To date, several approaches have been proposed and demonstrated for the generation of ultrashort deep-ultraviolet (DUV) pulses with shorter wavelengths than 300 nm. They rely on the frequency conversion from the visible or near-infrared (NIR) to the DUV through the supercontinuum generation [1], four-wave mixing (FWM) [2, 3], third-harmonic generation [4], and so forth [5, 6]. Such short pulses have been applied to spectroscopies in the gas phase [7, 8] as well as in the liquid phase [9]. Ultrashort DUV pulses are also useful means for the trace analysis of organic compounds [10–12]. Femtosecond DUV pulses have given a high ratio of a molecular-ion signal intensity to fragment signal intensities. In some spectroscopic applications, a light source that produces energetic multicolor DUV femtosecond pulses is useful. For instance, it allows simultaneous detection of several compounds in the trace analysis based on the laser-ionization time-of-flight mass spectrometry as well as nondegenerate pump-probe spectroscopies. Such an energetic multicolor source has, however, not been readily available in the DUV spectral range (200–300 nm).

The Raman-enhanced FWM in a gaseous medium generates multicolor laser emissions in a broad spectral range from the DUV to NIR [13–17]. By focusing two-color femtosecond laser pulses with the frequency spacing tuned to the vibrational Raman shift, multicolor femtosecond laser pulses have been generated via the cascaded FWM with molecular hydrogen [15–17]. Although the shortest wavelength of the generated femtosecond emissions reached to the DUV, the energy of the high-order anti-Stokes emissions generated in this wavelength range was much lower than those of the low-order anti-Stokes emissions generated in the visible range. Shitamichi et al. [16] employed three input pulses at 1200, 800, and 400 nm for higher intensities of the UV emissions. The intensities of the emissions at around 400 nm have been dramatically increased, while the intensities of the emissions in the DUV have been moderately enhanced.

In this letter, we have investigated an approach for the generation of energetic multicolor femtosecond pulses with pulse energies exceeding 1 μJ in the DUV region (around 220–300 nm). The Raman-enhanced FWM with three-color input pulses at 1200, 800, and 267 nm has been employed in hydrogen gas. For highly efficient frequency conversion by the FWM, the phase-matching condition needs to be satisfied. This is one of the dominant factors for the frequency conversion via the FWM in the DUV frequency range. The phase mismatch is notably higher than that in the near-ultraviolet or the longer wavelength range. For reducing the phase mismatch, a hollow fiber [18] is employed in this study [17, 19, 20]. Under these conditions, two regimes of the FWM have been investigated: (1) the FWM with the input DUV pulse co-propagating with the two NIR pulses and (2) the FWM with the DUV pulse delayed with respect to the NIR pulses. The two schemes give multicolor pulses with different spectral characteristics.

In the degenerate FWM pumped by two-color laser pulses, P1 (1200 nm) and P2 (800 nm), under the condition of the negligible pump depletion, the intensity of the first anti-Stokes emission is proportional to the intensity of one of the two pump pulses, I P1, and the square of the other pump pulse, I P2 [17, 21]: \(I_{{{\text{AS}}1}} \propto I_{{{\text{P}}1}} I_{{{\text{P}}2}}^{2} {\text{sinc}}^{ 2} ( - \Delta \beta_{{{\text{AS}}1}} z/2)\), where z is the propagation distance in the medium and I AS1 is the intensity of the first anti-Stokes emission. The phase mismatch for the first anti-Stokes generation, Δβ AS1, is Δβ AS1 = β P1 + β AS1 − 2β P2, where β P1, β P2, β AS1, respectively, stand for the propagation constants for P1, P2, and the first anti-Stokes emission. For a sufficiently high intensity of the first anti-Stokes emission, the higher-order anti-Stokes emissions with the following intensity are generated: \(I_{{{\text{AS}}N}} \propto I_{{{\text{P}}1}} I_{{{\text{P}}2}} I_{{{\text{AS}}N - 1}} {\text{sinc}}^{ 2} ( - \Delta \beta_{{{\text{AS}}N}} z/2)\). The phase mismatch Δβ ASN is expressed as β P1 + β ASN  − β P2 − β ASN-1 , where β ASN-1 and β ASN , respectively, are the propagation constants for the N–1th anti-Stokes emission and Nth anti-Stokes emission. The intensities I ASN-1 and I ASN correspond to those of the N–1th anti-Stokes emission and Nth anti-Stokes emission, respectively. In this cascaded scheme, a part of the energy of an anti-Stokes emission is converted into the higher-order anti-Stokes emission, indicating that the intensity of the anti-Stokes emission decreases with an increase in the order of the anti-Stokes emission. For the generation of the 8th anti-Stokes emission at 219 nm, eight processes of FWM need to be cascaded as schematically depicted in Fig. 1, leading to an intrinsically low intensity of the emission in the DUV wavelength range.

Fig. 1
figure 1

Energy diagram for the FWM in a two-color pumping scheme and b three-color pumping scheme

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By use of a DUV pulse emitting at 267 nm (P3) as an additional input pulse, the situation dramatically changes. The DUV emission in this scheme corresponds to AS6 in the two-color pumping approach discussed above and shown in Fig. 1a. The cascaded FWM process then starts from that generating AS7 at 240 nm as shown in Fig. 1b, and only two processes of FWM are involved for the generation of AS8 emitting at 219 nm. Furthermore, the energy of P3 is mainly converted into the multicolor femtosecond pulses in the DUV spectral range instead of being converted into the visible range. The energy of the multicolor DUV pulses is readily scalable by use of a high-energy DUV pulse as P3 that is able to be generated by frequency tripling an output NIR pulse from a Ti/sapphire chirped-pulse amplifier.

In the case of the Raman-enhanced FWM induced by the three-color pulses, the frequency conversion of the DUV pulse into the multicolor emissions is also observed for the DUV pulse delayed with respect to the two-color pulses, P1 and P2. The two-color NIR pump pulses excite the coherent molecular motion in hydrogen gas when the frequency separation between the two NIR pulses corresponds to the Raman shift frequency of the molecule. Even after the two pump pulses pass through the gas, the coherence is retained within the dephasing time. It modulates the frequency of the DUV pulse to generate multicolor DUV emissions even when the DUV pulse is delayed with respect to the two-color NIR pulses. Such a FWM called molecular phase modulation generating multicolor spectral emissions has been investigated elsewhere in the near-ultraviolet wavelength range [22, 23]. The phase modulation has also been used for pulse compression to generate isolated short pulses [24–27]. In these researches, the molecular coherence has been excited with a single-colored pump pulse. The process is linear with respect to the intensity of the pulse being modulated (the DUV pulse in the present research) [22]. In the following, the FWM processes with the DUV pulse co-propagating with the NIR pulses and that with the DUV pulse delayed with respect to the NIR pulses are investigated.

In the experiment, the setup shown in Fig. 2 was utilized. A part of the NIR pulse emitting at 800 nm emerging from a Ti/sapphire chirped-pulse amplifier (35 fs, 4 mJ, 1 kHz, Legend Elite-USP, Coherent Inc., Santa Clara, CA, USA) was used to pump an optical parametric amplifier (OPA, OPerASolo, Coherent Inc.) producing a signal at 1200 nm (P1). The pulse duration of P1 was about 50 fs. The remaining part of the NIR pulse at 800 nm was passed through a third-harmonic generator consisting of a frequency-doubling crystal (beta barium borate, β-BBO, 0.15-mm thick), α-BBO crystal for time delay control, dual-wavelength half-wave plate, and 0.1-mm-thick β-BBO crystal for the sum-frequency mixing. The generated third harmonic at 267 nm (P3) was horizontally polarized, which was then separated from other spectral components including the NIR pulse (800 nm, P2). After being sent to an optical delay line, the DUV pulse was spatially combined with the NIR pulses, P1 and P2, with horizontal polarizations after half-wave plates (WP2 and WP3 in Fig. 2). The resultant three-color laser beam was focused into a hollow fiber (made of fused silica, core diameter of 240 μm, 400-mm long) by use of an aluminum-coated concave mirror with a focal length of 500 mm. The pulse energies of the input P1, P2, and P3 were 200 μJ, 300 μJ, and 30 μJ, respectively. The hollow fiber was placed in a gas cell filled with hydrogen gas with a pressure of 0.6 atm. The output beam was collimated with another concave mirror with the same focal length and then was scattered on a diffuser made of fused silica for the spectral measurement of the beam using a multichannel spectrometer (Maya2000-Pro, Ocean Optics, Dunedin, FL, USA) with the calibrated spectral response in the wavelength range longer than 220 nm.

Fig. 2
figure 2

Experimental setup. OPA, optical parametric amplifier; SHG, 0.15-mm-thick β-BBO; TP, time plate; WP1–3, half-wave plate; L1, plano-concave lens, f = −150 mm; L2, plano-convex lens, f = 250 mm; THG, 0.1-mm-thick β-BBO; HM1, harmonic separator for 267, 400, and 800 nm; HM2, harmonic separator for 800 and 1200 nm; CM1,2, concave mirror, f = 500 mm; HF, hollow fiber chamber

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The spectrum of the output DUV pulse is shown in Fig. 3. The spectral shape of the output DUV pulse depended on the time delay of P3 with respect to P1 and P2. The two spectra measured for the time delays of 0 fs and 40 fs have sidebands originating from the FWM (Fig. 3). The spectral width of each sideband for the delay of 0 fs is broader than that for the delay of 40 fs. Besides, no notable variation was observed in the widths of the spectral peaks for time delays longer than 40 fs. The broader spectral width at the delay of 0 fs would be due to the cross-phases modulation (XPM) induced by the intense NIR pulses, P1 and P2. It means that the two phase modulation processes, FWM and XPM, have been simultaneously induced to modulate the frequency of P3 to form the multicolor DUV emissions and to broaden the spectrum of each multicolor emission. The XPM is arising from the electronic Kerr nonlinearity which is induced within the pulse envelopes of P1 and P2. In the case of the delayed P3 with respect to P1 and P2, this effect of spectral broadening disappears accordingly. The frequency of the DUV pulse is modulated solely by the FWM in this case. The pulse duration, spectral width, and frequency chirp of each multicolor emission are then determined by the corresponding parameters of the input pulse (P3) [22, 28] provided that the intensity of the DUV pulse is lower than the threshold for self-phase modulation, which was the case in the present research. The widths (the full width at half maximum) of the peaks at 240, 267, and 300 were, respectively, 3, 3, and 4 nm. These values suggest that the frequency widths of the emissions were the same within the uncertainty due to the resolution of the spectrometer.

Fig. 3
figure 3

Spectra of the output UV emission from the hollow fiber for the time delay of 40 fs (solid line) and 0 fs (solid area)

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The DUV pulse, P3, had a significant effect for the multicolor DUV laser emissions, although the DUV laser emissions are also generated by use of only the two-color pump pulses as reported elsewhere [15–17]. This is clearly shown in Fig. 4, in which the spectra of the output DUV pulse measured for the three-color pumping (1200, 800, 267 nm) and two-color pumping (1200, 800 nm) schemes are compared. The spectral intensities of the multicolor DUV pulses in the spectral range of 220–360 nm were much higher in the former than the latter where there was no detectable anti-Stokes emission in the wavelength range shorter than 240 nm. At wavelengths longer than 320 nm, spectral emission lines were generated in both the three-color and two-color pumping cases. For the spectral peak at 480 nm, there is no difference in the spectral intensity between the two different pumping schemes. This indicates that the spectral component at this wavelength is generated solely by the cascaded FWM induced by the two-color pump pulses. In the spectral range of 320–400 nm, both the two FWM processes would have contributed to the generation of the multicolor emissions.

Fig. 4
figure 4

Spectra of the multicolor DUV pulses generated by the two-color pulses (solid area) and three-color pulses (solid line). The spectra are normalized by the peak spectral intensity of the latter

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The peak area or pulse energy of the first anti-Stokes emission at the time delay of 40 fs was 1.7 times that of 0 fs, and the energy of the second Stokes emission in the former was considerably higher than the latter. These indicate the lower conversion efficiency from P3 to the multicolor DUV emissions in the latter case. This might be explained by the fact that the coherent vibration is continuously excited throughout the pulse envelopes of the two-color NIR pulses. The amplitude of the vibration then becomes the largest at the trailing edge of the two-color NIR pulses and results in highly efficient frequency conversion of P3 when P3 is slightly delayed with respect to the NIR pulses. For the P3 without the time delay, on the other hand, a part of the P3 is temporally overlapped with the leading edge of the two NIR pulses where the efficiency in the FWM is relatively low because of the low intensities of the two pulses in the leading edge.

The pulse energies of the generated multicolor laser emissions depended on the optical alignment of the input pulses into the hollow fiber. Careful alignment was necessary to lead to the highest output energies from the hollow fiber. To measure the pulse energy of each multicolor emission, the collimated output beam was passed through a fused silica prism followed by a joule meter (J3-09, Molectron). The typical pulse energies of each emission at the delay of P3 of 40 fs were, respectively, 2, 6, 4, 1, and 0.3 μJ at wavelengths of 300, 267, 240, 219, and 200 nm. The generation of the higher-order anti-Stokes emission at 185 nm was also confirmed by projecting the collimated output beam onto a phosphor screen following a fused silica prism. Although the anti-Stokes emission was also detected with a monochromator (VM502, Acton) equipped with a photomultiplier tube as shown in Fig. 5, the signal intensity of the vacuum ultraviolet emission was very low. This was because of the absorption by the oxygen through which the radiation passed before reaching the detector of the monochromator.

Fig. 5
figure 5

Spectrum of the multicolor emissions measured with the monochromator. The spectral sensitivity of the detector is not calibrated

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The spectral shape of the output multicolor DUV emissions depended on the energies of the two-color NIR pulses. By reducing the conversion efficiency into P3 in the third-harmonic generator, it was possible to increase the energy of P2 for a higher efficiency in the frequency conversion from P3 into the multicolor emissions. The conversion efficiency does not depend on the intensity of P3 [22], but depends on the intensities of the two-color NIR pulses. In the present research, the pulse energy of P3 was reduced to 10 μJ. As shown in Fig. 6, the conversion efficiency obtained in this case was higher than that obtained in Fig. 3, and the relative intensity of the first anti-Stokes emission was as high as 0.85 of the intensity of the output P3 at 267 nm (Fig. 6), although the pulse energy of each spectral emission became lower due to the reduction of the input energy of P3.

Fig. 6
figure 6

Spectrum of the output UV emission with the highest efficiency

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A gas cell without the hollow fiber was also employed for the FWM. The conversion efficiency into the spectral sidebands in this case was, however, much lower than the case of the hollow fiber, suggesting that the phase matching and the long interaction length provided by the hollow fiber are crucial for the efficient generation of multicolor DUV pulses similarly to the previous report on the two-color pumping regime [17]. One of the characteristics of the three-color pumping scheme is that the threshold of the gas pressure for the generation of the multicolor DUV pulses is independent of the intensity of P3 [22]. Instead, the threshold depends on the energies of the two NIR pulses, P1 and P2. Use of high-energy NIR pulses leads to the induction of FWM at a low gas pressure at which the phase mismatch for the wave mixing is small, which is crucial for the efficient generation of the multicolor DUV pulses through the cascaded FWM. This is in contrast to the previous scheme that used a single DUV input pulse [29]. In the approach, the first Stokes emission needs to be first generated for the subsequent generation of the anti-Stokes emission via FWM. The high gas pressure required for the generation of the first Stokes emission would have prevented the subsequent generation of the anti-Stokes emission due to a large phase mismatch originating from the high gas pressure.

As mentioned previously, the pulse durations of the multicolor DUV pulses generated by the molecular phase modulation are close to that of P3. The expected pulse duration of P3 given by a numerical simulation for the present experimental condition is 45 fs just behind the BBO crystal for the sum-frequency mixing. The group-delay dispersion in the air and the glass window placed in front of the hollow fiber stretches P3 to around 55 fs. These suggest that each of the generated spectral line is expected to have a duration around 55 fs and is positively chirped. For applications requiring shorter pulse durations, therefore, an external pulse compressor such as a pair of prisms is necessary to compress the pulses down to their transform-limited durations around 40-fs. When the three-color input pulses are temporally overlapped in the gas-filled hollow fiber, the bandwidth of each emission broadens due to the XPM induced by the NIR pulses as discussed above. The resultant width of each emission line supports a transform-limited duration shorter than 10-fs. The quasi-continuous spectrum consisting of the first Stokes, P3, and the first anti-Stokes emissions may be used to synthesize 2-fs optical pulses, although fine dispersion compensation would be necessary for the synthesis. Such dispersion compensation might be achieved by using a deformable mirror [30, 31]. The mutual phase coherence among the spectral components, which originates from the process of the four-wave mixing [32, 33], plays a key role for synthesis of ultrashort pulses with stable temporal intensity profiles.

In conclusion, an approach for the generation of energetic multicolor DUV femtosecond pulses has been investigated. Here, three-color laser pulses emitting at 1200, 800, and 267 nm generate intense multicolor laser pulses in the DUV through the FWM in hydrogen gas. The conversion efficiency from the input DUV pulse into the multicolor laser emissions is independent of the energy of the input DUV pulse. The conversion efficiency increases with an increase in the energy ratio of the NIR pump pulse to the input DUV pulse. This, however, decreases the energy of each multicolor laser emission, and hence there is an optimum energy ratio leading to the highest energy of the emission. In this work, a high-order anti-Stokes emission with the shortest wavelength of 185 nm has been generated, and the pulse energy of the emission generated in the spectral range longer than 200 nm exceeded 1 μJ. The multicolor DUV laser pulses are an attractive light source for applications such as the trace analysis employing laser-ionization time-of-flight mass spectroscopy as well as pump-probe spectroscopies. Simultaneous ionization of several organic compounds is expected to be demonstrated in the former. The femtosecond pulse duration of the multicolor laser emissions has also a crucial importance for the fragment-free ionization of organic compounds.