Generation of Terahertz Radiation by Relativistic Laser Pulses on the Surface of Thick Solid Targets and Thin Foils

Terahertz pulse generation from multiterawatt laser surface plasma near thick solid targets and thin foils has been studied. Pulses with energies up to 7 μJ were detected in the spectral region <3 THz in the direction of specular reflection from the surface of the CaF₂ target. The dependence of the terahertz pulse energy ${{W}_{{{\text{THz}}}}}$ on the laser pulse intensity $I_{L}^{\alpha }$ can be approximated by the power function ${{W}_{{{\text{THz}}}}} \sim I_{L}^{\alpha }$. For a fixed laser pulse duration and variable energy the power index lies in the range $\alpha \approx 1.5{-} 2.8$, while for a fixed energy and variable duration $\alpha \approx 1$.

INTRODUCTION

The study of high-power laser radiation interaction with solids has started shortly after the development of pulsed laser systems [1–3]. During irradiation of a solid target surface by high-intensity laser pulses, part of the laser pulse energy can be transferred to the target material and lead to the excitation of electronic currents both on the surface and inside the target. The mechanisms of the energy transfer to the electronic subsystem depend on the laser pulse intensity, pulse duration, the angle of incidence and the plasma density gradient scale length [4]. When using laser pulses with subrelativistic and relativistic intensities (10¹⁷–10¹⁹ W/cm² for a wavelength of 800 nm), the main mechanisms of energy transfer from the laser field to electrons are vacuum heating [5, 6], resonant absorption [7] and J × B heating [8]. Some electrons leave the interaction region, gaining relativistic kinetic energy [6, 9–11] and can be registered. Another part of the hot electrons is accelerated deep into the target surface, transferring the laser field energy to deeper electrons and leading to the collective motion of the electron plasma and the generation of secondary electromagnetic radiation—hard X-ray radiation [12–14], high harmonics of the incident laser field [15–19], as well as low-frequency radiation in the terahertz (THz) [20–23], subterahertz and microwave ranges [24–26], propagating in the direction of specular reflection from the target front surface. The energy of hot electrons may be sufficient for the electrons to move through the target if thin foils are used and form nonstationary electron density near the rear surface which in turn leads to the generation of powerful THz radiation behind the target [27–29]. THz pulses with record-high energy of up to 50 mJ were achieved in such a generation scheme from the rear surface when thin metal foils were irradiated with picosecond pulses of ultra-relativistic intensity [30].

Terahertz radiation sources are in great demand in biomedicine [31], molecular spectroscopy [32], studies of ultrafast dynamics of charge transfer in semiconductors [33], charged particle acceleration [34], X-ray high harmonic generation [35]. As high-peak-intensity THz pulses become more accessible, a whole class of studies is developing where THz radiation is used both as a probe and as a pump [36, 37]. There is increased interest in compact and convenient sources of THz radiation for pump-probe spectroscopic applications, that would be synchronized with the original laser pulses, as well as hot electron beams and high harmonic radiation [38–41].

Here, we present an experimental study of the generation efficiency of THz radiation from thick solid targets in the direction of specular reflection. Usually two different types of targets are used for the generation of THz radiation and high optical harmonics. In the vast majority of cases thin metal foils are chosen to generate THz pulses, while dielectric surfaces are used for the high harmonic generation. This work shows that surfaces of thick dielectric targets are also suitable for high-power THz pulse generation. Observed THz pulses were also compared to the ones generated from the front and rear surfaces of thin metal foils with different thicknesses. The spectrum of the emitted radiation was reconstructed and the dependence of the THz output on the initial laser pulse duration was measured. The maximal THz pulse energy for our acquisition geometry was about 7 μJ in the spectral range <3 THz when using a CaF₂ plate. The dependence of the THz signal energy ${{W}_{{{\text{THz}}}}}$ on the intensity of the laser pulse ${{I}_{L}}$ was studied as its duration and energy were varied.

EXPERIMENTAL SETUP AND DIAGNOSTIC METHODS

The experiments were performed at the National Research Center Kurchatov Institute on a Ti:Sapphire terawatt femtosecond laser system delivering pulses with the energy of up to 250 mJ and duration of 30–35 fs at 10 Hz repetition rate. A 60-mm-diameter beam entered into an experimental vacuum chamber (Fig. 1a) and was focused onto a target by a parabolic mirror with a focal length of 177 mm (f/3 focusing). To prevent the parabolic mirror contamination due to laser ablation of the target, a 150-μm-thick protective Mylar tape was placed between the mirror and the target and could be scrolled to a clean spot in case of contamination without opening the vacuum chamber. The beam profile at the focal plane was measured by a CCD camera with a pixel size of 1.1 × 1.1 μm. For these purposes, an attenuated replica of the beam could be reflected off the front surface of a wedge plate, introduced into the laser beam by a motorized translation stage. Careful adjustments of a deformable mirror installed before the optical compressor for spatial phase modulation allowed us to achieve the focal spot size of 10 μm FWHM (Fig. 1b). Copper foils with a thickness of 10, 20, 40 μm, as well as plane-parallel 1-mm-thick plates of CaF₂, polystyrene and aluminum were used as targets. To ensure the interaction of each laser pulse with a fresh spot on the target surface, a tape drive mechanism for foil targets was used while the solid plates were mounted on a rotating stage.

Fig. 1.

(Color online) (a) Experimental setup diagram. (M1) flip mirror, (P1–P5) parabolic mirrors, (W) flip wedge plate, (CCD) camera for the focal spot measurement, (S) shutter, (T) target, (3A-P-THz) sensor for the power measurement of the THz radiation. (b) Intensity profile of the pump beam at the focus at a pulse energy of 50 mJ.

THz radiation was observed in the direction of specular reflection for foils and thick plates. We have also detected THz emission on the rear side of the foil along the laser beam line (see Fig. 1). THz radiation was collimated by a parabolic mirror and then refocused into the Golay cell by a second parabolic mirror. A 3-mm-thick polypropylene window and a 5-mm-thick TPX output windows were used for guiding THz emission out of the vacuum chamber. The THz signal was collected in a solid angle of about 0.1 sr. A calibrated Ophir 3A-P-THz detector was used to measure the THz pulse energy. The optimal position of the target along the beam focus was determined by tunning to the highest THz signal.

EXPERIMENTAL RESULTS

The dependences of the THz output on the laser pulse energy and duration were studied. The laser pulse energy was adjusted by a half-wave plate and a thin-film polarizer. The range of intensities $1.5 \times$ 10¹⁸‒$2 \times {{10}^{{19}}}$ W/cm² used in the experiment corresponds to the change in the normalized vector potential a₀ = $eE{\text{/}}(m{{\omega }_{L}}c)$ = [I(W/cm²)$\lambda _{L}^{2}$(μm²)/(1.37 × 10¹⁸)(W/cm² μm²)]^1/2 ≈ $0.8{-} 3{\kern 1pt}$, where e, m are the charge and mass of the electron respectively, c is the speed of light in vacuum. The pulse temporal contrast was 10^–8 on the nanosecond scale and 10^–6 on the picosecond scale (8 ps before the main peak).

In Figs. 2a, 2b the dependence of the THz output on laser pulse energy is shown. The THz signal was observed in the direction of specular reflection for foils of different thicknesses and thick targets for a p‑polarized laser pulse at 45° angle of incidence. It can be seen that among the foils, the largest signal was observed for the foil of maximal thickness and was similar to the signal from a thick aluminum target. The maximal THz signal with the energy of about 7 μJ was detected from a thick CaF₂ target in a solid angle of 0.1 sr in the direction of specular reflection from the surface.

Fig. 2.

(Color online) Dependence of the THz signal on the laser pulse energy: (a) for the thin copper foil targets with a thickness of 40 μm (green triangles), 20 μm (blue squares), 10 μm (wine circles) and (b) for a 1 mm thick solid target made of CaF₂ (pink triangles), Al (blue squares), polystyrene (red circles) for the 45° angle of incidence of p-polarized radiation on the target. The dots represent experimental data, the solid lines are the fit of the experimental data by a power function ${{({{I}_{0}}\lambda _{0}^{2})}^{\alpha }}$, where (a) $\alpha = 1.5$ (green triangles), 1.9 (wine circles), 2.1 (blue squares) and (b) $\alpha = 1.8$ (pink triangles), 2.0 (blue squares), 1.7 (red circles). Each experimental point is the result of averaging over 10 laser pulses. (c) Dependence of the spectral intensity of visible radiation observed in the surface normal direction on the laser pulse energy for a 40 μm thick foil. Dashed lines indicate the calculated positions of $\frac{3}{2}{{\omega }_{L}}$ and $2{{\omega }_{L}}$ harmonics. (d) Dependence of the signal intensity at $\frac{3}{2}{{\omega }_{L}}$ frequency on the laser pulse energy.

Besides the observation of the THz signal, a spectrum of secondary emission in the visible frequency range was measured with an Ocean Optics spectrometer. Radiation was detected along the normal direction to the target surface and was extracted from the vacuum chamber through a system of folding mirrors. Figure 2c shows the spectral map of the visible radiation generated from the front surface of a 40 μm thick copper foil for various laser pulse energies. It can be seen that at intensity ${{I}_{L}} \approx 2 \times {{10}^{{18}}}$ W/cm² a signal at the wavelength of $\approx {\kern 1pt} 530$ nm appears corresponding to the $\frac{3}{2}{{\omega }_{L}}$ frequency. It is known that emission at a $\frac{3}{2}{{\omega }_{L}}$ is associated with the plasmon excitation and can only occur effectively at plasma density gradient scale lengths of $L \approx {{\lambda }_{L}}$ [42]. Measurements of the laser pulse temporal contrast using the third-order autocorrelation technique showed the presence of a prepulse at 8 ps before the main peak with 10⁶ times lower intensity. When the intensity of the main peak is at a level of 10¹⁸ W/cm², the prepulse intensity reaches 10¹² W/cm², which is sufficient to ionize a metal target [43]. Taking into account the plasma expansion velocity of 100 nm/ps [44] we obtain the value of the density gradient scale length $L \approx 800$ nm $\approx {{\lambda }_{L}}$, which is consistent with the appearance of emission at a $\frac{3}{2}{{\omega }_{L}}$. A weak scattered signal at a $2{{\omega }_{L}}$ was observed only at the maximal laser pulse energies. Detection of this signal was not optimized in these experiments, since it propagates in the direction of specular reflection from the target surface [42].

The plasma density gradient scale length is one of the important parameters affecting the efficiency of THz generation. The work [40] shows that the optimal THz yield from the front surface of a solid target is observed in the range of 0.2–0.5 ${{\lambda }_{L}}$. Thus, the use of glass targets, which requires intensities ${{I}_{L}} >$ 10¹³ W/cm² for ionization [45], allows us to avoid the formation of a preplasma with a length $L \approx {{\lambda }_{L}}$ by the prepulse at 8 ps before the main peak and observe the largest THz signal.

Scaling of the secondary emission signal with the laser pulse intensity is of great interest. The key scaling parameter is the value $a_{0}^{2} \sim {{I}_{L}}\lambda _{L}^{2}$. Fitting the obtained experimental dependences of the THz yield with a function of ${{({{I}_{0}}\lambda _{0}^{2})}^{\alpha }}$ gives the result for $\alpha = 1.5{-} 2.1$, indicating simultaneous contribution of vacuum heating and J × B heating in the process of hot electron acceleration for our range of intensities [4]. The ${{({{I}_{0}}\lambda _{0}^{2})}^{\alpha }}$ scaling of the THz output can be a tool for estimating the energy of fast electrons emitted from the target surface. Based on the experimental data obtained (Fig. 2) and numerical simulations performed in [41], it is possible to estimate the temperature ${{T}_{e}}$ of hot electrons at the level ${{T}_{e}} \approx 0.1{-} 1$ MeV for our range of intensities. A similar behavior with $\alpha \approx$ 2 is demonstrated by the dependence of the $\frac{3}{2}{{\omega }_{L}}$ signal on the laser field intensity (Fig. 2d).

Hot electrons generated on the front surface and accelerated into the target volume can move through the target and become a source of a THz signal due to the emission of coherent transition radiation (CTR) when crossing the rear target-vacuum interface [46]. In this case, the electron cloud near the rear surface and the uncompensated positive charge inside the target can be considered as a transient dipole, which also contributes to the generation of secondary electromagnetic radiation [27, 29]. In our experiment, the THz signal from the back surface of the copper foil was measured in the direction coinciding with the direction k of the laser field propagation. The work [29] shows that the angular distribution of the CTR has a maximum in the k direction, and the dipole radiation is directed predominantly along the target surface. Due to the technical design of our tape mechanism, the incidence angle of the laser beam was limited to the range from 0° (normal incidence) to 25° when detecting secondary radiation along the k direction behind the target. The THz signal was collected by a parabolic mirror with a focal length of 15 cm and an aperture of 5 cm, similar to the case of observation along the direction of specular reflection from the front surface. Thus, the detection geometry ensures the predominant contribution of the CTR to the measured signal. We have observed approximately 3 times higher THz signal at an angle of incidence $\theta = 25^\circ$ compared to $\theta = 5^\circ$ case (Fig. 3). In our range of laser intensities and target thicknesses THz yield is almost independent of the foil thickness in agreement with the results presented in [27]. Reducing the angle of incidence to $\theta = 5^\circ$ (almost normal incidence) makes the resonant absorption and vacuum heating mechanisms ineffective, preventing energy transfer from the laser pulse to the electronic subsystem of the target. The small THz signal observed at $\theta = 5^\circ$ also indicates the low efficiency of J × B heating at intensities ${{I}_{L}} \leqslant {{10}^{{19}}}$ W/cm².

Fig. 3.

(Color online) Dependence of the THz energy on laser intensity measured behind a copper foil target with a thickness of 40 μm (green triangles), 20 μm (blue squares), 10 μm (wine circles) at an angle of incidence of laser radiation on the target of 5° (a) and 25° (b). The dots show experimental data, the solid lines are the fit of the experimental data by a power function ${{({{I}_{0}}\lambda _{0}^{2})}^{\alpha }}$, where (a) $\alpha = 2.1$ (green triangles), 2.6 (wine circles), 2.4 (blue squares) and (b) $\alpha = 2.8$ (green triangles), 2.6 (wine circles), 2.5 (blue squares). Each experimental point is the result of averaging over 10 laser shots.

Recirculating electrons are a source of secondary radiation behind thin film targets. By using the Casino package we have performed simulations on scattering of the hot electrons while they travel through the volume of a material. It shows that for the electrons with an initial energy of 1 MeV passing through the 2-mm-thick material, less than 50 percent of the initial number of electrons have the maximal residual energy from 0.2 to 0.4 MeV and cannot make a significant contribution to the generation of THz radiation [41].

The scaling of the THz output on the laser pulse intensity changes significantly when the intensity was adjusted by varying the initial pulse duration, which is determined by the distance between the compressor gratings (Fig. 4a). It was found that in the intensity range $0.7 \times {{10}^{{19}}}$–$2 \times {{10}^{{19}}}$ W/cm² when detecting in the direction of specular reflection and $0.1 \times {{10}^{{19}}}$–$2 \times$ 10¹⁹ W/cm² for observation from the rear surface, the THz pulse energy ${{W}_{{{\text{THz}}}}}$ is almost independent of the intensity at a fixed laser pulse energy and decreases with a further decrease in intensity following the ${{W}_{{{\text{THz}}}}} \sim I_{L}^{\alpha }$ law with $\alpha \approx 1$. Such slow decay of the THz signal can be explained by the generation of a large number of hot electrons with increasing pulse duration due to chirping [47], which compensates for the decrease in the laser pulse peak intensity. The steeper dependence of the THz signal from the target front surface on the pulse duration needs further stu-dies.

Fig. 4.

(Color online) (a) Dependence of the THz pulse energy on the initial duration (chirp) of the laser pulse for a 40-μm-thick copper foil when observed from the front surface of the target (squares) and for a 20-μm-thick foil when detected from the rear side of the target (circles, 25° angle of incidence) at a laser pulse energy of 250 mJ. Note that logarithmic scale is used only along the ordinate axis. The solid curve is the fit of the experimental data with a power function. (b) Spectrum of THz radiation generated from the front surface of a thick polystyrene target (solid green curve) and from a 20-μm-thick copper foil behind the target (blue dashed curve, 25° angle of incidence).

The spectrum of the generated THz radiation (Fig. 4b) was reconstructed according to the method described in detail in [48] and based on measuring the THz signal energy passing through a set of different filters calibrated in the THz frequency range. A dependence was constructed in such a way as to minimize the discrepancy between the observed filtered signal and the numerically calculated one. It can be seen that the spectrum of THz radiation lies in the region <3 THz (Fig. 4b) for the signal from the front surface. We have also characterized low-frequency components of the secondary emission down to 5 GHz by directly measuring the temporal waveforms of electromagnetic radiation with coaxial-to-waveguide adapter connected to a fast oscilloscope with 23 GHz bandwidth.

CONCLUSIONS

In summary, efficient generation of THz radiation has been observed in the direction of specular reflection when irradiating the surface of thick dielectric targets with laser pulses of subrelativistic and relativistic intensity at a 45° incidence angle. The dependence of the THz pulse energy ${{W}_{{{\text{THz}}}}}$ on laser intensity is approximated by the power law function ${{W}_{{{\text{THz}}}}} \sim I_{L}^{\alpha }$. For the laser pulses with a fixed duration and variable energy, the power index lies in the range $\alpha \approx 1.5{-} 2.8$ while at a fixed level of energy and variable duration $\alpha \approx 1$. The generation efficiency of THz radiation from copper foils of different thicknesses and thick solid targets was compared. It has been shown that the highest THz pulse energy in the “reflection” scheme reaches 7 μJ in the spectral region <3 THz at laser intensities of $2 \times {{10}^{{19}}}$ W/cm² and is observed when using an optical glass as a target. The use of optical glasses simplifies the experimental procedure, that is facilitates surface preparation; allows one to avoid the use of a tape drive mechanism thus increasing the accuracy of target positioning in the beam focus; reduces contamination of optical elements in the interaction chamber due to the target material ablation. Such a THz radiation source can be useful in pump-probe spectroscopic applications that require time synchronization of THz pulse with the original laser pulse, as well as hot electron beam and high harmonic radiation.