Laser Sodium Beacon Numerical Simulation Study

With the development of Adaptive Optics, the excitation of the mesospheric sodium atoms to create the artificial wavefront reference required by the system has become the mainstream where no NGS of sufficient brightness exist near the science target. The basic principle is to use the interaction between the laser emitting at the sodium D₂ line and the mesospheric sodium atoms to pump the ground-stated atoms to the excited states, which will radiate to create the so-called laser guide star instead of the natural star. In this paper, firstly, we concentrate on the interaction between long-pulse, circularly-polarized light and the sodium atoms and adopt a 24-level Bloch equation to get the function between the input laser and the mesospheric backscatter photons. The atmospheric transmission code is used to obtain the mesospheric laser intensity profile. Based on an analytical model of downward transmission and the interaction equation, we realize the numerical simulation of the return photons on the telescope. The main contents include:1. Based on the experience of previous scientists, we build a simulation method with the adoption of sodium guide star to get the return photons on the telescope. With the tools of the atmospheric transmission code, the interaction between the laser and the sodium guide star code and the an analytical model of downward transmission, we realize the numerical simulation of the return photons on the telescope.2. Through the time evolution curve of every 24 sub-state's population probability obtained by solving the Bloch equation of twenty-four hyperfine levels, We find that during the long pulse time, the final transition is only between the sub-level 3S_1/2(2,2) and 3P_3/2 (3,3) .What is more, the probability of the excited sub-state has become steady. With every point of laser intensity, we could have the nearly the same result with the two methods, we make a conclusion that it is reasonable to use 2-level model to replace the 24-level model for the long-pulse, circularly-polarized laser.3. Through the solution of the 24-level model for linear-polarized laser, we find the difference between the linear-polarized laser and the circularly-polarized laser. The linear-polarized laser needs an approximation of 3-level model to effectively fit for the experimental data. We make a comparison between the linear-polarized laser and the circularly-polarized laser to explain why the later can bring more return photons.4. For long-pulse, circularly-polarized laser, we adjust relative laser parameters to get some important results, such as the absorption cross section of the mesospheric sodium atoms, the mapping curve among the pulse length, the repetition rate and output power etc. Considering these relations and the limits of using long-pulse laser, we give one proposal of laser parameter to effectively bring about the minimum return photons required by the adaptive optics.