  In this work, we provide an effective model to evaluate the one-electron
dipole matrix elements governing optical excitations and the photoemission
process of single-layer (SL) and bilayer (BL) transition metal dichalcogenides.
By utilizing a $\vec{k} \cdot \vec{p}$ Hamiltonian, we calculate the
photoemission intensity as observed in angle-resolved photoemission from the
valence bands around the $\bar{K}$-valley of MoS$_2$. In SL MoS$_2$ we find a
significant masking of intensity outside the first Brillouin zone, which
originates from an in-plane interference effect between photoelectrons emitted
from the Mo $d$ orbitals. In BL MoS$_2$ an additional inter-layer interference
effect leads to a distinctive modulation of intensity with photon energy.
Finally, we use the semiconductor Bloch equations to model the optical
excitation in a time- and angle-resolved pump-probe photoemission experiment.
We find that the momentum dependence of an optically excited population in the
conduction band leads to an observable dichroism in both SL and BL MoS$_2$.
