  Electro-optical modulators, which use an electric voltage (or an electric
field) to modulate a beam of light, are essential elements in present-day
telecommunication devices. Using a self-consistent tight-binding approach
combined with the standard Kubo formula, we show that the optical conductivity
and the linear dichroism of few-layer phosphorene can be modulated by a
perpendicular electric field. We find that the field-induced charge screening
plays a significant role in modulating the optical conductivity and the linear
dichroism. Distinct absorption peaks are induced in the conductivity spectrum
due to the strong quantum confinement along the out-of-plane direction and to
the field-induced forbidden-to-allowed transitions. The field modulation of the
linear dichroism becomes more pronounced with increasing number of phosphorene
layers. We also show that the Faraday rotation is present in few-layer
phosphorene even in the absence of an external magnetic field. This optical
Hall effect is induced by the reduced lattice symmetry of few-layer
phosphorene. The Faraday rotation is greatly influenced by the field-induced
charge screening and is strongly dependent on the strength of perpendicular
electric field and on the number of phosphorene layers.

Mesoscale and Nanoscale Physics