⇦Chinese Physics Letters, 2020, Vol. 37, No. 11, Article code 114202 Generation of Intense Sub-10 fs Pulses at 385 nm Fan Xiao (肖凡), Xiaohui Fan (范晓慧), Li Wang (王力), Dongwen Zhang (张栋文), Jianhua Wu (吴建华), Xiaowei Wang (王小伟)*, and Zengxiu Zhao (赵增秀)* Affiliations Department of Physics, National University of Defense Technology, Changsha 410073, China Received 5 August 2020; accepted 21 September 2020; published online 8 November 2020 Supported by the National Key Research and Development Program of China (Grant No. 2019YFA0307703), the Major Research Plan of NSF of China (Grant No. 91850201), and the National Natural Science Foundation of China (Grant Nos. 11974426, 11974425, U1830206 and 11604386).
*Corresponding authors. Email: xiaowei.wang@nudt.edu.cn; zhaozengxiu@nudt.edu.cn Citation Text: Xiao F, Fan X H, Wang L, Zhang D W and Wu J H et al. 2020 Chin. Phys. Lett. 37 114202    Abstract We demonstrated the generation and characterization of 9.7 fs, 180 μJ pulses centered at 385 nm via the frequency doubling of few-cycle near-infrared pulses. Both moderate conversion efficiency (9.5%) and broad phase matching bandwidth (20 nm) were achieved by shaping the spectra of the fundamental pulses. The strong intensity dependence of second-order harmonic generation and well controlled material dispersion ensured the inexistence of satellite pulses, which was confirmed by the self-diffraction frequency resolved optical gating measurement. DOI:10.1088/0256-307X/37/11/114202 PACS:42.65.Re, 42.65.Ky, 42.65.Jx © 2020 Chinese Physics Society Article Text With higher photon energies, the ultrashort laser pulses in ultraviolet (UV) region are preferred for efficient high-order harmonic generation (HHG),[1,2] time-resolved dynamics probing of wide-bandgap samples[3,4] with attosecond time resolution,[5] generation and diagnosis of warm-dense matter (WDM),[6,7] and so on. Therefore, it is valuable to develop schemes to efficiently convert the commercially available ultrashort pulses in near infrared (NIR) region to UV region. Several schemes have been proposed. Chang et al.[8] generated 4.4 fs blue pulses by coherently combining the spectra component from 300 nm to 500 nm with chirped mirrors after hollow-fiber (HF) injected with intense NIR pulses. However, the pulse energy was extremely low (6 µJ), since the spectra components above 500 nm accounted for the majority. With the same waveguide, if other near UV (NUV) pulses were input in addition to the broadband NIR pulses, sub-10 fs deep UV (DUV) pulses could be generated[9,10] via four-wave mixing, and theoretical simulations[11] predicted that the pulse energy can go up to millijoule level with chirped-pulse four-wave mixing technique. Another scheme was to perform the frequency upconversion with long pulses first, then compress the long UV pulses down to sub-10 fs with HF[12] or solid thin plates.[13,14] In spite of higher efficiency, significant satellite pulses existed due to the large high-order dispersion during spectral broadening process. Liu et al.[15] eliminated the satellite pulses with a deformable mirror system, but suffered from additional energy loss. The simplest scheme is to generate the second harmonic (SH) of ultrashort NIR pulses with nonlinear crystals directly.[16,17] An important advantage of this scheme is that the strong intensity dependence of second harmonic generation (SHG) can help to clean the satellite pulses.[18,19] However, the conversion efficiency is usually limited by the large phase match bandwidth for ultrashort laser pulses. SHG with microstructured quasi-phase-matching (QPM) crystals[20] and broadband frequency doubling (BFD)[21–23] technique were proposed to increase the bandwidth of SH with thick crystals. Different from the QPM and BFD, which engineer the nonlinear crystal and beam incident angle respectively, we propose to increase the SH bandwidth by engineering the spectrum of fundamental pulses. In this work, we generated 180 µJ UV pulses with 9.7 fs pulse duration by sending spectral shaped 1.9 mJ, 8 fs few-cycle NIR pulses to an 80-µm-thick beta-barium borate (BBO) crystal for SHG. The strong intensity dependence of second-order harmonic generation and well controlled material dispersion ensured the inexistence of satellite pulses, which was confirmed by the self-diffraction frequency resolved optical gating measurement. In the experiments, ultrashort NIR pulses were generated by sending 4.2 mJ, 800 nm multi-cycle pulses to a 1-m-long 250-µm-inner-diameter HF for spectral broadening, as shown in Fig. 1. The output pulses after fiber were re-collimated and dispersion over-compensated by chirped mirrors, which introduced about $-600$ fs$^2$ group delay dispersion (GDD). We obtained 1.9 mJ, 8 fs pulses by finely tuning the material dispersion with 5.75 mm fused silica plates (FS1). An 80-µm-thick substrate-free BBO cut at 29.2$^\circ$ for type-I phase-matching was used to double the frequency of NIR pulses without beam shrinking or focusing. The beam diameter of fundamental NIR pulses was about 8 mm in terms of full width at half maximum (FWHM). Chirped mirrors (CM82, Ultrafast Innovation) working at 350–450 nm were employed to over-compensate the dispersion of the blue pulses. Meanwhile, the residual NIR pulses after BBO were removed during the multiple reflectances on the chirped mirrors due to low reflectivity. Each reflection on the chirped mirrors introduces $-50$ fs$^2$ GDD. The blue pulses were then directed to a home-built self-diffraction frequency resolved optical gating (SD-FROG) setup for temporal characterization. Stackable fused silica plates were inserted before the SD-FROG optics to finely tune the dispersion.
cpl-37-11-114202-fig1.png
Fig. 1. Schematic of the experimental setup. HF: He-filled hollow-core fiber; FS1, FS2: fused silica plates; BBO: 80-µm-thick BBO crystal; CM: chirped mirrors for SH pulses; AM: aluminum mirrors; D-M: aluminum D-shape split mirror; DL: delay line; FM: focusing mirror (EFL = 1 m); FS: 50 µm fused silica plate for self-diffraction signal generation.
The material dispersion in the UV region is much more significant than the NIR region. Even the air should be paid attention to. One meter air introduces 49.5 fs$^2$ GDD for 400 nm pulses, which is comparable to the negative GDD introduced by the chirped mirrors used in our experiments. In contrast, some other chirped mirrors, e.g., 102144 from Layertec, introduces much less GDD ($-$25 fs$^2$) per pair. Usually the paired chirped mirrors are placed far away from each other, since near-zero incident angles and multiple reflections on each mirror are typically desired. The chirped mirror pairs together with the air in between may result in net positive GDD. So the total optical path in the air should be kept as short as possible. Besides the material dispersion, the phase matching bandwidth is another key factor to keep the pulses short. The time-bandwidth product for Gaussian pulses has a minimum of $\Delta \nu\tau\ge 0.441$,[24] then it is straightforward to calculate the time-energy product: $$ \Delta E \tau \ge 1.83~{\rm eV\cdot fs},~~ \tag {1} $$ which sets a bottom limit of 0.183 eV for the spectral width if sub-10 fs SH pulses are expected. For a given wavelength, perfect phase matching can be achieved by adjusting the phase matching angle $\theta$, i.e., the angle between the light propagation vector and BBO optical axis. However, all the other wavelength components are not phase matched, and the conversion efficiency will eventually drop to zero as the wavelength goes far away from the phase matched wavelength defined by $\theta$. The wavelength-dependent conversion efficiency $\eta$ for different $\theta$ can be approximately expressed as[25] $$ \eta (\lambda ,\theta) \propto {L^2} {\rm sinc} ^2\frac{\Delta k(\lambda ,\theta)L}{2},~~ \tag {2} $$ where $\Delta k(\lambda ,\theta) = 2\omega n(\lambda ,\theta)/c - \omega n(\lambda /2,\theta)/c$ is the phase mismatch.
cpl-37-11-114202-fig2.png
Fig. 2. (a) The normalized wavelength-dependent conversion efficiency of the 80-µm-thick BBO for different phase matching angles. (b) the SH spectrum widths in terms of photon energy for different BBO thicknesses versus the central SH wavelength. The horizontal red solid line indicates the minimum spectrum width for 10 fs Gaussian pulses.
The phase matching bandwidth can thus be estimated. In Fig. 2(a), normalized wavelength-dependent SH generation efficiency curves of 80 µm BBO are plotted for 8 different $\theta$'s according to Eq. (2). The FWHM of each curve, i.e., the phase matching bandwidth, decreases with increasing $\theta$ as shown in Fig. 2(a). Therefore, the longer the phase matched wavelength is, the greater the corresponding SH spectral width will be, assuming that the fundamental pulses have flat spectral shape. Instead of the spectral width in wavelength, photon energy width is a more intuitive indicator for pulse duration as described by Eq. (1). In Fig. 2(b), the FWHM of SH photon energy for different BBO thickness is calculated as a function of the central SH wavelength, which is half the phase matched fundamental wavelength. The horizontal solid line indicates the minimum $\Delta E$ supporting 10 fs SH pulses. The curves show that increasing the SH central wavelength can help to shorten the pulse duration. However, the central wavelength of efficiently generated SH pulses is usually smaller than 400 nm, since a typical fiber spectrum centers at below 800 nm due to blue-shift caused by ionization and high order non-linear effects during the pulse propagation in the fiber. Therefore, the thickness of BBO should be thinner than 100 µm. We used an 80-µm-thick BBO crystal, which was thin enough to ensure bandwidth and not too thin to maintain pulse energy. It is possible to further increase the SH bandwidth by shaping the NIR spectral distribution to be an M-like curve with a bump on each side of the central minimum. When the central minimum overlaps with the peak of Gaussian-like $\eta(\lambda)$ curve, the two bumps prevent $\eta(\lambda)$ dropping wings from narrowing the SH bandwidth. The same analysis may apply to other broadband phase matching problem in nonlinear optical frequency conversion process, e.g., optical parametric oscillators.[26]
cpl-37-11-114202-fig3.png
Fig. 3. (a) The spectra of fundamental NIR pulses when the HF input pulses have a GDD of 0 fs$^2$ (gray shaded line), +50 fs$^2$ (red solid line), +100 fs$^2$ (dashed line) and +200 fs$^2$ (dotted line). (b) The spectrum of optimized SH pulses, with the FWHM of 20 nm. The inset shows the focal spot profile of SH pulses.
As discussed above, appropriate spectral shaping of the NIR pulses, including the central wavelength red-shifting and M-like shape customization, is beneficial to improve the SH bandwidth while keeping reasonable conversion efficiency. Fortunately, the spectral shaping is possible and easy to implement in our experiments, since the spectral broadening process in the hollow fiber is highly sensitive to dispersion of the input pulses. Previous research showed that the blue shift can be suppressed by introducing a certain amount of positive chirp in the input NIR pulses before the fiber,[27] and the entire spectral shape will be changed accordingly. In our experimental setup, the spectral dispersion can be arbitrarily and precisely adjusted with an acousto-optic programmable dispersive filter (AOPDF)[28] integrated in the laser amplifier. When nearly Fourier-transform limited pulses were fed into the fiber, extremely broad and significantly blue-shifted spectra were generated as illustrated by the gray shaded line in Fig. 3(a). The red solid spectrum was obtained by adding +50 fs$^2$ GDD to the input pulses. It was red-shifted comparing to the gray shaded line and gained more weight on the long wavelength side, which was favorable for intense broadband SHG. When more positive GDD was added, the spectra trended to have narrow peaks on short wavelength side in spite of red-shifting of the overall spectra. Thus +50 fs$^2$ GDD provided better spectrum. More importantly, there were several M-shape structures in the red solid curve, such as the segments of 680–800 nm and 760–840 nm, which made it a perfect candidate spectrum for intense ultrashort SH pulses generation. The best balance between SH bandwidth and energy were found when 385 nm wavelength component was phase matched by tuning $\theta \approx 30^{\circ}$. The SH pulse energy was measured to be as high as 180 µJ, and the FWHM of spectrum is 20 nm, as shown in Fig. 3(b). The small spectral tails around 360 nm and 410 nm together with the huge central peak around 385 nm reproduced the $\eta(\lambda)$ structures as shown in Fig. 2(a). Although $\eta(\lambda)$ was very small around 720 nm and 820 nm, the spectral intensity in these regions was relatively strong, so that the SH spectrum had long tails on both side, which was very important for shortening the pulse duration. This was the benefit of our intentionally selected M-shape fundamental spectra with two bumps around 720 nm and 820 nm and a deep around 770 nm. The inset in Fig. 3(b) showed the focus of the SH pulses. It was focused down to $\sim$30 µm (FWHM) with a $f=200$ mm spherical mirror.
cpl-37-11-114202-fig4.png
Fig. 4. The calculated GDD of the 2.4 m air (dashed line), 0.75 mm fused silica plates (dashed line), 80 µm BBO (dot-dashed line), chirped mirrors (4 bounces, light gray solid line), and the total GDD (black solid line). The solid line with circle marker is the retrieved GDD from the SD-FROG trace.
Then the dispersion of SH pulses after BBO was over compensated by introducing about $-200$ fs$^2$ GDD with a pair of chirped mirrors. The gray solid curve in Fig. 4 showed the theoretical GDD introduced by 4 reflections on the chirped mirrors. The small oscillations in the GDD curve were the result of the multilayer coating on the chirped mirrors. The positive GDD mainly came from three mediums: the fused silica plate, the air and the BBO crystal. The latter two were constant and easy to be evaluated once the setup was optimized. Then the thickness of fused silica plate could be determined to yield zero net GDD. The optical path length in air was roughly 2.4 m, and the corresponding GDD was plotted as the dashed curve in Fig. 4. In contrast, the BBO introduced negligible GDD as shown by the dot-dashed curve. To cancel out the negative GDD, the thickness of fused silica plate was adjusted to be 0.75 mm with introduced GDD illustrated by the dashed line. The total material GDD shown by the solid black curve was then kept to be close to zero, although oscillations from chirped mirrors persisted.
cpl-37-11-114202-fig5.png
Fig. 5. The compressed 9.7 fs SH pulses measured by SD-FROG. (a) The experimental SD-FROG trace; (b) the retrieved SD-FROG trace; (c) the reconstructed spectra profile (solid line) and phase (dashed line); (d) the reconstructed intensity temporal profile (solid line) and phase (dashed line).
The non-tilted SD-FROG trace as shown in Fig. 5(a) indicated that near Fourier-transform limited pulses were generated. Projection algorithms[25] were used to retrieve the phase of the SH pulses, and the reconstructed trace with FROG error of $8.5 \times 10^{-3}$ is shown in Fig. 5(b). The retrieved spectrum shown in Fig. 5(c) is in agreement with the measured SH spectra as well. The GDD and third-order dispersion (TOD) at the central wavelength are estimated from the nearly flat spectral phase in Fig. 5(c) to be 21 fs$^2$ and 339 fs$^{3}$, respectively. To compare with the calculated material GDD, the retrieved GDD of the SH pulses is also plotted in Fig. 4 (solid line with circle markers). In our experiment, the retrieved GDD reproduced the oscillations quite well, although they did not coincide exactly with each other. The significant discrepancy of the oscillation amplitude in the spectra range of below 375 nm and above 400 nm came from the poor signal-to-noise ratio of the experimental data due to the weak signal there. Figure 5(d) shows the retrieved temporal profile with 9.7 fs FWHM. Owing to the strong intensity dependence of SHG and dispersion minimized optical path, the temporal intensity profile was clean. The slow rise leading edge of reconstructed temporal profile was caused by the uncompensated TOD, as indicated by the asymmetric pulse broadening. Although the pulse duration is longer than previously reported UV pulses of 4.4 fs,[8] 7.5 fs[15] and 8 fs,[12,13] the pulse energy in this work is much stronger, which is capable of reaching a peak intensity of $5.3 \times 10^{15}$ W/cm$^2$ by focusing the beam down to 30 µm. The pulse duration can be further shortened by maximizing the SH bandwidth through better NIR spectral shaping, which needs extensive studies on the spectral shape dependence of the HF output pulses upon the dispersion of input pulses. Moreover, the conversion efficiency can be improved by increasing the NIR pulse intensity on BBO via beam shrinking or focusing, in which the setup may have to be put in vacuum chamber to avoid air ionization. In conclusion, both moderate conversion efficiency (9.5%) and broad phase matching bandwidth (20 nm) have been achieved during the frequency doubling of properly spectral shaped 1.9 mJ few-cycle near-infra-red pulses with an 80-µm-thick BBO crystal. We obtain 180 µJ pulses centered at 385 nm with 9.7 fs temporal width after the dispersion compensation with chirped mirrors. The pulses are of great importance for efficient high-order harmonic and attosecond pulses generation, UV pump-probe measurements and laser induced warm dense matter research. 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