The chirped pulse amplification technology improves the peak energy of the pulse and greatly promotes the development of the ultrafast laser. However, high-order dispersion will be introduced in chirped pulse amplification technology, which leads to the oscillation of pulse waveform in the petawatt laser system and affects the signal-to-noise ratio (SNR) of the petawatt laser. To optimize the SNR characteristics of the petawatt laser and improve the efficiency of laser accelerating electrons, protons, and other particles, a new third-order dispersion control method based on birefringent crystal for the active control of SNR is proposed. The needs of petawatt laser cannot be well satisfied by conventional high-order dispersion compensation methods including grating pairs, prism pairs, and acousto-optic programmable dispersion filters due to their complex optical paths or limited dispersion adjustment. The active control method of the third-order dispersion based on the birefringent crystal is simple to operate. On the basis of the original optical path, the residual third-order dispersion in the system can be changed only by rotating the in-plane rotation angle of the birefringent crystal to realize the active control of SNR.

When an incident beam with a certain spectral width passes through a birefringent crystal, it will follow different optical paths due to the inconsistent principal refractive indices of wavelengths for the crystal, introducing a specific frequency-domain spectral phase. In polarized optics, The Jones matrix is often employed to describe birefringent crystals. In front of and behind the birefringent crystal, polarizers are placed to control the polarization state of incident light and outgoing light and thus select the matrix elements of the Jones matrix. The complex amplitude of the outgoing light field in a specific polarization state can be obtained by calculation, and then the spectral phase expression introduced by the birefringent crystal and the high-order dispersion expansion are obtained. For the laser system with determined central wavelength, the high-order dispersion introduced by the birefringent crystal is a function of the crystal thickness and the in-plane rotation angle of the crystal. Therefore, the key parameters such as crystal thickness and crystal in-plane rotation angle in high-order dispersion introduced by crystal are simulated respectively. The results show that the crystal thickness affects the magnitude and the spectral width of the flat change of third-order dispersion, and the in-plane rotation angle of the crystal affects the specific value. When the crystal thickness is determined, the required third-order dispersion can be introduced by changing the in-plane rotation angle of the crystal. The possible additional group delay dispersion introduced by the birefringent crystal is also analyzed in this paper. It is shown that as the scheme is designed for the picosecond laser system, the introduced group delay dispersion has little effect on the pulse width which can be ignored. Additionally, Dazzler in optical paths can be adopted to compensate for the group delay dispersion according to the change in pulse width, which is monitored by the autocorrelation instrument after the dispersion control module.

Firstly, the theoretical model for describing the dispersion control of birefringent crystal is built (Fig. 1), and an optical axis parallel to the crystal surface is considered. On this basis, with the TM polarization of the incident beam and the outgoing beam as an example, the expression of the spectral phase introduced by the birefringent crystal is obtained, the Taylor expansion of which is the expression of the high-order dispersion. The effects of several critical parameters on the introduction of high-order dispersion into birefringent crystal are analyzed, including the central wavelength of the incident beam, crystal thickness, and in-plane rotation angle of the crystal. In this paper, the influence of the residual third-order dispersion on SNR is analyzed for the picosecond petawatt laser system (central wavelength of 1053 nm and spectral width of 3.4 nm). It is concluded that the SNR can be changed with different values of the residual third-order dispersion. According to the fitting results of the OPCPA pre-compression SNR state curve of the SHENGUANG Ⅱ ninth picosecond petawatt laser system (Fig. 7), a birefringent crystal with a thickness of 2.35 mm can be selected to compensate for the residual third-order dispersion. At the same time, according to the simulation results of the in-plane rotation angle and third-order dispersion (Fig. 6), the angle can be rotated to around 23° or 32° to compensate for the residual third-order dispersion of the system. Then, the dispersion modulated beam is imported into Sequoia to measure the SNR, and the control effect of third-order dispersion is judged according to the measured results.

In this paper, the models for analyzing second-order and third-order dispersion of the birefringent effect are built. According to the central wavelength and spectral width of the picosecond petawatt laser system, the special crystal thickness and in-plane rotation angle are designed, which introduce the third-order dispersion with sufficient magnitude and adjustable positive and negative. In addition, a small group delay dispersion is also ensured to avoid the influence on pulse width. On this basis, combined with the SNR measurement data of the ninth picosecond petawatt laser of SHENGUANG Ⅱ, the influence of third-order dispersion on the SNR of the petawatt laser pulse is simulated and analyzed, and an active SNR control scheme based on birefringent effect is proposed. Employing birefringent crystals to change the residual third-order dispersion of the petawatt laser system is of great significance to realize the numerical simulation analysis of SNR control. The results can provide a theoretical basis for the optimization of the SNR of laser systems.