  An analytical theory of the nonlinear electromagnetic response of a
two-dimensional (2D) electron system in the second order in the electric field
amplitude is developed. The second-order polarizability and the intensity of
the second harmonic signal are calculated within the self-consistent-field
approach both for semiconductor 2D electron systems and for graphene. The
second harmonic generation in graphene is shown to be about two orders of
magnitude stronger than in GaAs quantum wells at typical experimental
parameters. Under the conditions of the 2D plasmon resonance the second
harmonic radiation intensity is further increased by several orders of
magnitude.
