Nonlinear optics in graphene: theoretical background and recent advances

We present a comprehensive review of the optical response of graphene, in both the linear and nonlinear regime. This will serve as a reference for both beginners and more experienced researchers in the field. We introduce, derive, and extensively discuss the Dirac–Bloch equations framework, central to describing electron–photon interaction in nonperturbative, gapless materials. We use this model to re-derive several known results in the linear regime, such as the universal absorption law, and to describe the nonlinear interaction of ultrashort pulses with graphene. We compare the validity of the Dirac–Bloch equations model with the traditional Semiconductor-Bloch equations and point out advantages and shortcomings of the two models. Lastly, we present a cutting-edge model for describing the nonlinear optical response of graphene when bending becomes important, a situation that deeply affects the output spectra, and can provide insight to a novel, effective way to manipulate light in two-dimensional media.