1. Introduction

Recent years the topic of terahertz (THz) radiation has been attracting continued interest because of its wide applications [1,2]. Nowadays most broadband pulsed THz sources are based on the excitation of different materials with ultrashort laser pulses. The incident laser intensity is normally restricted by ~10¹¹ W/cm² using conventional schemes such as through photoconduction [3] or optical rectification [4], due to the optical breakdown of matter. Efforts have been done to raise the energy conversion ratio of optical rectification by using phase matching methods on large-aperture crystals and pulse energy up to 30 $\mu J$single-cycle THz radiation has been achieved [5]. On the other hand, laser-driven plasmas, which have no thermal damage threshold and can sustain extremely intense light, have received considerable attention for THz radiation generation [6–9]. Since the first observation of THz radiation from plasmas [6], THz emission from femtosecond-induced breakdown of gases is studied widely [10,11], especially the “two-color” scheme [12], but the output THz energy tends to saturate with laser incident intensity ~10¹⁵ W/cm² [13]. Laser-solid interactions on the contrary show more potential on taking benefit of laser energy. Experiments on solid targets using ultrashort laser pulses so far show monotonously increased THz radiation output with the incident optical intensity up to 10¹⁹ W/cm² [14–17].

Irradiation of solid target by intense ultrashort laser beams results in a number of various regimes for the generation of hot electrons [18–20], which are potential to drive strong electromagnetic waves in a broadband region from x/γ-rays [21] to THz radiation. Resonance absorption, a major mechanism for hot electron generation at oblique incidence, plays an important role in laser-plasma interactions especially for moderate laser intensities [22]. It has been reported that x/γ-rays and second harmonic generation are greatly affected by resonance absorption [23]. In our previous experiments, high THz radiation yield is found corresponding to relative small plasmas in front of the target, where resonance absorption dominates [24]. The radiation was attributed to the self-organized transient electron currents formed along the target surface (Hereafter referred to as “surface current”) [16]. However, to our best knowledge so far, there is no direct observation reported which establishes a link between resonance absorption and the surface current induced THz radiation.

In this paper, we present simultaneous measurements of THz and second harmonic generation from femtosecond laser interaction with solid targets in the intensity region $I{\lambda }^2\simeq {10}^{16}~{10}^{18}$ W cm^-2$\mu m^2$. The THz yield $E_{THz}^{}$ ($\mu J$) at the front side of the target as a function of laser intensity show similar growth trend either by changing the laser pulse energy or the focal spot size, following a power scaling law $E_{THz}^{}\sim {(I{\lambda }^2)}^{1.0}$ basically. The THz emission is found strongly dependent on laser incidence angles. Besides, the emission is enhanced and decreased with specularly reflected second harmonic signal, which is considered as a signature of resonance absorption under our experimental conditions. Two-dimensional (2D) particle-in-cell (PIC) simulations have been carried out to investigate the impact of resonance absorption on the generation of surface current. Clear enhancement in surface current is observed when the incidence angle and the preplasma density scale length satisfy the optimal condition of resonance absorption. Hence we report our study which illustrates the relationship between the surface current, THz radiation and resonance absorption experimentally and theoretically.

2. Main diagnostics for experiments

The experiments were conducted using the Xtreme Light II (XL-II) Ti: sapphire laser system at the Institute of Physics, Chinese Academy of Sciences. It delivered up to 300 mJ energy in 100 fs at a repetition rate of 10 Hz with a shot-to-shot fluctuation around 10%. The main laser pulse was accompanied by a 4-ns amplified spontaneous emission (ASE) pedestal with an intensity contrast to the main pulse of 4 × 10⁻⁸. The contrast ratio was similar with the optimal case in Ref. 24, which results in a small preplasma with the scale length less than a laser wavelength in front of the target. The p-polarized laser pulse was focused with a f$f$/3.5 off-axis parabolic mirror (OAP) onto the target at an angle of incidence of 67.5° to the target normal. The full width at half maximum (FWHM) of the focal spot was measured to be around 5 $\mu m^{}$when the laser is tightly focused, which contained 35% of the total energy. The targets were single-side polished copper plates with a thickness of 1 mm mounted on a X-Y-Z motorized translational system to ensure a fresh surface for each laser shot.

The THz emission was collected in the specular reflection direction into a pyroelectric detector by a pair of polymethylpentene (TPX) lenses. The detector has a relative flat voltage response between 0.3 to 21 THz with an average responsivity of ~10⁴ V/W. The solid angle of THz radiation collection was 0.07 sr. A single-side polished high resistivity silicon (HR-Si) wafer was applied as the filter to reject the visible light.

Along with the THz radiation, we measured the reflected light spectrum using a fiber spectrometer with spectrum response from 200 to 1100 nm for laser-plasma interaction investigations [24]. The HR-Si wafer in the path of THz radiation was tilted to reflect the visible light out of the vacuum chamber through suitable selected glass filters. The spectra of the reflected light were found second harmonic dominant, which indicates that resonance absorption is an effective mechanism in the interaction process. The fiber spectrometer (200-1100 nm) was used to monitor the second harmonic generation shot by shot. A detailed description of the experimental setup can be found in Ref. 24.

3. Measurements and discussions

In the first series of experiments, a scan of defocusing distance was carried out by moving the OAP toward or backward the target, by 100 $\mu m^{}$each time. In the scanning, the laser pulse duration was essentially invariant, and the pulse energy at the target surface was kept as 210 mJ, with a shot to shot fluctuation less than 7%. At each given position, the THz signals were measured by ~10 shot to reduce the effect of fluctuation. The observed THz signal as a function of defocusing distance is shown in Fig. 1(a).We also measured THz radiation at the best focus by changing the laser pulse energy. The comparison of the THz yield as a function of laser intensity either by changing the pulse energy or the focal spot size is shown in Fig. 1(b). The solid square stands for data obtained at different defocusing distances with 210 mJ laser pulse energy, while the open square represents that obtained by different laser pulse energies at minimum focal spot. Power exponents of 0.9 and 1.2 are derived from the data with constant and varied laser pulse energy, respectively. Comparing with the earlier measurement [14], where a power law with an exponent of 1.1 by varying laser pulse energy is reported, we can conclude that the THz yield basically follows an intensity scaling law $E_{THz}^{}\sim {(I{\lambda }^2)}^{1.0}$. Since the laser pulse duration was essentially constant ignoring the time jittering in the experiment, Fig. 1(b) also suggests that the laser fluence (J/cm²) has only weak superiority on the observed THz radiation compared with the laser irradiance (W/cm²). This is very different from the case of x/γ-rays, which is found significantly affected by laser fluence than by laser intensity in previous experiments [25].

 

Fig. 1 (a) THz signal intensity from Cu targets as a function of laser defocusing distance at constant laser pulse energy ~210 mJ. (b) THz emission yield in a collection angle of 0.07 sr as a function of laser intensity either by changing the laser pulse energy (open square) or the focal spot size (solid square) by p-polarized laser pulses at an incidence angle of 67.5°.

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To understand the generation mechanisms for the observed THz radiation, the first step is to identify the electron (current) sources. The angular distribution of hot electrons is strongly dependent on laser intensities [22,26]. At low laser intensities, electron emission along plasma density gradient direction has been observed for p-polarized incidence [27]. At high laser intensities and with large incidence angles, electron beams will be accelerated mainly in two directions: along the laser propagation direction [26], or along the target surface [28]. THz radiation imposes a surface current behavior, i.e., the THz radiation observed at the front side of the target should not be induced from inner electrons, since the effective plasma layer for the generation of long wavelength radiation should be very thin on the target surface due to the skin effect. In our recent discussions, the observed THz radiation is attributed to the self-organized transient electron currents formed along the front target surface [16].

At oblique incidence for p-polarized light, an existence of plasma in front of the target will give rise to resonance absorption and generate hot electrons near the critical density surface [18]. Some of the generated hot electrons will penetrate into the dense region of the target and produce x/γ-ray radiation [29]; some will emit back to the low density region [27]. The electrons generated from resonance absorption are initially accelerated by longitudinal electron plasma waves along the direction of density gradient. However, the electron ejecting direction may be changed during propagation. Some of the electrons will be trapped by the surface quasi-static electric and magnetic fields [30] and form electron flows along the target surface, which are capable to give rise to radiation in THz region. With relative small plasmas in front of the target, resonance absorption is found effective for THz radiation generation previously [24], the plasma condition of which is similar with that in this experiment.

It is well-known that the coefficient of resonance absorption closely depends on laser incidence angles [18]. According to the linear theory of resonance absorption, the absorption rate f_RA can be expressed as [31]

In experiments, the measurement of specularly reflected second harmonic light is a powerful tool of laser-plasma interaction investigations related with resonance absorption [23,24]. In order to study the role played by resonance absorption in THz radiation generation, an incidence-angle-dependent experiment has been carried out by simultaneous measurements of THz radiation and specularly reflected second harmonic light, the setup of which is illustrated in Fig. 2(a).The laser pulse energy at the target surface was kept as 230 mJ, with a shot to shot fluctuation around 15%. The incidence angle θ was successively changed from 67.5°, 45°, to 22.5° by rotating the target surface (detection geometries marked as 1 to 3, respectively). The pyroelectric detector in junction with collection optics was always set at a direction of 22.5° with respective to the target surface with a collection angle of 0.036 sr. Specularly reflected light from the target at all three incidence angles were picked up by the same fiber spectrometer (200-1100 nm) in junction with collection optics and selected glass filters. The solid angle of the light collection was kept as 0.057 sr.

 

Fig. 2 (a) Schematic setup for the incidence-angle-dependent experiment. Target was rotated from 1 to 3 with the corresponding incidence angle of 67.5°, 45°, and 22.5°, respectively. The pyroelectric detector in junction with collection optics is always set at a direction of 22.5° with respective to the target surface. Specularly reflected light was measured by a fiber spectrometer (200-1100 nm). (b) Averaged THz radiation (solid square) and second harmonic (open square) signals with respective to incidence angles θ, with standard deviation as error bars. Each data point represents an average of ~20 laser shots. The p-polarized laser pulse energy at the target surface was kept as ~230 mJ.

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The angular-dependent experimental results are shown in Fig. 2(b). Two features can be immediately seen: the THz radiation (solid square) is strongly affected by the laser incidence angle with an optimal value of around 45°; the THz radiation and second harmonic signals (open square) exhibit a same trend of growth and decline with respect to incidence angles. Since resonance absorption accounts for almost all the second harmonic yield in the case of small preplasmas at oblique incidence for p-polarized light [23], our measurements suggest a positive effect of resonance absorption on THz radiation generation. The optimium angle of incidence is around 45°, which indicates a preplasma scale length of $L/\lambda \approx 0.2$ [18]. In our previous experiments [16], p-polarized light was found more effective to generate THz radiation compared to the s-polarized light, which also support our understanding here.

2D-PIC simulations have been carried out to investigate the correlation between resonance absorption and surface current. In the simulations, the target is a plasma slab located in the region $21-33\lambda$. The profile of the plasma density n is set to be an exponential rise along x-axis with a density scale length $L={\left(d\ln n/dx\right)}^{-1}$ up to 10$n_c$ and then followed by a plateau, where $n_c$ represents the critical density. $L/\lambda$ is set to be 0.2 according to the experimental observations. Along y-direction the plasma is uniform. A p-polarized Gaussian pulse is incident from the left side of the simulation box and irradiated on the front target surface with peak amplitude a₀ = 1, which $a_0$ is related to the laser intensity by $I{\lambda }_{}^2=a_0^2\times 1.37\times {10}^{18}$ W/cm² $\mu m^2$. The laser pulse duration is $35{\tau }_0$ and the waist is $6\lambda$, where ${\tau }_0=\lambda /c$ and c is the speed of light. We investigate the variation in target surface current by changing the laser incidence angles.

Figure 3(a) shows the distribution of the normalized surface current $j_y$ at the time of 60 laser cycles after incidence. The maximum values of $j_y$ at each incidence angle are given as green squares in Fig. 3(b). The resonance absorption rate acquired by Eq. (1) is given as the blue curve for comparison. One can see clearly that $j_y$ is positively correlated to the resonance absorption rate. Note that the maximum value of $j_y$ is much larger at the laser incidence angle of 60° compared with that at 30°, which indicates that a larger incidence angle is better for the surface current generation. This is consistent with previous experimental observations [28] and is also in good agreement with our angular-dependent measurement result of THz radiation in Fig. 2(b).

 

Fig. 3 (a) The distribution of surface currents normalize by $n_{c}ec$ at the time of 60 laser cycles after incidence with the angle of incidence of 30°, 45°, 60° from left to right, respectively. Green squares in (b) show maximum values of surface current at different incidence angles θ, while the blue line gives the relationship between the resonance absorption rate and the incidence angle calculated by Eq. (1). The plasma density scale length L is set to be$0.2\lambda$ in the simulations.

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Previous studies have shown that a small scale plasma is better for THz radiation [24] and for surface current generation [28]. Larger incidence angles will cause a reduction of preplasma and favor the surface current production. Furthermore, the optimum incidence angle for resonance absorption is given by ${\theta }_m=\arcsin \left[0.68{\left(2\pi L/\lambda \right)}^{-1/3}\right]$, which indicates that the occurrence of resonance absorption requires a large incidence angle ${\theta }_m$ with a small preplasma scale length L. However, the rate of resonance absorption will drop significantly at very large incidence angles. Hence a careful selection of the laser incidence angle under typical plasma conditions should be done to optimize the THz yield.

It has been pointed out by Nakamura et al. [32], that the quasistatic surface-magnetic field plays an irreplaceable role in the formation of surface current. The surface-magnetic field is initiated from electrons accelerated near the target surface. Laser ponderomotive forces at grazing incidence can account for such electron flows. This may partially re-explain the earlier model proposed by Hamster et al. [6], which emphasizes the role played by laser ponderomotive force in the generation process of THz radiation. Due to the high plasma density in solid targets, electrons accelerated along the laser incident direction by the laser ponderomotive force normally cannot contribute to the THz radiation directly, unless the laser incidence angle is large enough to allow the electrons to be pushed near the target surface. In other words, the laser ponderomotive force is expected playing an increasingly important role in the surface current generation with an increase of laser intensity at grazing incidence. Since laser ponderomotive force acceleration will result in a hot electron temperature scaling law of ${(I{\lambda }^2)}^{1/2}$ [22], we suggest that the surface current induced THz yield E_THz ($\mu J$) might probably scales with laser intensity as $E_{THz}~{(I{\lambda }^2)}^{1/2}$with ultraintense lasers. To confirm this assumption, experiments in the ultrarelativistic intensity regime need to be done.

4. Summary

To summarize, we investigate the intensity-dependence law of THz radiation in the specular reflection direction either by changing laser focal spot size at constant incident energy or by varying laser pulse energy at best focus. The THz radiation is found scaling almost linearly with laser intensity from 10¹⁶ to 10¹⁸ W/cm² in both cases, which indicates that it is not the laser fluence (J/cm²) but the laser irradiance (W/cm²) which plays an active role for the THz radiation generation. The observed THz radiation is attributed to the self-organized transient surface current on the front side of the target. Spectral measurement of the specularly reflected light suggests resonance absorption as an active absorption mechanism in the laser-plasma interaction process. Angular-dependent experiments show that the THz yield is enhanced by resonance absorption. The positive correlation between resonance absorption and the surface current is verified by 2D-PIC simulations. Possibilities of contributions of other laser absorption mechanisms, such as laser ponderomotive force, for the surface current generation are discussed. In order to make more effective use of the incident laser energy, we suggest a tightly focused pump laser and a careful selection of laser incidence angle taking plasma conditions into account.