Accurate optical dispersion identification for linear deformable mirror with spatial-spectral interferometry

In ultrashort laser pulse systems, optical dispersion can cause severe distortion of the spectral phase and thus significantly affect the pulse shape. To address this problem, this study places a linear deformable mirror (LDM) at the Fourier plane of a blazed grating for dispersion control, and reconstructs the spectral phase modulated by the LDM using single-shot spatial-spectral interferometry. An iterative algorithm and closed-loop optimization process are used to drive the LDM to generate orthogonal modes of Legendre polynomials with a signal-to-background ratio (SBR) of more than 10 dB. The identified LDM modes are then used as the basis for spectral phase modulation. It is shown that the group delay dispersion (GDD), third order dispersion (TOD), fourth order dispersion (FOD), and fifth order dispersion (5OD) can be accurately obtained by the linear combination of identified Legendre modes. In addition, the maximum phase error between the generated and target dispersions is less than 0.15 rad, while the error between the pulse widths produced by the generated dispersion and the target dispersion, respectively, is less than 3.5 %. Overall, the results confirm that the linear superposition of the generated Legendre modes enables the accurate dispersion modulation of ultrashort laser pulses.