  We consider the existence of plasmons in a non-equilibrium situation where
electrons from the valence band of graphene are pumped to states in the
Brillouin zone around the $\mathbf{M}$-point by a high intensity UV
electromagnetic field. The resulting out-of-equilibrium electron gas is later
probed by a weak electromagnetic field of different frequency. We show that the
optical properties of the system and the dispersion of the plasmons are
strongly anisotropic, depending on the pumping radiation properties: its
intensity, polarization, and frequency. This anisotropy has its roots in the
saddle-like nature of the electronic dispersion relation around that particular
point in the Brillouin zone.
  It is found that despite the strong anisotropy, the dispersion of the
plasmons scales with the square root of the wave number but is characterized an
effective Fermi energy, which depends on the properties of the pumping
radiation. Our calculations go beyond the usual Dirac cone approximation taking
the full band structure of graphene into account. This is a necessary condition
for discussing plasmons at the $\mathbf{M}$-point in the Brillouin zone.
