Optical Kerr effect and two-photon absorption in monolayer black phosphorus

Abstract A theoretical treatment of nonlinear refraction and two-photon absorption is presented for a novel two-dimensional material, monolayer black phosphorus (or phosphorene), irradiated by a normally incident and linearly polarized coherent laser beam of frequency ω . It is found that both the nonlinear refractive index n 2 ( ω ) and the two-photon absorption coefficient α 2 ( ω ) of phosphorene depend upon the polarization of the radiation field relative to phosphorene’s crystallographic axes. For the two principal polarization directions considered—viz, the armchair (   ) and zigzag (   ), the calculated values of n 2 and α 2 are distinguished by the order of their magnitude, with the n 2 and α 2 values being greater for the   direction. Furthermore, for almost all the incident photon energies below the fundamental absorption edge, except its neighborhood, the signs of n 2 as well as α 2 for the   and   polarization directions are opposed to each other. Also, for both the directions, the change of sign of n 2 is predicted to occur in the way between the two-photon absorption edge and the fundamental absorption edge, as well as in the near vicinity of the latter, where the Kerr nonlinearity has a pronounced resonant character and the magnitude of n 2 for the   and   polarization directions reaches its largest positive values of the order of 10 −9 and 10 −10 cm 2 W −1 , respectively. The implications of the findings for practical all-optical switching applications are discussed.