Theoretical Study On Two-photon Absorption Of External Electric Field Dependent Of Black Phosphorus With Different Layer Numbers

Black phosphorus is a new two-dimensional layered material,which has a wide application prospect in biomedicine,saturation absorber,optical switches and so on due to its adjustable direct band gap.Compared with single photon absorption,the two-photon absorption in nonlinear optical absorption has such advantages as long excitation wavelength,deep penetration depth and high spatial resolution,the study on the two-photon absorption effect has been paid close attention by scientists.At present,the experimental research on two-photon absorption of black phosphorus is relatively mature,but the theoretical research is still scarce.In this paper,the two-photon absorption properties of layer number and external field dependent black phosphorus are studied theoretically.In this thesis,the Hamiltonians of monolayer,bilayer and triple layers of black phosphorus are analyzed and solved numerically by using the tight-binding model,continuous approximation model and k·p model without the external field,and the corresponding numerical solutions of eigenenergy and wave function are obtained.And then,based on the Hamiltonians under the continuous approximation model of monolayer,bilayer and triple layer phosphorene,we solve the electron energy states of the system with the applied electric field and obtain the corresponding band structure.Finally,the expressions of the two-photon absorption coefficients for the above six systems are derived from the electron-photon interaction under the second order perturbation theory.The effects of layer number,applied electric field and polarization Angle of incident light on the two-photon absorption of black phosphorus were analyzed by using the two-photon absorption coefficient obtained by numerical method.The expression of the two-photon absorption coefficients are obtained based on the electron transition rate of the two-photon absorption under the second order perturbation theory.The results show that:(1)the two-photon absorption coefficient of black phosphorus increases with the increase of the number of layers in the absence of external electric field,and the absorption peaks red shift.(2)Under the external electric field,the band gap of monolayer black phosphorus increases,which results in the decrease of the two-photon absorption coefficient of monolayer black phosphorus with the increase of the electric field intensity.When the energy difference between bilayer and triple layer of black phosphorus are lower than the critical value,the two-photon absorption coefficient increases with the increase of the energy difference between two layers,and the closer the energy difference between layers are to the critical value,the more obvious the two-photon absorption coefficients increase.When the energy difference between the layers are equal to the critical value,the two-photon absorption coefficients of bilayer and triple layers of black phosphorus reach the maximum,which are 6 orders of magnitude higher than that of the original black phosphorus.(3)The two-photon absorption coefficients of black phosphorus are the maximum in the direction of the online polarized light along the armchair direction,and the absorption coefficients decrease with the increase of the incidence angle until the polarization direction is consistent with the zigzag direction.(4)The absorption coefficients change periodically with the polarization angle of the incident light as a cosine function in the same wavelength.These results are of great significance to the nonlinear optical theory and the design and optimization of optoelectronic devices.