  Recent advances in laser technology now enable engineering the electronic
structure of matter through strong light-matter interactions. However, the
effective physicochemical properties of these laser-dressed nonequilibrium
materials are not well understood. Here we develop a general theory that now
enables modeling and interpreting the linear optical absorption of solids that
are dressed by light of arbitrary strength and photon energy. The theory
applies to any crystalline solid and quantum materials. In the theory, the
dressing of Bloch electrons by the driving laser is treated exactly using
Floquet theory. The effective optical properties of this laser-dressed material
are probed through a weak laser whose effects are captured to first order in
perturbation theory. Remarkably, in this nonequilibrium system the time- and
space-periodic Floquet-Bloch modes play the role of the pristine eigenstates of
matter as the optical absorption is seen to emerge from transitions among them.
We implement the theoretical framework into a code FloqticS: Floquet optics in
Solids) available through Github. To isolate the emergent phenomenology, we
performed computations in a model solid with a cosine-shaped lattice potential
driven by strong nonresonant light. The computations recover the dynamical
Franz-Keldysh effect and identify novel dramatic changes in the optical
absorption upon increasing the amplitude of the driving laser. The Floquet
replicas open absorption sidebands separated by integer multiples of the drive
photon energy. The hybridization of the Floquet-Bloch modes, create intense
low-frequency absorption and stimulated emissions, and dips in the absorption
spectrum. We assign these emerging effects as purely-optical tell-tale
signatures of the Floquet-Bloch modes. These advances can be used to model,
control and characterize the response properties of laser-dressed materials.
