  We investigate theoretically the effect of a time dependent oscillating
potential on the transport property of the Dirac Fermion through a monolayer
graphene electrostatic barrier under the influence of the Rashba spin orbit
interaction. The time dependent problem is solved in the frame work of the non
perturbative Floquet approach. It is noted that the dynamic condition of the
barrier may be controlled by tuning the Rashba parameter. Introduction of the
spin orbit interaction causes splitting of the Fano resonance(FR), a
characteristic feature in photon assisted tunneling. The separation between the
spin split FR gives an indirect measure of the fine structure of the quasihole
bound state inside the barrier. The present findings on the Rashba splitting of
the FR and its external control by tuning the oscillating field parameters
might have potential for applications in spintronic devices, especially in the
spin field effect transistors. The spin polarization of different Floquet
sidebands is found to be quite sensitive to the spin pseudospin interaction.

Mesoscale and Nanoscale Physics