  We study theoretically the optical response of the surface states of a
topological insulator, especially the generation of helicity-dependent direct
current by circularly polarized light. Interestingly, the dominant current, due
to an interband transition, is controlled by the Berry curvature of the surface
bands. This extends the connection between photocurrents and Berry curvature
beyond the quasiclassical approximation where it has been shown to hold.
Explicit expressions are derived for the (111) surface of the topological
insulator Bi_{2}Se_{3} where we find significant helicity dependent
photocurrents when the rotational symmetry of the surface is broken by an
in-plane magnetic field or a strain. Moreover, the dominant current grows
linearly with time until a scattering occurs, which provides a means for
determining the scattering time. The dc spin generated on the surface is also
dominated by a linear-in-time, Berry curvature dependent contribution.
