Second-order nonlinear optical response of graphene

Abstract

Although massless Dirac fermions in graphene constitute a centrosymmetric medium for inplane excitations, their second-order nonlinear optical response is nonzero if the effects of spatial dispersion are taken into account. Here we present a rigorous quantum-mechanical theory of the second-order nonlinear response of graphene beyond the electric dipole approximation, which includes both intraband and interband transitions. The resulting nonlinear susceptibility tensor satisfies all symmetry and permutation properties, and can be applied to all three-wave mixing processes. We obtain useful analytic expressions in the limit of a degenerate electron distribution, which reveal quite strong second-order nonlinearity at long wavelengths, Fermi-edge resonances, and unusual polarization properties.

Probing Polaritons in 2D Materials

“…Difference frequency generation (DFG), a second‐order nonlinear optical effect, was recently discovered to trigger plasmon polaritons in graphene and topological insulators (TIs) due to the intrinsic nonlinear optical response of these materials . Figure d presents a schematic diagram of DFG.…”

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

“…, where all higher-order conductivities should be considered as functions of non-equilibrium chemical potentials µ e , µ h and temperature T . However at present the functions σ (5) , σ (7) , etc., are unknown and the function σ αβγδ (ω 1 , ω 2 , ω 3 ; µ 0 , T 0 ) was calculated [28][29][30] only for the quasi-equilibrium case with µ 0 and T 0 . Therefore in this paper we restrict ourselves by the approach (23) - (25), postponing developing of more general theories for future publications.…”

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

“…While for σ (2) this would hold if the material lacked inversion symmetry, in the presence of such symmetry (such as in graphene), at least the dependence on k to first order must be kept, which corresponds to keeping electricquadrupole-like and magnetic dipole-like contributions to the second order nonlinear response [51,52,55]. Note that for 2D nano structures there will be scattered light with many different wave vectors, for some of which the k dependence of the conductivity could be important.…”

“…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, and doping levels. When scattering is described within a phenomenological relaxation time approximation, the calculated eff 3 c ( ) are about two orders of magnitude smaller than most values extracted from earlier experiments for lightly doped graphene [43][44][45][46]48].…”