With the rapid development of high-order harmonic extreme ultraviolet coherent light sources and attosecond pulses, they have caught widespread attention in free electron laser seed injection, time-resolved angular resolved photoelectron spectroscopy measurement, and nondestructive nanostructure detection. There are many ways to generate extreme ultraviolet light sources, including synchrotron radiation, laser produced plasma, and free electron lasers, which can also be employed to generate high-energy extreme ultraviolet light sources. Compared to other light sources, high-order harmonics feature good coherence, short pulse duration, and device miniaturization. Currently, the high-order harmonic mechanism has been widely adopted to generate coherent light sources in the extreme ultraviolet region. We utilize a self-developed 200 TW titanium sapphire laser system with a maximum single pulse energy that can reach 8 J, and a main pulse energy of 7.9 J after beam splitting is transported to the free electron laser experiment for generating an electron beam source based on the acceleration mechanism of laser wakefield. The second laser beam is leveraged for high-order harmonic generation experiments. Both experiments are conducted synchronously to facilitate the simultaneous injection of electron beams and extreme ultraviolet seed beams into the oscillators in the future.

As shown in Fig. 1(a), the whole system is placed in a vacuum chamber to avoid strong absorption of extreme ultraviolet pulse, and the vacuum system maintains the background pressure of 10^-3 Pa. The driving laser parameters include a center wavelength of 800 nm, repetition rate of 1 Hz, pulse width of 30 fs, and energy of 35 mJ. A plano-convex mirror with a focal length of 5000 mm and a focal spot diameter of about 400 μm is adopted. The length of the Ne-filled gas cell is 50 mm. The harmonic radiation propagates with the residual driving laser and then transmits through the iris to the measurement section. Two Mo mirrors and a 350 nm-thick Zr filter are placed behind the iris to attenuate the fundamental laser field. Then, the harmonic signals can be divided into two different paths via the moveable gold-coated spherical mirror. Absolute harmonic energy is measured with an XUV (extreme ultra violet) photodiode detector which is calibrated by the Beijing Synchrotron Radiation Facility to get the real spectrum response curve. When the spherical mirror moves into the beam path, the HHG (high-order harmonic generation) spectrum is detected by a home-built flat-filed grating spectrometer. The spatial harmonic distribution is obtained by calculating the longitudinal spectrum of the XUV charge-coupled device.

Figures 1(b) and 1(c) show the generated harmonic spectra. From the 41st to the 69th harmonics (19.5 nm to 11.6 nm wavelength), the total energy of HHG is about 78.7 nJ. According to the HHG spectral distribution, the single harmonic energy of the 61st harmonic (13.1 nm) and 59th harmonic (13.5 nm) is 13.5 nJ and 11.1 nJ, respectively. The conversion efficiency is 3.6×10-7 for 61st harmonic and 3×10-7 for 59th harmonic. The divergence of the output beam measured at 61st and 59th harmonics is about 0.32 mrad and 0.33 mrad (full width at half maxima, FWHM). To obtain the optimal HHG extreme ultraviolet source at the wavelength of 13 nm, we investigate the 61st and the 59th harmonic intensity generated in Ne as a function of the gas pressure and driving laser energy. Figures 2(a) and 2(e) present the optimal phase-matching conditions for driving laser energy with the position of gas cell. With the increasing laser energy, the optimal phase-matching position moves to the negative position. Then the optimal phase-matching conditions for the gas pressure at 9×1014W/cm2 are studied. As shown in Figs. 2(c) and 2(g), two optimal phase-matching conditions for 61st harmonic are 6.0 kPa at -100 mm position and 7.6 kPa at -160 mm position, respectively. The optimal gas pressure for the 59th and 61st harmonics is basically the same, but 59th harmonic matching range of gas pressure is wider, with the matching gas pressure slightly higher than that for the 61st harmonic. Figures 2(b), 2(d), 2(f), and 2(h) demonstrate the theoretical results in Ne that generates harmonics as a function of driving laser energy and gas pressure respectively. Based on the experimental and theoretical simulation results in Fig. 2, the spectra of three different focal positions with maximum harmonic signals are selected for analysis in Fig. 3, which shows the harmonic spectra at different focal positions. The beam divergence of the 61st and the 59th harmonics is about 0.30 mrad and 0.31 mrad at position of 0, 0.32 mrad and 0.33 mrad at position of -100 mm, and 0.57 mrad and 0.65 mrad at position of -160 mm. The fitting results of harmonic distribution and curve at positions 0 and -100 mm are better than those at -160 mm. Additionally, the Gaussian-like distribution shows that the phase-matching conditions are well achieved. The simulated changes in gas pressure and driving laser energy in phase-matching conditions are basically the same as the experimental results. Finally, the optimal phase-matching conditions for the current laser parameters are obtained by combining the longitudinal distribution of the 13 nm spectra obtained at different focal positions. Combined with the experimental and simulation results, the relationship between phase-matching conditions and focal positions is realized by optimizing parameters such as driving laser energy and gas pressure. Meanwhile, the longitudinal spatial distribution of harmonic signals at different focal positions is measured, and numerical fitting proves that the spectrum has a good Gaussian distribution with a minimum divergence angle of 0.30 mrad. The results combining these two aspects verify that the optimal phase-matching conditions under the current laser parameters are achieved.

Extreme ultraviolet pulses with low divergence angle and high conversion efficiency are obtained by loosely focused beams, with a total energy of 78.7 nJ in the spectral wavelength range of 11.6 nm to 19.5 nm. We employ a 200 TW laser system homologous to free-electron lasing (FEL) and optimize the HHG extreme ultraviolet light source under this system platform to facilitate synchronous injection of FEL seed laser. In the future, wavefront correction technologies (such as deformable mirrors and wavefront sensors) will be adopted to further optimize beam quality, and higher repetition frequency lasers can be utilized to increase the average power of harmonics. This will have important application prospects in strong attosecond pulse generation, extreme ultraviolet pump-probe spectroscopy, and FEL seed source injection.