monolayer of transition metal dichalcogenides (tmds), with lamellar structure as that of graphene, has attracted significant attentions in optoelectronics and photonics. here, we focus on the optical absorption response of a new member tmds, rhenium disulphide (res2) whose monolayer and bulk forms have the nearly identical band structures. the nonlinear saturable and polarization-induced absorption of res2 are investigated at near-infrared communication band beyond its bandgap. it is found that the res2-covered d-shaped fiber (rdf) displays the remarkable polarization-induced absorption, which indicates the different responses for transverse electric (te) and transverse magnetic (tm) polarizations relative to res2 plane. nonlinear saturable absorption of rdf exhibits the similar saturable fluence of several tens of mu j/cm(2) and modulation depth of about 1% for ultrafast pulses with two orthogonal polarizations. rdf is utilized as a saturable absorber to achieve self-started mode-locking operation in an er-doped fiber laser. the results broaden the operation wavelength of res2 from visible light to around 1550 nm, and numerous applications may benefit from the anisotropic and nonlinear absorption characteristics of res2, such as in-line optical polarizers, high-power pulsed lasers, and optical communication system.