Gate-tunable third-order nonlinear optical response of massless Dirac fermions in graphene

Abstract

Materials with massless Dirac fermions can possess exceptionally strong and widely tunable optical nonlinearities. Experiments on graphene monolayer have indeed found very large third-order nonlinear responses, but the reported variation of the nonlinear optical coefficient by orders of magnitude is not yet understood. A large part of the difficulty is the lack of information on how doping or chemical potential affects the different nonlinear optical processes. Here we report the first experimental study, in corroboration with theory, on third harmonic generation (THG) and four-wave mixing (FWM) in graphene that has its chemical potential tuned by ion-gel gating. THG was seen to have enhanced by ~30 times when pristine graphene was heavily doped, while difference-frequency FWM appeared just the opposite. The latter was found to have a strong divergence toward degenerate FWM in undoped graphene, leading to a giant third-order nonlinearity. These truly amazing characteristics of graphene come from the possibility to gate-control the chemical potential, which selectively switches on and off one-and multi-photon resonant transitions that coherently contribute to the optical nonlinearity, and therefore can be utilized to develop graphene-based nonlinear optoelectronic devices.

Strong Light–Matter Interactions Enabled by Polaritons in Atomically Thin Materials

“…Fortuitously, the unique linear electronic dispersion relation of graphene, giving rise to its universal 2.3% broadband light absorption and facile electrical tunability, also endows this 2D material with an intrinsically anharmonic response to external electromagnetic fields: low‐energy charge carriers within a single Dirac cone have energies ε k = ℏ v F | k |, where k is the electron wavevector and v F ≈ c /300 is the Fermi velocity, endowing them with a velocity of fixed magnitude that instantaneously changes sign when crossing the Dirac point; an applied ac electric field E ( t ) = E 0 cos( ωt ) thus leads to a square‐wave surface current density J ( t ) = − env F sign{sin ( ωt )} in the E 0 → ∞ limit that is weighted by the charge carrier density n and contains significant contributions from all odd harmonics in its Fourier decomposition (see Figure a) . However, despite a large optical nonlinearity associated with intraband charge carrier motion near the Dirac point, most experiments in graphene nonlinear optics have only probed the interband response linking vertical transitions between Dirac cones, presumably due to the availability of interband transitions at all photon energies that could potentially enhance nonlinear processes involving multiple light frequencies, and the wider abundance of high‐powered lasers operating in the near‐IR and visible regimes that are routinely employed in nonlinear optical experiments. The initial report of a large optical nonlinearity in graphene was demonstrated in a four‐wave‐mixing experiment using intense near‐IR/visible light pulses, followed by explorations of harmonic generation, the optical Kerr effect, and other four‐wave‐mixing schemes, with reported values of the third‐order nonlinear susceptibility χ (3) ranging from ≈10 −15 –10 −19 m 2 V −2 (≈10 −7 –10 −11 esu in Gaussian units) .…”

“…The initial report of a large optical nonlinearity in graphene was demonstrated in a four‐wave‐mixing experiment using intense near‐IR/visible light pulses, followed by explorations of harmonic generation, the optical Kerr effect, and other four‐wave‐mixing schemes, with reported values of the third‐order nonlinear susceptibility χ (3) ranging from ≈10 −15 –10 −19 m 2 V −2 (≈10 −7 –10 −11 esu in Gaussian units) . The ability to electrically modulate the nonlinear optical response in graphene has recently been demonstrated, along with high‐harmonic generation (HHG) by the carbon monolayer when driven by intense terahertz and mid‐IR light pulses.…”

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...…”

“…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].…”

Temporally Resolving Synchronous Degenerate and Nondegenerate Two‐Photon Absorption in 2D Semiconducting Monolayers

“…Beyond the linear optical regime, extensive efforts in recent years have been devoted to investigating nonlinear optical responses of TMD monolayers up to the third order. These studies provided valuable information of lattice structure, nonlinear absorption coefficients, fine structures of excitonic levels, and realized subband photodetection, tunable nonlinear optical response, quantum coherence, etc.…”