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Abstract
THz emission in air under the irradiation of a pair of tightly-focused femtosecond laser pulses (800nm, 35fs) with nanosecond time delay and micro-meter spatial offsets is studied with polarization-sensitive THz time-domain spectroscopy and time-resolved imaging. The pre-pulse irradiation induces air-breakdown at its focus, which results in the expansion of shockwave front traveling outward. When the main pulse irradiates such shockwave front far from the pre-pulse focus with nanosecond delay, THz emission intensity was enhanced up to ∼13-times and its linear polarization was aligned along the line between the two focus positions of the pre- and the main pulses which is parallel to the expansion direction of the shockwave front. Asymmetric density profiles of the shockwave fronts prepared by the pre-pulse irradiation define the polarization of THz emission. Mechanisms are discussed from the viewpoint of electron diffusion in such asymmetric density profiles.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
THz science and technology have been expanding their fields in recent years [1,2]. One direction of such advancements is in the field of nonlinear phenomena [3,4] with intense THz sources. One major laser-based THz emitter is so far based on LiNbO$_3$ crystals [5]. However, under intense femtosecond laser irradiation, solid materials are irreversibly damaged, therefore further intensity increase of THz radiation becomes limited. On the other hand, hydrodynamic targets such as gases/clusters and liquids [6–14] are naturally free from such limitation due to laser breakdown and can be supplied to laser focus in continuous flow.
Studies on THz emission mechanisms from gas targets have been carried out and intensity enhancements of THz emission are reported, especially under two-color/double pulse excitation conditions since the early reports [15–17]. Among them, two-color excitation with the fundamental and the second harmonic with a zero time delay (phase-matched) is expected to effectively drive non-linear processes of four-wave mixing by changing the optical excitation conditions; with pressure dependence in Ar below 1-bar [18] or in CO$_2$ below 10-bar [19], chirp effects in air [20], various gas targets such as rare-gases, nitrogen, oxygen, and carbon dioxide [21], numerical simulations of wave mixing [22]. A further study with coherent three-color excitation was also reported for THz emission in air [23]. Though the most of the studies were usually made with the excitation laser at the wavelength of 800 nm, there is also a study with the wavelength longer at $3.9\,\mu$m and its second harmonic [24]. As for the double pulse excitation with a single color, there are much less studies if compared with those for the two-color excitation. Y. Liu, $et$ $al.$ reported the angular and polarization properties of THz emission from two long plasma columns in air working as a transmission line [25]. K. Mori, $et$ $al.$ studied THz emission from Ar cluster in a vacuum chamber on the effects of the incident pulse width and the delay time up to 20 ps [26]. J. -M. Manceau, $et$ $al.$ reported a THz emission with double pulse excitation with spatial offset at 2 mm along the laser propagation direction ($\Delta z$) [27]. K. Mori, $et$ $al.$ also studied THz emission from Ar cluster in a vacuum chamber under double pulse excitation with spatial offsets on the vertical plane to the laser propagation (on x-y plane, $\Delta x$ and $\Delta y$) and with delay time up to 500 ps [28].
Unlike the established approach reported so far by controlling the excitation E$-$field conditions such as the two-color excitation methods described above, in this paper, we scientifically focus our interests on the density profile at the target for the main pulse irradiation. Technically, we study THz emission from air under double pulse irradiation conditions at the single color (wavelength of 800 nm) with nanosecond time-delay up to 10 ns. Not only conventional coaxial irradiation of the two pulses, double pulse irradiation but with spatial offsets ($\Delta x$ and $\Delta y$) up to $50\,\mu$m for the focus positions are well examined. Under such irradiation conditions with spatio-temporal offsets, THz emission with enhanced intensity and aligned polarization is clearly observed. Mechanisms are discussed considering the interaction of the main pulse and the supersonically-expanding shockwave front with asymmetric density profiles which are prepared by the pre-pulse irradiation.
2. Methods
Details of the experimental setup are described elsewhere [29] and are briefly outlined next (Fig. 1). A pulsed femtosecond laser ($t_p = 35$ fs, transform-limited, $\lambda = 800$ nm, 1 kHz, Mantis, Legend Elite HE USP, Coherent, Inc.,) was used and the output pulses were split into the pre-pulse (0.2 mJ/pulse) and the main pulse (0.4 mJ/pulse). THz emission was induced by the main pulse irradiation into air (along with z-axis as in Fig. 1) with time-delay, $\Delta t$, after the pre-pulse irradiation by an off-axis parabolic mirror (1-inch diameter, focal length $f$ = 50.8 mm, 47-097, Edmund Optics). Under the focusing conditions with effective numerical aperture (NA) at 0.125, the laser focus area and its depth was estimated to be about $8\,\mu$m in diameter and $120\,\mu$m, respectively [29]. Spatial offsets along the x- and y-axes, $\Delta x$ and $\Delta y$, were applied to the pre-pulse irradiation. Steering mirrors for the pre-pulse alignment were automatically controlled by a piezo-transducer system (POLARIS-K2S2P, KPZ101, Thorlabs) to change the pre-pulse focus position with a micrometer precision. THz time-domain spectroscopy (THz-TDS) with a $\langle 110\rangle$-oriented ZnTe crystal (1-mm thick, Nippon Mining $\&$ Metals Co., Ltd.) [8,9,29] was performed for THz measurements toward the directions along the z-axis (co-axial) and the x-axis (from the side to the laser incidence). THz polarization measurements were carried out with wire-grids following the standard procedure [30–32]. This experiment was carried out with lock-in detection, so that the effective repetition of the laser excitation is at 0.5 kHz. During the THz-TDS experiments with the spatial offsets and the time-delay for the pre-pulse, the main pulse and the probe for THz-TDS were never re-aligned after they were once well aligned.
Fig. 1. Schematic diagram of the experimental setup with temporal ($\Delta t$) and spatial offsets ($\Delta x$ and $\Delta y$) for the pre-pulse irradiation.
Time-resolved shadowgraphy and time-integrated luminescence imaging were also carried out from the laser focal region along the x-axis (from the side to the laser incidence) and the y-axis with objective lenses (M Plan Apo 10$\times$, MITUTOYO) and CMOS cameras (Blackfly S USB3, FLIR Systems, Inc.). The shadowgraphy was utilising the pre-pulse and a white light continuum ($\sim 1$ ps, 580 $\pm$ 30 nm selected with color filters, as a strobe light) converted from the main pulse with a 10-cm-long water cell. The back-illumination with the white light continuum was along the x-axis as shown in Fig. 1. In this configuration with the shutter-less camera, since the breakdown luminescence is too strong, the breakdown luminescence from the pre-pulse focus was inevitably captured in addition to shadowgraphs of the expanding shockwave front. The luminescence imaging was with both of the pre- and main pulses, which visualized the interaction of the main pulse with the air-breakdown induced shockwave expansion by the pre-pulse. In this mode of image acquisition, all the emission in broad-band spectra by the two-pulse irradiation was time-integrated. All the experiments were carried out at the normal conditions; in air under atmospheric pressure (1 atm) and at room temperature (296 K) with humidity at 40-50%.
3. Results
Figure 2 shows the polarization status of THz emission from air under the double pulse irradiation conditions when it is observed in the direction along the z-axis (co-axial). In panel (a), the delay time, $\Delta t$, is at 1.5 ns and the laser polarization for the pre- and main pulses are linearly-vertical (y-pol.) and linearly-horizontal (x-pol.), respectively, while for (b), $\Delta t$ is at 4.7 ns and the laser polarization for the pre- and main pulses are reversed as x-pol. and y-pol., respectively.
Fig. 2. Polarization status of THz emission dependent on the pre-pulse offsets from air under the double pulse irradiation condition. The intensities of the pre- and the main pulses are 0.2 mJ/pulse and 0.4 mJ/pulse, respectively. Horizontal and vertical axes, $\Delta x$ and $\Delta y$, represent the spatial offsets of the pre-pulse irradiation, respectively. (a) The delay time, $\Delta t$, is fixed at 1.5 ns and the laser polarization of the pre- and the main pulses is vertically-linear (y-pol.) and horizontally-linear (x-pol.), respectively. (b) $\Delta t$ at 4.7 ns and the laser polarization of the pre-pulse and the main pulse is x-pol. and y-pol., respectively. The inset shows the THz emission spectrum as |Ey| obtained by Fourier-transform of the TDS signal at ($\Delta x$, $\Delta y$) = ($0\,\mu$m, $24\,\mu$m).
THz intensity increases as the pre-pulse offset becomes larger up to a certain point and it decreases as the offset extends further. Such THz intensity peak also shifts from $\Delta y$ = $13\,\mu$m for $\Delta t$ = 1.5 ns to $\Delta y$ = $24\,\mu$m for $\Delta t$ = 4.7 ns. Furthermore, regardless to the incident laser polarization, THz polarization shows its stretched characteristic and radial-nature when the offsets are at the appropriate for each delay time. THz polarisation is preferentially aligned in the direction defined by two offsets $( \Delta x,\; \Delta y)$. Indeed, when the spatial offset is at $( \Delta x,\; \Delta y)$ = ($10\,\mu$m, $10\,\mu$m) or ($16\,\mu$m, $16\,\mu$m), diagonally-stretched linearly-polarization of THz emission is clearly observed as shown in Fig. 2(b). This indicates that THz polarization is aligned to the direction along the line connecting the focus points of the pre- and the main-pulses. When THz emission is observed from the side to the laser incidence along the x-axis, under the same laser irradiation conditions, no apparent THz emission is observed (not shown). This indicates that the experimental condition is completely different from the case with an objective lens with much higher numerical aperture (NA=0.85) [33] where the charge separation along the laser incident axis due to ponderomotive forces is considered as the main THz emission mechanism.
Figure 3(a) shows THz polarization for the pre-pulse vertical offset with the fixed horizontal offset at 0 $\mathrm{\mu}$m, ($\Delta x$, $\Delta y$) = (0 $\mathrm{\mu}$m, $\Delta y$), at different delay times. A similar tendency of the vertically-aligned THz polarization is observed even at the longer delay time at 9.7 ns. Fig. 3(b) shows the square of peak-to-peak electric field intensity of THz emission, $|{\boldsymbol{E}}_{\textrm{peak-to-peak}}| ^2$, along the major axis of slightly-elliptic trajectories on the projection of the electric field vector to the $E_x-E_y$ plane as shown in the inset of Fig. 2(a), as a function of the pre-pulse vertical offset. As the delay time increases from 1.5 ns to 4.7 ns and 9.7 ns, the position of the vertical offset for the highest THz emission intensity shifts radially-outwards from 13 $\mathrm{\mu}$m to 24 $\mathrm{\mu}$m and 33 $\mathrm{\mu}$m. The highest intensity observed at $\Delta t$ = 9.7 ns is at least 13-times higher than the case under the single-pulse excitation only with the main pulse. Considering the report on the energy conversion efficiency from the laser at 800 nm to THz emission with a ZnTe$\langle 110\rangle$ crystal at 1.25x10$^{-5}$ [34], when we compare THz intensities from the ZnTe crystal and the shockwave with the main pulse irradiation at 0.4mJ/pulse, the photon-number-based conversion efficiency under the double pulse irradiation to the shockwave front can be estimated 2.1x10$^{-5}$. The horizontal dotted lines in Fig. 3 represents the position of the shockwave front observed in the shadowgraphy shown in Fig. 4 for each delay time. The radial shockwave expansion is clearly observed (Fig. 4(a)) with the initial velocity of 6.45 km/s at 1.5 ns, which corresponds to Mach 18.8 (Fig. 4(b)). Apparently, the peak position for the highest THz emission intensity for each delay time corresponds to the position of the shockwave front.
Fig. 3. (a) Polarization status of THz emission from air which is dependent on the vertical offset of the pre-pulse irradiation (the horizontal offset, $\Delta y$ is fixed at 0 $\mu$m) under the double pulse irradiation condition with different delay times. The laser polarization of the pre-pulse and the main pulse is vertically-linear (y-pol.) and horizontally-linear (x-pol.), respectively. (b) The intensity of $|{\boldsymbol{E}}_{\textrm{peak-to-peak}}| ^2$ shown in the inset of Fig. 2(a) as a function of the vertical offset, $\Delta y$, at different delay times. The horizontal dotted lines represent the position of shockwave front for each delay time estimated from the shadowgraphy shown in Fig. 4. The vertical dotted line in red represents THz emission intensity under the single pulse irradiation only with the main pulse. The arrows show the shockwave front region with asymmetric profile of THz emission generation.
Fig. 4. (a) Time-resolved shadowgraphy in air with the pre-pulse (y-pol.) irradiation at 0.2 mJ/pulse without the main pulse. The area indicated by a red dotted line indicates the estimated focal volume of the pre-pulse. The polarization of the white light continuum as the back illumination is mainly parallel to z-axis. The breakdown luminescence from the pre-pulse focus was inevitably captured in addition to shadowgraphs of the expanding shockwave front since the breakdown luminescence is too strong. (b) The distance of the shockwave front from z-axis and the calculated instantaneous expanding velocity (Mach number) as a function of the delay time. (c) Estimated density, $\rho$, and pressure, $P$, at the shockwave front when the pre-pulse intensity is at 0.2 mJ/pulse.
4. Discussion
The results described above clearly indicate that the characteristics of THz emission are not directly defined by the polarisation of incident laser pulses, while the shockwave front plays a defining role to the THz intensity enhancements and its polarization. This consideration is further supported by the experimental results in imaging. Fig. 5 shows time-integrated luminescence images with different pre-pulse vertical offsets while the delay time is fixed at 9.7 ns; bright spots and shadows as shown in Fig. 5(b) are mainly observed from the positions where the main pulse comes across the shockwave front.
Fig. 5. (a) Overlaid images of time-integrated luminescence from the focuses of the pre-pulse and the main pulse. The two images were taken separately when only the pre-pulse or the main pulse was present, and then superimposed. (b) Time-integrated luminescence images of the laser focus from the side and their schematics when the delay time, $\Delta t$, is 9.7 ns. The upward arrows in thick black represent the total current, therefore the total electron diffusion goes to the other direction. The black dots in the schematics represent the cross-section between the main pulse and the shockwave front. (c) Time-integrated luminescence images of the laser focus along y-axis. Horizontal dotted lines represent the optical path of the main pulse (z-axis). Scale bars are 100 $\mathrm{\mu}$m.
One characteristic observed in Fig. 3(b), especially at $\Delta t$ = 9.7 ns, is that THz emission intensity has longer and shorter tails for the the smaller and the larger offset with the peak at 33 $\mathrm{\mu}$m respectively, which is indicated by the upward and downward arrows in green in Fig. 3(b). Fig. 5(b) shows a dominant luminescence centered on the focal region of the main pulse for the vertical offset $\Delta y = 20\,\mathrm{\mu}$m. Interaction between the shockwave front and the main pulse is not expected when the the vertical offset is larger than 46 $\mathrm{\mu}$m. The bright emission is localised in the regions of the cross section of the main pulse focus region and the shockwave front expanding from the pre-pulse focus (see the schematics of the interaction region in the inset). For the very initial process right after the electron ejection at the shockwave front by the main pulse irradiation toward THz emission, where the contribution of positive ions are negligible, we discuss the mechanisms as follows.
4.1 Transient electron diffusion in asymmetric profile
The discussion above suggests that the interaction of the main pulse with the shockwave front is crucial for the enhanced THz emission with the linearly-aligned polarization. As shown in Supplement 1, THz emission spectra at different delay times have similar nature as long as the main pulse irradiates the shockwave front. This strongly indicates that the related mechanisms of THz emission are the same even at different delay times. The main pulse interaction with such shockwave front with high density, when the main pulse is tightly-focused, surely results in air-breakdown leading to plasma formation at the shockwave front. As shown in Supplement 1.2, the electron density $n$ in plasma is comparable to the molecular density of the air or multiplied through non-linear processes of the incident main pulse. Since the density of the shockwave front is about 5-6 times higher than that of the ambient air as shown in Fig. 4(c), the plasma with electron density $n_e \sim 2 \times 10^{20} \,\textrm{cm}^{-3}$ and electron temperature $T_e\sim 100\,\textrm{eV}$ is induced when the shockwave front is irradiated by the main-pulse. The electron diffusion constant $D = k_B T_e / m \gamma _{ei}$ is estimated to be $\sim 100\,\textrm{m}^2/s$ where $\gamma _{ei} = n \sigma _{ei} v_e$ is the electron-ion collision frequency, $\sigma _{ei} = ( 1/ 4 \pi \epsilon _0) ^2 \pi e^4/ m^2 v_e^4$ is the electron-ion collision cross-section, and $v_e = \sqrt {2 k_B T_e/m}$ is the electron velocity where $k_B$, $\epsilon _0$ and $e$ are the Boltzmann constant, the permittivity of vacuum, and the elementary charge, respectively. The width of the boundary between the shockwave front and the outer ambient air is expected to be the order of mean free path of the molecules that is $\sim 70\,\textrm{nm}$ for the ambient air. Since the molecular density $\rho$ of the shockwave front is about $6 \rho _0$ at maximum where the density of the outer ambient air $\rho _0$ is about $3 \times 10^{19} \,\textrm{cm}^{-3}$, the change in the molecular density at the boundary is in order of $\sim 10^{20} \,\textrm{cm}^{-3}$. As shown in Supplement 1.2, the electron density $n_e$ of the plasma induced by the main pulse irradiation is comparable to the air density or higher, which suggests that the change in $n$ at the boundary is in the same order as the air ($\sim 10^{20} \,\textrm{cm}^{-3}$) or higher.
When there is an electron density gradient at the shockwave front, electron diffusion naturally takes place. This leads to induction of transient current;
Fig. 6. (a) A schematic diagram of the density (mass density of air, electron and ion plasma) $n$ profile around the shockwave front induced by the pre-pulse irradiation at shorter and longer delay times. When the pre-pulse offset is positive ($\Delta y$ > 0) or negative ($\Delta y$ < 0), the main pulse irradiates the shockwave front traveling downward or upward, respectively. (b) The THz-TDS waveforms of y-component (Ey) when the delay time between the pre-pulse and main pulse irradiation is at 1.5 ns. The spatial offset for the pre-pulse irradiation is ($\Delta x$, $\Delta y$) = ($0\,\mu$m, $-13\,\mu$m) or ($0\,\mu$m, $+13\,\mu$m). The datum for ($\Delta x$, $\Delta y$) = ($0\,\mu$m, $-13\,\mu$m) is reproduced from the inset of Fig. 2
In Fig. 5(b), the positions of the laser focus and the shockwave front at $\Delta t = 9.7\,\textrm{ns}$ are schematically shown. On the basis of the discussions above, the thick black arrows in Fig. 5(b) display the position and the direction of the total transient diffusion current that is perpendicular to the shockwave front. When the pre-pulse offset is 33 ${\mu}\textrm{m}$, the direction of the current is perpendicular to the z-axis for THz detection as shown in the middle panel of Fig. 5(b), which results in the maximum intensity of THz emission as observed in Fig. 3(b). As the pre-pulse offset decreases from 33 ${\mu}\textrm{m}$, the direction of the current is tilted along the curvature of the shockwave surface as shown in the left panel of Fig. 5(b). The tilt of the current leads to the reduced intensity as observed in the pre-pulse offset dependence of THz emission as shown in Fig. 3(b).
Another characteristic which should be pointed out is that the peak intensity of THz emission decreases as the delay time becomes shorter (Fig. 3(b)); 8.5, 7.0, and 5.0 for $\Delta t$ at 9.7, 4.7, and 1.5 ns, respectively. This seems to be contrary to the expectation based on the fact that the peak density at the shockwave front increases with decreasing the delay time since the air density for ionization increases as shown in Fig. 4(c). When the delay time is short, the profile can be sharp and steep on the both sides of the shockwave front as shown in Fig. 6(a). The diffusion currents inducing THz emission flow toward the outside and the inside of the shockwave front within the focus of the main-pulse. These two current components compensate each other, which results in the reduction of the THz emission intensity at the shorter delay time. As the delay time increases, such a density profile becomes mild but asymmetric along the distance, $\boldsymbol {r}$. Then, the electron diffusion current toward the outside of the shockwave front becomes dominant, which results in the higher intensity of THz emission though the peak density is less at 9.7 ns than at shorter delay time.
The discussions so far can be re-considered from a viewpoint of well-accepted discussions in THz emission from semiconductors (Supplement 1.3). In photo-excited semiconductors, THz emission is induced by sub-picosecond transient current described as in Eq. (1), that is called photo-Dember current [37–39]. The diffusion constant of such electron in semiconductors is typically $\sim 1 \textrm{m}^2/s$, while the constant in air at the shockwave front is estimated to be much higher at $\sim 100\,\textrm{m}^2/s$ as aforementioned. Considering the width of the boundary at the shockwave front, the value of the spacial gradient in $n_e$ in Eq. (1) at the shockwave front can be up to $\left |\partial n ( \boldsymbol {r}) / \partial \boldsymbol {r} \right |\sim 10^{25} \textrm{cm}^{-4}$. With this value and the diffusion constant estimated above, the electron diffusion in this study considered as transient current is sufficient for the THz emission observed. Furthermore, the phase flip in THz-TDS as shown in Fig. 6(b) can be considered as "lateral photo-Dember currents" in solid samples [37]. In cases of gases or fluids such as air or water, however, the density profiles to be excited by the main pulse for THz emission can be modified by the irradiation of multiple pre-pulses with controlled spatio-temporal offsets. This can be an advantage as a versatile THz source with tailored polarization statuses.
4.2 One consideration on ponderomotive force
So far, there have been papers on THz wave emission from air with a single femtosecond laser pulse in single color though the numbers are quite limited if compared with those on double pulses in two different colors for optical rectification. Discussions have been done mainly with the concepts of ponderomotive action/wake-field acceleration [33,40–42] or Cherenkov radiation [43,44] (especially for higher laser irradiation conditions) with experimental results such as the conical profile of THz emission with z-polarization [45]. Discussions in the previous papers have been considering air with homogeneous density distribution. Here, we discuss the possibility of ponderomotive action on x-y plane for the main pulse interaction with the shockwave front with asymmetric density profile along its expansion direction caused by the pre-pulse irradiation (Fig. 7).
Fig. 7. Schematic diagram of the ponderomotive action in respect to asymmetric air density change with the main pulse irradiation (a) outside, (b) on, and (c) inside of the shockwave front. (d) THz TDS from air at $\Delta t$ = 9.7 ns with the main pulse irradiating across the shockwave front.
With this asymmetric spatial profile of the air density at the shockwave front, electron ionization is effectively induced in the rising slope of the incident main pulse along z-axis. The number of electrons has the similar (or steeper due to multi-photon ionization) asymmetric density profile along the y-axis to that of air. After the effective ionization, the electrons generated start to escape from the volume of the intense laser to the outside on the x-y plane due to ponderomotive action. Then the return current is induced because of the positive charge left at around the shockwave front along z-axis. When the main pulse is irradiating right on the shockwave front as shown in Fig. 7(b), the number of electrons generated through ionization is higher at the top half (in red, inside of the shockwave front) than at the bottom half (in blue, outside of the shockwave front) due to the asymmetric air density profile. This finally causes higher population of the electron return current from the inside of the shockwave front. This electron trajectory is schematically shown with the thick red and the thin blue arrows. On the other hand, when the main pulse irradiates the inner part of the shockwave front as shown in Fig. 7(c), the number of electrons generated is higher at the bottom half than at the top half, which results in higher population of the electron return current from the outside of the shockwave front. This hypothetical analysis based on ponderomotive action may indicate that the resultant THz emission signal should show its phase flip depending on the main pulse irradiation positions at around the shockwave front. However, the data set shown in Fig. 7(d) does not show such phase flips. Therefore, the ponderomotive action does not play the major role for THz emission this time.
5. Conclusion
We show THz emission control in terms of its intensity and polarization (linear) by shockwave front/plasma with asymmetric density profiles prepared by the tightly-focused pre-pulse irradiation. In air, the photon intensity of THz emission was enhanced 13-times at maximum if compared with the single pulse irradiation. More advanced control of THz emission has been also examined with a water flow for circular-polarization under the similar conditions of double pulse irradiation [29]. With appropriate spatio-temporal offsets, in the case of water, THz emission intensity is also enhanced 1500-times. This corresponds to the photon-number-based conversion efficiency from the laser to THz at $7.1\times 10^{-3}$, while the efficiency in the case of air under the double pulse irradiation is $2.1\times 10^{-5}$. These studies indicate that manipulation of such air/plasma density profile controls the direction of the instantaneous electron motion. Further control can be envisaged by the use of multiple pre-pulses with different spatial offsets (and time-delays) to control the spatial density distribution at shockwave front. Additionally, similar experiments with different gases such Ar are currently under preparation.
Funding
Japan Society for the Promotion of Science (JSPS) KAKENHI (20K05371); Ministry of Science and Technology, Taiwan (107-2112-M-001-014-MY3, 110-2112-M-001-054).
Acknowledgments
T. N. is grateful for the support by JSPS KAKENHI Grant Number 20K05371. K. H. is grateful for the supports by the Ministry of Science and Technology (MOST) of Taiwan (107-2112-M-001-014-MY3, 110-2112-M-001-054), the Cooperative Research Program of “Network Joint Research Center for Materials and Devices”, Nanotechnology Platform (Hokkaido University), and the Collaborative Research Projects of Laboratory for Materials and Structures, Institute of Innovative Research (Tokyo Institute of Technology). K. H. also acknowledges Prof. Saulius Juodkazis (Swinburne University of Technology, Australia) for his discussion on this project. K. H. also acknowledges the Japan Science and Technology Agency (JST) PRESTO (Precursory Research for Embryonic Science and Technology) Program (SAKIGAKE, Innovative use of light and materials/life) for its supports on the original project on X-ray/THz wave simultaneous emission, “Ultrawide band light conversion by controlling structures of microdroplets and ultrashort laser pulse (2009-2013)” and for the laser facilities for the current project.
Disclosures
All other 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.
Supplemental document
See Supplement 1 for supporting content.
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