Graphene, a newly discovered carbon based material, is predicted to have a strong nonlinear electromagnetic response over a broad spectral range. Its unique carrier transport and terahertz properties have gained ample attention. Recently, it has been demonstrated that graphene has an extraordinary high nonlinear response with third-order susceptibility X3∼ 10-7 esu, which is 105 times higher than that of silicon.
In this thesis, we examine the nonlinear response of electron dynamics in graphene using the new derived optical Bloch equations. The thesis is divided into three sections. In the first part, we provide an overview of the derivation of the extended optical Bloch equations from the time-dependent Dirac equations. Then, we use these derived optical Bloch equations to demonstrate the coupling of light and field interaction in graphene, and the generation of the photon echo signals. Next, we describe the nonlinear response in graphene in terms of the current density, and we show that the enhanced interband dynamics reduces nonlinearity in the electric current. Finally, we illustrate that the strong interplay between the interband and intraband dynamics leads to large harmonic generations, where harmonics of up to 13th order are generated.