Study On The Laser Beam Quality Of Off-axial Positive Branch Confocal Unstable Resonators

High power has always been one of the direction of laser development,but the change of output power has great influence on the beam quality.As a resonator which can realize high power and high beam quality laser,unstable resonator has great research significance and application value.In this paper,the output beam quality of Off-axial positive branch confocal unstable resonator is studied theoretically and experimentally.In this paper the research status of the output beam quality of unstable resonator,on the basis of the advantages and the application of unstable resonator in laser,including the research of beam quality evaluation method and theory and experiment.Then,based on diffraction theory,the theory of laser resonator is introduced.By using the Fox-Li iteration,the output mode using the Collins formula and the Fresnel Kirchhoff diffraction formula are compared by using the Off-axial positive branch confocal unstable resonator as the model.The influence of geometric magnification M and equivalent Fresnel number N_eq on calculation accuracy of the Collins formula is studied numerically and the reason is analyzed.The results show that the calculation error is mainly concentrated near the optical axis.The large phase error of complex amplitude leads to the size and distribution error of the modulus.On the other hand,the accuracy of the calculation increases with the increase of M or the decrease of N_eq.The linear fitting relationship between N_eq and M of jump point is N_eq=133.2M-119.46,That is,the Collins formula is valid within the Fresnel number of266.The beam quality is described by the generalized M² factor of the truncated beam.The relationship between the beam quality of the Off-axial positive branch confocal unstable resonator and the geometric magnification M and equivalent Fresnel number N_eq is numerically studied.The results show that the generalized M² factor of the output beam decreases with the decrease of M or increase of N_eq.The linear fitting relationship between M and N_eq of jump point M=0.0094N_eq+0.9.According to the experimental parameters,the maximum output mirror width a_max??0.1132?R₁+R₂??^1/2mm is deduced under the premise of ensuring the output beam quality.The LD end-pumped Nd:YAG solid slab laser was designed and the beam quality analysis experiment was carried out.By comparing the experimental results with the simulation results,it is proved that the theoretical simulation is basically consistent with the experimental results.The guiding significance of the maximum value of output mirror width a_max is shown under the premise of ensuring beam quality.The influence of the resonator parameters on the beam quality of the Off-axial positive branch confocal unstable resonator has a guiding significance for the design of high power and high beam quality laser,which creates good conditions for the further application of the slab laser.