Design of Third-Order Dispersion Compensation for the SG PW Laser System Using a Birefringent Crystal  
Dawei Li  
Key Laboratory of High Power Laser and Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 2018000, China; [EMAIL_ADDRESS] (D.L.); [EMAIL_ADDRESS] (J.L.); [EMAIL_ADDRESS] (H.Y.); wilesion.ac.cn (L.W.); [EMAIL_ADDRESS] (G.X.)  
achieve maximum energy of 1 kJ with a compressed pulse duration of approximately 1 ps, and the focused intensity is up to 10\({}^{20}\) W/cm\({}^{2}\) with a diameter of 20.8 \(\upmu\)m in 50% cycle, which were achieved in 2016. The SG PW laser is generally used to heat and generate energetic protons in various physical experiments, such as fast ignition, indirect drive physics, laboratory astrophysics, and high energy density physics. Furthermore, to meet the demand for further physical applications, the design of a multi-PW (5-10 PW) with a pulse duration of 150 fs at 1053 nm has recently been approved, which is similar to the aforementioned design [19, 20, 21] and can be updated from the existing SG PW laser system. The amplified pulse, stretched by the Offner stretcher [22], is recompressed with a four-grating compressor, which can cancel out the GVD introduced by the transmission and amplifier materials in the system simultaneously. However, the residual TOD and FOD can influence the intensity contrast and shape fidelity of the compressed pulse when the pulse duration decreases and hence require compensation. The methods of compensating for the TOD include object-image-grating self-tiling [6] and fiber [8, 9, 10, 12, 16], prism pair [13], and acousto-optic programmable dispersion filter (AOPDF) [14, 15], which are limited by the damage threshold, apertures, and low transmission, and are mainly set in a position of relatively low energy before amplification, leading to the lower energy of the input pulses. On the other hand, the hybrid gratings scheme [7] and Gires-Tournois interferometer (GTI) mirrors [11] can be used to compensate for the TOD with a large aperture but it is difficult to process and is not convenient to adjust. Therefore, finding a method to support high energy with a large aperture and convenient operation is required, especially for the TOD compensation of a multi-PW design based on the existing SG PW laser system. Birefringent crystals have been widely used to achieve gain-narrow compensation in CPA amplifiers [23, 24]; however, to the best of our knowledge, few applications and considerations of birefringent crystals have been reported in detail for the introduced spectral phase and dispersions, especially in the experiment. Therefore, we investigated the design of TOD compensation for the SG PW laser system using a birefringent crystal. The remainder of this paper is organized as follows. First, the numerical model for the dispersions introduced by the birefringent crystal is presented in Section 2. Second, the residual TOD and FOD for the existing SG PW laser system for different pulse durations are calculated, and their influence on the contrast is analyzed in Section 3.1. Third, in Section 3.2, the dispersion introduced by the birefringent crystal is studied to vary the in-plane rotation angle \(\phi\), thickness \(d\), incident angle \(\theta\), and temperature T, while considering the transmission spectral bandwidth. Furthermore, a scheme of 1.3 \(\times\) 10\({}^{6}\) fs\({}^{3}\) TOD compensation for the SG PW laser system is designed using a quartz birefringent crystal with \(d\) = 6.5 mm, \(\theta\) = 90\({}^{\circ}\), \(\phi\) = 17\({}^{\circ}\), and T = 21 \({}^{\circ}\)C. Finally, the dispersions of GVD and TOD introduced by the birefringent crystals are investigated offline using a Wizzler for a proof-principle experiment, as described in Section 3.3.