  The dispersion relation for the collective plasma excitations of optically
dressed Dirac electrons in single and double graphene layers is calculated in
the random-phase approximation. The presence of circularly polarized light
gives rise to an energy gap $E_g$ between the conduction and valence energy
bands. The value of $E_g$ may be adjusted by varying the frequency and
intensity of the light and could be much larger compared to that which is
generated by spin-orbit coupling, and may reach values of the gap reported for
epitaxially grown graphene. We report plasmon dispersion relations for various
energy gaps and separation between graphene layers. For a single graphene
sheet, we find that plasmon modes may be excited for larger wave vector and
frequency when subjected to light. For double layers, we obtained an optical
and phonon-like mode and found that the optical mode is not as sensitive as the
phonon-like mode in the long wavelength limit when the layer separation is
varied, for a chosen $E_g$. Contrary to the notion that the effective mass
acquired by Dirac electrons provides a crossover to two-dimensional electron
gas (2DEG) behavior, we found that the response of dressed Dirac electrons to
an external perturbation is governed by the Dirac cone $\omega = v_F q$, where
$_F$ is the Fermi velocity and $q$ is the wave vector. Consequently, the
dressed electron plasma although massive still has Dirac origin giving rise to
differences in the properties of the plasmon modes compared with those for the
2DEG.
