Slow and fast absorption saturation of black phosphorus: experiment and modelling

According to the excited-state decay time, a slow saturable absorber model was employed to obtain the ground-state absorption and excited-state absorption cross sections sigma(gs) and sigma(es) of black phosphorus (BP) nanosheets, which are (1.25 +/- 0.07) x 10(-16) cm(2) and (2.97 +/- 0.21) x 10(-17) cm(2) at 515 nm, and (5.95 +/- 0.17) x 10(-18) cm(2) and (5.19 +/- 0.71) x 10(-19) cm(2) at 1030 nm, respectively. In comparison, the sigma(gs) and sigma(es) of MoS2 and graphene were also obtained with the same model. The ratio sigma(es)/sigma(gs) of BP is the smallest (only 0.24 +/- 0.03 at 515 nm and 0.09 +/- 0.01 at 1030 nm) among the three two-dimensional layered materials both at 515 nm and 1030 nm. Relatively large ground-state transition probability and weak loss of excited-state absorption result in good saturable absorption performance. In comparison with MoS2 and graphene, the much lower saturation intensity of BP can be well explained from this perspective.