Light conveys electric and magnetic fields that are polarized perpendicularly with respect to the propagation axis due to its transversal nature. It has been decades since such a discreet definition of light was experimentally overturned, as a result of the realization of radially polarized Bessel–Gauss and Laguerre–Gaussian beams [1–4]. When radially polarized beams are tightly focused, the longitudinal components will be constructively added together and provide finite field amplitude at the focus, while the transversal components cancel out. Such a unique property of electromagnetic radiation finds a myriad of applications in optics, including molecular orientation control [5], optical tweezers and atom traps [6], and high-resolution fluorescence microscopy [7], to name a few. The field sensitivity in terahertz (THz) time-domain spectroscopy has revealed fundamental natures of Bessel beams in a more complete form than in the visible spectral regime, notably in the temporal phase evolution at the focus [8,9]. Furthermore, THz spectra contain various elementary excitations in solids; hitherto, the unique polarization state is expected to be useful in observing the transitions which cannot be measured with usual plane waves, including plasmons, longitudinal optical phonons, and two-dimensional systems such as intraband transitions of quantum wells, surface states of topological insulators, etc. [10,11]. In addition, owing to the recent advances in nonlinear THz spectroscopy [12], several works have been conducted in this direction to obtain longitudinally polarized THz fields with high field amplitude. For example, the demand for high-field longitudinal polarization is particularly important for particle acceleration studies [13], where acceleration structures can be miniaturized to several millimeters in size for accelerating lighter charged particles, thereby shrinking the medium-scale facilities that use the conventional microwave technologies.

Compared to the optical frequencies, successful generation of longitudinally polarized THz radiation is relatively recent. Many schemes have been proposed towards this end, such as photoconductive antenna [14], optical rectification with segmented electro-optic (EO) crystals [15], and plasma filaments [16]. THz pulses with transverse field amplitude over MV/cm are frequently achieved [17–19]; however, the maximum longitudinal field strength reported so far still stays in the range of 11 kV/cm [20]. Here we present a scheme that can be employed to generate quasi-single-cycle and longitudinally polarized THz transient with an unprecedented amplitude of 1.5 MV/cm. Our experimental setup is shown in Fig. 1. Multiterawatt pulses from the JETI (JEna TI-Saph) laser system at the University of Jena were focused onto thin metallic foil placed inside a vacuum chamber. JETI delivers 1J pulses with 30 fs duration and a central wavelength of 800 nm at a 10 Hz repetition rate. The focused laser pulse instantaneously ionizes the foil surface, resulting in dense plasma formation and acceleration of charge particles. The lighter electrons, which gain energy from the laser pulse, can travel through the thin target and escape at the rear surface. Upon exiting, they create a charge separation field of the order of TV/m at the rear surface in the target normal direction [21]. This field is transient in nature and is responsible for the acceleration of the ions, which in turn results in a dipole-like THz emission [22–25].

 

Fig. 1. Illustration of the high-power laser pulse interaction with a thin foil target. The intense laser pulses can instantaneously ionize the front side of the foil, generating plasma and accelerating charge particles. The charged particle dynamics inside the foil target and the subsequent particle acceleration process at the rear surface lead to the emission of subcycle, broadband THz pulses [22]. The THz emission process and collection optics consisting of an ellipsoidal mirror (4.12 Sr solid angle) are also shown.

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We collected only the THz radiation emitted from the rear surface of the metallic foil by using an ellipsoidal mirror, which covers almost 4.12 Sr solid angle from the normal projection of the interaction point at the foil rear surface. The collected THz radiation is collimated and focused by a pair of parabolic mirrors after proper attenuation either onto a calibrated pyroelectric detector to measure the total energy or onto an EO crystal to measure the temporal waveform.

Figure 2 shows the single-shot, noncollinear measurement technique for recording the THz waveform. The THz radiation is normally focused onto the EO crystal and generates birefringence inside the crystal due to the instantaneous electronic response to the THz polarization. A linearly polarized, collimated near-infrared (NIR) probe beam is incident at an angle and covers the whole THz spot on the EO crystal and experiences induced ellipticity [25]. Due to this skewed geometry between the THz and NIR probe pulse, the temporal waveform of the THz electric field is directly encoded onto the spatial profile of the probe pulse in the horizontal direction. The elliptically polarized probe pulse is then sent through a quarter-wave plate and a polarizer (“analyzer”) so that the ellipticity information is converted into intensity modulation, which can be imaged by a CCD camera.

 

Fig. 2. Sketch of the experimental setup. The collimated THz radiation is focused onto an electro-optic (EO) crystal using an off-axis parabola (OAP) for coherent detection. A single-shot noncollinear EO detection scheme is employed to measure the temporal waveform of the THz pulse. The THz waveform is obtained by subtracting the two CCD images measured for two orthogonal directions of the analyzer. The horizontal axis of the recorded image provides temporal information whose resolution is defined by the angle subtended between the THz and optical beam at the EO crystal and the imaging system. The vertical axis provides the spatial profile of the THz spot. A THz wire grid (WG) polarizer, along with a circular metallic mask placed in the collimated beam, was used to unambiguously determine the polarization state of the THz beam. The circular metallic mask transmitted the THz beam only in one quadrant, while blocking the rest enabled us to distinguish the azimuthal and radial polarization components. Inset: GaP crystals with two different orientations of the crystal planes were employed to detect longitudinal (500 μm thick $⟨100⟩$) and transverse (100 μm thick $⟨110⟩$) polarization components of the THz pulse.

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The THz field was measured using electro-optic crystals (GaP) with two different crystal cuts. In order to record the longitudinally polarized electric field (${ϵ}_z$), we employed a $⟨100⟩$-cut GaP crystal with 500 μm thickness [26,27]. For detecting the transverse polarization component (${ϵ}_y$ in our configuration), a $⟨110⟩$-cut GaP crystal with 100 μm thickness was used. Figure 3(a) presents the measured THz waveform using two crystals. The field amplitudes for longitudinal (${ϵ}_z$) and transversal (${ϵ}_y$) components measured with GaP $⟨100⟩$ and GaP $⟨110⟩$ crystals are estimated to be 1.50 MV/cm and 3 MV/cm, respectively. Indeed broadband silicon attenuators were inserted in the collimated beam path to avoid saturation or over-rotation of the EO signal. These results agree well with the values that are evaluated from pulse energy detected by the pyrometer. Focusing a radially polarized beam, compared to linear polarization, creates a strong and tightly focused longitudinal field, where the ratio between the longitudinal to the transverse field is given by the numerical aperture (NA) of the focusing optics. For the optical scheme employed in our study ($\mathrm{NA}=0.33$), this ratio was 0.5 from experimental measurements and 0.43 from theoretical estimates. Further analysis also reveals that the detected THz pulse exhibits quasi-single-cycle waveform with temporal durations of approximately 220 fs and 600 fs for transverse (${ϵ}_y$) and longitudinal (${ϵ}_z$) polarizations, respectively. This difference in the detected temporal structure of the waveforms can be ascribed to the difference in the response function of the two crystals used here [24,28], clearly supported by the respective THz spectra shown in the inset of Fig. 3(a). By taking this factor into account, the actual field amplitude of ${ϵ}_z$ component can be slightly larger.

 

Fig. 3. Results: (a) temporal waveform of the longitudinal (${ϵ}_z$) and transverse (${ϵ}_y$) field components measured at the focus of the THz beam. Inset: corresponding spectral amplitudes. (b) Dependence of longitudinal field strength of the THz pulse with respect to the incident laser power.

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In the next step, we investigated the influence of the incident laser power on ${ϵ}_z$. The results presented in Fig. 3(b) indicate that ${ϵ}_z$ scaling with $P_{\text{laser}}$ follows a power-law coefficient of $P_{\text{laser}}^{0.76\pm 0.02}$. This agrees well with the behavior expected from the plasma expansion model, which phenomenologically describes the THz generation mechanism under intense laser–solid interaction [24]. It says that THz radiation is emitted by the charge particle acceleration process at the foil rear surface, and the polarization of the radiation is radial. Thus, the THz intensity is proportional to the square of the particle number [25], which in turn scales with a power-law coefficient of 1.5 with respect to the incident laser intensity. Therefore, the THz electric field should increase following a power law of $P_{\text{laser}}^{0.75}$, agreeing very well with the experimental observation.

Consequently, the spatial profiles of the two polarization components at the focal position [Fig. 4(a)] show distinct characteristics. In contrast to the $I_z$ component, which exhibits a single peak with a near-Gaussian profile, $I_y$ shows a clear double-peak structure. This is a clear indication of the destructive interference of the transversal polarization components in the radial beam at the focus. In addition, a phase difference of $\frac{\pi }{2}$ observed between the two components is a clear feature of focusing radial and linear polarizations [14,29]. Similarly, the focal spot size ratio ($I_z/I_y$) was 0.5 experimentally and 0.41 theoretically. Further confirmation was obtained from spot size measurements providing $0.0017{\lambda }^2$ and $0.0029{\lambda }^2$, respectively, where $\lambda =600\mathrm{\mu m}$ is taken as the central wavelength of the spectrum for the employed focusing conditions.

 

Fig. 4. Spatio-temporal characteristics of THz focus: (a) cross section of the intensity profile of transverse (red line) and longitudinal (blue line) polarizations at the focus obtained from the intensity profile (along the vertical direction) of the THz signal on the CCD image. (b) The strength of ${ϵ}_z$ obtained from $z$-scan measurements. (c) The temporal evolution of the ${ϵ}_z$ obtained from $z$-scan measurements. (d) Gouy phase estimated for various THz frequencies around the focus. Vertical error bars represent the shot-to-shot fluctuations.

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In the next step, we characterized the spatial and temporal evolution of the THz pulse along its propagation axis ($z$ direction). We measured the THz waveforms while scanning the GaP $⟨100⟩$ crystal around the focus. The peak amplitude as a function of the $z$ position is presented in Fig. 4(b). It demonstrates a clear maximum strength of ${ϵ}_z$ as the crystal is moved along the $z$ axis. The experimental data can be optimally fitted with the equation for a Gaussian beam, and it indicates a maximum of 1.9 MV/cm, higher than the recorded value. The vertical error bars are due to shot–shot fluctuations. Figure 4(c) presents the temporal evolution of the THz pulse for different $z$ positions after compensating for the path difference between the two beams at the cross-point on the crystal as it is moved along $z$. A temporal shift in phase is observed but not a phase flip of $\pi$ when the beams go through the focus. We can attribute this to the fact that the noncollinear geometry at which the THz pulse and the optical probe enter the crystal is very sensitive to the accurate positioning of the crystal, and thereby moving the crystal on the $z$ axis can lead to unequal path difference between the beams, resulting in a slightly different time of arrival for the probe pulse and thereby suppressing the phase flip. Even after carefully correcting this temporal delay between the pulses at the focus, a systematic shift in the temporal waveform is observed, which can be attributed to the Gouy phase shift. At the focus, all the frequencies are well-focused on axis, and hence the temporal duration is also minimum. Away from the focus, the high-frequency components do not converge, which leads to the extension in the temporal axis. This argument is clearly supported by the spectral phase shift plotted in Fig. 4(d), where the spectral phases for different frequencies with respect to $z$ positions are plotted. It can be seen that the phase acquires overall shift of $\pi$, when the EO crystal surpasses the focus position (amplitude peak position). The phase shift can also be fitted with the equation ${\varphi }_{\mathrm{Gouy}}(z)=-{\tan }^{-1}(z/z_0)$ [30], which describes the Gouy phase of longitudinal polarization.

Even though the above measurements established the generation of record-breaking longitudinally polarized THz radiation, we performed a final set of novel measurements to eliminate any ambiguity in our evaluation. To this end, we measured the spatial distribution of the beam polarization in the collimated part. First, we placed a simple wire grid (WG) polarizer, without the mask, before the focusing parabolic mirror (see Fig. 2) and detected the total transmitted THz power using the pyrometer for various rotation angles of the WG. The results shown in Fig. 5 (middle) indicate that the beam is radially polarized in the collimated path. To characterize more precisely, the temporal waveform of the THz pulse was measured using the GaP $⟨100⟩$ crystal, which is only sensitive to the longitudinal polarization component. In order to aid us, the WG was partially attached to a metallic mask, which allowed THz radiation to pass only through a selected quadrant (see Fig. 2). By carefully adjusting the relative angle between the WG and the mask, transmission of either the radial or azimuthal component can be selected [16]. The waveforms measured for all the quadrants (top, down, left, and right) of the beam are plotted in Fig. 5 at corresponding positions. It can be seen that the waveforms corresponding to the radial component appear similarly for all the quadrants, while the azimuthal component is absent, which reconfirms that the detected signal correctly measures only the ${ϵ}_z$ component. Interestingly, an asymmetric field pattern is visible between the left and right sides of the beam, which may be attributed to the presence of different THz generation processes. THz generation due to ponderomotively driven electrons in the laser propagation direction gives rise to the asymmetric THz emission pattern compared to the uniform dipole-like emission from the ion acceleration process [24].

 

Fig. 5. Temporally resolved beam profile measurements: polarization measurements based on a conventional wire grid polarizer and pyrometer (center) and EO detection scheme (outer figures). The outer figures represent the THz field measured with the wire grid polarizer and quadratic aperture oriented at different directions. The solid arrows indicate the direction of the quadratic aperture.

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Concluding, we have demonstrated that tighter focusing of a radially polarized THz beam can create MV/cm longitudinally polarized THz beams. To this extent, we generated radially polarized, subpicosecond THz pulses from the interaction of a terawatt laser with thin metal foils. The longitudinal field obtained at the focus exceeds 1.5 MV/cm, the highest available in the laboratory. The $z$-scan measurements and the Gaussian fit indicate that the longitudinal field strength could be 1.9 MV/cm, higher than the observed value. However, in addition to the strong on-axis longitudinal field, the presence of a strong transverse field, albeit off-axis, in the vicinity of the focus should be noted. Developing a technique to suppress or even exploit the transverse field component, for example in direct particle acceleration in vacuum [31], is vital in order to fully harness the potential of such a strong longitudinal field. Furthermore, the ${ϵ}_z$ scales with incident laser power to a power-law coefficient of $P^{0.76\pm 0.02}$ agree also with the predicted THz generation process. Simultaneously, the measurements of the spatial distribution of intensity, polarization, and spectral phase evolution agree well with the expected radial polarization of the beam. A phase shift of $\frac{\pi }{2}$ between the transverse (${ϵ}_y$) and longitudinal (${ϵ}_z$) fields at the focus is observed. Further analysis to estimate the spectrally resolved phase shift shows the contribution from the Gouy phase anomaly leading to a phase shift of $\pi$ as the pulse travels through the focus.

Creating strong longitudinal fields in the THz regime is nontrivial. In this regard, plasma-based THz generation schemes offer endless possibilities. Hence, the availability of ultrastrong longitudinal THz radiation would enable highly efficient acceleration of charged particles in free space, novel experiments in nonlinear spectroscopy of 2D materials, etc.