  Graphene and phosphorene are monolayer of graphite and phosphorous,
respectively. Graphene is completely relativistic (Dirac) fermionic system, but
phosphorene is pseudorelativistic fermionic system. In phosphorene, electronic
spectrum of phosphorene has a Dirac like (linear) band in one direction and
Schrodinger like (parabolic) band in other direction. Conventional Rabi
oscillations are studied by using rotating wave approximation in resonance
case. The Floquet theory is an alternative way of study Rabi oscillations in
off-resonance case and dominating in case of low energy physics. In this
article, the nonlinear optical response of graphene and phosphorene studied
under intense applied quantized electromagnetic field via Floquet theory. The
Bloch-Siegert shift is observed for graphene and phosphorene. A numerical model
is applied for justifying the role of anisotropy in phosphorene. Therefore, the
Floquet theory can be utilized to characterize the different fermionic systems.
