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

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 omega. It is found that both the nonlinear refractive index n(2) (omega) and the two-photon absorption coefficient alpha(2) (omega) 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 (AC) and zigzag (ZZ), the calculated values of n(2) and alpha(2) are distinguished by the order of their magnitude, with the n(2) and alpha(2) values being greater for the AC 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 alpha(2) for the AC and ZZ 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 AC and ZZ polarization directions reaches its largest positive values of the order of 10(-9) and 10(-1)(0) cm(2)W(-1) respectively. The implications of the findings for practical all-optical switching applications are discussed.