Nonlinear quantum optical properties of graphene

Abstract

We present a semiclassical theory of the linear and nonlinear optical response of graphene. The emphasis is placed on the nonlinear optical response of graphene from the standpoint of the underlying chiral symmetry. The Bloch quasiparticles in the low-energy limit around the degeneracy points are dominantly chiral. It is shown that this chiral behavior in conjunction with scale invariance in graphene around the Dirac points results in the strong nonlinear optical response. Explicit expressions for the linear and nonlinear conductivity tensors are derived based on semiconductor Bloch equations (SBEs). The linear terms agree with the result of Kubo formulation. The three main additive mechanisms contribute in the nonlinear optical response of graphene: pure intraband, pure interband and the interplay between them. For each contribution, an explicit response function is derived. The Kerr-type nonlinearity of graphene is then numerically studied and it is demonstrated that the nonlinear refractive index of graphene can be tuned and enhanced by applying a gate voltage. It is also discussed that a strong Kerr nonlinearity can be achieved in a gated graphene monolayer. However, this nonlinearity is accompanied with a significant amount of absorption loss.

Quantum theory of the third-order nonlinear electrodynamic effects of graphene

“…At higher (infrared, optical) frequencies the inter-band quantum transitions between the electron and hole bands should be taken into account and a quantum theory is needed. Recently, a quantum theory of the third-order nonlinear electrodynamic response of graphene to a uniform external electric field has been proposed in several publications 28,[32][33][34]48 . For example, in Ref.…”

Giant enhancement of the third harmonic in graphene integrated in a layered structure

“…[19][20][21][22][23][24] the third-order nonlinear response functions of graphene have been calculated for a single, freely hanging in vacuum (or in air) mono-atomic graphene layer. In reality graphene lies of a dielectric substrate (of thickness d).…”

“…More general, quantum theories, which take into account both contributions, have been recently proposed in Refs. [19][20][21][22][23][24]. It was shown that, apart from a strong resonance at low (hω ≪ 2E F ) frequencies, the third-order nonlinear conductivity σ αβγδ (ω 1 , ω 2 , ω 3 ) demonstrates a number of resonances at the frequencies corresponding to the one-, two-and three-photon interband absorption.…”

Nonlinear graphene plasmonics

“…The series of studies on graphene's numerous nonlinear optical processes, as shown in figure 7, can be traced back to contributions by Mikhailov since 2007 [58][59][60][61][62][63] [78][79][80] and more recently by other groups [81][82][83][84][85][86][87][88][89].…”

“…Perturbative models are developed to supplement the interband physics, for example the quantum mechanical (QM) Dirac equation model [61,62,64,66,67,89], and also the semiconductor Bloch equations [73,75,76,85]. The QM model replaces v g in equation (3.1) with v g = ψ|∂ H/∂k|ψ , where ψ is the wave function of graphene and H is the Dirac Hamiltonian, which replaces N(p) with N(p) = f (−ε k ) − f (ε k ), the Fermi distribution difference between the conduction and valence bands.…”