nonlinear optical phenomena, including harmonic generation, parametric processes, optical bistability, modulational instability, and soliton propagation [17][18][19][20][21][22][23][50][51][52][53][54][55][56][57][58][59][60][61][62]. One of the most remarkable properties enabled by antiparallel wave and Poynting vectors in NIMs is a novel, backward phase-matching mechanism.…”

“…One of the most remarkable properties enabled by antiparallel wave and Poynting vectors in NIMs is a novel, backward phase-matching mechanism. Backward phase-matching in combination with the strong frequency dependence of the metamaterial parameters was shown to facilitate new regimes of second-harmonic generation (SHG) [17,53] and optical parametric amplification (OPA) [17][18][19][20][21][22][23].…”

Microscopic mirrorless negative-index optical parametric oscillator

“…One is a three-wave mixing (TWM) BWMOPO that implements ͑2͒ nonlinearities of the NIMs [2,3]. The other option, a four-wave mixing (FWM) BWMOPO [4], proposes independent engineering of a ͑3͒ nonlinearity through embedded, resonant, NLO centers. In the vicinity of the resonances, ͑3͒ is exceptionally strong and optical properties of the composite can be tailored by means of quantum control.…”