Spatio-temporal control of THz emission

Intense THz sources are expected for further progresses in nonlinear THz science and technology. Liquids like water are durable and continuously-reusable under intense laser irradiation for THz emission though such studies on THz emission from water targets are so far limited. Polarisation fine control of THz emission is demonstrated with a tilted micro-thin water flow by the irradiation of two cross-linearly-polarised femtosecond laser pulses (800nm, 35fs, transform-limited) with spatio-temporal offsets. With an optimized horizontal offset at ∼11 μm between the ∼8 μm focal spots and time delay at 4.7ns, circularly-polarised THz emission is obtained with its intensity enhancement more than 1,500-times if compared with the single pulse irradiation. It is shown that the photon-number-based efficiency from the laser to THz at 7.1 x 10−3 is achieved with the optimisation of the double pulse irradiation. Polarisation-resolved THz time-domain spectroscopy and time-resolved shadowgraphy imaging reveal that the circularly-polarised THz emission originates from the focal volume in front of the water flow. Coupling between a shockwave due to air-breakdown and water ablation-mediated mass transport by the pre-pulse with a laser wake-field along the optical path of the main pulse is responsible for the point-like single-cycle THz emission. Intense irradiation of flowing liquid has emerged as a means of generating THz emission with fine control. Here, a double-pulse THz generation scheme is demonstrated that relies on spatial and temporal off-sets of a pre-pulse to control both polarization and emission intensity.

I ntense THz sources are expected for further progresses in nonlinear THz science and practical implementation of nonionizing radiation in sensing and communications 1 . Solid crystalline-based sources under laser irradiation have an inherent limitation due to the polarisation (pol.) and orientation sensitivity as well as due to material breakdown especially for intense laser excitation for the developments of intense THz sources. On the other hand, an intense laser irradiation to liquids is an emerging promising technique for THz emission [2][3][4][5][6] . It has a possibility to tailor compositions of liquids and to explore conditions of different plasma densities from under-dense to dense and different temperatures even for simultaneous hard X-ray emission 7 . Especially appealing is the capability to refresh the irradiation spot on a liquid flow/jet for a stable THz or X-ray emission source. It was empirically found that water-based THz emission shows intensity enhancements up to 10 3 times when laser-pulse pairs with nanosecond delay are applied 8 . This prompted a detailed experimental study of this phenomenon. Spectral characterisation of light emission, light localisation and shockwave formation studied by imaging, and polarisation-resolved timedomain spectroscopy (TDS) revealed detailed picture of the lightmatter interaction which realises a renewable pulsed (on demand) point-like THz source as described in this study.
Such studies on THz emission from laser-induced plasma are partly summarized in a review paper 9 especially in cases with gas or solid targets. On fine control of THz polarisation, there are some experimental trials with two-color laser-induced plasma with gas targets. With linearly-polarised two-color lasers, linearlypolarised THz emission is finely controlled in its angle of the linear polarisation by the relative phase between the two lasers, technically by the position of BBO crystal and its rotation angle 10 . Under the similar experimental condition but with circularly-/ elliptically-polarised two-color lasers, such THz polarisation control is attained by keeping the THz amplitude constant 11 . Afterward, another trial with external double helix electrodes is also reported 12 , where elliptically-polarised THz emission is obtained. Theoretical studies on THz polarisation control with magnetized plasma are also reported 13,14 . These reports so far are with gas targets and the concept related is mainly on the optical control/manipulation of electron trajectories under intense laser irradiation conditions, while no reports with a concept of spatiotemporal control are reported.
Here, a concept on fine-control of THz emission with the prepulse offsets under double pulse excitation conditions is described (Fig. 1). With nanosecond-temporal and micrometer-spatial offsets of the pre-pulse irradiation under the double pulse excitation to a tilted water flow, THz emission can be finely controlled in its intensity and polarisation. This geometry verifies the theoretically-predicted coupling in under-dense gaseous plasmas at~10 17 W cm −215 . As one possible hypothesis, we have discussed a mechanism on the basis of the transverse (t) plasma density gradient ∇n ðtÞ e (water ablation by the pre-pulse irradiation) which is coupled with the longitudinal (l) electron velocity in the Langmuir plasma wave v ðlÞ p (of the main pulse). This mechanism generates circular electron current ½∇n ðtÞ e v ðlÞ p , which induces circularly-polarised THz emission.

Results
Experimental results of the imaging and spectral characterisation of the focal volume where the laser pulse interaction with the water flow and ablated plume takes place is presented in the dedicated sections. Polarisation analyses using TDS allowed us to reveal polarisation and to pinpoint the location of THz emission. Details of the experimental conditions are presented in Experiments Section.
Single pulse excitation of water flow. The polarisation status of THz emission under the main pulse irradiation is shown in Fig. 2a. The polarisation of the incident main pulse is horizontally-linear (x-pol. as usual, p-pol. to the water flow), circular, or vertically-linear (y-pol., s-pol. to the water flow). Though a circular-component is slightly observed when the main pulse is circularly-polarised, but even then, the resultant THz emission is dominantly horizontally-linearly polarised.
Time-integrated luminescence images under such irradiation condition are shown in Fig. 2b; blue emission components and a red spot are clearly observed. The component indicated by the light blue arrow is due to air-ionization at the tight laser focus since such emission is also observed even in air without the water flow. UV-visible emission spectroscopy also confirmed emission peaks of atoms and ions such as oxygen or nitrogen 16 at different ionisation states. Another blue component indicated by the dark blue arrow is due to laser ablation, ejection of ionised water into ablation plume from the water flow. This component is always vertical to the water flow with different laser incident angles as shown in Supplementary Fig. 1. Distinguished line emission from hydrogen shown in Fig. 2c is a signature of water breakdown. The red spot is at the tight laser focus due to laser-plasma on the flow surface; the effective laser focus size on the water flow can be estimated from this image to be 8 μm at largest. The emission spectrum shown in Fig. 2c indicates that the incident main pulse is blue-shifted due to self-phase modulation (SPM) by the selfgenerating plasma 17,18 , which is usual in the case of hard X-ray emission from a water flow 19 , while such SPM in the case only with air is shown in Supplementary Fig. 2, Supplementary Note 1. This blue-shift is an indication of the laser-plasma coupling, which is essential feature at the used 1 − 10 PW cm −2 intensities. The temporal frequency shift ω(t) = ω 0 + α S t due to SPM is defined by the nonlinear refractive index of the medium n 2 , interaction length L, and the laser pulse intensity I l , and duration t p as α S ¼ 4πLn 2 For typical values in this experiment L = 100 μm, t p = 40 fs, I l = 10 PW cm −2 and Δω 0 /ω 0 = 10% (Δλ = 80 nm), the effective value of n 2 = 60 × 10 −20 cm 2 W −1 in the region of the pre-pulseinduced plume, which is almost an order of magnitude larger than the typical n 2 = 8 × 10 −20 cm 2 W −1 of air at 800 nm 17 Fig. 1 A concept of THz emission controlled by spatio-temporal offsets. A concept of THz emission control under the double pulse excitation with the pre-pulse spatio-temporal offsets and the tilted water flow. With such offsets, THz emission is finely controlled in its polarisation from linear to circular with its handedness (helicity); left-handed circular (LHC, clock-wise when it is observed from the later time to the earlier time) and right-handed circular (RHC, counter-clock-wise) for the transmission and the reflection sides (or vice versa), respectively. apparently change as shown in Fig. 3a; as the delay time between the two pulses increases, the polarisation status of THz emission dynamically changes to circular-polarisation from horizontallylinear under the single pulse excitation as shown in Fig. 2a. As a representative data set, THz polarisation when the delay time is at 4.7 ns is left-handed circular (LHC, clock-wise when it is observed from the later time to the earlier time) and right-handed circular (RHC, counter-clock-wise) for the transmission and the reflection sides, respectively. Furthermore, with the spatio-temporal offsets (Δx, Δy, Δt)= (11 μm, 0 μm, 4.7 ns), THz emission intensity increases 1500-times higher than in the single pulse irradiation as |E| 2 -intensity in discrete Fourier transform (DFT) spectra over the 0-3 THz region 8 . Considering the report on the energy conversion efficiency from 800 nm to THz with a ZnTe〈110〉 crystal at 1.25 × 10 −520 , the photon-number-based conversion efficiency under the double pulse irradiation can be estimated 7.1 × 10 −3 .  c Time-integrated luminescence spectra at the positions indicated by the arrow in (b) and the laser emission spectrum (in black). Sharp emission lines observed in air-ionization can be assigned to be from ions of oxygen, nitrogen, and argon 16 . The blue-shift of the emission from the focal spot is due to self-phase modulation of laser pulse. Spectral region at wavelengths shorter than ∼320 nm has lower sensitivity due to reduced transmission of a signal collection optics.
As shown in Fig. 3b, close look-up of the TDS signal waveforms shows their peaks delay as the delay time increases. Furthermore, THz emission spectra obtained as discrete Fourier transform of TDS signals generally show their peak shift toward the shorter frequency as shown in Fig. 3c; more precisely the shift is larger in the transmission side than in the reflection side. Figure 4a shows time-integrated luminescence images at different delay times only with air (without the water flow). The pre-pulse spatial offset is fixed at (Δx, Δy) = (11 μm, 0 μm). In the case only with air, though a stretched rugby ball-like blue emission is observed at the focus under the single pulse excitation, the spatial distribution of the blue emission, which reflects the intensity spatial distribution of the incident main pulse, shows distorted shapes under the double pulse irradiation with the prepulse with the spatial offset. As the delay time increases, the spatial distribution changes. This is due to the shockwave expansion from the volume of air-ionization due to the prepulse irradiation. The expansion velocity of the shockwave front is estimated to be about 7 km s −1 initially at Δt = 2.0 ns and it slows down to about 1 km s −1 at Δt = 14.7 ns as shown in Supplementary Fig. 3.
Under the double pulse excitation with the water flow shown in the time-resolved shadowgraphy shown in Fig. 4b and the luminescence images shown in Fig. 4c, another shockwave formation due to laser ablation by the pre-pulse excitation to the water flow (therefore this shockwave front carries ablation  Fig. 2a to circular. b TDS signals measured without the wire-grids under the double pulse excitation in the transmission side (normalized). As the delay time between the two pulses increases, the signal peak delays. The similar tendency of the peak shift is also observed for the reflection side. c THz emission spectra obtained from discrete Fourier transform of TDS signals (normalized). As the delay time increases, the emission spectra shifted towards the lower frequency (red-shift in wavelength).
plume of ionised/atomised water), its expansion in front of the flow, and formation of cavitation bubbles in the flow are clearly observed. In the shadowgraphy, a white dotted line and black dotted lines represent the focus of the incident main pulse on the flow surface and the expanding shockwave front, respectively. The expansion velocity of the shockwave front from the water flow surface is estimated to be about 8-10 km s −1 initially at Δt = 2.0 ns. In the luminescence image, the positions indicated by the arrows in orange and red match the shockwave front and the focus of the incident main pulse on the flow surface in the shadowgrapy, respectively. Figure 4d shows the emission spectra for the shockwave front (orange) and the flow surface (red) with the peak wavelength at 720 nm and 770 nm, respectively. These spectral shifts are due to the SPM-based blue-shift from the original laser pulse at 800 nm as discussed in the previous section. The results obtained indicate that the main pulse interacts with the shockwave front under this double pulse excitation condition and injects ablation plume/plasma, which is driving a wake-field at incident intensity of~10 16 W cm −2 . Even in the double pulse irradiation in air, luminescent halo is formed when ionised air is pushed from the side into the main-pulse (unpublished results). This injection from the side is an important aspect of THz emission from sub-wavelength focal region of~100 μm length.
Double pulse excitation: dependence on the pre-pulse spatial offset. Experiments were extended to reveal the effects of spatial offsets between the two pulses for control of THz emission. Figure 5 shows the results of TDS measurements with the wiregrids for the transmission (a) and the reflection (b) sides. The delay time between the two pulses is fixed at 4.7 ns. In the transmission side, as the horizontal offset becomes large along the x-axis from the condition in Fig. 3 (a) at (Δx, Δy) = (11 μm, 0 μm), THz polarisation changes from elliptical to horizontallylinear. As the vertical offset with the fixed horizontal offset at Δx = 11 μm, THz polarisation changes to horizontally-linear and back to circular but with opposite handedness, LHC (in blue) to RHC (in red). An apparent THz intensity enhancement nor THz circular-polarisation were not observed when the pre-pulse irradiates the water flow with the horizontal offset with negative values. On the other hand in the case only with air without the water flow, as shown in Supplementary Fig. 4, the tendency of the THz polarisation dependent on the pre-pulse spatial offset is homogeneous in its radial direction (as expected from its symmetry). This indicates that the asymmetric characteristic of the tilted water flow is important. In the reflection side as shown in Fig. 5b, distorted THz polarisation is clearly observed. Similar to the case in the transmission, THz intensity enhancement or THz circular-polarisation is not observed when the pre-pulse irradiates with the horizontal offset at negative values (the pre-pulse irradiates the water flow before its focus). Another characteristic observed is that the handedness (helicity) of the circular-polarisation is always opposite to that in the transmission side; when the polarisation is LHC in the transmission, it is RHC in the reflection and vice versa. Furthermore, another tendency observed clearly is that the distortion of the polarisation especially along the vertical offset with the fixed horizontal offset at Δx = 11 μm shows a radial characteristic of polarisation. Figure 6 shows (a) time-integrated luminescence images in air without the water flow with different pre-pulse horizontal offsets with the fixed vertical offset at 0 μm, (b) time-resolved shadowgraphy under the pre-pulse excitation without the main pulse, and (c) time-integrated luminescence images with the water flow under the double pulse excitation. The delay time between the main pulse is fixed at 4.7 ns. Similar to the images shown in Fig. 4a, the intensity spatial profile of the incident main pulse is distorted but it is dependent on the pre-pulse horizontal offset. The pre-pulse irradiation position on the water flow also changes with the offset as shown in Fig. 6b since the water flow is 60 ∘ -tilted to the laser irradiation axis. As described previously, a shockwave expansion due to the air-ionization induced by the pre-pulse irradiation is observed as shown in the inset of Fig. 6, which is indicated by the black arrows. Such shockwave due to the air-ionization is still observed when the horizontal offset is 11 μm, while such shockwave is not observed when the horizontal offset is −19 μm. This is considered to be due to the 60 ∘ -tilted water flow; the pre-pulse irradiates the water flow after or before the focus in air when the offset is at 11 μm or −19 μm, respectively. In luminescence images shown in Fig. 6c, orange emission is observed when the prepulse offset is even at −19 μm as well as at 11 μm. However, in the case with the offset at −19 μm, the emission is from the shockwave from the water surface due to laser ablation and its structure can be different from the structure when the offset is at 11 μm. The details will be discussed later in the Discussion section.

Discussion
A charge current or redistribution on~1 ps time scale will generatẽ 1 THz emission. Polarisation of detected signal depends on the current direction and the position of detectors. Linearly-oscillating current will generate toroidal pattern of E-field. Depending on the position of detector, polarisation can be undefined (on the axis of oscillating dipole along which there is no dipole emission) or linear (perpendicular view to the oscillating linear current). Circularlyoscillating/redistributing charges will emit circularly-polarised Efield when observed perpendicular to the current loop.
As observed in THz emission from gas jets in vacuum, radial (linear) polarisation was observed and was defined with orientation of concentration gradient of expanding ion-clouds 21 .
Our group also observed recently such THz emission dependent on the density gradient at the shockwave front in air even at atmospheric pressure under the same experimental condition as in this paper (unpublished results). The gradient of injected material (ablation plume and ionised air) into the path of the main-pulse observed in the experiments is important for further discussion. The pre-pulse irradiation creates such plasma/gas gradients which are injected into the optical path of the mainpulse from side at different time moments. Apparently, optimisation of space and time of such injection defines efficiency and polarisation of THz emission. The irradiated spot on the water flow was close to the geometrical focus of diameter 2w 0 = 2 × 0.61λ l /NA ≈ 8 μm as determined by direct imaging; NA = 0.125 is the effective numerical aperture of the off-axis parabolic mirror (see Supplementary Note 2 for details). The axial extent of the focal region, the depth of focus 2z R ¼ 2nπw 2 0 =λ % 120 μm exactly what was observed in experiment. Under such focusing conditions, there was no considerable change of the light-matter interaction volume due to self-focusing, which is typically used in THz emission in air. Hence, THz emission is induced from the volume of subwavelength (for THz) cross sections and constitutes a point-like emitter which is useful for THz optical applications. In the following sections, we present a mechanism discussion as one possible hypothesis on how circularly-polarised THz emission, cyclotron-like electron trajectories in other words, is induced under the double pulse excitation (see Supplementary Note 3 and Supplementary Fig. 5 for the basics and details).
Single pulse excitation. The laser irradiation conditions are in the range of 6-26 PW cm −2 with ponderomotive field action and wake-field formation far from the relativistic conditions defined by the ratio of electron quiver velocity to the speed of light a 0 ≡ v q /c ≈ 0.14 for the highest intensity. The plasma under consideration is underdense ω > ω c for the used laser wavelength λ = 800 nm, where ω c is the critical density and ω = 2πc/λ. At the used intensities, ionisation of air takes place at the waist of the beam even without the water flow. Self-action of instantaneous ionisation and propagation of laser pulse creates a coupled plasma-light system, the wake-field. The ponderomotive force which for electron is F p ¼ À e 2 4m e ω 2 ∇I, where I is the laser intensity forming the wake structure, a longitudinal plasma wave.
A circular focal diameter of the laser focus projects onto the water flow as an ellipsis which is twice-wider elongated since cosð60 Þ ¼ 0:5 as compared with its extension along y-axis. This corresponds to the moving ionisation pattern on the water flow surface schematically shown in Fig. 7a. After the laser pulse ionisation, the charge relaxation is expected to occur along the direction of the initial surface of water flow. Hence, the strongest current component is expected to be along x-axis. This determines the polarisation of THz emission. Regardless the polarisation of the incident pulse, THz emission was E x -polarised. Even when the incident polarisation was circular, the THz emission was only slightly elliptical with prevailing linear component as for any other irradiation with the linear polarisation.
Double pulse excitation; the delay time effect. In the experiments with different delay times, TDS signal peak delays (Fig. 3b) and spectra shifts of THz emission toward the shorter frequency (Fig. 3c) are clearly shown. Furthermore, the positions of the expanding shockwave front in the shadowgraphy match the positions of the light emission observed in luminescence images (Fig. 4b and c). This tendency, with the emission spectrum of the shockwave front shown in Fig. 4d, indicates that the THz emission under the double pulse excitation is mainly from the shockwave front. Figure 8a shows the TDS peak delay as the function of the delay time and the distance estimated from the TDS peak delay under the assumption that the THz emission passes though additional volume with water component due to laser ablation from the water flow. If the volume is with a half density of water, the slope shown as a dotted line in Fig. 8a match the shockwave expansion dynamics observed in the imaging experiments shown in Fig. 8b. This data analysis indicates that the THz emission under the double pulse excitation is induced mainly at the front of the expanding shockwave, the upstream side far from the flow surface which is the case of the single pulse excitation.
Double pulse excitation; pre-pulse spatial offset. One apparent result shown in Fig. 5, is that THz intensity enhancements and the polarisation change are induced only when the pre-pulse spatial offset along x-axis is positive. The results shown in Fig. 6 indicate that the shockwave due to the air-ionization, which has been also observed and results in linearly-polarised THz emission in air under the same double pulse excitation (unpublished results), plays a key role for such characteristic changes under the double pulse excitation. Air breakdown by the pre-pulse pushes ionised air into the optical path of the main pulse and the condition is very different for the +x and −x positions. Based on the results described, Fig. 9 shows schematic diagrams of the configurations in front of the water flow from the top for the cases Δx = −19 μm (a) and +11 μm (b). When the offset is at Δx = −19 μm, the pre-pulse irradiates the water flow before the focus and a shockwave material transport into the optical path of the main pulse is not efficient (a weaker ablation of water and not synchronised with the wake-field). When the offset is at Δx = +11 μm, the pre-pulse irradiates the water flow after it focuses tightly in air. This is because the water flow is tilted at 60 ∘ . Apparently, such interference between the shockwaves due to the air-ionization and the water ablation is observed clearly when the pre-pulse horizontal offset is at Δx = +11 μm as shown in Fig. 9d, while such shockwave formation due to air-ionization is not observed at all when the pre-pulse horizontal offset is at Δx = −19 μm as shown in Fig. 9c. Water ablated by the pre-pulse irradiation is expanding and entering into the optical path of the main-pulse. A more dense region formed by the pre-pulse at the focal breakdown in air facilitates the formation of the wake-field as the main pulse propagates into the matter/plasma driven by the shockwave from the water ablation by the pre-pulse. The wake-field is schematically shown in Fig. 7, which pushes electrons with the advancing front at velocity v p . If the pre-pulse-induced plume is pushed into the right location (the space and time synchronisation is essential), there will be an effective coupling of the wakefield velocity v p and the perpendicular electron density gradient ∇ n e (see Supplementary Note 3 for details). However,   Fig. 8 Correlation between thetime-domain spectroscopy (TDS) peak delay and the images. a TDS peak delay (shown in Fig. 3b) as a function of the delay time. The TDS peak delay is converted to the distance under the assumption that the THz emission in front of the water flow experiences the passage through water considering that the refractive index of water at 1-THz is 2.12 32 . The solid line is an eye guide and the dotted line is a converted distance under the assumption that the THz emission passes through water but with the density at 0.5. b The distance of the shockwave expansion (a) shown in Fig. 4b and c. if the injection of the pre-pulse-induced plume is arriving a half period of the wake-field later (Fig. 7b), electrons will be pushed back (an opposite direction of the wave-field-induced electron transport). It was predicted theoretically that circularly-polarised THz emission will result from such coupling ∇ n e × v p 15,22,23 and the polarisation handedness depends on the sign of the cross-product. Change of the sign of v p depends on the geometrical location of the pre-pulse and the geometrical structure of the wake-field. Apparently, the expanding plume which entered the optical path of the main pulse from the above caused the RHC THz emission and from the below caused the LHC THz emission (this is consistent with the side view structure of the wake-field shown in Fig. 7b). The factors which break the top-bottom (vertical) symmetry along y-axis are combined due to the water flow and the gravity acting on an aerosol formed by the low repetition 0.5 kHz laser pulses in the experiment. The plume due to water ablation is chargecoupled and composed of very different masses: electrons, protons, and ionised oxygen atoms. The period of the wake-field λ pe = 2π/k pe ≈ 5.9 μm (in time 2π/ω pe = 20 fs) is defined by the Langmuir frequency ω pe ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n e e 2 =ðε 0 m e Þ p and the skin depth k pe = ω pe /c ≈ 0.9 μm for the plasma density which is by 30% higher than the molecular air density n e = 1.3 × [2.5 × 10 19 ] cm −3 (as seen by the main pulse); then the group velocity v g ¼ c 2 k=ω ¼ c ffiffi ε p ¼ 0:99c. The maximum of THz emission was observed at Δx = 11 μm offset under the optimised (Δt = 4.7 ns) double pulse exposure with the diameter of the focal spot at~8 μm. Maximising the plasma density gradient ∇n ðtÞ e (transverse) coupling with electron velocity v ðlÞ e (longitudinal) is required for the generation of the circular current 15 . Formation of the electron density gradient ∇ n e (transverse) facilitates induction of a rotational current ∇ × j = e ∇ n e × v ≠ 0, where v is the longitudinal electron velocity in the wake, hence, ∇ × v ≡ 0 22 (see Supplementary Note 3 and Fig. 9).
THz emission in the reflection and transmission directions in respect to the water flow has similar intensities but opposite polarisation handedness. The highest intensity of THz emission from the water flow under the double pulse excitation in |E| 2 (as photon numbers) is about 1 GW cm −2 based on the THz emission from the ZnTe crystal at the saturation regime 24 . For the incident laser power of~1 PW cm −2 , the conversion efficiency from the near-infrared laser to THz emission in this study is estimated to be 10 −6 . Further enhancements are expected in other liquids such as gold nano-colloidal aqueous suspensions as reported in hard X-ray emission 25 .

Conclusion and outlook
A simple two-laser pulse irradiation with micro-meter spatial offsets and nanosecond time delay to a micro-thin water flow is shown to generate circularly-polarised THz emission from a laser wake-field formed in front of the water flow. Further control of THz polarisation, from linear to circular and from left-handed to right-handed, can be well performed by adjusting such spatial offsets and time delay. With the appropriate offsets, THz emission intensity is also enhanced 1500-times if it is compared with the single pulse irradiation. This corresponds to the photonnumber-based conversion efficiency from the laser to THz emission under the double pulse irradiation at 7.1 × 10 −3 . It has a length of approximately Rayleigh length of optical focus 60 μm or a sub-wavelength for the THz emission. The mechanism responsible for the increased efficiency of THz emission as compared with the single pulse irradiation of solid/liquid/gas targets is related to mass transport of ablated material/plume by the pre-pulse into the focal volume of the main pulse. The strong shockwave front makes the region of the highest efficient THz emission when it enters the optical path of the main pulse. It realises mass/charge delivery from the side into the laser wakefield. The water ablation condition for THz emission is optimal at the delay time of 4.7 ns after the pre-pulse irradiation when a horizontal offset between the pulses was approximately diameter of the focal spot (the strongest plasma density gradient is formed). Theoretically-predicted emission of circularly-polarised THz emission, when the electron wake-field velocity is coupled (a cross product) with the electron density gradient, is realised experimentally in this study. The radial current transients restoring the axially depleted charges in the wake-field determines the spectral extent (a shorter transient broader spectrum as related via Fourier transform) and the circular polarisation of such THz wave emission. Circular polarisation is a result of radially-spiraling currents.
Circularly-polarised THz emission opens new possibilities as a polarisation control toolbox for THz technologies which can open new applications for opto-mechanics where large torsion can be generated upon absorption, reflection, or scattering and for rotational/vibrational molecular spectroscopy where polarisation wave-plates are not readily available or lossy. THz radiation can be used to better understand highly dynamic laser triggered explosions which find increasing number of application in laser machining/fabrication and creation of high temperature/pressure phases of new materials. Among different methods of electromagnetic field generation, sub-wavelength emitters are promising due to unmatched flexibility in wave front and polarisation engineering. THz radiation can be used to characterised internal wake-field current structures in the filaments.

Methods
All the experiments shown in Fig. 10 were carried out in air under atmospheric pressure (1 atm) at room temperature (296 K).
Polarisation-sensitive THz time-domain spectroscopy. The setup is as shown in Fig. 10a. A pulsed femtosecond laser (t p = 35 fs, transform-limited, λ = 800 nm, 1 kHz, Mantis, Legend Elite HE USP, Coherent, Inc.,) is used and the output pulses are split into the pre-pulse (E 1 , linearly-polarised parallel to y-axis, y-pol., 0.2 mJ per pulse), the main pulse (E 2 , linearly-polarised parallel to x-axis, x-pol., 0.4 mJ per pulse), and the probe for THz time-domain spectroscopy (TDS) with a series of half-wave plates and polarisation beam splitters (65-906, 47-048, Edmund Optics) 7,8,26 . THz emission is induced by the main pulse irradiation with timedelay, Δt, to the pre-pulse irradiation onto a thin water flow (~17 μm thick) by an off-axis parabolic mirror (1-in. diameter, effective focal length f = 50.8 mm, 47-097, Edmund Optics). The laser incident angle along z-axis is at 60 ∘ to the water surface normal. With this incident angle at 60 ∘ , effective coupling between the incident laser and the self-generating plasma is highly expected thorugh resonance absorption 27 , which has been confirmed in hard X-ray generation from water 28 . Under this condition, the polarisations of the main and the pre-pulses are p-pol. and s-pol., respectively. The optical delay between the two excitation pulses, Δt, is controlled with automatic stages (SGSP46-800 and SGSP26-150, Sigma Koki). A water flow is prepared with two colliding water jets and the system is set on an automatic stage (KS701-20LMS, Suruga Seiki) along the z-axis to adjust the flow surface for optimal X-ray emission measured by a Geiger counter (SS315, Southern Scientific). The detection of the THz emission is carried out by the electro-optic sampling method in the transmission direction through the water flow and in the reflection direction with 〈110〉-oriented ZnTe crystals (1-mm thick, Nippon Mining & Metals Co., Ltd.). Lock-in measurements are carried out with an optical chopper (3502, New Focus) and a lock-in amplifier (SR830, Stanford Research System), therefore the effective repetition rate of the laser excitation is 0.5 kHz. Following the usual method reported previously [29][30][31] , two wire grids (WGs, MWG40FA-III, Origin) are additionally used for the measurements of polarisation status in THz emission. One of the WGs, WG2, is used at the fixed angle 0 ∘ (parallel to x-axis), while the other WG, WG1, is used at two different angles, +45 ∘ and −45 ∘ for two independent TDS signals as E +45 and E −45 , respectively. The xand y-components of THz electric field, E x and E y , are then calculated from E x = E +45 + E −45 and E y = E +45 − E −45 , respectively.
Time-resolved imaging. Imaging experiments for the laser focus from the side (along x-axis) and the top (6 ∘ -tilted from y-axis) are as shown in Fig. 10b and carried out in two different methods with an objective lens (M Plan Apo 10×, or M Plan UV 10×, MITUTOYO) and CMOS cameras (Blackfly S USB3, FLIR Systems, Inc.) with filters for IR-cut and for intensity control in the visible region. One is with the pre-pulse and white light continuum (~1 ps, 580 ± 30 nm, as a strobe light) converted from the main pulse with a water cell. With this method, transient refractive index changes and/or scattering due to pre-plasma formation and/or laser ablation induced by the pre-pulse irradiation can be visualized. Another imaging is with the pre-pulse and the main pulse, which visualizes the interaction of the main pulse with the water flow with structures prepared by the pre-pulse irradiation. The exposure time for the camera setting was fixed at 2 ms for single shot imaging. In this mode of image acquisition, all the emission in broad-band spectra by the two-pulse irradiation of the water flow is time-integrated. In associated with the imaging, time-integrated UV-visible emission spectroscopy is also performed with a commercially-available spectrometer (HR4000, OceanInsight), which is position-dependent with a fiber input.
Pre-pulse spatial offsets. In addition to the time-delay as the temporal offset, spatial offsets along x-and y-axes, Δx and Δy, are applied to the pre-pulse irradiation in the experiments described above as shown in Fig. 10c. One steering mirror for the pre-pulse alignment is automatically controlled by a piezo-transducer system (POLARIS-K2S2P, KPZ101, Thorlabs) to change the pre-pulse focus position with micron-order precision. The origin, (Δx, Δy) = (0, 0), is defined experimentally with a Newton-ring like pattern in far field to the transmission side as an interference pattern with the pre-pulse and the main pulse focuses in air. The focus position of the prepulse with offsets is experimentally confirmed by the imaging setup described above.

Data availability
Data underlying the results presented in this paper are not publicly available at this time but can be obtained from the authors upon reasonable requests.