  We present a semiclassical theory of 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 low energy limit, around the degeneracy points are dominantly chiral. It is
shown for the first time 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 studied and it is demonstrated that its Kerr
nonlinear coefficient is several orders of magnitude higher than that of many
other known semiconductors. In addition, the nonlinear refractive index of
graphene can also be tuned and enhanced by applying a gate voltage.
