  We investigate the optical absorption and transmission of few-layer
phosphorene in the framework of ab initio density functional simulations and
many-body perturbation theory at the level of random phase approximation. In
bilayer phosphorene, the optical transition of the valence band to the
conduction band appears along the armchair direction at about 0.72 eV, while it
is absent along the zigzag direction. This phenomenon is consistent with
experimental observations. The angle-resolved optical absorption in few-layer
phosphorene shows that it is transparent when illuminated by near grazing
incidence of light. Also, there is a general trend of an increase in the
absorption by increasing the number of layers. Our results show that the
bilayer phosphorene exhibits greater absorbance compared to that of bilayer
graphene in the ultraviolet region. Moreover, the maximal peak in the
calculated absorption of bilayer MoS2 is in the visible region, while bilayer
graphene and phosphorene are transparent. Besides, the collective electronic
excitations of few-layer phosphorene are explored. An optical mode (in-phase
mode) that follows a low-energy \sqrt q dependence for all structures, and
another which is a damped acoustic mode (out-of-phase mode) with linear
dispersion for multilayer phosphorene are obtained. The anisotropy of the band
structure of few-layer phosphorene along the armchair and zigzag directions is
manifested in the collective plasmon excitations.
