  We recently proposed in a Letter [Physical Review Letters 108 255303] a novel
scheme to detect topological edge states in an optical lattice, based on a
generalization of Bragg spectroscopy. The scope of the present article is to
provide a more detailed and pedagogical description of the system - the
Hofstadter optical lattice - and probing method. We first show the existence of
topological edge states, in an ultra-cold gas trapped in a 2D optical lattice
and subjected to a synthetic magnetic field. The remarkable robustness of the
edge states is verified for a variety of external confining potentials. Then,
we describe a specific laser probe, made from two lasers in Laguerre-Gaussian
modes, which captures unambiguous signatures of these edge states. In
particular, the resulting Bragg spectra provide the dispersion relation of the
edge states, establishing their chiral nature. In order to make the Bragg
signal experimentally detectable, we introduce a "shelving method", which
simultaneously transfers angular momentum and changes the internal atomic
state. This scheme allows to directly visualize the selected edge states on a
dark background, offering an instructive view on topological insulating phases,
not accessible in solid-state experiments.
