Transient nonlinear plasmonics in nanostructured graphene

Abstract

Plasmons in highly doped graphene offer the means to dramatically enhance light absorption in the atomically thin material. Ultimately the absorbed light energy induces an increase in electron temperature, accompanied by large shifts in the chemical potential. This intrinsically incoherent effect leads to strong intensity-dependent modifications of the optical response, complementing the remarkable coherent nonlinearities arising in graphene due to interband transitions and anharmonic intraband electron motion. Through rigorous time-domain quantum-mechanical simulations of graphene nanoribbons, we show that the incoherent mechanism dominates over the coherent response for the high levels of intensity required to trigger nonperturbative optical phenomena such as saturable absorption. We anticipate that these findings will elucidate the role of coherent and incoherent nonlinearities for future studies and applications of plasmon-assisted nonlinear optics.

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

“…The strong intrinsic field enhancement provided by the long‐lived and electrically tunable plasmons of monolayer graphene (cf. Section ) has naturally launched explorations of its ability to enhance nonlinear optical phenomena, stimulating fertile research efforts in nonlinear graphene plasmonics . 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) .…”

“…HHG is one such process, predicted to be particularly effective in highly doped, nanostructured graphene due to the synergetic combination of plasmonic near‐field enhancement and anharmonic intraband charge carrier motion near the Dirac point (see Figure b). Plasmon‐assisted HHG in graphene is however competing with its strong intrinsic saturable absorption, which diminishes the in‐plane plasmonic near‐field enhancement in the material; the coherent saturable absorption is augmented by an incoherent saturation originating in the optical heating of electrons, which becomes substantial due to enhanced light absorption at the plasmon resonance …”

“…Plasmon-assisted HHG in graphene is however competing with its strong intrinsic saturable absorption, [170] which diminishes the in-plane plasmonic near-field enhancement in the material; the coherent saturable absorption is augmented by an incoherent saturation originating in the optical heating of electrons, which becomes substantial due to enhanced light absorption at the plasmon resonance. [145] Several experimental investigations probing nonlinear plasmonic phenomena in both extended and nanostructured graphene resonators with intense pulsed laser fields are highlighted in Figure 11. In particular, the electronic heating associated with resonant excitation of plasmons constitutes an incoherent but substantial source of optical nonlinearity that can be exploited to realize all-optical switching with relatively lowfluence pulses.…”

Terahertz Nonlinear Optics of Graphene: From Saturable Absorption to High‐Harmonics Generation

“…Besides standard “continuous” graphene samples, nonlinear THz spectroscopy was also performed on patterned graphene, featuring the confinement of THz field, and thus leading to enhancement of the THz nonlinearity. For example, it was theoretically predicted and experimentally verified that enhancement of the nonlinear interaction of the light field in graphene can be achieved by local field confinement via resonant plasmonic absorption if the graphene is patterned in subwavelength structures such as ribbons. Using THz FEL, Jadidi et al demonstrated nonlinear THz absorption at plasmonic resonance in lithographically patterned epitaxial graphene ribbons (see Figure a), following one‐color pump–probe scheme with THz field polarization perpendicular to the patterning direction.…”

Single-Plasmon Thermo-Optical Switching in Graphene

“…[13][14][15] In this context, electrically doped graphene -the atomically-thin carbon layer-appears as an excellent infrared plasmonic material 16,17,[17][18][19][20][21][22][23] in which a comparatively small number of electrons rule its optical and thermal properties in the ultrafast regime, thus displaying extraordinary thermo-optical properties that hold strong potential for all-optical modulation. 21,[24][25][26][27][28] Following excitation by an ultrafast optical pump, graphene plasmons decay on typically longer timescales than their noble metal counterparts into energetic electrons and holes, 23,29 which subsequently thermalize on ultrafast timescales. 25,26 Owing to its linear electronic dispersion relation, which endows graphene with a low electronic heat capacity, the large amount of optical energy absorbed through resonant excitation of plasmons can dramatically elevate the temperature of conduction electrons in the 2D material.…”