1. Introduction

The way of ultrashort two-color laser fields to pump gas plasma is good at generating efficiently broadband terahertz (THz) fields [1–4], which benefits many applications [5–7]. Accordingly, developing an efficient THz source in this way is still drawing considerable attention in THz field. To enhance the THz radiation, one of the methods is creating multi-filaments, instead of single filament, pumped by femtosecond laser pulses. If pumped by single-color laser pulses, the two spatially overlapped filaments can enhance THz radiation by one order of magnitude than the THz radiation from the single filament [8], whereas two filaments separated in space can also boost the THz radiation [9–11] by the square of the number of filaments [12–14]. Two beams with elliptically or circularly polarization are used to enhance the THz radiations, which can effectively avoid the difficult control of the relative time delay between two linearly polarized pumps [15–17]. Recent report shown that under a two-color laser pump, two parallel filaments were able to enhance THz radiation by 200% from the single filament [18].

As is known, the controllable polarization is also interesting and important in THz region [19], which can promote the understanding of the light-matter interaction. For example, the circularly polarized THz fields can be used for birefringent materials imaging [20] and angular streaking the relativistic electron beams [21]. The handedness of the circularly polarized THz fields would benefit the study of the chiral molecules and THz communications [22,23]. Conventionally, the polarization of the THz field can be adjusted with THz wave plates [24–27]. To overcome the undesirable material absorption and bandwidth limitation of the THz wave-plates, the directly polarization-controlled THz field in gas plasma has been studied in recent decades. The circularly polarized THz fields can be generated by applying an external electrical field [28], controlling the gas pressure [29], tunning the time delays/intensity ratio of multi-pump pulses [30] or using circularly polarized two-color laser fields in long distance plasma [31], and so on. Recently, the flexible polarization-controllable THz field was realized in long filament pumped by a circularly polarized laser pulse together with its linearly polarized second-harmonic [32].

The polarization of the THz radiation from two filaments has the potential to be controlled. Here, we intend to create two paralleled filaments pumped by two-color laser fields for both an efficient enhancement and a controllable polarization of THz radiation. Correspondingly, we arrange two noncolinear laser paths to create two paralleled pumps by using a parabolic mirror with a through central hole. This arrangement ensures the full utility of the available laser power. In each filament, the two pulses constituting the two-color laser field in the reaction region always have a parallel polarization by rotating a zero-order dual-wavelength wave plate. And the polarizations of the two-color laser fields in the two paths can be adjusted to be parallel or orthogonal with each other by inserting a half-wave plate of fundamental wave in one of the paths. If the polarizations in the paths are set to be orthogonal mutually, the generated THz fields have mutually orthogonal polarization, too. Accordingly, the polarization of the superposed THz field can be controlled by changing the relative time delay between the two THz fields, which allows us to control flexibly the polarization of the superposed THz field, or the total THz field.

2. Experimental setup

The experimental setup is schematically illustrated in Fig. 1(a). A 3.0 W-100 fs-800 nm p-polarized femtosecond laser pulse chain is outputted from a 1 kHz Ti: sapphire amplifier system with a diameter of 10 mm at e⁻² level. The pulse chain is split into two beams by a beam splitter (BS1). The transmitted beam with an average power of ∼2.98 W is further split by anther beam splitter (BS2) to generate two pump arms which are marked as Arm1 (p-polarization, ∼1.45 W) and Arm2 (p-polarization, ∼1.45 W), respectively. The two pumps are arranged and focused to generate two parallel filaments by using a convex lens in Arm2 and a parabolic mirror with a through hole in Arm1. The focal distance is set to 100 mm or 150 mm in the Arm1 or in the Arm2. In each of the Arms, a pair of lenses is inserted to reduce the beam size and position longitudinally the filament. The previous study suggests the slightly change of the spatial separation wouldn’t affect the propagation direction of THz fields when the two pumps are synchronized temporally [13], so the transverse separation of the two paralleled filaments is experimentally estimated at 0.15 ± 0.05 mm, where the two plasma channels are spatially separated completely. The 400 nm (second-harmonic, SH) pulse chain is converted from the 800 nm chain (fundamental-wave, FW) by using a 200-μm-thick type-I β-BBO crystal with an efficiency of ∼15%. In Arm1, the s-polarized FW can be adjusted by a half-wave plate (HWP1) together with a rotation of the type-I β-BBO crystal by 90° for effective generation of the orthogonally polarized two-color laser fields (s-polarized FW and p-polarized SH). A zero-order wave plate, DWP, 1/2 wave for 800 nm and full wave for 400 nm, with its optical axis along 45° is used to adjust accurately the polarization of the FW to be parallel to that of the SH both for Arm1 and Arm2. The delay between the two arms is controlled by a delay stage (DS). The emitted THz radiations from two filaments are collimated and focused by a pair of parabolic mirrors, then detected with a 2 mm-thick (111)-cut zinc telluride (ZnTe) crystal for electro-optical (EO) sampling. A silicon wafer and a Teflon plate are used to reflect and block the optical pumps, as displayed in Fig. 1(a). Besides, a THz polarizer can be inserted between the parabolic mirrors to pick out the s- or p-polarized components of the generated THz fields.

 

Fig. 1. (a) Schematic diagram of the experimental apparatus. DWP: zero-order dual-wavelength wave plate (1/2 wave for 800 nm and full wave for 400 nm); HWP1,2,3: half-wave plate of fundamental wave; QWP: quarter-wave plate of fundamental wave; α-BBO: alpha-barium borate crystal; β-BBO: beta-barium borate crystal; BS1, BS2: beam splitters; PM: parabolic mirror; Spec: spectrometer; DS: delay stage; the THz detector system contains a pair of PMs, silicon wafer, Teflon plate and Golay cell. (b) The measured power of THz radiation as function of the power of a two-color laser field with different focal length.

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The THz fields are measured by spectral interferometry-based single-shot THz EO sampling [33], which is performed by the probe reflected beam from BS1. As shown in Fig. 1(a), the probe (15 mW) is temporally stretched up to ∼ 6 ps (chirp value ∼ 3.6 × 10⁵ fs²) by a prism pair. Its polarization direction can be adjusted by a half-wave plate (HWP3). A plano-convex lens after HWP3 is used for the spatial profile matching between the probe and the THz beam on the ZnTe crystal. After another half-wave plate (HWP2), a 7-mm-thick α-BBO crystal and a polarizer work to generate a pulse pair for spectral interferometry with high modulation depth and signal-noise ratio, and the pulse pair is finally received by a spectrometer (spectral resolution 0.06 nm, temporal resolution 3 ms).

3. Experimental results

In order to check the effect of the intensity clamping on THz emission, we firstly use a Golay cell to measure the THz emission which is a function of the two-color laser power for single filament under a given focal condition. During this measurement, a mirror is inserted in front of BS1 so that the pump power can be up to 2.75 W for the THz generation, as displayed in Fig. 1(a). Two silicon wafers and a Teflon plate are used to block the near-infrared optical pump and some others from the filaments. Figure 1(b) presents the measurements with the focal lengths of 125, 175 and 300 mm, where we find the THz powers would reach saturation, even decrease as the pump powers increase continuously. The results indicate that our pumps are powerful enough to enhance THz radiations by increasing the filament volume with two-filament configuration. The phenomenon is also verified that the saturation power of THz radiation grows with the incremental plasma distance.

For convenience of description, the THz electric fields from Arm1 and Arm2 are labeled as E_THz1(t) and E_THz2(t), respectively. As a result, the total electric THz field emitted from two filaments is marked as E_THz(t). Figure 2(a) displays the measured E_THz(t), E_THz1(t) and E_THz2(t) with the parallel polarization. E_THz1(t) and E_THz2(t) are synchronized by tunning DS. As we see, all of them display similar temporal profiles, as well as the spectra as shown in Fig. 2(b). It indicates the pumps for two filaments can effectively enhance the THz radiation than that for the single filament, which agrees with the previous result [18]. Figure 2(a) shows the amplitude of the THz radiation from two filaments is ∼1.83 times that from either of the two filaments. Besides, the intensities of THz radiations with different laser pulse powers are also measured. As displayed in Fig. 2(c), the red, blue and black curves correspond to the intensities of E_THz1(t), E_THz2(t) and E_THz(t), respectively. We can see that the intensity saturations of THz fields occur at a pump level of ∼ 0.71 W, where the intensity of E_THz(t) is about 4.04 times that of E_THz1(t), and 2.23 times that of E_THz2(t). In a word, our two-filament design can make an obvious enhancement for THz generation.

 

Fig. 2. The measured THz fields from the two filaments by parallel polarized two-color laser fields (a), the corresponding spectra (b), and the measured intensity and power of the THz radiation as a function of laser pump power (c, d). Arm1 and Arm2 mean the THz signals from Arm1 and Arm2 paths, respectively.

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We also confirm the relationship of the THz powers from the two filaments by a Golay cell at different pump levels. Here, we only increase the laser power in Arm2 to strengthen E_THz2(t) while keep the power to be 0.3 W in Arm1. The laser power in each arm is controlled by adding an iris and changing its aperture so that the SH efficiency of the β-BBO crystal is almost insusceptible for different the pump powers. As shown in Fig. 2(d), when the pump power rises to 0.71 W, the output THz power from Arm2 increases monotonously, and the total THz power from two filaments (black square line) is approximately equal to the sum of that from the Arm1 (blue triangle line) and Arm2 (red circle line). The maximum of the total THz power is 1.5 times of that from Arm2. From Fig. 2, it can be concluded that both the power and intensity of the total THz radiation can be enhanced effectively than that from single filament.

To control the polarization of the THz radiations from the filaments, the laser polarization is adjusted to the vertical direction with HWP1 in Arm1 but kept horizontally in Arm2. Correspondingly, the THz field from the filaments can be regarded as the vector superposition of two orthogonal THz electric fields, i.e., E_THz(t)${\boldsymbol {\hat{e}}}$ =[E_THz1(t)$\hat{e}_z$+E_THz2(t+τ)$\hat{e}_y$], where τ stands for the time delay between E_THz1 and E_THz2. We use a (111) ZnTe crystal as a detector for the three-dimensional (3D) trajectories of THz fields. The vertically and horizontally polarized THz components are picked out through rotating a THz linearly polarizer between the parabolic mirrors and a half-wave plate (HWP2) for the probe as shown in Fig. 1(a). Figure 3 shows the measured 3D THz electric fields with different relatively phases by changing the time delay τ. When the relatively phases are 0, 0.25π and 0.5π, the THz fields perform linear, elliptical and circular polarizations as shown in Fig. 3(a-c), respectively. From Fig. 3(c) and 3(d), we find the circularly polarized THz fields can be switched from anti-clockwise to clockwise by inversing the relative phase between the two THz fields. It is implied that the ellipticity of the THz field can be manipulated by changing the relative time delay between the pumps of the two Arms. Figure 3(b) shows the measured amplitude of the s-polarized THz field deviates from that of the p-polarized, which may be disturbed by the external conditions during its measurement.

 

Fig. 3. The measured 3D electric fields of THz radiations at ϕ_THz = 0, 0.25π, 0.5π and -0.5π.

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Compared with the THz fields from the two filaments with an identical polarization [13], our design can avoid the spatial interference in E_THz(t) from E_THz1(t) and E_THz2(t) due to their orthogonal polarizations while keeping flexibly manipulation of E_THz(t) polarization by varying the delay τ. In addition, E_THz(t) power is scarcely influenced during the manipulation because the orthogonally polarized THz generation are independent with each other. The description above means the polarization of the THz radiation E_THz(t) can be flexibly controlled with no change of its spatial structure and power.

4. Discussions

To deepen the understanding of the polarization-controlled THz radiation, the photocurrent model [34] is used to simulate the THz radiation from two paralleled filaments pumped by two-color laser fields. It is well known the free electron density and current J(t) are governed by $\partial \rho \left( t \right)/\partial t = W\left[ {E\left( t \right)} \right]\left[ {\rho _0-\rho \left( t \right)} \right]$ and $\partial J\left( t \right)/\partial t = (q^2/m)\rho \left( t \right)E\left( t \right)-J\left( t \right)/\tau _c$. Here E(t) and $W\left[ {E\left( t \right)} \right]$ are the laser fields and the static tunnel ionization rate [35], while $\rho _0$, q and m are the density of neutral atoms, the charge and mass of the electron, respectively. τ_c is the current decay time with τ_c = 5 ps. The two-color pump fields from Arm1 or Arm2 can be written as E₁(t)=f_1FW(t)cos(ωt)ê_z+f_1SH(t)cos(2ωt+ϕ₁)ê_z and E₂(t_d)=[f_2FW(t_d)cos(ωt_d)+f_2SH(t_d)cos(2ωt_d+ ϕ₂)]ê_y, where t_d = t + τ. In our simulations, the THz radiations generating from two filaments are independently calculated without interference as in Fig. 4. While setting τ value so that the relative phase between E_THz1(t) and E_THz2(t) from two filaments ranges from 0, 0.25π to 0.5π, E_THz(t) polarization is from linear to circular. And the E_THz(t) spin can be inverted when the phase varies from 0.5π to -0.5π. The simulated results agree well with the measurements as shown in Fig. 3, which verifies that the THz polarization can be controllable feasibly.

 

Fig. 4. Simulations of 3D THz electric fields at ϕ_THz = 0, 0.25π, 0.5π and -0.5π.

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The conventional method of the polarization-controlled broadband THz radiation is hard to control freely the polarization states. An interesting way to manipulate THz polarization was reported by changing the relative phase between the two-color laser field composed of a circular polarized FW and its linearly polarized SH or the length of the filament [24]. It can precisely manipulate the azimuthal angle and ellipticity of the output THz fields. In comparison, our method has advantages in ellipticity control. The recent research suggested that the phases and spectra of the THz fields radiated from the long-distance plasma can be suffered by the plasma length [36]. The THz radiation from each filament in our experiment is independent, so the THz power and spectrum almost keep unchanged during the polarization manipulation. It means that it is free from the intensity or spectral perturbations during the polarization manipulation, which may be important for some THz applications.

As we know, one of the advantages of the air-plasma-based THz source can avoid the limitation of the pump damage threshold. However, the intensity clamping in filaments would constrain the efficiency of the THz radiation as the measured results in Fig. 1(b). While creating the THz fields by the high-power laser pulses, employing the long-distance plasma is an effective way to enhance the THz radiation. Unfortunately, as the linear-dipole array model [37] described, the phase delay between the THz fields in different longitudinal positions of the long gas-plasma would result in the final output THz field stretching to be multicycle, which would lose the unique advantage over the THz radiations from nonlinear crystals. Comparatively, to boost THz radiation with the paralleled multiple filaments is an effective way without pulse broadening.

5. Conclusions

In summary, we present experimentally an obvious enhancement of THz radiation with two paralleled filaments pumped by two-color laser fields. The intensity clamping effect is experimentally verified by measuring the THz power from each of the filaments at different pump levels, which prevents the further enhancement from the THz power by increasing the pump power. By use of two laser pumps for two parallel closely filaments, we can avoid effectively this prevention, and allow us make a full use of the higher pump power. By measuring the intensities of the THz fields at different pump levels, we verify that the total THz field with two paralleled filaments was effectively enhanced by a factor of 4.04 times that of Arm1and 2.23 times that of Arm2 while the laser pumps increase to intensity clamping. More importantly, the polarization-controlled THz radiation can be carried out by using two orthogonally polarized laser fields. While controlling the relative phase from 0 to 0.5π, the total THz field polarization gradually varies from linear to circular. Notably, our efficient enhancement of THz radiation with controllable polarization is suitable for high-quality applications because both the power and the spectrum are almost unchanged during polarization manipulation.