Observation of energetic terahertz pulses from relativistic solid density plasmas

We report the first experimental observation of terahertz (THz) radiation from the rear surface of a solid target while interacting with an intense laser pulse. Experimental and two-dimensional particle-in-cell simulations show that the observed THz radiation is mostly emitted at large angles to the target normal. Numerical results point out that a large part of the emission originates from a micron-scale plasma sheath at the rear surface of the target, which is also responsible for the ion acceleration. This opens a perspective for the application of THz radiation detection for on-site diagnostics of particle acceleration in laser-produced plasmas.


Introduction
Plasmas produced by high-power (10 12 -10 15 W) lasers are unique laboratories for the investigation of matter at high density and temperature, such as those found in astrophysical environments [1,2]. Besides the relevance to fundamental physics, hot laser plasmas have the potential for innovative applications ranging from generation of coherent electromagnetic radiation [3,4] to the acceleration of charged particles with table-top-size settings [5,6]. Progress in the investigation of both fundamental and applied aspects of hot laser plasmas necessarily requires powerful diagnostic tools to understand and eventually control their complex dynamics. In this context, characterization of laser plasmas using external probes is challenging because of the small spatio-temporal scales involved (a few tens of microns in space and several hundreds of picoseconds in time) [7]. A promising alternative is represented by the analysis of radiation generated by the internal dynamics of hot plasmas [8][9][10]. For instance, the higher-order harmonic radiation generated during laser-plasma interaction provides details of the electron dynamics at the critical density surface and related nonlinear optical effects in the plasma [10][11][12]. To date, studies of self-emitted radiation were mainly focused in the shortwavelength range [13] suitable to understand the electron dynamics happening on a short time scale [9]. Terahertz (THz) radiation from laser-produced plasmas in gases has been observed by various groups [14][15][16][17]. However, limited work has been reported on the observation of THz radiation from high-power laser-produced plasmas in solids [18][19][20]. In the earliest study, the generation of linearly polarized infrared radiation emitted from a solid target was attributed to a ponderomotively induced space-charge field [18]. The authors observed peak THz emission in the specular reflection direction of the incident laser pulse. The recent observation of THz radiation from the front surface of a solid target by Sagisaka et al [19] led them to propose the antenna mechanism, where the electrons generated by the laser pulse moving along the target surface emit THz radiation. The polarization of the emitted radiation is similar to that of the incident laser pulse. Previous observations were all from the front surface of the target where the high-power laser pulse impinges, and hence can be related to the electron dynamics. However, emission from the rear surface does not directly link to the incident laser pulse or to the THz radiation generated at the front surface as it is not able to travel through the dense solid plasma. Moreover, the radiation from the electrons exiting the rear surface falls mainly in the optical or in the high-frequency regime [21][22][23]. Therefore, the observation of THz radiation from the rear 3 side of the target should account for the ion acceleration process, where the transient dynamics of the accelerating sheath field acts as a source.
In this paper, we report the first observation of self-generated non-collinear THz pulses from the rear surface of a solid target during relativistic laser-solid interaction. No less than 2 µJ of radiation with frequency between 0.15 and 2 THz was measured by focusing 30 TW (terawatt) femtosecond laser pulses at relativistic intensities onto a thin titanium foil. Our experiments and two-dimensional (2D) particle-in-cell (PIC) simulations show that the measured THz radiation is emitted from the rear surface of the target, predominantly at large angles with respect to the target normal. Furthermore, the numerical results and experiment indicate that a substantial fraction of the observed radiation is linked to the dynamics of the ion acceleration process at the rear surface of the laser-irradiated target.

Experimental setup
The experiment was performed using the 30 TW JETI (JEna TI-Sapphire) laser system at the Institute of Optics and Quantum Electronics at the University of Jena. The JETI laser delivers 1.0 J, 800 nm and 30 fs pulses at a 10 Hz repetition rate. A schematic diagram of the experimental setup is shown in figure 1. P-polarized laser pulses were used to irradiate 5 µm thick titanium foils placed inside the experimental vacuum chamber. The laser beam was focused to a peak intensity of 10 19 W cm −2 using an off-axis parabolic mirror with 12 cm focal length. In order to collect the THz radiation emitted in the perpendicular direction to the target normal, a metallic ellipsoidal mirror ( f -number = 1.18) was employed. The target and the focal point of the laser pulse were located at the first focus of the ellipsoidal mirror, oriented with its semi-major axis perpendicular to the target surface. The target holder was designed in such a way that no radiation emitted from the target front surface entered our collection optics. The ellipsoidal mirror was designed to collect THz radiation emitted from the rear surface of the target at elevations between 0 • and 41 • (equivalent to a solid angle of 4.12 sr), and refocus it at the second focus of the ellipse. Here, a motorized iris diaphragm (max. diameter 34 mm) was placed to scan the radial intensity distribution of the THz radiation. This design rejects efficiently the radiation emitted in the forward direction (in target normal direction) and within the field of view of the iris (±4 • at full aperture, corresponding to a solid angle of 10 −3 sr). Behind the iris diaphragm, a collimation off-axis parabola and a sequence of plane mirrors were used to relay the THz radiation through a Zeonex window onto a calibrated hybrid pyroelectric Joule meter [24], placed outside the vacuum chamber. The detector was coated with organic black material to extend the sensitivity to a large spectral window ranging from 0.1 to 30 THz. Detection of parasitic electromagnetic radiation (such as laser light, background radiation, etc) and signal saturation was prevented by means of suitable calibrated filters and attenuators placed in front of the detector. Along with the THz radiation, the ion spectra were recorded simultaneously by means of a Thomson parabola detector, thanks to a 3 mm hole drilled in the center of the T-ray collimation parabola. The focusing of the laser pulse was tuned to ensure the maximum ion energy and number.

Results
The optical components in the beam path were calibrated using a Fourier transform infrared spectrometer. By accounting for the transmission/reflection of each optical component in the beam relay path, the readout of the detector could be used to measure the absolute energy  THz emitted non-collinearly from the rear surface was collected using a metallic ellipsoidal mirror and was focused onto the pyroelectric detector placed outside the vacuum chamber.
of the THz radiation generated during the experiment. For incident laser energies of 650 mJ (estimated intensity-10 19 W cm −2 ), we detected T-ray pulses with energy not less than 2 µJ in the 0.15-2 THz band. Considering the coupling losses in the beam relay system the actual emitted energy should be an order higher than the measured signal. Assuming that the THz radiation is a single optical cycle pulse the peak power of the radiation should be above 2 MW. In addition, the polarization of the THz radiation was measured using wire grid polarizers. The signal level reduced to half when a wire grid polarizer was placed in front of the detector. This shows that the observed THz is radially polarized (as expected from a dipole emission) or unpolarized.

Spectral analysis
The spectral analysis of the T-rays was performed using a collection of lowpass and bandpass filters. The bandpass filters are a combination of bandpass/lowpass filters; they are exact Spatial distribution of THz radiation at the iris diaphragm. Numerical simulation of the spatial distribution of THz radiation for various iris diameters (blue line). Experimentally measured spatial distribution of the THz radiation for various iris diameters (red diamonds). Inset: simulated effective 2D spatial distribution of THz radiation behind (5 mm) the iris. The distribution clearly shows that the emission is strongly non-collinear.
replicas of the far infrared filters used on the ISOPHOT instrument [25]. The lowpass filters are commercially available and are made of wire grids of various diameters and separation. The filters were placed in front of the detector. The observed T-ray signal contained spectral information for frequencies between 0.15 and 2 THz (which was the cut-off frequency of the attenuators and the chamber window). The spectral analysis shows that about 60% of the total detected energy is distributed in the 0.6-0.9 and 1.6-2 THz regions. Only 30% of the transmitted energy is between 0.3 and 0.6 THz.

Spatial distribution
The spatial distribution of the collected THz radiation was measured by recording the transmitted signal for various apertures of the iris diaphragm at the second focus of the ellipsoidal mirror. The bi-logarithmic plot of figure 2 shows that for iris diameters d smaller than 8 mm the measured signal strength scales as d 3 . For larger apertures, the signal is nearly constant, indicating that almost the entire energy of the focused T-ray beam is distributed within a radius of 4 mm. The power-law scaling shows that the center of the THz beam is hollow rather than filled. Because the spatial spectrum of a hollow beam has peaks off-axis, our observation is compatible with non-collinear THz emission. The spectral content of the THz radiation from the experiments is used to simulate the expected detected signal behind the iris diaphragm. The best fit is represented by the blue line of the plot in figure 2. The effective spatial distribution of the THz radiation behind the iris is shown in the inset of figure 2. In the simulation we assumed that the observed pattern has a radial polarization state, as expected from dipole emission. Despite a small quantitative mismatch between the experiment and the numerical simulation, the powerlaw trend is accurately reproduced by the numerical model. Additional measurements were carried out by placing a metal coin of diameter 15 mm behind the target at a distance of 10 mm so that all the forward emitted radiation is blocked (see figure 3). Such an arrangement would cast a shadow cone of base diameter 18 cm on the iris, hence blocking all the forward emitted radiation. Moreover, the geometry of the beam block is such that the reflected THz radiation from the coin back to the target will propagate at elevation angles larger than 54 • , and thus cannot be reflected by the ellipsoidal mirror inside the iris. The THz detector placed outside the vacuum chamber did not observe any significant change in the energy of the THz radiation. In contrast, when the metal coin was placed at the second focus of the ellipsoidal mirror the signal on the THz detector vanished to the background level. These tests show unequivocally that the radiation is emitted at elevation angles between 0 • and 41 • and corroborate the interpretation of the aperture scanning measurements.

Particle-in-cell simulations
In order to identify the source of the THz radiation, we performed 2D PIC simulations [26]. A simulation box of 20 µm × 200 µm × 100 µm in the x-, yand z-directions, respectively, and a spatial resolution of 50 nm was used together with absorbing boundary conditions. An aluminum target 1 µm thick, 10 µm wide and 30 µm long was placed 25 µm from the entrance plane (x y) of the simulation box. The code calculates the field ionization rates and can handle populations of neutral and ionized Al atoms. The focused intensity of the laser was 1.3 × 10 19 W cm −2 and the density was 6 × 10 22 cm −3 . The laser pulse was polarized in the plane perpendicular to the plane of incidence and propagating in the z-direction had a central wavelength of 800 nm. For the evaluation of the THz field we chose a 2D simulation plane along the y-z-direction in the center of the simulation box (see figure 4(b)). In order to measure the THz radiation field lineout was taken on a semicircle of 30 µm radius from the center of the target rear surface. The fields were extracted every 1.44 fs for a total duration of 738 fs. The retrieved spatio-temporal field structure was Fourier transformed in time and filtered to reject optical frequencies. In order to make sure that the observed field can propagate as 7 radiation, the Poynting vectors were plotted. The radiation was selected in frequency using a lowpass filter with a hard cut-off at 25 THz. A suitable timeframe was chosen to observe dipolelike emission. A more extended spatial emission can be observed for temporally integrated emission, which is due to the hot electrons or the surface plasmons traveling along the target surface. The magnitude of the isotropic emission is much smaller/negligible when the number of particles per cell is reduced by a factor of 7, a clear indication that the dipole field is due to the plasma sheath at the rear surface of the target, which is accelerating the positive charges.
Upon hitting the target at t = 80 fs (time elapsed from the beginning of the simulation), the femtosecond pulse completely ionizes the aluminum atoms and excites a low-frequency, expanding electromagnetic wave at the back of the target. The radiation flux is visualized in figure 4(a), where a snapshot (at t = 194 fs) of the magnitude and direction of the Poynting vector is shown. The emitted radiation has a rather complex spatio-temporal structure whose analysis revealed the existence of three main mechanisms, each responsible for the generation of THz radiation featuring characteristic spatio-temporal and spectral signatures. The fields are represented in normalized quantities. The analysis was carried out on time evolution data of the outward component of the Poynting vector, sampled along a semi-circle of radius 30 µm centered at the interaction point of the laser pulse and the target and extending on the rear side of the aluminum foil (see figure 4(b)). The radiation was frequency filtered with a bandpass filter centered at 60 ± 30 THz. The leading edge of the radiation front (time of arrival t = 200 fs) is characterized by a strong, asymmetric emission peak at θ = +53 • from the target normal (see figure 4(c), blue line). The emission lasts as little as 14 fs, revealing a broad frequency spectrum extending from the optical to THz frequencies. The radiation pattern can easily be modeled by the dipole emission associated with a bunch of electrons propagating at β = v c = 0.73 (v is the velocity of the electron and c is the speed of light) along the direction of the incident heating pulse and deflected by an electric field normal to the target surface. Consistently, the charge diagnostic of the simulation revealed accordingly the presence of a negatively charged cloud propagating at β = 0.75 at θ = +21 • from the target normal.
At intermediate times of arrival (230 fs < t < 430 fs) a low-frequency emission ( f < 25 THz) is observed in the simulation. The overall angularly resolved flux is plotted in figure 4(c) (green line), revealing a characteristic dipole emission symmetric around the target normal. The emission is peaked at angles of θ = ±47 • from the target normal, a value consistent with the emission of charged particles propagating at a speed of β = 0.37 parallel to the target normal, and accelerated along the same direction. The correspondingly modeled emission pattern is superimposed on the plot of figure 4(c) (dotted red line) 8 . The remarkable agreement of the model with the simulated radiation pattern suggests that a possible source of the noncollinear THz radiation is related to the dynamics of the TNSA mechanism. By irradiating a thin foil target with ultra-short laser pulses at intensities greater than 10 18 W cm −2 , a population of extremely energetic hot electrons (several MeV) is generated. Some of these electrons travel through the target and escape at the rear surface, thereby generating a micron-scale plasma sheath with a space charge field of the order of TV m −1 [28,29]. The sheath field is strong enough to field ionize the rear surface and accelerate protons and ions to very high energies. The energetic electrons leading the plasma sheath, which is of the order of a few microns, experience deceleration while the ions and protons are accelerated to several MeV energies. Because of the accelerating and decelerating dynamics of charged particles, radiation of electromagnetic waves is expected to be emitted according to a dipole-like pattern.
At later times (t > 430 fs), the radiation pattern is peaked at angles θ = +90 • from the target normal. The field snapshots clearly show that this radiation originates from a surface plasmon hitting the edge of the target, as reported previously by Sagisaka et al [19]. The low-frequency ( f < 25 THz) time integrated flux across the observation plane shows that the emission is far from being uniform and most of the radiation is emitted off-axis with respect to the target normal. If the experiment was capable of detecting this emission, we would have observed that the flux passing directly through the aperture would represent 9.4% of the total collected radiation.
These three sources of THz radiation do not contribute on an equal footing to the experimentally observed emission. The contribution of the radiation generated by the deflected electrons fades rapidly at low frequencies, while a major contribution of the surface plasmon emission can be ruled out by the relatively large size of our target (3 cm). The excited plasmon is indeed expected to decay within a few mm of propagation, thus well before the edge of the foil is reached. The experimental setup indeed was capable of collecting only radiation emitted non-collinearly. Indeed, the angular distribution, polarization and the metal coin measurements indicate that the observed radiation is dipole like. This suggests that the target normal sheath acceleration (TNSA) emission could play a role in explaining the high yield of T -ray emission observed in the experiments. In fact, figure 5 is consistent with this conjecture. It shows the charge dynamics and distance at the center of the target rear surface over time. The zero time corresponds to the time the laser pulse hits the target. The ions (red) move more slowly compared to the electrons. The electrons escaping the rear surface develop a space charge field. Later on, the ions gain energy and get accelerated by the field generated by the charge separation. The charge separation drives the field and in turn leads to emission in the non-collinear direction.

Conclusions
In conclusion, the rich phenomenology observed in the simulation indicates that spatiotemporally resolved diagnostics of self-emitted THz radiation could be used to identify and monitor the acceleration of charged particles in relativistic plasmas. Various target geometries can be tested to obtain the contribution from the surface plasmons. Such diagnostics could therefore be used to optimize both the laser-driven particle acceleration process and/or the generation of THz radiation. Using a laser-driven particle accelerator as a source of THz radiation could be promising; it is to be noted that the energy measured in our experiments was mainly in the off-axis direction and between 0.15 and 2 THz. According to the simulations, higher yields (up to ×10) are expected in the 0.1-30 THz band, a value which would make the source competitive with other THz-generation methods. The average power of such a source depends on the repetition rate of the laser system, which in our case is 10 Hz, while the peak power is in the megawatt range, comparable with the existing synchrotron sources. The remarkable high energy of the T-ray pulses generated during relativistic laser-plasma interaction could find relevant applications in biological imaging and material science. Moreover, characterization of self-emitted T-rays has the potential of being a unique diagnostic for laser-plasma acceleration schemes, with relevance to the optimization of table-top laserdriven particle accelerators.