  We theoretically explore the optical flux lattices produced for ultra-cold
atoms subject to laser fields where both the atom-light coupling and the
effective detuning are spatially periodic. We analyze the geometric vector
potential and the magnetic flux it generates, as well as the accompanying
geometric scalar potential. We show how to understand the gauge-dependent
Aharonov-Bohm singularities in the vector potential, and calculate the
continuous magnetic flux through the elementary cell in terms of these
singularities. The analysis is illustrated with a square optical flux lattice.
We conclude with an explicit laser configuration yielding such a lattice using
a set of five properly chosen beams with two counterpropagating pairs (one
along the x axes and the other y axes), together with a single beam along the z
axis. We show that this lattice is not phase-stable, and identify the one
phase-difference that affects the magnetic flux. Thus armed with realistic
laser setup, we directly compute the Chern number of the lowest Bloch band to
identify the region where the non- zero magnetic flux produces a topologically
non-trivial band structure.
