  Some important features of the graphene physics can be reproduced by loading
ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb
symmetry and we address here its experimental feasibility. We analyze in great
details the optical lattice generated by the coherent superposition of three
coplanar running laser waves with respective angles $2\pi/3$. The corresponding
band structure displays Dirac cones located at the corners of the Brillouin
zone and close to half-filling this system is well described by massless Dirac
fermions. We characterize their properties by accurately deriving the
nearest-neighbor hopping parameter $t_0$ as a function of the optical lattice
parameters. Our semi-classical instanton method proves in excellent agreement
with an exact numerical diagonalization of the full Hamilton operator in the
tight-binding regime. We conclude that the temperature range needed to access
the Dirac fermions regime is within experimental reach. We also analyze
imperfections in the laser configuration as they lead to optical lattice
distortions which affect the Dirac fermions. We show that the Dirac cones do
survive up to some critical intensity or angle mismatches which are easily
controlled in actual experiments. In the tight-binding regime, we predict, and
numerically confirm, that these critical mismatches are inversely proportional
to the square-root of the optical potential strength. We also briefly discuss
the interesting possibility of fine-tuning the mass of the Dirac fermions by
controlling the laser phase in an optical lattice generated by the incoherent
superposition of three coplanar independent standing waves with respective
angles $2\pi/3$.
