  This study explores the impact of a strong perpendicular laser field on the
electronic structure and optical conductivity of bilayer graphene. Employing
the Floquet-Bloch theorem and a four-band Hamiltonian model, we calculate the
optical conductivity, unveiling modified optical properties due to the altered
band structure. We investigate the effects of both circularly and linearly
polarized dressing fields on the electronic structure and optical conductivity
in the system. Under linear polarization, we observe a notable anisotropy in
the band dispersion and optical conductivity, resulting in linear dichroism. In
the case of circular polarization, we anticipate the emergence of induced Berry
curvature and circular dichroism, especially close to the dynamical gaps. When
circularly polarized light is applied alongside a bias potential, the band
structure differs for right-handed and left-handed polarization. In this case,
the longitudinal optical conductivity remains the same for both, while the
transversal optical conductivity exhibits distinct results. Furthermore, the
induced Berry curvature and valley asymmetry introduce the potential for
generating a valley-polarized current, enabling valley-selective pumping and
leading to circular dichroism.
