1. Introduction

There are increasing demands of ultrashort pulses in the vacuum UV and soft X-ray regions for various scientific and industrial applications. Thus, new light sources, such as free electron lasers and high harmonic generation systems, have been developed and continuously improved over the last two decades.

Non-resonant four-wave mixing in filamentation is an alternative method to generate vacuum UV radiation at high repetition rates (kHz) [1–6]. Although the laser wavelengths generated by this method so far are longer than 140 nm, shorter output wavelengths are expected for this method. The prime advantages of this method are its simplicity and efficiency. The method only requires a temporal and spatial overlap of intense femtosecond laser pulses in a rare gas cell. The intense laser pulse alters the local refractive index of the gas and self-focuses, which causes ionization of the gas. Since the ionized gas species reverses the spatial gradient of the refractive index with respect to that of the neutral gas, the overall effect enables propagation of a collimated laser pulse over the Rayleigh length [7]. When two-color femtosecond pulses are introduced, even if each laser pulse is not sufficiently intense to create filamentation, cooperative interaction between the two-color fields and the gas medium can produce filamentation [8]. Alignment of two laser beams in a gas cell is considerably easier than into a narrow hollow fiber. The physics of the four-wave mixing process in filamentation is not identical with that in a hollow fiber [9], as manifested by different gas-pressure dependencies [8]. Intensity clamping and mode cleaning effects of the filamentation provide stable and spatially clean output pulses [10, 11]. By controlling the laser peak power and gas pressure one can avoid multiple filaments that cause beam break-up and pointing instability. Pulse energies from several hundred nJ to several μJ are obtained by filamentation four-wave mixing at 1 kHz.

Here we present simultaneous generation of sub-20 fs deep and vacuum UV pulses from a single filamentation cell. As we reported previously [8, 12], generation of the pump and probe pulses by filamentation four-wave mixing in a single gas cell ensures very precise and stable optical pump-probe delay. The cascaded four-wave mixing processes employed in our previous study for simultaneous generation of the third and fourth harmonics (3ω and 4ω, respectively) were already capable of producing the fifth harmonics (5ω); however, the optical path in air was not transparent to 5ω. In this study, therefore, the optical paths from the filamentation cell to the target are evacuated. Furthermore, we eliminate transmissive optics in the paths after the four-wave mixing; an output optical window of the filamentation cell and an input optical window of the photoelectron spectrometer employed in our previous system [8, 13] were removed. In this study, the 3ω, 4ω, and 5ω pulses are separated and transported only using reflective optics, so that grating compressors to compensate material dispersion are no longer necessary. This modification not only simplifies the system but also improves the pulse characteristics. Beutler et al. [4] have previously demonstrated generation of sub-20 fs vacuum UV pulse by filamentation four-wave mixing of 3ω and ω; their method was focused on generation of a short pulse of 5ω, but not 3ω and 4ω and, it required spectral phase transfer [1] and compression using MgF₂. Our system requires no dispersion compensation to obtain sub-20 fs pulses of 3ω, 4ω, and 5ω pulses. We demonstrate time-resolved photoelectron imaging of the non-adiabatic wave packet dynamics in CS₂ molecule.

2. Experiment

Figure 1(a) shows a schematic diagram of our apparatus. A cryogenically cooled Ti:sapphire multipass amplifier delivered ~770 nm pulses (25 fs, 1.5 mJ) at 1 kHz. The fundamental frequency pulse (ω) was split into two beams with a ratio of 3:7. The higher intensity beam was converted to the second harmonic, 2ω, in a β-barium borate crystal (β-BBO, θ = 29°, t = 0.3 mm). A dielectric concave mirror (r = 2,000 mm) was used to focus the second harmonic into a neon gas cell through a Brewster-angled calcium fluoride (CaF₂) window (t = 1 mm). This concave mirror was also used to separate the second harmonic from the residual fundamental. The fundamental beam was focused into the cell with another dielectric concave mirror (r = 2,000 mm). A flat dichroic mirror was used to recombine the fundamental and second harmonic beams. The relative polarization of two beams was parallel to each other. The pulse energies of the fundamental and the second harmonic were 0.43 and 0.37 mJ, respectively. The laser and the optical configuration for the input beams were identical to those employed in our previous study [8] except that the fundamental output from the Ti:sapphire amplifier was 25% lower than in [8].

 

Fig. 1 (a) Schematic diagram of the experimental setup. (b) Schematic drawing of the differential pumping system. All dimensions are given in millimeters.

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When the ω and 2ω pulses overlap temporally and spatially, a bright filament (plasma column) with the length of ca. 120 mm was created. We used a pinhole instead of an output window for the filamentation cell in order to create efficient differential pumping and transmit the deep and vacuum UV pulses generated by four-wave mixing. The pinhole was made by the filament itself. We placed a flat aluminum disk (t = 1.5 mm) at the end of the filamentation cell, and let the laser beam drill a through-hole. The subsequent laser pulses are transmitted through this hole (ca. 0.1 mmϕ). Behind the pinhole, a narrow channel (1.25 mm in diameter and 20 mm in length) and an aperture (3 mmϕ) were installed for differential pumping, as shown in Fig. 1(b). The pressure of neon gas in the gas cell was ~3.7 × 10² Torr. The neon gas leaking through the pinhole was evacuated with a dry pump (580 L/min). The pressure in this first differential pumping section was below 3.0 × 10⁻¹ Torr. The region between the channel and the aperture was evacuated with another dry pump (500 L/min). The flow rate of neon gas was estimated to be 0.5 Torr･L/s.

The laser pulses finally entered a high-vacuum optics chamber that houses an optical delay stage and mirrors. A UV-enhanced aluminum mirror with an aperture of 3 mm diameter was used to spatially separate the central and peripheral parts of the beam. The central part was transmitted through this holed mirror and reflected four times with dielectric mirrors (Layertec) for 5ω in order to attenuate other colors (ω, 2ω, 3ω and 4ω). The peripheral part reflected by the holed mirror was used to sample 3ω or 4ω, using dichroic mirrors. The timing of the 5ω pulse was varied using a vacuum-compatible translational stage with 5 nm resolution (Sigma-tech). The vacuum UV and deep UV pulses were independently focused onto a molecular beam with two Al concave mirrors (r = 1,000 mm). The intersection angle between the vacuum UV and deep UV pulses was estimated to be ca. 1°. The entire optics chamber was evacuated using two turbo molecular pumps (300 L/s) to maintain the pressure below 2 × 10⁻⁶ Torr when operating the filamentation gas cell.

The photoelectron imaging apparatus with a doubly-skimmed molecular beam source was employed [13] with an Even-Lavie pulsed valve [14]. Photoelectrons generated by (1 + 1’) resonantly enhanced two-photon ionization of jet-cooled samples were accelerated in an electric field and projected onto a dual microchannel plate (MCP, effective area of 75 mmϕ) backed by a phosphor screen (P46). The linear polarization vectors of the vacuum UV and deep UV pulses were aligned parallel to each other and also set parallel to the MCP detector face [15]. Photoelectron images were recorded as a function of the delay time between deep UV and vacuum UV pulses and analyzed by pBASEX method [16] to obtain time-dependent photoelectron kinetic energy and angular distributions.

3. Results and discussion

The spectra of 3ω, 4ω, and 5ω pulses generated by cascaded four-wave mixing are shown in Fig. 2. The 5ω spectrum was measured using a spectrometer purged with nitrogen gas. The transform-limited (TL) pulse widths are estimated as 9, 7, and 6 fs for 3ω, 4ω, and 5ω, respectively, by Fourier transform of the observed spectra assuming a constant spectral phase. In this study, we set a pinhole near the end of the filament. The spectra of the pulses were the same using the pinhole and a CaF₂ optical window. When the pinhole was set too close to the filament, four-wave mixing efficiency diminished.

 

Fig. 2 Typical spectra (a) 3ω, (b) 4ω, and (c) 5ω.

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Figure 3(a) compares the pressure dependence of the output pulse energies when using the pinhole and the window. The energies of the ω and 2ω input beams were respectively 430 and 370 μJ. We measured the output energies of 3ω and 4ω using a thermal sensor (3A, Ophir) in air after separating them using a CaF₂ prism. The 5ω beam was separated from other colors using three dielectric mirrors for 5ω, and the pulse energy was measured using a vacuum compatible thermal sensor (12A-TEC, Ophir) under vacuum. As for 5ω, contribution of the stray light from the intense ω and 2ω input beams was not negligible, so the stray light was measured by pumping Ne gas out of the cell and subtracted from the energy measured with the Ne gas to evaluate an accurate energy of the 5ω pulse. Accurate measurement of the 5ω pulse energy was difficult at low energies (20~30 nJ) due to thermal drift of the power meter, and their values are not shown here.

 

Fig. 3 (a) Pressure dependence of the measured pulse energies for 3ω (diamonds), 4ω (squares) and 5ω (circles). The energies of the ω and 2ω input beams were 430 and 370 μJ, respectively. The filled/open symbols indicate the energies measured with/without an output pinhole. (b) A typical cross-correlation trace between 4ω and 5ω measured by non-resonant (1 + 1’) two-photon ionization of Xe (circles). The solid line shows a Gaussian with FWHM of 18 fs. The vertical scale corresponds to averaged ion counts per 10 seconds.

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As seen in Fig. 3(a), the pulse energies of 3ω and 4ω initially increased with the Ne gas pressure, but they were saturated at ca. 600 Torr. The pulse energy of 5ω reached the maximum at 400 Torr and gradually descended at higher gas pressures. The maximum pulse energy of 5ω obtained using the pinhole was ~100 nJ at a Ne gas pressure of 400 Torr. The typical values of transmittance through the pinhole were ~30, 45, and 40% for 3ω, 4ω, and 5ω, respectively. The losses of the pulse energies are well compensated for by superior pulse characteristics and a simpler setup achieved by the pinhole.

We also examined the spatial modes of the output beams using a Ce:YAG phosphor plate. The spatial profiles of the 3ω and 4ω beams were clean throughout the pressure range from 200 to 700 Torr, even when using the pinhole. On the other hand, the beam mode of 5ω gradually degraded at the gas pressure over 400 Torr to become a non-uniform spatial distribution. Consequently, the transmission of the 5ω pulse through the pinhole diminished at high pressures.

The cross-correlation trace between 4ω and 5ω measured using non-resonant (1 + 1’) two-photon ionization of Xe is shown in Fig. 3(b). The background signal (~80) originates from two-photon ionization by individual one-color ionization processes. As shown in Fig. 3(b), the observed trace is well expressed by a single Gaussian with a full width at half maximum of 18 ± 2 fs (a solid line). This value is two times larger than 9 fs expected for the transform-limited pulses of 4ω and 5ω; however, it is shorter than the cross-correlation time (22 fs) of 3ω (14 fs) and 4ω (17 fs) of our previous system [8].

Finally, we demonstrate an application of our new light source to study predissociation dynamics of CS₂ from the ¹B₂(¹Σ_u⁺) excited state. CS₂ is linear in the electronic ground state (¹Σ_g⁺). Photoexcitation to ¹B₂(¹Σ_u⁺) in the wavelength region of 192 – 208 nm makes the molecule a bent (or quasi-linear) structure and induces symmetric stretching (ν₁ = 392 cm⁻¹) and bending (ν₂ = 426 cm⁻¹) vibrations [17]. At 198 nm, the molecule is above the barrier for linearity, so that a large bending vibration occurs between the linear and bent geometries. Although the ¹B₂(¹Σ_u⁺) state is bound in the linear geometry, it undergoes avoided crossings with the repulsive ¹B₂(¹Π_g) state at large bending angles, so that the molecule predissociates into CS(¹Σ⁺) + S(¹D) and CS(¹Σ⁺) + S(³P) [18, 19].

In our previous study [20], we performed time-resolved photoelectron imaging of this reaction using 4ω and 3ω for the pump and probe pulses, respectively. The 4ω (200 nm, 6.2 eV) pulse created a vibrational wave-packet on the ¹B₂(¹Σ_u⁺) state and a time-delayed 3ω (260 nm, 4.8 eV) pulse induced photoionization. However, as shown in Fig. 4(a), photoionization from the bent geometry in the ¹B₂(¹Σ_u⁺) state requires a high probe-photon energy, as the ground state of CS₂⁺ has the linear equilibrium geometry. Consequently, the 3ω pulse is unable to induce photoionization from the bent geometry. Shown in Fig. 4(b) is a two-dimensional (2D) map of the photoelectron kinetic energy distributions measured in our previous study [20]; ionization is induced only near the linear Franck-Condon region and the outer turning point is not observed.

 

Fig. 4 (a) Schematic potential energy diagram of CS₂. Two-dimensional (2D) map of photoelectron kinetic energy (PKE) distributions as a function of the pump-probe delay time using (b) 3ω probe pulse and (c) 5ω probe pulse. Figure 4(b) is reproduced from [20].

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In the present work, we employed 5ω (159 nm, 7.8 eV) as a probe pulse and succeeded in observing the wavepacket motions between the turning points. Figure 4(c) shows a 2D map of the photoelectron kinetic energy distributions measured as a function of the pump-probe time delay. The high and low photoelectron-energy signals originate from the linear and bent geometries, respectively. The oscillatory motion of the photoelectron kinetic energy is mainly ascribed to the bending mode. The weak signal in the very low kinetic energy region might be attributed to the wavepacket on the ¹B₂(¹Π_g) state accessed by non-adiabatic transition; detailed analysis of the experimental results is now in progress and will be presented elsewhere.

The result clearly demonstrates the necessity of sub-20 fs vacuum UV radiation as a probe pulse in time-resolved photoelectron spectroscopy of this reaction. A short pulse in the vacuum UV region is also useful as a pump pulse to access higher valence and Rydberg states and explore vacuum UV photochemistry. Other scientific and industrial applications are certainly possible.