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Abstract
Understanding the process of terahertz (THz) wave generation from liquid water is crucial for further developing liquid THz sources. We present a systematic investigation of THz wave generated from laser-irradiated water lines. We show that water line in the diameter range of 0.1-0.2 mm generates the strongest THz wave, and THz frequency red shift is observed when diameter of the water line increases. The pump pulse energy dependence is decoupled from self-focusing effect by compensating the focal point displacement. As the pump pulse energy increases, saturation effect in THz peak electric field is observed, which can be mainly attributed to the intensity clamping effect inside the plasma and have never been reported previously, using water line or water film as the THz source. The proposed mechanism for saturation is supported by an independent measurement of laser pulse spectrum broadening. This work may help to further understand the laser-liquid interaction in THz generation process.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Great interest in terahertz (THz) science and technology has arisen from its wide-range applications including nondestructive imaging [1–5], biomedical analyzing [6–8], novel electron accelerator [9,10] and THz field-materials nonlinear interaction [11–13] etc. Achieving intense and broadband table-top THz wave sources is crucial for further exploring THz wave applications. A large variety of THz sources have been proposed and developed in the past decades, such as nonlinear optical crystals [14–20], gas plasmas [21–29], photoconductive antennas [30,31] and free electron lasers [32]. Among these sources, nonlinear optical crystals, such as ZnTe and LiNbO3 crystals, have been widely used. However, the damage threshold of the crystal limits incident laser intensity, leading to a limited THz power scaling. Additionally, phonon absorption in THz frequency range of the crystals leads to a narrow THz wave emission bandwidth [33,34]. Therefore, laser induced plasma comes to be seen as a promising THz source due to considerable high intensity, dramatically broad bandwidth and non-limitation on excitation damage threshold. However, due to the relatively low molecular density in gases, the scaling of THz emission from gas plasma might be limited by the plasma density. Liquid water has lower ionization energy and higher molecular density than air as an ionized medium. Ionized liquid water has been successfully exploited as a source of high harmonics [35], super-continuum (white light) [36,37], or X-ray [38], but it has been considered impossible to be developed as a THz source because of its strong absorption of THz radiation.
Recently, THz wave generation from ionized liquids with different geometries was reported. In one of the works, THz radiation can be generated from intense ultrafast laser induced filament in a 50-mm long cuvette filled with various liquids [39]. Their setup is similar to the one that was used to investigate optical pulse spectrum broadening [40] And similarly, the THz wave generation process is attributed to spectrum broadening of the pump laser pulse. In another work, a gravity-driven, free-flowing water film with thickness of 200 µm was employed to reduce the absorption of THz radiation by liquid water, and THz radiation was generated by focusing a sub-picosecond laser pulse into the water film [41]. In the follow-up works, the geometries of water were further optimized. Water jet generated by a homemade flattened nozzle at fixed pressure can provide a thinner water film, further reducing the absorption of THz radiation [42,43] by the generation media themselves. But the stability and controllability of the water jet need to be improved. As a jet source, water jet can provide higher molecular density than gas molecular jet [44] and gas cluster beam [45]. Thus, water jet is a promising THz source to achieve higher optical-to-THz conversion efficiency. Very recent report shows thin water column formed by syringe needles or round-hole nozzles provides an easier access to water flow optimum for THz wave generation [46–48]. Parameters for maximum THz generation were systematically investigated, such as the relative position between the water line and the laser focal spot, the diameters of the water line and the laser pulse duration. The dependence of THz waveform [47] and optimal pulse duration [48] on the diameter of water line is also investigated, respectively. Besides, the double-pump method was used to boost THz wave generation in liquids jets [49] and water lines [50]. However, the relationship between THz waveform and diameter of water line under its optimal pulse duration has not been investigated. Considering nonlinear refractive index coefficient of liquid water is relatively large [51], the Kerr nonlinearity effect should not be ignored in the THz generation process. Moreover, due to the self-focusing effect in the air before the laser pulse hits the liquid water column, movement of the focal spot inside the liquid sample is another factor that needs to be considered experimentally. Therefore, some physical phenomena need to be decoupled from these effects caused by Kerr nonlinearity.
In this article, we further systematically investigate the THz wave generation process from liquid water lines and discuss the Kerr nonlinearity effects in the pump pulse propagation and in the THz wave generation process. The water lines with different diameters were used for THz wave generation under its optimal laser pulse duration. The water line produced by the 0.20-mm inner diameter needle generates largest THz wave amplitude. And THz peak electric field decrease and THz pulse broadening are observed when the diameter of water line increases in excess of 0.20 mm. Furthermore, we decouple the pump energy dependence from self-focusing effect by compensating the focal point displacement caused by self-focusing effect. We observed THz emission is saturated when the pump pulse energy increases to over 0.8 mJ using 2-inch focusing length lens and pump pulses with 400 fs pulse duration. We attribute the saturation effect to the intensity clamping inside plasma and consequently saturation of the plasma density as the pump intensity increase to certain extent. An independent measurement result on pump pulse spectrum broadening indicates the laser intensity inside the plasma is saturated as the input laser pulse energy is further increased, which can be seen as an evidence of our proposed mechanism. The trends of the spectrum broadening measurements agree well with the results on THz wave amplitude dependence on the pump laser pulse energy.
2. Experimental setup
A schematic diagram of the experimental setup is shown in Fig. 1(a). A commercial femtosecond Ti: sapphire amplified laser with 800 nm central wavelength and 1 kHz repetition rate is used. Different laser pulse duration can be achieved by changing the pre-chirp of the laser pulse. Negatively chirped pulses are used in our experiments. The laser beam is split into pump beam and probe beam. The pump beam is focused into a water line by a 2-inch focal length lens. The THz wave generated from water line is collected by an off-axis parabolic mirror (PM1) with 6-inch effective focal length (EFL). A high-resistivity silicon wafer is used as a long-pass-filter to block the residual pump light. THz waves pass through the silicon wafer and are refocused by an off-axis parabolic mirror (PM2) with 4-inch effective focal length. An ITO-coated glass plate is used to combine the optical probe beam and terahertz wave. An 1-mm thick <110> ZnTe crystal followed by a balanced detector (BD) is used to detect the THz waveform. Deionized distilled water is utilized as the THz emission medium. An industrial dispensing needle pumped by a digital peristaltic pump is used to produce a stable water line. To avoid the impact of prepulse, the flow rate of water line is kept to be 6 mm/ms, ensuring each optical pump pulse (pulse-to-pulse separation is 1 ms for 1-kHz laser system) to excite a completely refreshed water volume. We define that laser propagates along z-direction and water line flows along y-direction. The position of water line can be precisely controlled by a 2D-translation stage. A fiber-coupled spectrometer (Ocean Optics USB2000+) is placed along x-direction (perpendicular to the laser pulse propagation direction) to test the spectra broadening effect. A 2-inch focal length lens (L3) is used to collect the light from plasma in water line in the direction perpendicular to the laser pulse propagation direction for the spectra measurement and a short-pass optical filter (F) to partially block the pump light reflected from the water surface or scattered from the plasma, as shown in Fig. 1(a).
Fig. 1. (a) Schematic diagram of the experimental setup. BD: balanced detector, PM1-2: parabolic mirror, L1-3: optical lenses, F: short-pass filter, Si: silicon wafer. (b) THz waveform generated from water line with 0.4 mJ laser pulse energy. Inset: Corresponding Fourier transform spectrum of the THz wave.
Figure 1(b) plots the THz waveform generated from water line under 0.4 mJ laser pulse energy. The water line with 0.20-mm diameter is placed at optimized position where the THz wave peak amplitude is maximum. The corresponding Fourier transform spectrum is shown in the inset. Both the central wavelength and the full width at half maximum (FWHM) of the THz signal are about 0.7 THz.
3. Influence of the diameter of water line
First, we investigate the influence of the diameter of water line on THz wave generation efficiency. A set of needles with different inner diameters are used to produce different water lines. Figure 2(a) shows THz waveforms generated from water lines with different diameters. For each water line, the relative position and laser pulse duration are optimized to achieve the maximal THz peak amplitude. The amplitude of generated THz wave is related to the pulse duration of pump laser. Figure 2(c) shows the THz peak amplitude dependence on pump pulse duration for a 0.20-mm diameter water line. The optimal pulse duration for 0.20-mm diameter water line is about 400 fs and the optimal pulse duration for other different diameter water lines is shown in Fig. 2(d). These results are in agreement with the previous one [48].THz wave generated from water line with 0.20-mm diameter has the highest peak amplitude and it decreases as the diameter increases or decreases from 0.20 mm. Furthermore, we can observe an obvious THz pulse timing delay and pulse width broadening when the water line diameter increases. We attribute the pulse delay to the optical path length increase as water line diameter increases. Figure 2(b) shows those corresponding Fourier transform spectra. A frequency red shift occurs when the water line diameter increases, which is correspond to the THz pulse broadening. There are two reasons for this effect: First, the generated THz waves have larger optical path in thicker water lines. Considering the absorption coefficient of water increases with frequency in the range of 0.1–10 THz, high frequency components of the generated THz wave experience higher absorption in the thicker water lines. The absence of high frequency components leads to the spectrum red shift and THz pulse broadening. Second, the optimized pump pulse durations for thicker water lines are larger, which may directly lead to larger pulse duration of the THz pulse.
Fig. 2. THz waveforms and their corresponding spectra when water lines with different diameters are used. (a) THz waveforms generated from 0.11 mm, 0.20 mm, 0.28 mm, 0.34 mm, 0.39 mm, 0.47 mm, 0.56 mm, 0.70 mm, 0.82 mm diameters water line, respectively. (b) Corresponding Fourier transform spectra. (c) THz amplitude as a function of pump pulse duration for 0.20 mm-diameter water line. (d) Optimal pulse duration for water lines of different diameters.
4. Pump pulse energy dependence
In order to investigate the pump pulse energy dependence, we employ a circular variable metallic neutral density filter to control the incident laser pulse energy, and a water line with 0.20-mm diameter is used to generate THz wave, as shown in the Fig. 3(a). Firstly, we optimize THz peak amplitude by changing the water line position when the pump pulse energy is set at 0.4 mJ. The generated THz peak amplitude decreases when we simply increase incident pulse energy. However, if we optimize the water line position under 2.8 mJ pump pulse energy, the THz peak amplitude decreases when the pump pulse energy is gradually attenuated from 2.8 to 0.4 mJ. These two trends are completely inconsistent. To find out the possible mechanism, we look into the previous works. A linear relationship between THz energy and pump pulse energy was obtained from both the free-flowing water film [35] and the water jet [36]. However, they believe the linear dependence rather than a quadratic one is mainly caused by the plasma position displacement. In the follow-up work, a quasi-quadratic dependence between THz energy and pump pulse energy was demonstrated with water jet scheme [43]. For water line scheme, the linear scaling of the THz field strength (quadratic scaling of the THz energy) with the laser energy is verified by experimental and particles in cell (PIC) results [46]. Although the influence of plasma position displacement is noticed, no effective solution has been demonstrated to reduce the impact of it. And no saturation is observed in either water jet scheme or water line scheme previously.
Fig. 3. (a) Normalized THz peak amplitude as a function of the incident pulse energy. Red dot: water line position optimized under 0.4 mJ. Blue dot: water line position optimized under 2.8 mJ. (b) Schematic diagram of the relative position between the water line and the laser focal point under different pulse energy. (c) THz amplitude dependence on pump pulse energy for water lines with 0.11-mm, 0.20-mm and 0.39-mm diameters, respectively. (d) Lens position as a function of pump pulse energy. Blue dots represent experimental results and red line represents calculation results.
Since the water line scheme is extremely sensitive to the plasma position [48], the above discrepancy can be attributed to plasma displacement when we optimize the THz signal at different pump energies. Due to self-focusing effect in both air and liquid water, variable incident pulse energy leads to effective focal length change. Figure 3(b) schematically shows the displacement in the laser focal point with respect to the water line as the laser pulse energy varies. Yellow solid line defines as the laser beam path when the water line position is optimized for the highest THz peak amplitude. Red dashed line represents the optical axis of the laser beam. When laser pulse is attenuated to lower pulse energy, the focal point moves forward along the optical axis. Vice versa, the focal point moves backward along the optical axis. On the other hand, THz wave coupled out of water line is highly dependent on the relative position between the water line and the laser focal point. Considering the impact of the water line position with respective to plasma in the x-axis direction (perpendicular to the laser propagation direction), it is related to the THz wave coupling out of cylindrical surface of the water line, and the most critical issue is how to more efficiently couple the generated THz wave out of the cylinder (water line). Based on the dipole model proposed in Ref. [42], when the pump beam passes through the center of the water line, there is extremely weak THz radiation that can be coupled to the forward direction. Therefore, to make more THz radiation couple to the forward direction, the pump laser beam has to move away from the center of water line. The deviation of the pump beam from center of the water line has been experimentally obtained in the previous work done by Prof. X.-C. Zhang’s group in Ref. [48]. Their work is quite systematic, and so we didn’t re-perform further experiments on this. Nevertheless, during the optimization of the THz signal we also obtained optimal deviation for most efficient THz wave coupling is about 70% of the radius of the water line, independent of the diameter of water line. It is noteworthy that when the pump beam is set away from the center of the water line, the overall THz wave generation efficiency will be slightly dropped even though the detected signal is increased. In this case, likely, considerable amount of the THz radiation is trapped inside water line due to the total internal reflection along the water/air interface. Moreover, when the pump beam deviates from the center of the water line, the optical intensity at the focus is dropped at low pump energy due to the additional astigmatism before it gets saturated, compared to the case when the pump beam passes through the center of the water line. The variation trend of THz peak amplitude will be unpredictable if we simply change the incident pulse energy without further optimizing the relative position between the water line and the laser focal point. To obtain the intrinsic pump pulse energy dependence, we move the focusing lens along z-direction to compensate the focal point displacement caused by self-focusing effect in both air and inside the liquid water sample. In this condition, the variation trend of THz peak amplitude is independent with the initial pump pulse energy. As shown in Fig. 3(c), THz peak amplitude increases rapidly at lower pulse energy and tends to be saturated at higher pulse energy. The saturating pulse energy increases with the water line diameter, as the vertical dashed lines indicate. The saturating pulse energy is about 0.4 mJ for 0.11 mm, 0.8 mJ for 0.20 mm and 1.0 mJ for 0.39 mm-diameter water lines, respectively. Different from the linear result in Ref. [46], in our case, saturation effect can be observed when pulse energy is higher than saturating pulse energy. This phenomenon can be attributed to intensity clamping effect and consequently plasma density saturation in liquid water. The intensity clamping effect limits maximum laser intensity inside the plasma, and subsequently, plasma density [52], thus limiting the peak amplitude of generated THz wave. It is worth noting that the pump pulse energy dependence of water lines with different diameters were tested under their optimized pulse durations. Since the saturation effect is attributed to intensity clamping, the increase in saturation pulse energy is partially associate with the increased optimal pulse durations.
In order to give a clearer picture about the impact of self-focusing effect, we record the focusing lens position after compensating the focal point displacement under different pump energy for the water line with a 0.20-mm diameter. Also, we carry out a simplified calculation on the self-focusing induced focal point displacement. In the calculation, the lens is calculated to be at different position along z-axis to counteract the self-focusing effect in water and air, thus keep the focal point in water fixed under different pulse energy. The formula we used to trace the beam propagate is shown below:
In order to prove that intensity clamping in plasma is the origin of THz emission saturation, a measurement of laser intensity inside plasma is necessary. However, due to the high laser intensity inside plasma, precise measurement of the intensity distribution is difficult. An alternative and independent way to determine relative intensity inside the plasma can be achieved by measuring the pump pulse spectral broadening. In the work done by Prof. S.L. Chin’s group [40], the spectrum broadening for laser pulse in water can be written as:
$f(t )\; $ is the temporal profile of the laser pulse, and ${I_0}$ is the peak intensity. The first term on the right represents a frequency shift due to nonlinear refractive index of water, and the second term is associated with plasma generation via multiphoton excitation (m=5 for 1.55eV photon energy) which causes a blue-shift of the entire spectrum only. Thus, the frequency blue shift $\varDelta {\omega _ + }\; $ is expected to be dominated by the second term in the equation when the peak intensity is getting higher. In this case, the frequency blue shift is directly in correlation with the peak intensity: $\varDelta {\omega _{Max + }} \propto I_0^m.\; $Since the $\varDelta {\omega _{Max + }}\; $ essentially depends on the peak power intensity, the saturation of $\varDelta {\omega _{Max + }}\; $ occurs when the laser intensity inside plasma is saturated. Because the absorption near 800 nm is very low (absorption coefficient is much less than 0.1/cm [53]), we concluded that liquid water absorption near 800 nm can be neglected and won’t affect the spectrum broadening saturation when the diameter of the water line is less than 1 mm. Thus, $\varDelta {\omega _{Max + }}$ saturation at high laser pulse energies can be therefore used as an indication of the saturated peak intensity. To verify the peak intensity inside the plasma in our experiment is saturated. A fiber-coupled spectrometer (Ocean Optics USB2000+) is employed to monitor the laser pulse spectrum as the laser pulse energy is increased. The probe of the spectrometer is placed along x-axis after a short-pass filter and a collecting lens, as shown in Fig. 1(a). The spectrometer records the broadened spectrum under different pump laser pulse energy when the water line position is optimized to the maximum THz peak amplitude as Fig. 4(a) shows. The black line represents the spectrum of initial pump beam and the colored line represent the broadened spectra from plasma. A saturation effect of spectrum broadening can be observed from the short wavelength side, as indicated by the blue dots in Fig. 4(b), $\varDelta {\omega _{Max + }}$ increases rapidly at low laser energy and tends to be saturated at high laser energy. Our results agrees well with that those reported in Ref. [40], which verifies that intensity clamping or plasma density saturation is the main mechanism for THz peak electric field saturation since the generated THz peak amplitude highly depends on the laser intensity or plasma density.Fig. 4. (a) Broadened spectra from plasma in water line under different pump energy. The black line represents the spectrum of initial pump beam and the colored line represent the broadened spectra from plasma. (b) Maximum blue shift of the broadened spectra as a function of the pump energy.
5. Conclusion
We systematically investigate THz wave emission from water lines under excitation of sub-picosecond laser pulse. Our experimental results on the water-line-diameter dependence show that the water line with a diameter of about 0.1- 0.20 mm generates the highest THz wave peak amplitude and a THz frequency red shift is observed when the water line diameter increases. An intrinsic pump pulse energy dependence is obtained by compensating the focal point displacement caused by self-focusing effect. As the laser pulse energy increases, saturation in THz peak amplitude is observed and can be explained by intensity clamping and subsequently plasma density saturation inside the plasma. An independent measurement of laser spectrum broadening further verify the intensity clamping effect plays a major role in preventing THz peak amplitude from further increasing as the pump laser pulse energy increases, which has never been reported. Our investigation may help to further optimize the scheme of THz wave generation from liquid samples and could contribute to better understanding the Kerr nonlinearity effects in the THz generation process in liquids.
Funding
National Natural Science Foundation of China (61875151); National Key Research and Development Program of China (2017YFA0701000).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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