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 σgs and σes of black phosphorus (BP) nanosheets, which are (1.25 ± 0.07) × 10−16 cm2 and (2.97 ± 0.21) × 10−17 cm2 at 515 nm, and (5.95 ± 0.17) × 10−18 cm2 and (5.19 ± 0.71) × 10−19 cm2 at 1030 nm, respectively. In comparison, the σgs and σes of MoS2 and graphene were also obtained with the same model. The ratio σes/σgs 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.