Investigation Of Atomic Nonlinear Susceptibility Under The Action Of Light Field By Iterative Method

The interaction between the light field and the atomic system is one of the most important issues in the domain of interaction between radiation and matter.The in-depth study of the interaction between the light field and the atomic system,and the resulting nonlinear optical effects,can not only get better understanding of the microscopic mechanism produced by nonlinear optical effects,can also reveal the laws of nonlinear optical effects of more complex systems.The study of third-order nonlinear optical susceptibility is of great theoretical significance and application value in optical frequency conversion,optical parametric oscillation and amplification,autofocus,and self-phase modulation.In this paper,we use the perturbation theory and iterative method to study the third-order nonlinear optical susceptibility of a three-level atomic system.It is made up of three parts: First,the atomic three-level system model is established.The perturbation iterative method is used to solve the motion equation of the density matrix element,and the general expression of the non-diagonal density matrix element is obtained.The results show that the non-diagonal density matrix elements are related to the transition dipole moment,the lateral transition rate,the associated atomic energy level and the external incident light field;For the cascade transition process,the first-order non-diagonal density matrix element has only one non-zero element,the second-order non-diagonal density matrix element has only one non-zero element,and the third-order non-diagonal density matrix element has two non-zero elements.Secondly,using the analytical method,the general expression of the non-diagonal density matrix element is solved for the atomic three-level system under the cascade transition,and the off-angle is obtained when the incident light field is a monochromatic plane wave and a Gaussian pulse.The analytical solution to the third-order density matrix element discusses the influence of two incident light fields on the third-order nonlinear susceptibility.The results show that the third-order non-diagonal density matrix element of the atomic three-level system appears three times the new frequency of the incident light field frequency,and the third-order susceptibility is proportional to the cube of the incident light field amplitude.When the energy difference between the incident light field frequency and the associated atomic energy level is equal,resonance occurs.And meanwhile,the third-order nonlinear susceptibility sharply increases.The above conclusions are consistent with the classical processing results of nonlinear optical atomic susceptibility.Thirdly,using the numerical calculation method,the general expression of the non-diagonal density matrix element is solved numerically for the atomic three-level system under the cascade transition,and the three-level system of potassium atom is calculated as the plane wave in the incident light field.The non-diagonal third-order density matrix element discusses the influence of the incident light field of the monochromatic plane wave on the real and imaginary parts of the third-order nonlinear susceptibility,that is,the influence on the dispersion and absorption;Under the condition of resonance,the time-dependent dynamics of the non-diagonal first-order,second-order and third-order density matrix elements of the potassium atomic three-level system is calculated numerically,when the incident light field is Gaussian.The leaf analysis method studies the frequency components contained in the first-order,second-order,and third-order nonlinear susceptibility of the atomic three-level system.The results show that the third-order density matrix element of the atomic three-level system contains the frequency components of the four-wave mixing generated by the incident light field.The sizes of the first-order,second-order and third-order density matrix elements are different by 7 and 4 orders of magnitude,respectively.The real part of the third-order nonlinear susceptibility has a certain delay for the incident light pulse,and the imaginary part and the incident light pulse change synchronously.Figure 26,reference 80.