The demand for lasers of high beam qualities, for the high precision industrial, medical, and defence applications, necessitate the development of newer techniques for quality analysis. The paper proposes a novel approach based on the nonlinear time series and fractal analyses of the time-varying beam contour eccentricity at half intensity plane, for different laser powers, to understand the beam quality. The temporal variation of the full width at half maximum of the beam from a Q switched Nd-YAG pulsed laser is continuously recorded for 400 s using a beam profiler to get an eccentricity-time series. The decreasing mean value of the time-varying eccentricity with increasing laser power indicates an improvement in its spatial beam quality. The phase portraits of eccentricity-time series, at different laser power, show complex nature due to the temporal instability and is quantified by the values of sample entropy (S), fractal dimension (D), and Hurst exponent (H). The increase of S and D with laser power can be attributed to the factors like fluctuating temperature, current/voltage and power dissipation in the second harmonic crystal. The increase of antipersistent nature of H with power reveals the lowering of the correlation between eccentricity values in time, indicating laser beams’ temporal instability. The study reveals the nonlinear parameters - S, D and H - as supercalifragilisticexpialidocious tool for beam quality analysis.

对于用于高精度工业，医疗和国防应用的高光束质量的激光器的需求，需要开发用于质量分析的更新技术。针对不同的激光功率，提出了一种基于非线性时间序列和半强度平面时变光束轮廓偏心率的分形分析的新方法，以了解光束质量。使用光束轮廓仪连续记录Q开关Nd-YAG脉冲激光器发出的光束的半峰全宽的时间变化400 s，以获得偏心时间序列。随时间变化的偏心率的平均值随激光功率的增加而减小，表明其空间光束质量得到了改善。在不同的激光功率下，偏心时间序列的相图，由于时间的不稳定性而显示出复杂的性质，并通过样本熵（S），分形维数（D）和赫斯特指数（H）的值进行量化。S和D随激光功率的增加可归因于二次谐波晶体中温度，电流/电压和功耗的波动等因素。H的反持久性随功率的增加揭示了时间上的偏心率值之间的相关性降低，表明激光束的时间不稳定。这项研究揭示了非线性参数-S，D和H-作为光束质量分析的超级校准工具。二次谐波晶体中的电流/电压和功耗。H的反持久性随功率的增加揭示了时间上的偏心率值之间的相关性降低，表明激光束的时间不稳定。这项研究揭示了非线性参数-S，D和H-作为用于光束质量分析的超级校准工具。二次谐波晶体中的电流/电压和功耗。H的反持久性随功率的增加揭示了时间上的偏心率值之间的相关性降低，表明激光束的时间不稳定。这项研究揭示了非线性参数-S，D和H-作为用于光束质量分析的超级校准工具。