Flowing cryogenic liquid target for terahertz wave generation

Terahertz wave emission from condensed matter excited by intense laser pulses not only reflects the details in laser-matter interaction but also offers bright terahertz wave sources. Flowing liquid targets possess the advantage of providing a fresh area for each laser pulse. To demonstrate a debris-free target under laser excitation, we investigate the use of liquid nitrogen as a target. By creating a flowing liquid nitrogen line in the ambient environment, we successfully observe broadband terahertz wave emission under short pulse excitation. Our cryogenic line is able to sustain the excitation of a high-repetition-rate (1 kHz) laser. The terahertz peak field emitted from liquid nitrogen is comparable to that from liquid water, yet a broader bandwidth is observed. This demonstration prompts new opportunities in choosing potential materials for studying terahertz wave generation process and in understanding laser-induced ionization in different liquids.

The rapid development of advanced laser technology provides great opportunities to study nonlinear processes in laser-matter interaction. In terahertz (THz) regime, there is an increasing demand for intense THz sources to enable fundamental studies in ultrafast phenomena, 1-3 such as hidden phase transition, 4 high harmonic generation, 5 alignment and orientation of molecules. 6 Currently, a THz field over MV/cm is attainable by employing nonlinear crystals. 7,8 Further improvement is limited by the optical damage under intense laser irradiation. Additionally, THz pulse energy above 50 mJ has been reported, with a solid metal target under-single-shot excitation by an intense laser pulse (60 J). 9 However, because of the contamination issue caused by debris as well as the target damage, solid targets are hardly applied to lasers with a high repetition rate (1 kHz). Therefore, developing a durable target is imperative to provide a solution for intense lasers.
Liquid targets with a similar density as solid are the potential candidates due to their capability of providing a fresh area for each pulse. Moreover, liquid targets have been studied for decades in generating extreme ultraviolet and X-ray radiation. 10,11 Since the first observation of THz wave generated from liquid water, 12,13 more experiments and discussions based on liquid targets for THz wave generation have been reported. Remarkably, THz field strength up to 0.2 MV/cm has been demonstrated by using a 200 µm water line as the target. 14 The broadband THz wave generated from liquid metal is also observed. 15 Also, the enhancement of THz wave emission induced by a pre-existing plasma in a double-pump excitation geometry is studied to reveal more details in laser-liquid interaction. 16,17 In contrast to an air plasma, the preference for subpicosecond excitation pulses suggests a different ionization processes in liquids, in which collisional ionization plays an important role in increasing the electron density. 18 On the other hand, unlike a solid target, the fluidity of liquids can support a continued operation without interruption. Nevertheless, there is still debris when laser intensity is high enough to create a "mist" from the target, which not only contaminates the optics nearby, but also absorbs and scatters the signal. It should be noted that while gas is a good debris-free target, it hardly supports a high-density plasma because of the relatively low molecular density.
To demonstrate a debris-free target for THz wave emission, we create a free-standing, flowing liquid nitrogen (LN2) line in the ambient environment. Applying single color excitation, coherent THz emission is detected in the forward direction by electro-optic sampling (EOS).
Compared with the signal from liquid water under the same excitation condition, the signal from LN2 has a comparable peak field but a broader bandwidth, which is attributed to the low absorption of LN2 at higher THz frequency. The LN2 target can support the excitation by laser pulses with a 1 kHz repetition rate without interruption.  As a target, the surface smoothness and stability of the flow is key to getting a good signalto-noise ratio. In fluid mechanics, a flowing liquid can be characterized by Reynolds numbers (Re), 19 which is a dimensionless quantity defined as where r, v, r and h are the density, flow rate, radius and dynamic viscosity of the liquid, respectively. When Re < 2300, laminar flow is formed with no lateral mixing or turbulence, 20 in which the liquid is regarded as several layers moving smoothly. Laminar flow offers a good-quality target for optical excitation. From Eq. (1), we know that a low flow rate and a high viscosity are in favor of a small Re number. However, as a target designed for the laser with 1 kHz repetition rate, the flow rate (v) needs to be greater than 1 m/s to provide each pulse a fresh area. LN2 has a relatively low viscosity (h = 150 µPa×s at 77 K) leading to the difficulty in creating a Laminar flow.
In our case, to avoid a turbulent flow, Re is kept at 2150 by selecting the syringe with appropriate diameter.
It should be noted that the LN2 line is flowing in the ambient environment. This is possible because of the Leidenfrost effect, 21,22 in which an insulating layer is created at the surface by the vaporized LN2 to keep the liquid from boiling rapidly. The liquid line will break into droplets eventually due to the surface energy minimization. The break-up distance L from the needle tip can be calculated by 23  Fig. 2. Currently, the peak field from LN2 is 0.4 times weaker than that from water. However, the THz signal from LN2 shows a shorter pulse duration. The corresponding spectra without normalization are shown in the inset for comparing the real magnitude between two signals. Under the same excitation and detection conditions, the LN2 shows a broader bandwidth with more high-frequency components. There are two possible reasons.
LN2 has a low absorption in THz frequency because it's a nonpolar liquid. Additionally, the vaporized N2 keeps purging the system to preserve the high frequency components. The cutoff frequency is about 2.5 THz, which is limited by the detection crystal. THz wave emission from bulk LN2 under a two-color or double pump excitation was recently reported, 24 in which a bolometer is used for detection. Distinctively, we are using a flowing LN2 line and measuring a temporal THz waveform.
The THz wave emission from liquids is extremely sensitive to the position of the liquid target across the focus. Fig. 3 shows the cross section of a liquid line and the laser beam. By scanning the position of the LN2 line in x direction from x = 0, the incident angle (a) at the air/liquid interface is continuously increasing from 0° to 90°, which can be calculated by a = arcsin(Dx/r).
Dx is the distance of liquid centroid away from the z direction. The laser beam refracts at the air/liquid interface, leading to a deviation from z direction. As it has been discussed in our previous work, 25 there is an optimized incident angle to get the maximal THz field coupled out from the liquid, which is determined by the dipole projection in the direction of detection and the total internal reflection of the THz wave at the liquid/air interface. signal is obtained at Dx = ± 170 µm, showing that the optimal incident angle is 50.6°. As a nonpolar liquid, LN2 has a much lower absorption coefficient (0.8 cm -1 at 1 THz) 26 than that of water (220 cm -1 at 1 THz) 27 . A lower refractive index is expected, which results in a smaller optimal incident angle. For the laser beam, the difference of refractive index between liquid water (1.3) and LN2 (1.2) is too small to be a dominant factor here. The baseline offset in Fig. 4a is the amplitude of THz emission from air plasma when the liquid target is moved away from the laser focus. Then, the field amplitude gradually increases when the liquid line is moved towards the focus. It can be explained the molecular density near the liquid line gradually increased by the vaporization of LN2.
Additionally, the result clearly shows that under the excitation of sub-picosecond pulse the signal from a liquid is stronger than that from air. Fig. 4b shows the waveforms when Dx = ± 170 µm, respectively. The waveforms have the same shape with an opposite polarity. This is because that the projection of dipole created by electrons has an opposite direction, which clearly indicates that the THz signal is from a liquid phase rather than a vaporized gas phase. This demonstration also shows that the flowing liquid target can be applied to both normal and cryogenic liquid. Moreover, flowing liquid nitrogen is a debris-free target, the mist is vaporized immediately without contamination and scattering.
Currently, THz wave generation from liquids under single-color excitation is explained by the ponderomotive force induced dipole. However, many properties remain unclear. Namely, which properties of liquids can lead to a high field and a broad bandwidth? Besides liquid water, two nonpolar liquids have been tested, a-pinene 16 and liquid nitrogen (in this paper). Both of them provide a broader bandwidth of THz signal than that from water, which suggests the significance of the low absorption. On the other hand, a much brighter white light from liquids than that from air plasma is observed in the experiment, which indicates that the liquid does provide more electrons in the ionization process. But the way of making full use of the ionized electrons to improve the generation efficiency needs more theoretical and experimental studies.
In summary, we report a temporal THz waveform from a flowing cryogenic line under the single-color excitation. Comparing to the THz signal from liquid water, a comparable electric field but with a broader bandwidth is observed. Our results show that LN2 has the potential to be a THz source for generating broadband THz pulses without producing debris. Furthermore, ionized LN2 can also emit X-ray. Along with THz ray, they are able to reflect different dynamics of ionized electrons, respectively. Detecting two synchronized pulses (X-ray and THz ray) as well as the white light in the same ionization process is meaningful to portray a full picture of electron dynamics from excitation to recombination. Also, developing flowing liquid target (line/droplets) The corresponding spectra are shown in the inset. The LN2 signal shows a narrower pulse duration, and its spectrum has a broader bandwidth.