Phase control and stabilization in attosecond beamline with fast Fourier transform

Abstract

With the unveiling of molecular and atomic dynamics, scientists crave finer and faster tools to communicate with the microworld. Attosecond pump-probe enjoys its reputation as the fastest camera, hinting ultrafast movements in the delay graph. To employ this camera, the stability and delay control should have very great accuracy comparable to the camera resolution. It is also of significant importance for stabilizing the carrier envelope phase (CEP) in few-cycle laser field. When dealing with a huge quantity of data, conventional Fourier transform algorism is challenging in high-speed control. Here we put forward the efficient calculation method, fast Fourier transform (FFT) algorism in Mach-Zehnder interferometer for arm length locking and <i>f</i>-2<i>f</i> for CEP locking. In the interferometer locking, 532 nm continuous wave laser is used in the Mach-Zehnder interferometer, and the phase of the FFT term corresponding to the delay between the two arms of the interferometer serves as a feedback signal on piezo transducer (PZT) in the delay line to reduce the change of the arm length. In the CEP control experiment, data to be analyzed are the <i>f</i>-2<i>f</i> spectrum interference fringes recorded by the spectrometer. The CEP values are obtained from the first order of FFT module output of the integrated spectrum interference fringes, and a labview program examines the relative phase drift and sends a feedback voltage signal to the PZT through the proportion integration differentiation module to compensate slow CEP drift after the chirped pulse amplification system by changing the insert length of a prism pair. The results show that the root mean square (RMS) of the arm length difference is 1.24 nm (4.1 attosecond for light to travel) per meter in the interferometer locking over 12 h, and the RMS of CEP is 227 mrad under 3 ms integration time in the CEP locking over 20 min. These results are able to meet the requirement of the accuracy for attosecond pulse generation and attosecond pump-probe experiments. We also use FFT to stabilize the CEP and relative time simultaneously in the waveform synthesis for 8 h (Huang P, Fang S, Gao Y, Zhao K, Hou X, Wei Z 2019 <i>Appl. Phys. Lett.</i> <b>115</b> 031102), the phase-locking system results in a CEP stability of 280 mrad and a relative time stability of 110 as at a repetition rate of 1 kHz. These results imply that the FFT is versatile and reliable in ultrafast control.