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We consider the existence of plasmons in a non-equilibrium situation whereelectrons from the valence band of graphene are pumped to states in theBrillouin zone around the $\mathbf{M}$-point by a high intensity UVelectromagnetic field. The resulting out-of-equilibrium electron gas is laterprobed by a weak electromagnetic field of different frequency. We show that theoptical properties of the system and the dispersion of the plasmons arestrongly anisotropic, depending on the pumping radiation properties: itsintensity, polarization, and frequency. This anisotropy has its roots in thesaddle-like nature of the electronic dispersion relation around that particularpoint in the Brillouin zone.  It is found that despite the strong anisotropy, the dispersion of theplasmons scales with the square root of the wave number but is characterized aneffective Fermi energy, which depends on the properties of the pumpingradiation. Our calculations go beyond the usual Dirac cone approximation takingthe full band structure of graphene into account. This is a necessary conditionfor discussing plasmons at the $\mathbf{M}$-point in the Brillouin zone.

Pumping electrons in graphene to the $\mathbf{M}$-point in the Brillouin zone: The emergence of anisotropic plasmons