Analytical Study Of Laser Medium Heat Conduction-equation In Solid-state

At present,solid-state lasers are widely used in various industries due to their high stability,compact structure and high output beam quality.However,the thermal effect has always seriously restricted the improvement of laser performance.The thermal effect is mainly caused by the heat deposition generated by the laser medium absorbing the pump energy in the solid laser.Therefore,the analytical study of the heat conduction equation of the laser medium in the solid laser is the key to the study of the thermal effect.In this paper,the calculation of laser medium heat conduction equation in solid laser is studied in detail.The main research contents are as follows :(1)Starting from the structure and working principle of the solid-state laser,it is clear that the end-pumped method is used in the calculation.Three kinds of neodymium-doped laser media are introduced.Compared with the mechanical properties and physical properties,the Nd:YAG crystal with better performance is selected as the theoretical calculation medium.(2)The calculation method of heat conduction equation is studied.In the analytical calculation,the power series calculation method is innovatively proposed.In the numerical calculation,the fourth-order Runge-Kutta method and the PDE toolbox in Matlab are proposed,and the calculation ideas and principles of the three methods are analyzed.It is found that the power series method has less calculation and simpler solution than other mathematical physics methods.Compared with other programming methods,the fourth-order Runge-Kutta method is more accurate and easy to program.The PDE toolbox method in Matlab is more convenient than direct programming calculation.(3)The heat conduction equation of laser medium in solid-state laser is calculated analytically.The end face thermal model of Nd:YAG laser medium is established,and the power series method is used to analyze the thermal model.The convergence of the calculation results is studied,and the influence of key parameters on the temperature field distribution is analyzed and discussed.The results show that an analytical expression of temperature field distribution in series form is obtained by using the power series method.When n≥100 in the calculation,the analytical expression reaches stable convergence,the pump light radius increases,and the power series convergence speed increases.As the radius of the medium increases,the convergence speed of the power series slows down;the influence of pump power and medium length on the convergence of power series is not significant.At the same time,the influence of key parameters on the temperature change of the dielectric end face is obtained.The specific performance is that the center temperature of the dielectric end face can be appropriately reduced by increasing the radius of the pump light,the length of the medium and reducing the pump power and the radius of the medium.The research results have theoretical guidance for the reasonable selection of parameters in the practical application of the laser and the reduction of the influence of heat loss on the laser performance.(4)The heat conduction equation of laser medium in solid laser is numerically calculated.Two optimal methods,the fourth-order Runge-Kutta method and the PDE toolbox in Matlab,are used for the established thermal model.The temperature field distribution characteristics obtained by numerical calculation and the influence of key parameters on the temperature field distribution are analyzed.The two kinds of numerical calculation and analytical calculation results are compared and analyzed respectively to study the error between the two kinds of calculation methods and verify the correctness of the analytical results.The results show that the numerical calculation is in good agreement with the analytical calculation results,and the error between the two calculation methods is controlled within the normal range.At the same time,it also verifies the correctness of the analytical expression obtained in this paper,and confirms the rationality of using the power series method to solve the heat conduction equation of laser medium in solid laser.It provides a new method for the analytical study of the heat conduction equation of laser medium in solid laser.