Optical frequency comb (OFC) technology has revolutionized the field of optics by providing precise measurement tools for light frequencies. Comprising a series of even spaced spectral lines resembling the teeth of a comb, OFCs have found widespread applications in timekeeping, precision spectroscopy, and fundamental physics. Extending this technology into the X-ray regime to achieve ultra-high precision probing of atomic and molecular structures has long been a significant challenge in the scientific community. Recently, researchers in Shanghai Advanced Research Institute, Chinese Academy of Sciences, have proposed an innovative theoretical method that utilizing the chirped frequency-beating seed laser to generate tunable X-ray frequency combs (XFCs) at the Shanghai Soft X-ray Free-Electron Laser Facility (SXFEL).
Figure 1. The schematic layout of the proposed method (a) and the design of the chirped frequency-beating seed laser system (b). The movement direction of the movable platform is indicated by black bidirectional arrows.
The schematic layout of the method is illustrated in Figure 1, mainly consisting of an echo-enabled harmonic generation (EEHG) FEL setup and a chirped frequency-beating seed laser system. The EEHG-FEL setup can generate fully coherent XFEL radiation pulses at several tens of harmonics of the seed laser. The chirped frequency-beating seed laser system can provide an initial bunched seed laser combs and ultimately facilitates the generation of XFCs in the EEHG-FEL setup under optimized conditions. There are two external seed lasers (Laser1, Laser2) are needed in the whole configuration. Among them, Laser2 is the dedicated designed chirped frequency-beating seed laser.
The chirped frequency-beating seed laser system mainly includes a pair of parallel gratings (G1, G2), a beam splitter (BS), an optical delay line, a beam combiner (BC) and so on, as shown in Figure 1(b). An ultrafast laser pulse (~100 fs) firstly go and come back through the parallel gratings to introduce linear chirping and temporal broadening. Then the chirped laser pulse (~ps) is introduced into the upper right blue line by the reflector and split into two identical beams by the beam splitter. An optical delay line is implanted with a tunable time delay, resulting in these two identical laser beams to intersect at the beam combiner and form a chirped frequency-beating seed laser (Laser2) as shown in Figure 2.
Figure 2. Schematic diagram of the Wigner distribution (a) and envelope (b) of the chirped frequency-beating seed laser
The chirped frequency-beating seed laser is used to generate the X-ray OFC through the EEHG-FEL scheme. The principle of EEHG is that the frequencies of the FEL and the seed laser share the relationship:
where m is normally several tens here. For the amplification of the XFC, the chirp of the seed laser must be taken into consideration and mitigated. The researchers have studied profoundly of this problem and devised an optimization method here:
where is the relative time delay, is the chirp, N is any natural number (N') plus any positive fraction (P) not exceeding 1/2, the repetition frequency of the XFC (frep) is corresponding to the beating frequency as:
By adjusting the linear chirp and the time delay of the two laser pulses according to Equation 2, same frequency components will appear after Fourier transformation and the XFC pulses can be amplified. This adjustment enables us to achieve an effect equivalent to traditional mode-locked lasers. To validate the accuracy and efficacy of the method, the researchers conducted simulations with N = 1, according to Equation 2. The radiation results of the XFC power and spectra are presented in Figure 3. The peak power is near 600MW with a central wavelength around 4.36nm being into the water window regime. It is evident that efficient mode-locked amplification and generation of an XFC has been achieved.
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Figure 3. Radiation performance of the proposed method. Spectra (a) and saturation power distributions (b) of the XFC.
This research introduces a novel theoretical method to generate high power tunable X-ray frequency combs by utilizing a chirped frequency-beating seed laser in an EEHG-FEL scheme. This approach overcomes the limitations of traditional technologies and provides the feasibility for realizing frequency combs in the X-ray spectrum. The realization of tunable XFCs will significantly improve the capacity of X-ray spectroscopy, promoting in-depth studies of the microstructures of matter. High power XFCs can also be used in the research field of resonant inelastic X-ray scattering (RIXS) and Terabit-level coherent optical communication, exploring new states of matter, and investigating fundamental interactions. Furthermore, the research team is preparing to validate this method experimentally in the SXFEL facility. And the chirped frequency-beating seed laser system has already been set up and tested. The researchers anticipate that this approach will significantly enhance the possibilities of the spectroscopic experiment in seeded FELs.
This study presents a feasible method for achieving continuous tunability high power XFCs using the chirped frequency-beating laser technique in a seeded FEL. By manipulating the Wigner distribution and beating frequency of the seed laser, a suitable seed laser pulse can be generated. The seed laser can be effectively preserved and amplified in the EEHG-FEL process based on the optimization conditions, resulting in high-power XFC radiation.
The work has been published in High Power Laser Science and Engineering, vol. 12, Issue 5 (Lanpeng Ni, Yaozong Xiao, Zheng Qi, Chao Feng, Zhentang Zhao, "Tunable X-ray frequency comb generation at the Shanghai soft X-ray Free-Electron Laser facility," High Power Laser Sci. Eng. 12, 05000e60 (2024)).
