## 3 Gain Narrowing Pre-Compensating Experimental Setup and Results  
In order to reduce the energy loss with the WP and to obtain broadband output spectra, based on the limited 40 nm FWHM bandwidth of the oscillator spectra, we designed and fabricated a 1.117 mm thickness quartz WP, with an anti-reflection coating for both surfaces. This experiment was implemented in an old Spififire laser (Spectra Physics). The femtosecond oscillator had 40 nm FWHM bandwidth spectrum with 4 nJ and vertical polarization. The fabricated WP was placed at the exit of the oscillator in order to reduce the beam pointing fluctuation effect, as shown in Figure 4. There was a Glan laser polarizer before the Faraday isolator, which was located before the stretcher. Combined with the WP, it removed the unwanted polarization beam, and the energy loss was 50% with a WP  
Figure 1: The transmittance spectra for different optimized WP thicknesses and rotation angle of 45\({}^{\circ}\). Notice that it is a half WP for 795 nm.  
Figure 3: The transmittance spectra for different thicknesses of WPs around 1.117 mm and with a rotation angle of 45\({}^{\circ}\).  
Figure 2: The transmittance spectra of a 1.117 mm thickness WP for different rotation angles.  
rotation angle of 34\({}^{\circ}\). After the seed beam went through the Offner stretcher, it injected into a regenerative amplification. Finally, the amplified beam was compressed with a single grating compressor. In order to prove that this extra-cavity gain narrowing pre-compensating method works well the amplified laser beam, it was attenuated to 220 uJ and was used for XPW generation.  
The spectra of the seed beam before the regenerative amplifier were measured with a spectrometer (BWTEK) and are shown in Figure 5 for different rotation angles of the WP. As the rotation angle increases, the attenuation depth of the attenuation curve increases, and the central wavelength of the attenuation curve keeps at 795 nm, which is consistent with the calculated results in Figure 2.  
After regenerative amplification, the spectral bandwidths were both 25 nm without the WP or with the WP's angle of 0\({}^{\circ}\). When the WP rotation angle was rotated to 30\({}^{\circ}\), the amplified spectral bandwidth was 37 nm. When the WP rotation angle was rotated to 34\({}^{\circ}\), the amplified spectral bandwidth was 40 nm, and spectral center had a small dip, as shown in Figure 6. When the rotation angle was turned from 0\({}^{\circ}\) to 34\({}^{\circ}\), the seed trips in the regenerative amplification increased by one round, and the amplified beam energy remained the same at 1.5 mJ. As a result of the stable oscillator spectra and good beam pointing stability with the WP at the exit of the oscillator, the amplified spectra remained essentially unaffected for operation for periods of days. After optimizing the compressor, the pulse duration and spectral phase were measured by a Wizzler (Fastlite). A low energy beam was sent to the Wizzler, and the measured pulse duration and the spectral phase are shown in Figure 7, without the WP and with the WP's angle of 34\({}^{\circ}\), respectively. The FWHM of the measured pulse duration was 42.5 fs without the WP and 33.2 fs with the WP with an angle of 34\({}^{\circ}\), with the same optimized grating incident angle. Residual high-order dispersion from the measured spectral phase was a limitation for the pulse compression, after optimizing the compressor angle. At the same time, we also measured the pulse duration and spectral phase with the WP at an angle of 0\({}^{\circ}\), which was as same as that without the WP. This indicates that the WP worked well for gain narrowing pre-compensation.  
Figure 4: The outline of the experimental setup of gain compensating and XPW generation.  
Figure 5: The spectra of the oscillator and the spectra of the seed beam before the regenerative amplifier for different rotation angles of the WP.