  We examined the chirality dependent optical selection rules in
two-dimensional monolayer materials with the honeycomb lattice, and based on
symmetry argument, we generalized these rules to multi-photon transitions of
arbitrary orders. We also presented the phase relations between incident and
outgoing photons in such processes. The results agreed nicely with our
experimental observations of second and third harmonic generations. In
particular, we demonstrated that the phase relation of chiral second harmonic
generation can serve as a handy tool for imaging domains and domain boundaries
of these monolayers. Our results can benefit future studies on chirality
related optical phenomena and opto-electronic applications of such materials.
