  Here, we report first principles calculations and analysis of laser-induced
photocurrents at the surface of a prototype Rashba system. By referring to
Keldysh non-equilibrium formalism combined with the Wannier interpolation
scheme we perform first-principles electronic structure calculations of a
prototype BiAg$_2$ surface alloy, which is a well-known material realization of
the Rashba model. In addition to non-magnetic ground state situation we also
study the case of in-plane magnetized BiAg$_2$. We calculate the laser-induced
charge photocurrents for the ferromagnetic case and the laser-induced spin
photocurrents for both the non-magnetic and the ferromagnetic cases. Our
results confirm the emergence of very large in-plane photocurrents as predicted
by the Rashba model. The resulting photocurrents satisfy all the symmetry
restrictions with respect to the light helicity and the magnetization
direction. We provide microscopic insights into the symmetry and magnitude of
the computed currents based on the ab-initio multi-band electronic structure of
the system, and scrutinize the importance of resonant two-band and three-band
transitions for driven currents, thereby establishing a benchmark picture of
photocurrents at Rashba-like surfaces and interfaces. Our work contributes to
the study of the role of the interfacial Rashba spin-orbit interaction as a
mechanism for the generation of in-plane photocurrents, which are of great
interest in the field of ultrafast and terahertz spintronics.
