Graphene’s nonlinear-optical physics revealed through exponentially growing self-phase modulation

Abstract

Graphene is considered a record-performance nonlinear-optical material on the basis of numerous experiments. The observed strong nonlinear response ascribed to the refractive part of graphene’s electronic third-order susceptibility χ(3) cannot, however, be explained using the relatively modest χ(3) value theoretically predicted for the 2D material. Here we solve this long-standing paradox and demonstrate that, rather than χ(3)-based refraction, a complex phenomenon which we call saturable photoexcited-carrier refraction is at the heart of nonlinear-optical interactions in graphene such as self-phase modulation. Saturable photoexcited-carrier refraction is found to enable self-phase modulation of picosecond optical pulses with exponential-like bandwidth growth along graphene-covered waveguides. Our theory allows explanation of these extraordinary experimental results both qualitatively and quantitatively. It also supports the graphene nonlinearities measured in previous self-phase modulation and self-(de)focusing (Z-scan) experiments. This work signifies a paradigm shift in the understanding of 2D-material nonlinearities and finally enables their full exploitation in next-generation nonlinear-optical devices.

Evaluation of graphene optical nonlinearity with photon-pair generation in graphene-on-silicon waveguides

“…4(c) and 4(d) exhibit the P 1 p -dependence of the single-count rates rather than the P 2 p -dependence associated with SFWM. This P 1 p -dependence indicates that noise photons are generated via processes other than SFWM (e.g., SPM [18,21,24,25] and inelastic scattering [47]) and the CAR of the GSWs has been reduced due to the graphene-induced loss and such unwanted photon-generation events.…”

Transforming silicon into a high performing in tegrated nonlinear photonics platform by integrati on with 2D graphene oxide films

“…To quantitively analyze the spectral broadening of the output spectra, we introduce the concept of a broadening factor (BF) [52,53]. The width of the optical spectra is described by the root-mean-square (RMS) width, defined as [52] ∆ω rms…”

Nonlinear optics of graphene and other 2D materials in layered structures

“…Various experiments with graphene in free-space configurations, on waveguides, and on photonic crystals have been performed to investigate different nonlinear phenomena, including PFC [13,21], third harmonic generation (THG) [21][22][23][24][25], second harmonic generation (SHG) [26][27][28][29][30][31], Kerr effects (or self-phase modulation, SPM) and two photon absorption [32][33][34][35][36][37][38][39], and coherent current injection [40,41]. The extracted effective bulk third order susceptibilities eff [37,38,42], the ability to tune the nonlinearity by varying the chemical potential [21,25], and the possibility of having quasi-exponentially growing SPM in graphene on waveguides [39]. Most of the existing microscopic theories [43][44][45][46][47][48][49][50][51][52][53][54][55][56] focus on the dependence of the sheet conductivities σ ( n) ( i n eff wc µ-( ) ) on incident light frequencies, temperature...…”

“…Several effects have been considered that might bring theory in better agreement with these experiments, including saturation of the optical nonlinearity [47,54], the influence of cascaded second order processes [55,57], and novel plasmonic effects [55,58], but none of them can sufficiently enhance the calculated conductivities. Recently, free-carrier refraction has been shown to play an important role for understanding the above mentioned strong SPM in graphene, where a perturbative approach fails [39]. However, agreement with perturbative calculations is satisfactory in recent free-space experiments, where the doping level of graphene is tuned over a large range [21,25].…”

“…Besides involving a product of two second order conductivities, the cascaded process coefficient k k , c p s 3 h ( ) in equation (39) is also proportional to the term k d ( ). This illustrates how the structure underneath the graphene can be used to tune the cascaded process: In the experiment by Constant et al [57], this term is maximized by matching k d with the surface plasmon polariton (SPP) resonance of the entire structure.…”