1. Introduction

The generation of electromagnetic waves with frequencies between 0.1 and 10 THz (THz radiation) has recently attracted considerable attention. Many promising applications of THz radiation have been proposed, such as analysis of materials including biomolecules, medical diagnostics, inspections for illegal drugs and bombs in mail, and detection of flaws in structures without the use of X-rays. Efficient and bright radiation sources in the THz region are required to realize these potential applications. Laser-produced plasma is one of the promising candidates to be an efficient generator of THz radiation [1]. Thus far, various schemes for generating THz pulses using laser-produced plasma have been proposed and studied. After the pioneering work of Hamster et al. [2], THz pulse generation from biased plasmas [3], air plasma filaments [4], and plasma excited by two-color optical pulses [5] have been reported. All these studies used gas targets. Although many schemes of THz pulse generation have been studied, there are only a few studies focusing on the targets. Chen et al. have shown that the amplitude of THz pulses from gas targets generated by a two-color scheme increases when using gas with lower ionization potential [6].

Recently, laser–cluster interactions have been studied intensively [7–10]. The cluster size is smaller than the laser wavelength, and the distance between neighboring clusters is larger than the laser wavelength. The laser can interact with a well-isolated solid-state target. Therefore, high laser-cluster coupling efficiency can be expected. We have studied THz radiation from such laser–cluster interactions.

In this article, we show that THz pulses are radiated from argon clusters irradiated with intense femtosecond laser pulses. We conclude that the average power of the THz pulses from the cluster targets is significantly enhanced by the considerable absorption of laser light by the clusters. The laser polarization dependence and the angular distribution of the average power of the THz pulses suggest that the radiation originates from the charge separation along the laser propagation direction in the laser focal spot.

2. Experiment

Schematic diagrams of the experimental setup are shown in Fig. 1 . To produce atomic argon clusters, high pressure argon gas (<8 MPa backing pressure) was injected into a high-vacuum chamber through a conical nozzle. The repetition rate of the gas injection was 1.25 Hz, which was synchronized with the laser pulses. Details of the gas injection are described in Ref. 9. The mean size of the clusters, which depends on the backing pressure, was ~10⁴ atoms at 8 MPa. This value was obtained by applying the Rayleigh scattering method [10] and corresponds to a diameter of ~10 nm. The mean distance between the clusters is estimated to be ~1 μm at 8 MPa.

 

Fig. 1 Schematics of setup with detection systems using (a) EO sampling and (b) a bolometer.

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Laser pulses with a center wavelength of 800 nm, a pulse duration of 130 fs, and a pulse energy of <50 mJ from a chirped-pulse amplified Ti:sapphire laser [11] were focused onto the argon cluster beam through a plano-convex lens with a focal length of 200 mm. The spot diameter was ~17 μm. The laser pulses were horizontally polarized (see the inset of Fig. 1). When the gas jet was irradiated with the laser pulses, high energy ions generated by the Coulomb explosion of the clusters were detected by using time-of-flight measurements [9,10], which were used to confirm the production of clusters.

The setup shown in Fig. 1(a) employs an electro-optic (EO) sampling technique to measure the waveforms of the THz pulses in the direction of 45 degrees with respect to the propagation direction of the laser pulses. The THz pulses were collected and collimated with a Tsurupica lens [12] with a focal length of 70 mm. The collection angle was ~32 degrees. The window of the chamber was a plate of fused silica that is transparent below ~1.5 THz. The collimated THz pulses were focused on a ZnTe (110) crystal with a thickness of 3 mm by using an off-axis paraboloidal mirror placed outside the chamber. Probe laser pulses divided from the main laser pulses were also focused on the beam spot of the THz pulses on the ZnTe crystal. The ellipticity of the probe laser pulses that is proportional to the electric field of the THz pulses was detected with balanced photodiodes. In this EO detection scheme, laser pulses with a repetition rate of 2.5 Hz were used. The output signal of the balanced photodiodes synchronized with the gas injection (1.25 Hz) was measured with a lock-in amplifier.

In order to measure the angular distribution and the backing pressure dependence of the average power of the THz pulses, a detection system using the liquid-helium-cooled InSb bolometer shown in Fig. 1(b) was used by replacing the EO detection. THz pulses radiated in the directions of 0, 45, 90, and 135 degrees with respect to the propagation direction of the laser pulses were collected and collimated with a polyethylene lens with a focal length of 400 mm and a collection angle of ~7 degrees. The collimated THz pulses were focused on the bolometer with an off-axis paraboloidal mirror. In this scheme, pump laser pulses with the same repetition rate as the gas injection rate were used. In both detection systems, a thick polystyrene foam plate and a black polyethylene sheet were placed in front of the detectors to block the pump laser pulses and unwanted infrared and visible light emitted or scattered from the clusters.

In addition, the energy of the laser pulses transmitted through the cluster gas jet was measured by using a thermopile detector. Here, the laser absorption fraction is defined as 1-E _gas/E ₀, where E _gas and E ₀ are the detected energies with and without the gas injection, respectively. By measuring the spectra of the transmitted laser pulses, we confirmed that the light components with wavelengths other than 800 nm can be ignored. The power of the scattered light in the direction of 90 degrees measured with the thermopile detector was undetectable.

3. Results and discussions

Figure 2(a) and (b) shows the waveform of the THz pulses at a backing pressure of 7 MPa as measured in the EO detection and the spectra obtained by performing a Fourier transform of the waveforms at various backing pressures, respectively. The intensity of the laser pulses was ~1 × 10¹⁷ W/cm². As shown in Fig. 2(a), the radiation of the THz pulses is observed for a duration of ~2 ps. The maximum frequency of the radiation is ~1.0 THz. There is a dip at ~0.2 THz. It is confirmed that the dip is not due to interference effects of the THz pulses in the window or the lens. The laser-produced plasma can be treated as an array of coherent THz radiation sources [13]. The interference of the radiation from each source will affect the spectrum of the observed THz pulses. There is a possibility that destructive superposition of the THz pulses at an observation angle of 45 degrees occurs at ~0.2 THz. However, the origin of the dip is unclear at present.

 

Fig. 2 (a) Waveform of THz pulses radiated in the direction of 45 degrees and (b) their spectra at various backing pressures.

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In Fig. 2(b), there is no resonant radiation at the plasma frequencies that Hamster et al. [2] observed in their studies using gas targets. The plasma frequency of the laser-produced plasma in this study is estimated as follows. The density of the atoms n at the focal point at the backing pressure p is estimated by using the equation n(x)/n ₀ = 0.150 (x/d)⁻² for monatomic gases [14], where n ₀ = p/k _B T, d, and x are the atomic density of the injection gas at temperature T, the diameter of the orifice of the nozzle, and the distance between the focal point and the orifice of the nozzle, respectively, and k _B is the Boltzmann constant. By using the experimental parameters of T = 300 K, p = 7 MPa, d = 0.5 mm and x = 32 mm, the density of atoms n ~6.2 × 10¹⁶ cm⁻³ is obtained. The energy distribution of the ions that Coulomb-exploded as a result of the double laser pulses indicates that almost all atoms in the clusters are ionized when the laser intensity is above ~10¹⁷ W/cm² [9]. Assuming that all atoms are ionized and the average valence of the ions is 8 [9,10], the plasma frequency of the laser-produced plasma is estimated to be ~6.3 THz. The frequencies of the THz pulses observed in this study are limited mainly by the low transmittance of the silica window above ~1.5 THz and are much lower than the estimated plasma frequency.

Although no resonant radiation is observed at plasma frequencies in Fig. 2(b), there is a peak just below 0.5 THz. Note that the EO detection system in this study, which uses a 3 mm thick ZnTe crystal, has an almost flat frequency response below ~0.8 THz since the coherent buildup length between the THz radiation and laser pulses is longer than 3 mm in this frequency region. The length of the interaction between the laser pulses and the cluster gas jet is as long as the Rayleigh length. This indicates that plasma regions with a length comparable to the Rayleigh length are produced in the cluster gas jet by the focused laser pulses. The Rayleigh length in this study is ~400 μm. This length is about a half of the wavelength of the THz radiation at the peak frequencies in Fig. 2(b), which implies that plasma regions on the scale of the Rayleigh length produced by the focused optical pulses work as half-wave antennae of THz radiation.

Figure 3 shows the power of the horizontally and vertically polarized THz pulses radiated in the directions of 0, 45, 90, and 135 degrees. The laser intensity and the backing pressure are 3.2 × 10¹⁶ W/cm² and 7 MPa, respectively. Intense THz radiation is observed in the directions of 45 and 135 degrees. In both directions, the horizontally polarized component is much more intense than the vertically polarized component. In addition, we confirmed that the polarization state and the angular distribution of the THz wave mentioned above are independent of the polarization of the laser pulses, which suggests that the contribution to the observed THz radiation from nonlinear optical processes based on third-order susceptibility [5,15] and the nonlinear current in inhomogeneous plasmas [2] are negligible. The angular dependence and the polarization state of the THz radiation are consistent with the predictions of the models based on the existence of charge separation in the direction of the laser propagation in the plasma caused by the laser wake field [2,4]. Although the details of the physics of THz generation are still under discussion, the present experimental results indicate that THz radiation is generated as a result of the dynamics of the charge separation induced in the direction of propagation of the laser by the intense laser pulse.

 

Fig. 3 Angular distribution of the average power of the polarized THz pulses radiated from argon cluster targets at a backing pressure of 7 MPa and a laser intensity of 3.2 × 10¹⁶ W/cm². Solid and open circles correspond to the horizontally and vertically polarized THz pulses.

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Figure 4(a) and (b) shows the backing pressure dependences of the average power of the horizontally polarized THz pulses and the laser absorption fraction, respectively. Note that the laser absorption fraction is large (~40% at maximum when the laser intensity is 9.9 × 10¹⁶ W/cm², as shown in Fig. 4(b)), which is consistent with previous reports [7,8]. The laser absorption fraction increases as p^x with x~0.8, where p is the backing pressure. Since the laser intensities in the experiment for Fig. 4 are sufficiently high to ionize almost all atoms in the clusters [9], the laser absorption fraction is expected to be proportional to the total density of the atoms, that is, the backing pressure (p^x with x = 1), which is consistent with the experimental results (x~0.8). The fact that the x values observed in the experiments are slightly smaller than 1 suggests the existence of partially ionized clusters.

 

Fig. 4 Backing pressure dependences of (a) the average THz power radiated in the direction of 45 degrees and (b) the laser absorption fraction at laser intensities of 5.0 × 10¹⁶ (solid circles) and 9.9 × 10¹⁶ (open circles) W/cm².

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As shown in Fig. 4(a), the THz power increases with the backing pressure as expected. However it seems to saturate at higher backing pressures. Since the THz pulses are coherent radiation, as shown in Fig. 2(a), the average power of the THz pulses should increase as the square of the energy E_abs ∝ p ^0.8 absorbed by the cluster targets, that is, p ^1.6 when the laser intensity is constant. In fact, the backing pressure dependence of the average THz power at laser intensities of 5.0 × 10¹⁶ and 9.9 × 10¹⁶ W/cm² changes as ~p ^1.6 below 5 and 6 MPa, respectively, which is consistent with the above predictions. However, at higher backing pressures, the rate of increase of the THz power is smaller than p ^1.6, which is explained as follows. The complex refractive index of plasmas with a density n _e at an angular frequency ω is

where e, m, and γ are the charge, the rest mass, and the scattering rate of the electrons, respectively, and ε ₀ is the dielectric constant of vacuum. The THz pulses generated inside the plasmas are transmitted into free space with a power transmittance T(ω) ∝ |t|²/|N(ω)| = 4|N(ω)|/|1 + N(ω)|², where t = 2N(ω)/[1 + N(ω)] is the complex amplitude transmittance [16]. Since, as discussed above, the plasma frequency described by (en _e/4π² ε ₀ m)^1/2 is well above the frequencies of the THz radiation observed in this study, |N(ω)| is much larger than unity. At higher backing pressures, |N(ω)| becomes large, which results in the decrease of T(ω). Therefore, the rate of increase of the THz power at higher backing pressures is decreased by the reduced transmittance.

Finally, we show that the average power of the THz radiation is significantly increased by the large laser absorption ratio of the cluster targets as compared to that of gas targets. Separately, we measured the power of the THz radiation from gas targets and their laser absorption fraction as follows. The chamber was filled with argon gas with a pressure of ~670 Pa. The density of the argon atoms at the interaction point between the gas target and the laser pulses is ~1.6 × 10¹⁷ cm⁻³. Although this atomic density for the gas target is slightly larger than 6.2 × 10¹⁶ cm⁻³ for the cluster targets with a backing pressure of 7 MPa derived above, the power of the THz radiation from the gas target radiated in the direction of 45 degrees was ~1/40 of that from the cluster target with a backing pressure of 7 MPa. The laser absorption fraction of the gas was ~2% which is one order of magnitude smaller than that of the cluster target. This shows that the power of the THz radiation from the cluster targets is gained by the strong absorption of the laser pulses by the cluster targets.

4. Summary

We have successfully observed the radiation of the THz pulses generated by laser–cluster interactions. The average power of the THz pulses from the cluster targets is strongly enhanced compared to that from gas targets. It can be shown that the enhancement of the THz radiation originates from the large laser absorption by the clusters. The lack of laser polarization dependence and the angular distribution of the average power of the THz pulses suggest that the radiation originates from the motion of the charges in the laser focal spot that are spread along the laser propagation direction.