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Ultrashort pulses with a 25-μJ output energy were generated at 200 nm by dual broadband frequency doubling with a thin KBe2BO3F2 (KBBF) crystal at 1 kHz as the fourth harmonic of a high power Ti:sapphire laser. The spectrum was broadened to a spectral width of 2.25 nm. The pulse duration of 56 fs was measured by single-shot autocorrelation with two-photon fluorescence from self-trapped excitons in a CaF2 crystal.
©2012 Optical Society of America
1. Introduction
Ultrashort high power lasers opened a new field of high order harmonic generation, which has been applied to new optics frontiers such as the generation of attosecond pulses [1] and nonlinear optics in the extreme ultraviolet (EUV) region [2]. More recently, practical harmonic light sources with a repetition rate above 1 kHz are being used for photoelectron spectroscopy in solids [3–5]. For this purpose, high intensity harmonics are always required. One of the methods to generate strong harmonics is to use a short-wavelength driver [2,6], because the atomic dipole moment is proportional to λ-5.3 (λ is the wavelength of a driver) [7], although the cutoff energy (proportional to Iλ2, I is the intensity of a driver) becomes low, while phase matching in a long distance is also effective for strong harmonics [8,9].
One method to generate ultrashort high power ultraviolet (UV) and vacuum ultraviolet (VUV) pulses is spectral broadening or four-wave mixing through filamentation in rare gases [10–14]. The output energy of 300 μJ was obtained at 268 nm [12] but the energy decreased to ~μJ at 200 nm [11] or VUV [13]. Another stream is frequency doubling by nonlinear crystals. The energy was over 1 mJ in sub-10 fs at 400 nm [15,16] but was about 50 nJ at 180 nm [17]. The energy and pulse width are limited by spectral narrowing and resultant pulse broadening due to group velocity mismatch (GVM) between the fundamental and second harmonic pulses in the case of direct frequency doubling (DFD) in the short-wavelength region. To overcome this defect, broadband frequency doubling (BFD) [18,19] is proposed and demonstrated from 800 nm to 400 nm [15,16], where angular dispersion from a grating is converted to the desired dispersion of phase matching angle, and GVM is cancelled. However, we cannot reach to deep UV by a single stage. If we use two stages of BFD sequentially, the efficiency will be considerably low because four gratings are necessary. Dual broadband frequency doubling (dual-BFD), which we propose in this paper, is a scheme to combine the two stages of BFD together, and to generate broadband fourth harmonic with only two gratings.
In this paper, we developed a multi-color laser source for harmonic generation based on the fundamental (ω), second harmonic (2ω) and fourth harmonic (4ω) of a Ti:sapphire laser with a special emphasis on 4ω at 1 kHz. The scheme of dual-BFD was applied to generate the 4ω pulses by a thin KBe2BO3F2 (KBBF) crystal [20,21]. 25-μJ pulses with a pulse width of 56 fs arround 200 nm were obtained at 1 kHz. The pulse width was measured by single-shot autocorrelation with two-photon fluorescence (TPF) in a CaF2 crystal.
2. Calculation of frequency doubling in two cases: DFD and BFD
In this section, we calculate the spectral width and the pulse duration for frequency doubling from 2ω to 4ω pulses in two cases: direct frequency doubling (DFD) and broadband frequency doubling (BFD).
The bandwidth is limited due to GVM between 2ω and 4ω pulses at the case of DFD in the KBBF crystal. The type-I phase matching angle of KBBF [22] from 2ω (400 nm) to 4ω (200 nm) pulses is θpm = 52.7°, and the temporal walk-off due to GVM [23] in the phase matched condition is given by
where D is the optical-path length in the KBBF crystal. The thickness of KBBF (L) is 230 μm, then the optical-path length is D = L/cos(θpm) = 380 μm in KBBF. no and ne are the ordinary and extraordinary refractive indices. The acceptable spectral width (FWHM, full width half maximum) [24] at the 2ω pulse is expressed aswhere λ is the wavelength, c is the light velocity. If we assume the spectral function f(2ω) is transferred to f 2(4ω) by frequency doubling and a Gaussian spectral shape at 2ω, the spectral width of 4ω can be expressed asEven though the spectral shape is sinc2 at 2ω, the prefactor is almost the same (0.36). Then we assume a Gaussian shape for simplicity and harmonize with the expression in the case of BFD. The corresponding transform-limited pulse duration iswhere k is the time bandwidth product. Figure 1(a) shows the calculated results of DFD. At the central wavelength of 400 nm, GVM between 2ω and 4ω pulses is 167 fs, and then the acceptable bandwidth at 2ω is 1.4 nm. The bandwidth at 4ω is 0.5 nm, corresponding to the shortest pulse width of 116 fs.
Fig. 1 Calculation of the acceptable spectral width and corresponding pulse width for frequency doubling from 2ω to 4ω pulses in two cases. (a) Direct frequency doubling (DFD). GVM, acceptable spectral widths (Δλ2ω and Δλ4ω), corresponding shortest pulse duration (τp) at 4ω are plotted against the wavelength at 180-220 nm (4ω) and 360-440 nm (2ω), respectively. (b) Broadband frequency doubling (BFD). Acceptable spectral widths (Δλ2ω-BFD and Δλ4ω-BFD), corresponding shortest pulse duration (τp-BFD) at 4ω are plotted by changing the wavelength at 4ω and 2ω pulses, respectively.
In the case of broadband frequency doubling (BFD), an acceptable spectral width (FWHM) at 2ω can be calculated as [18,19]
where θ is the phase matching angle. The prefactor of 1.33 comes because we use FWHM instead of the width corresponding to the first zero of a sinc2 function. The change of spectral shape during BFD is not as simple like in case of DFD where the spectral width is rather narrow. In BFD, 4ω pulses are generated more by mixing of a broader range of frequency components. However, we assume a simple frequency conversion described in DFD, and also a Gaussian pulse (spectral) shape for simplicity. Then the acceptable spectral width of 4ω isand the corresponding transform-limited pulse duration isAs shown in Fig. 1(b), the acceptable spectral width at 2ω and 4ω in BFD are 10.5 and 3.7 nm, respectively. Then the corresponding shortest pulse duration at 4ω is 16 fs, which is about 7-8 times shorter than the case of DFD in the KBBF crystal. This improvement should be noted because pulse shortening by BFD from ω to 2ω in β-barium borate (BBO) is only a factor of 2-3. This fact shows that BFD in KBBF is so essential to generate ultrashort pulses at 4ω.
3. Experimental setup
Based on the above calculations, BFD has the advantages of broader acceptable spectral width and shorter pulse duration. Therefore, to generate broadband fourth harmonic pulses, we usually adopt the BFD technique both at 2ω and 4ω. A simple and intuitive way is to use a two-stage BFD, which generate broadband 2ω and 4ω pulses independently. However, this system is complicated and inefficient, because four gratings (two for BFD at 2ω and another two for BFD at 4ω) are necessary. In this experiment, we applied a more efficient scheme: dual-BFD, where two gratings were removed and the system became more compact, as shown in Fig. 2 .
Fig. 2 Schematic diagram of the dual-BFD system and the structure of a KBBF prism coupled device (KBBF-PCD). G1 and G2: diffraction gratings, the groove densities are 300 and 1200 lines/mm, respectively. M1 and M2: plane mirrors, HR (high reflection)@750-850 nm; C1 and C2: concave mirrors (radii of curvature are RC1 = 3000 mm and RC2 = 1500 mm), HR@750-850 nm; WP: zero order half waveplate@400 nm; C3-C4: concave mirrors (RC3 = 2000 mm and RC4 = 750 mm), HR@370-430 nm; C5-C6: concave mirrors (RC5 = 750 mm and RC6 = 4000 mm), HR@195-205 nm; M3: plane mirror, HR@195-205 nm. Thicknesses of BBO and KBBF are 150 μm and 230 μm, respectively. The KBBF is stacked between two fused quartz prisms with an apex angle of 52°.
Fundamental pulses were generated by a 1 kHz, Ti:sapphire laser, which was composed of an oscillator, a stretcher, a regenerative amplifier, a three stage multi-pass amplifiers and a compressor [25,26]. Mode-locked pulses from the oscillator were broadened by an Offner-type stretcher from 12 fs to about 250 ps. The broadened pulses were injected into the regenerative amplifier, and cleaned up by a fast pulse slicer. During the three-stage multi-pass amplification, the power of the pulses can be greatly amplified by a factor of 100. The amplified output beam was magnified by a factor of 2 with a telescope to a beam size of about 12 mm in diameter. A compressor composed of a newly-designed transmission grating (provided by Canon Inc.) was established in the experiment. This transmission grating was improved on phase distortion and diffraction efficiency compared with that reported in Ref [26]. The diffraction efficiency was over 95% at 800 nm, resulting in an overall throughput of the compressor about 80%. As a result, 20-fs, 10 mJ, 800-nm pulses were generated from this laser system.
The fundamental pulses are directed to the dual-BFD system, as shown in Fig. 2. Spectral angular dispersion (dβ/dλ) of diffracted beam is generated from grating G1 (300 lines/mm), and after a telescope different spectral components enter at their phase matching angles into the BBO crystal. That means angular dispersion from grating G1 is converted to the desired dispersion of phase matching angle (dθ/dλ), and GVM is cancelled out in this BFD scheme.
From the calculation, when the incident angle of grating G1 is α1 = 5°, angular dispersion is dβ1/dλω = 3 × 10−4 rad/nm at 800 nm. The dispersion of phase matching angle in BBO is dθ1/dλω = 6.4 × 10−4 rad/nm [18], therefore, the required magnification factor is M1c = (dβ1/dλω)/(dθ1/dλω) = 0.48. In the experiment, the image on the grating G1 was relayed by the telescope with two concave mirrors (C1, RC1 = 3000 mm and C2, RC2 = 1500 mm) onto the BBO crystal, then the magnification factor is M1 = 0.5 which is matched to the calculated value (M1c).
The 2ω beam (400 nm) was generated after the BBO crystal. The angular dispersion after BBO is twice that of the first grating G1 (300 lines/mm) and the frequency is doubled. As a result, the angular dispersion after BBO is equivalent to that caused by a 1200-lines/mm grating with an incident parallel 2ω beam. Therefore, we can understand simply by inserting an imaginary grating Gi with a 1200-lines/mm groove density at the position of BBO. The angular dispersion is dβ2/dλ2ω = 12 × 10−4 rad/nm, and the calculated dispersion of phase matching angle in the KBBF crystal is dθ2/dλ2ω = 3.4 × 10−3 rad/nm. As a result, the required magnification factor is M2c = (dβ2/dλ2ω)/(dθ2/dλ2ω) = 0.35. In the experiment, another telescope with a magnification factor of M2 = 0.375 was set up to match the calculated value (M2c). It was composed of two concave mirrors (C3 and C4) with radii of curvature of 2000 and 750 mm respectively, and the image on the BBO was relayed onto the KBBF crystal.
For the KBBF crystal, the phase matching angle at 400 nm is 52.7°, and the thickness is too small to be cut to z axis for frequency doubling. Therefore, an optically-contacted prism-coupling device (PCD) [20,21] is essential, as shown in Fig. 2. The thickness of KBBF is L = 230 μm, and the prisms are made by fused quartz. Fourth harmonic beam is generated after this KBBF-PCD, and the image on KBBF is relayed onto grating G2 (1200 lines/mm) by two concave mirrors (C5, RC5 = 750 mm and C6, RC6 = 4000 mm). It should be noted that the optical arrangement before and after KBBF is asymmetric. By using the mirror C6, whose radius of curvature is twice that of C3, the angular divergence on G2 becomes half. Then the groove density of 1200 lines/mm can be used to retrieve the parallel beam at 4ω. After the grating G2, the parallel 4ω beam was generated.
4. Experimental results
Figure 3 shows the experimental results of the second harmonic pulses. The maximum output power after BBO was 1.4 W for a 150-μm-thick BBO at an input fundamental power of about 5.7 W, then the conversion efficiency was 24.5%. By adding a telescope for 2ω symmetric to that before BBO and a 600-lines/mm grating after BBO [16], the 2ω beam was retrieved to a parallel beam. The 2ω output power at this stage was 1 W by considering a grating efficiency of 70%. On this condition, the pulse duration was measured to be 16 fs by self-diffraction frequency-resolved optical gating (SD-FROG) with a 100-μm-thick CaF2 plate, as shown in Fig. 3(b) [15,16].
Fig. 3 (a) Output power after BBO versus input power of fundamental pulses. The maximum output power after BBO was 1.4 W with a 150-μm-thick BBO. (b) The retrieved pulse shape and phase of the 2ω pulses measured by SD-FROG with a 100-μm-thick CaF2 plate. The pulse duration was 16 fs. The used grid size was 128 × 128, and the root mean square (RMS) error was 1.53%.
The output power and the spectrum of 4ω obtained by the configuration of Fig. 2 are shown in Fig. 4 . Output power after KBBF-PCD versus input power of 2ω beam is shown in Fig. 4(a). The maximum output power was 40 mW with a conversion efficiency of 2.9% when the power of 2ω pulses was 1.4 W. After two concave mirrors (C5, C6) and grating G2, the final output of 4ω pulses was 25 mW, resulting in a pulse energy of 25 μJ. Measured spectra of 2ω and 4ω pulses are shown in Fig. 4(b). The spectrum of 4ω pulses is ranged from 196 to 205 nm (7 nm). The FWHM spectral width is 2.25 nm, and the corresponding Fourier transform-limited pulse duration is 19 fs.
Fig. 4 (a) Output power after KBBF-PCD versus input power of 2ω pulses. (b) Measured spectrum of 4ω and 2ω pulses. The spectrum of 4ω pulses is ranged from 196 to 205 nm, and the FWHM spectral width is 2.25 nm.
Since the wavelength of 4ω pulses (200 nm) is short, there is no nonlinear crystal for autocorrelation. SD-FROG is of course a possible method as used in 2ω pulses. However, SD signal was so weak to discriminate from strong scattering of the 4ω beam with the same wavelength. Furthermore, FROG need a long time for data acquisition and retrieval, and is not adequate for the real time adjustment where the optimum condition cannot be calculated exactly. Here we adopt single-shot autocorrelation by using two-photon fluorescence (TPF) [27,28]. The schematic of TPF process in CaF2 is shown in Fig. 5(a) [29]. The two-photon energy of the 4ω pulses (12.4 eV) is higher than the band gap of CaF2 (10.0 eV). The electron-hole pair formed by two-photon excitation relaxes to self-trapped excitons, resulting in UV fluorescence. The intensity of this fluorescence is proportional to the square of the intensity of 4ω pulses, which enables the autocorrelation measurement. The spectrum of TPF is shown in Fig. 5(b). The central wavelength is around 290 nm, and the spectrum is ranged from 225 to 400 nm. Pulses from the dual-BFD system were sent to the measurement system, as shown in Fig. 5(c). A thin fused quartz lens was used to focus and an Al mirror M1 was used to split the input beam spatially into two beams. The two splitted beams overlapped at a 10-mm long CaF2, and the signal of two-photon fluorescence was collected by a Nikon UV lens (UV Nikorr) into a CCD (ANDOR DV420A-BU) on a 1-m optical rail. An UV filter was used to eliminate the unnecessary background, and then the image inside CaF2 was finally observed by the CCD. The image in CaF2 is magnified by ~9 to the CCD. The Rayleigh length of the focusing in Fig. 5(c) is 12.5 mm for a 5-mm diameter input beam and much larger than that of a TPF image (~30 μm). The region of fluorescence is much smaller than the Rayleigh length, therefore the intensity drop outside the beam waist did not cause artificial shortening in the autocorrelation trace.
Fig. 5 (a) Schematic of two-photon fluorescence (TPF) process. (b) Measured spectrum of two-photon fluorescence in CaF2. (c) Schematic of the autocorrelation measurement system by TPF. M1-M3: Al mirrors; the thickness of CaF2 is 10 mm.
Figure 6(a) shows a typical image on the CCD, where a bright circle can be seen in the center because of the overlapping of two pulses inside the CaF2 crystal. Figure 6(b) shows the corresponding autocorrelation trace. The pulse duration is 56 fs by assuming a Gaussian shape, which is about 3 times the Fourier transform limit. The calibration of pulse width was done by inserting a 2-mm-thick CaF2 plate on one side of two beams.
Fig. 6 (a) A typical image on the CCD, the inset scale indicates 50 μm in CaF2. (b) The autocorrelation trace of the 4ω pulses. The FWHM pulse width is 56 fs by assuming a Gaussian shape.
5. Discussion
In the experiment, the conversion efficiency in KBBF was about 2.9%. There would be some possible reasons for low efficiency, such as self phase modulation (SPM) at 2ω in the front fused quartz prism, nonlinear absorption in KBBF or in the rear fused quartz prism, and other technical problems like quality of KBBF and optical contact. Besides the technical problems, we discuss about SPM and nonlinear absorption. In the experiment, SPM was not observed and the spectrum of 4ω did not change as shown in Fig. 4(b). Nonlinear absorption did not appear considerably as shown in Fig. 4(a) where the slope is below quadratic but above linear. From the data of nonlinear absorption coefficient around 200 nm in a fused quartz [30], nonlinear absorption may be taken into account with further increase of power output.
After KBBF, the 4ω pulses pass through some materials including the fused quartz prism after KBBF, the fused quartz lens and the CaF2 crystal in the measurement setup. If we assume 5-mm fused quartz and 5-mm CaF2, the second-order and third-order dispersions are 3363 fs2 and 1190 fs3. The pulse will be broadened to about 490 fs after these materials with an assumption of a 19-fs transform-limited pulse after KBBF. Pre-compensation before frequency doubling is a possible solution for pulse shortening. In the experiment, we changed the distance of the transmission gratings in the compressor for optimization. However, this cannot control the 4ω pulses directly, but also change the fundamental. The measured optimized pulse duration was 56 fs, which was about three times the Fourier transform limit. From this experimental result, pre-compensation certainly works, but is not perfect to compress the pulses to near Fourier transform limit. For further pulse shortening, a prism pair compressor at 4ω would be more appropriate, because it can compensate the residual dispersions directly.
6. Conclusion
In this paper, we applied the dual-BFD technique to generate fourth harmonic pulses from the Ti:sapphire laser system. BBO and KBBF are used as the nonlinear crystals in this scheme. High energy pulses (25 μJ) centered at 200 nm with a broad spectrum (196-205 nm) were generated. The FWHM spectral width was 2.25 nm, and the corresponding Fourier transform-limited pulse duration was 19 fs. The pulse duration was measured to be 56 fs by single-shot autocorrelation with two-photon fluorescence from self-trapped excitons in CaF2. By optimizing the dual-BFD system, it is possible to increase further the power of 4ω pulses.
Acknowledgments
The authors would like to thank Canon Inc. for providing the transmission gratings and Dr. Takashi Onose for helpful discussions.
References and links
1. P. B. Corkum and F. Krausz, “Attosecond science,” Nat. Phys. 3(6), 381–387 (2007). [CrossRef]
2. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004). [CrossRef] [PubMed]
3. T. Kiss, F. Kanetaka, T. Yokoya, T. Shimojima, K. Kanai, S. Shin, Y. Onuki, T. Togashi, C. Zhang, C. T. Chen, and S. Watanabe, “Photoemission spectroscopic evidence of gap anisotropy in an f-Electron superconductor,” Phys. Rev. Lett. 94(5), 057001 (2005). [CrossRef] [PubMed]
4. S. Mathias, L. Miaja-Avila, M. M. Murnane, H. Kapteyn, M. Aeschlimann, and M. Bauer, “Angle-resolved photoemission spectroscopy with a femtosecond high harmonic light source using a two-dimensional imaging electron analyzer,” Rev. Sci. Instrum. 78(8), 083105 (2007). [CrossRef] [PubMed]
5. K. Ishizaka, T. Kiss, T. Yamamoto, Y. Ishida, T. Saitoh, M. Matsunami, R. Eguchi, T. Ohtsuki, A. Kosuge, T. Kanai, M. Nohara, H. Takagi, S. Watanabe, and S. Shin, “Femtosecond core-level photoemision spectroscopy on 1T-TaS2 using a 60-eV laser source,” Phys. Rev. B 83(8), 081104 (2011). [CrossRef]
6. D. Yoshitomi, T. Shimizu, T. Sekikawa, and S. Watanabe, “Generation and focusing of submilliwatt-average-power 50-nm pulses by the fifth harmonic of a KrF laser,” Opt. Lett. 27(24), 2170–2172 (2002). [CrossRef] [PubMed]
7. K. L. Ishikawa, K. Schiessl, E. Persson, and J. Burgdörfer, “Fine-scale oscillations in the wavelength and intensity dependence of high-order harmonic generation: Connection with channel closings,” Phys. Rev. A 79(3), 033411 (2009). [CrossRef]
8. A. Rundquist, C. G. Durfee 3rd, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft X-rays,” Science 280(5368), 1412–1415 (1998). [CrossRef] [PubMed]
9. E. Takahashi, Y. Nabekawa, and K. Midorikawa, “Generation of 10- microJ coherent extreme-ultraviolet light by use of high-order harmonics,” Opt. Lett. 27(21), 1920–1922 (2002). [CrossRef] [PubMed]
10. C. G. Durfee 3rd, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24(10), 697–699 (1999). [CrossRef] [PubMed]
11. T. Fuji, T. Horio, and T. Suzuki, “Generation of 12 fs deep-ultraviolet pulses by four-wave mixing through filamentation in neon gas,” Opt. Lett. 32(17), 2481–2483 (2007). [CrossRef] [PubMed]
12. M. Ghotbi, P. Trabs, and M. Beutler, “Generation of high-energy, sub-20-fs pulses in the deep ultraviolet by using spectral broadening during filamentation in argon,” Opt. Lett. 36(4), 463–465 (2011). [CrossRef] [PubMed]
13. M. Ghotbi, M. Beutler, and F. Noack, “Generation of 2.5 μJ vacuum ultraviolet pulses with sub-50 fs duration by noncollinear four-wave mixing in argon,” Opt. Lett. 35(20), 3492–3494 (2010). [CrossRef] [PubMed]
14. T. Nagy and P. Simon, “Generation of 200-microJ, sub-25-fs deep-UV pulses using a noble-gas-filled hollow fiber,” Opt. Lett. 34(15), 2300–2302 (2009). [CrossRef] [PubMed]
15. T. Kanai, X. Zhou, T. Sekikawa, S. Watanabe, and T. Togashi, “Generation of subterawatt sub-10-fs blue pulses at 1-5 kHz by broadband frequency doubling,” Opt. Lett. 28(16), 1484–1486 (2003). [CrossRef] [PubMed]
16. T. Kanai, X. Zhou, T. Liu, A. Kosuge, T. Sekikawa, and S. Watanabe, “Generation of terawatt 10-fs blue pulses by compensation for pulse-front distortion in broadband frequency doubling,” Opt. Lett. 29(24), 2929–2931 (2004). [CrossRef] [PubMed]
17. F. Seifert, J. Ringling, F. Noack, V. Petrov, and O. Kittelmann, “Generation of tunable femtosecond pulses to as low as 172.7 nm by sum-frequency mixing in lithium triborate,” Opt. Lett. 19(19), 1538–1540 (1994). [CrossRef] [PubMed]
18. O. E. Martinez, “Achromatic phase matching for second harmonic generation of femtosecond pulses,” IEEE J. Quantum Electron. 25(12), 2464–2468 (1989). [CrossRef]
19. G. Szabó and Z. Bor, “Broadband frequency doubler for femtosecond pulses,” Appl. Phys. B 50, 51–54 (1990). [CrossRef]
20. C. Chen, J. Lu, T. Togashi, T. Suganuma, T. Sekikawa, S. Watanabe, Z. Xu, and J. Wang, “Second-harmonic generation from a KBe2 BO3F2 crystal in the deep ultraviolet,” Opt. Lett. 27(8), 637–639 (2002). [CrossRef] [PubMed]
21. T. Togashi, T. Kanai, T. Sekikawa, S. Watanabe, C. Chen, C. Zhang, Z. Xu, and J. Wang, “Generation of vacuum-ultraviolet light by an optically contacted, prism-coupled KBe2BO3F2 crystal,” Opt. Lett. 28(4), 254–256 (2003). [CrossRef] [PubMed]
22. C. Chen, G. Wang, X. Wang, Y. Zhu, Z. Xu, T. Kanai, and S. Watanabe, “Improved sellmeier equations and phase-matching characteristics in deep-ultraviolet region of KBe2BO3F2 crystal,” IEEE J. Quantum Electron. 44(7), 617–621 (2008). [CrossRef]
23. W. H. Glenn, “Second-harmonic generation by picosecond optical pulses,” IEEE J. Quantum Electron. 5(6), 284–290 (1969). [CrossRef]
24. R. C. Miller, “Second harmonic generation with a broadband optical maser,” Phys. Lett. 26A, 177–178 (1968).
25. Y. Nabekawa, Y. Kuramoto, T. Togashi, T. Sekikawa, and S. Watanabe, “Generation of 0.66-TW pulses at 1 kHz by a Ti:sapphire laser,” Opt. Lett. 23(17), 1384–1386 (1998). [CrossRef] [PubMed]
26. C. Zhou, T. Seki, T. Sukegawa, T. Kanai, J. Itatani, Y. Kobayashi, and S. Watanabe, “Large-scale, high-efficiency transmission grating for Terawatt-class Ti:sapphire lasers at 1 kHz,” Appl. Phys. Express 4(7), 072701 (2011). [CrossRef]
27. K. Hata, M. Watanabe, and S. Watanabe, “Nonlinear processes in UV optical materials at 248 nm,” Appl. Phys. B 50(1), 55–59 (1990). [CrossRef]
28. N. Sarukura, M. Watanabe, A. Endoh, and S. Watanabe, “Single-shot measurement of subpicosecond KrF pulse width by three-photon fluorescence of the XeF visible transition,” Opt. Lett. 13(11), 996–998 (1988). [CrossRef] [PubMed]
29. R. T. Williams, J. N. Bradford, and W. L. Faust, “Short-pulse optical studies of exciton relaxation and F-center formation in NaCl, KCl, and NaBr,” Phys. Rev. B 18(12), 7038–7057 (1978). [CrossRef]
30. S. A. Slattery and D. N. Nikogosyan, “Two-photon absorption at 211 nm in fused silica, crystalline quartz and some alkali halides,” Opt. Commun. 228(1-3), 127–131 (2003). [CrossRef]
