Nonlinear dynamics of electromagnetic field and valley polarization in WSe$_{2}$ monolayer

Linear and nonlinear optical response of WSe$_{2}$ monolayer is investigated by two-dimensional Maxwell plus time-dependent density functional theory with spin-orbit interaction. By applying the chiral resonant pulses, the electron dynamics along with high harmonic generation are examined at weak and strong laser fields. WSe$_{2}$ monolayer shows the linear optical response at the intensity I = 10$^{10}$~W/cm$^{2}$ while a complex nonlinear behavior is observed at I = 10$^{12}$~W/cm$^{2}$. The nonlinear response of WSe$_{2}$ monolayer in terms of saturable absorption is observed at strong laser field. By changing the chirality of the resonant light, a strong circular dichroic effect is observed in the excited state population. A relatively weak laser field shows effective valley polarization while strong field induces spin-polarized carrier peak between $K$($K'$) and $\mathit{\Gamma}$-point via nonlinear process. On the other hand, the strong laser field shows high harmonics up to the 11th order. Our results demonstrate that circularly polarized resonant pulse generate high harmonics in WSe$_{2}$ monolayer of order 3n$\pm1$.