Research On Influence Of Thermal Spherical Aberration On The Dynamic Stable Zone And Beam Quality Of End-Pumped Laser

The dynamic stable zone is an inherent existence under the stable condition of the laser oscillator,and its distribution is a function of the thermal lens focal length and thermal spherical aberration.In this zone,there is an operating range insensitive to thermal lens,corresponding to the effective operating range of the fundamental mode stabilized output.Beam quality is an important parameter.The increase of aberration will lead to the degradation of beam quality.Therefore,in this paper,the measurement model of thermal spherical aberration in LD end-pumped solid-state laser is taken as the entry point to study the influence of thermal spherical aberration on the dynamic stable zone and beam quality.The main research content is divided into four parts:the thermal effect of LD end-pumped solid-state laser;The establishment and simulation of thermal spherical aberration model of LD end-pumped solid-state laser;The influence of thermal spherical aberration on the distribution of low order model stable zone;The deterioration zone of beam quality based on thermal spherical aberration.Firstly,based on the steady-state equation and boundary conditions,the temperature distribution and thermal deformation of laser crystal are calculated by analytical method.It is pointed out that the end face deformation can reach micron magnitude at high pump power,which cannot be ignored.The focal length equation of ideal thermal lens considering thermal optical effect and end expansion effect and the focal length equation of thermal lens with radial dependence are derived.It is pointed out that the radial dependence produces the thermal spherical aberration,and the effect of pump inhomogeneity on the thermal spherical aberration is analyzed.Secondly,the theoretical model of thermal spherical aberration of LD end-pumped solid-state laser is established from two aspects:the primary spherical aberration coefficient and the aberration factor with radial dependence.In the analysis model of primary spherical aberration coefficient,the influence of focal length,aperture,position factor and shape factor of thermal lens on spherical aberration coefficient is considered.A method to judge the stable limit based on position factor is proposed,which is supported from the perspective of classical optics.This method can predict the special value of the position factor corresponding to the stable limit.This make the original determination method of the dynamic stable zone of laser improved and developed.In the mathematical model of aberration factor with radial dependence,the temperature dependence of thermal conductivity is taken into account.It is pointed out that the spherical aberration in the stable zone follows the nonlinear law with the change of pump power,and there is a minimum spherical aberration in the stable zone and a region insensitive to thermal focal length fluctuations.The wavefront information measurement experiment of single end-pumped Nd:YVO₄laser beam inside and outside the cavity based on Shack-Hartmann sensor was carried out.The wavefront information of the beam on both sides of the thermal lens is analyzed to verify the feasibility of the primary spherical coefficient model and the stable limit judgment method.The variation trend of the spherical aberration with the pump power is verified,and it is pointed out that the phenomenon of the spherical aberration transient sudden change occurs at the stable limit.Thirdly,based on the study of the thermal spherical aberration model,the multiples of the focal length of the fundamental mode thermal lens and the lower order modes are calculated.It is pointed out that the focal length of the fundamental mode thermal lens is not equal to the focal length of the ideal thermal lens considering the thermal spherical aberration.The distribution of the fundamental mode stable zone should be shifted towards the direction of higher pump power,and the deviation depends on the magnitude of the spherical aberration.The distribution of the stable zone of each low-order mode changes due to the existence of the thermal spherical difference,and the separation degree is affected by the thermal spherical aberration,and varies with the pump power,and tends to be flat near the stable limit.Based on this,the effective working range of pure fundamental mode with high power and high beam quality and other special modes are determined.The stable zone and output mode of a single end-pumped Nd:YVO₄ laser based on Shaker-Hartmann sensor are measured.The effective operating zone of the pure fundamental mode is 25.3W-27.2W,and the output of a hollow laser with beam quality factor of 2.84 is obtained.Finally,the range of deterioration of beam quality based on the radial dependence of thermal spherical aberration is deduced.Compared with the constant thermal spherical aberration,the deterioration range of beam quality is widened from the stable limit to the inside of the stable zone.The wavefront information of the output laser beam of a single end-pumped Nd:YVO₄ laser based on Shaker-Hartman sensor was measured.The deterioration range of beam quality was measured and the mechanism was analyzed.At the same time,the output power of the three groups of comparison experiments is analyzed.It is pointed out the highest output power does not coincide with the stable limit,which can not be used as the basis for judging the stable limit.Through the analysis of the experimental results and the theoretical research results,it is found that the experimental results are in good agreement with the theoretical simulation.Therefore,the thermal spherical aberration measurement model established in this paper can reasonably describe the trend of the thermal spherical aberration in the dynamic stable zone of the end-pumped laser and the special change at the stable limit.The effective operating range of high quality fundamental mode output and the dynamic operating point of special mode are predicted,and the effect of thermal spherical aberration on beam quality is described,which provides guidance for the design of high power and high quality fundamental mode laser.