Theory of the strongly nonlinear electrodynamic response of graphene: A hot electron model

Abstract

An electrodynamic response of graphene to a strong electromagnetic radiation is considered. A hot electron model (HEM) is introduced and a corresponding system of nonlinear equations is formulated. Solutions of this system are found and discussed in detail for intrinsic and doped graphene: the hot electron temperature, non-equilibrium electron and holes densities, absorption coefficient and other physical quantities are calculated as functions of the incident wave frequency ω and intensity I, of the equilibrium chemical potential µ0 and temperature T0, scattering parameters, as well as of the ratio τǫ/τrec of the intra-band energy relaxation time τǫ to the recombination time τrec. The influence of the radiation intensity on the absorption coefficient A at low ( ω 2|µ0|, dA/dI > 0) and high ( ω 2|µ0|, dA/dI < 0) frequencies is studied. The results are shown to be in good agreement with recent experimental data.

Hot carriers in graphene – fundamentals and applications

“…35 4.1.3 Nonlinear conductivity. The nonlinear optical properties of graphene have been investigated extensively, both theoretically 120,122,[141][142][143][144] and experimentally. Of particular interest are the observation of high-harmonics generation (HHG), 56,145 third-harmonic generation (THG), [146][147][148][149][150] fourwave mixing (FWM) [151][152][153] and different kinds of intensityinduced changes of the refractive index, such as saturable absorption (SA) 154,155 and the Kerr effect.…”

Predicting Graphene's Nonlinear‐Optical Refractive Response for Propagating Pulses

“…To implement the approach outlined above for modeling graphene's nonlinear response for propagating pulses in the non‐perturbative regime, we need to find explicit functional dependences of the chemical potential μ and temperature T on the carrier concentration. In principle, one should consider Fermi–Dirac distributions with different temperatures [ 18 ] and chemical potentials [ 27 ] for the electrons and the holes. However, supported by the conclusions of refs.…”

Asymmetric Si-slot Coupler with Nonreciprocal Response Based on Graphene Saturable Absorption

“…Graphene, a 2D semi-metal or zero bandgap semiconductor [10], can be cast as a high-contrast SA material in the NIR, owing to its mono-atomic thickness and the gap-less Dirac-cone dispersion. Various theoretical models have been proposed for its nonlinear behaviour, in perturbative [19], [20] and non-perturbative [12], [21], [22] regimes, using semiclassical and/or thermodynamic tools. These models lead to standard third-order nonlinear response (Kerr effect, self/crossphase modulation, four-wave mixing, parametric conversion) or to a more complicated response, when coupled to the photoexcited carrier plasma [23]- [25].…”