Unwrapping the laser beam quality through nonlinear time series and fractal analyses: A surrogate approach

Abstract

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.