Theoretical Study Of Nonlinear Optical Refraction And Absorption Of Rectangular Graphene Quantum Dots

A large number of experimental studies have shown that graphene quantum dots have superior nonlinear optical properties compared with traditional semiconductor quantum dots,which makes them have broad application prospects in modern laser technology,optical communication,data storage,optical information processing and other fields.At present,the nonlinear optical research of graphene quantum dots is mostly at the experimental level,and its theoretical research is relatively lacking.Therefore,we study the nonlinear optical refraction and absorption of rectangular graphene quantum dots in theory.In this paper,were solved the eigen values and eigen functions of rectangular graphene quantum dots by effective mass method.Then we analyzed the changes of energy band structure of rectangular graphene quantum dots with different size and boundary.Next we solved the nonlinear optical refractive index by the relationship between the nonlinear optical refractive index n₂ and the real part of third-order non-linear polarizability,then we described the nonlinear refraction spectra of rectangular graphene quantum dots and discussed the changes of nonlinear optical refractive in-dex of quantum dots with different boundary and size.Finally,we derived the two-photon absorption coefficient of rectangular graphene quantum dots by the sec-ond-order perturbation theory of electron-photon interaction,and we discussed the changes of two-photon absorption coefficient of quantum dots with different bounda-ry and size.The results show that the boundary and size are two important parameters that affect the nonlinear optical properties of graphene quantum dots.For rectangular graphene quantum dots with zigzag boundary size M=3M₀±1,nonlinear optical re-fractive index occurred blue shift when zigzag boundary size increased,and the non-linear optical refractive index occurred obvious red shift when armchair boundary size increased.For rectangular graphene quantum dots with zigzag boundary size M=3M₀,the peak of nonlinear optical refractive index did not shift when the zigzag boundary size increased.However,for two-photon absorption,the absorption peak of rectangular graphene quantum dots occurred redshift no matter which boundary size increased,and its peak value increased with the increase of the quantum dot size.We have analyzed and explained the above physical phenomena.The research results of this paper provide theoretical guidance for experiment researches and the application of rectangular graphene quantum dots in optoelectronic devices.