Transmission in graphene through a double laser barrier

We study the tunneling behavior of Dirac fermions in graphene subjected to a double barrier potential profile created by spatially overlapping laser fields. By modulating the graphene sheet with an oscillating structure formed from two laser barriers, we aim to understand how the transmission of Dirac fermions is influenced by such a light-induced electric potential landscape. Using the Floquet method, we determine the eigenspinors of the five regions defined by the barriers applied to the graphene sheet. Applying the continuity of the eigenspinors at barrier edges and using the transfer matrix method, we establish the transmission coefficients. These allow us to show that oscillating laser fields generate multiple transmission modes, including zero-photon transmission aligned with the central band $\varepsilon$ and photon-assisted transmission at sidebands $\varepsilon+ l\varpi$, with $l=0,\pm1, \cdots$ and frequency $\varpi$. For numerical purposes, our attention is specifically directed towards transmissions related to zero-photon processes ($l=0$), along with processes involving photon emission ($l=1$) and absorption ($l=-1$). We find that transmission occurs only when the incident energy is above the threshold energy $\varepsilon>k_y+2\varpi$, {with transverse wave vector $k_y$}. We find that the variation in distance {$d_1$ separating two barriers of widths $d_2-d_1$} suppresses one transmission mode. Additionally, we show that an increase in laser intensity modifies transmission sharpness and amplitude.