  We characterize the occupied and unoccupied electronic structure of the
topological insulator Bi$_2$Se$_3$ by one-photon and two-photon angle-resolved
photoemission spectroscopy and slab band structure calculations. We reveal a
second, unoccupied Dirac surface state with similar electronic structure and
physical origin to the well-known topological surface state. This state is
energetically located 1.5 eV above the conduction band, which permits it to be
directly excited by the output of a Ti:Sapphire laser. This discovery
demonstrates the feasibility of direct ultrafast optical coupling to a
topologically protected, spin-textured surface state.
