Research Article | Open Access
Zhiqiang Yu, Lu Sun, Nan Zhang, Jianxin Wang, Pengfei Qi, Lanjun Guo, Quan Sun, Weiwei Liu, Hiroaki Misawa, "Anti-Correlated Plasma and THz Pulse Generation during Two-Color Laser Filamentation in Air", Ultrafast Science, vol. 2022, Article ID 9853053, 7 pages, 2022. https://doi.org/10.34133/2022/9853053
Anti-Correlated Plasma and THz Pulse Generation during Two-Color Laser Filamentation in Air
The THz generation efficiency and the plasma density generated by a filament in air have been found anti-correlated when pumped by two-color laser field. The plasma density near zero delay of two laser pulses has a minimum value, which is opposite to the trend of THz generation efficiency and contradicts common sense. The lower plasma density cannot be explained by the static tunneling model according to the conventional photocurrent model, but it might be attributed to the electron trapping by the excited states of nitrogen molecule. The present work also clarifies the dominant role of the drifting velocity accelerated by the two-color laser field during the THz pulse generation process. The results promote our understanding on the optimization of the THz generation efficiency by the two-color laser filamentation.
In the past decades, terahertz (THz) pulse generated by the interaction between femtosecond laser pulse and gas plasma, i.e., filament, has attracted broad attention owing to its advantages of ultrabroad band and high field strength [1–3]. In order to coherently control the output THz wave, two-color laser (TCL) field, commonly synthesized by a Ti: sapphire femtosecond laser pulse (FL) centered around 800 nm and its second harmonic (SH), is frequently used as the pumping source [4–9]. In common sense, the superposition of two laser pulses will not only enhance the free electron density inside a filament , but also boost the efficiency of the THz wave generation [11–16]. The terahertz field strength strongly depends on the laser wavelength and relative phase between the two-color laser beams. When the time delay of the two-color field is close to zero delay, the phase difference is π/2, which increases the magnitude of the net current, thereby realizing strong terahertz wave radiation . The cross-section of the THz wave generated by the dual-color laser filamentation is Gaussian distribution , and the beam divergence angle can be adjusted by changing the diameter and length of the plasma. Recent studies on THz generation using two-color lasers demonstrate that, as the pump laser energy increases, the THz generation energy increases, and when the laser energy continues to increase, secondary ionization occurs, and the THz intensity continues to increase [18–20]. Finally, due to intensity clamping and THz energy reabsorption in plasmas, the THz energy tends to saturation. In addition, researchers also use longer pump wavelength, transparent dielectric tape target to enhance the radiation of THz wave [19, 20]. Besides, increasing the plasma density is also reported an important method to improve the THz generation efficiency . However, there are few experimental reports on the plasma density of the two-color laser filamentation that radiates THz. In the present work, the anticorrelation between the terahertz wave generation efficiency and the plasma density found in the two-color laser filamentation experimental breaks the cognition that the superposition of the two laser pulses would increase the free electron density and the efficiency of terahertz wave generation simultaneously.
In the current work, the variation of the THz amplitude generated by TCL in air has been studied as a function of the temporal delay between two laser pulses, which were centered around 800 nm and 1600 nm, respectively. At the same time, the plasms density generated by TCL has also been characterized. Surprisingly, the experimental results demonstrate an anti-correlation between the THz amplitude and the plasma density. THz amplitude reaches the maximum when there is zero delay between the two laser pulses, while the free electron density was recorded minimum, contrary to common sense. Our finding might provide new insight into the underlying mechanism of THz generation by TCL.
2. Experiment Setup
Figure 1 shows the schematic diagram of our experimental setup. During the experiments, a 1 kHz Ti: sapphire femtosecond amplifier (Solstice, Spectra Physics Inc.) which delivered 35 fs pulses with a central wavelength of 800 nm was employed. The pulse with a total energy of 5 mJ was split into two paths by a beam splitter (BS1). One path with 3 mJ pulse energy was used to pump an optical parametric amplifier (OPA, TOPAS), producing the pulse (POPA) whose wavelength can be tunable from 1200 nm to 1600 nm.
The other path was further divided into two beams by the second beam splitter (BS2). The main pulse (PFL) was combined with the OPA output POPA by a dielectric mirror, yielding a filament in air. Two identical lenses (L1, L2), whose focal lengths were mm, were used to focus two lasers before reaching DM. The laser beam radiuses (1/e2) of and on the front surface of the focusing lens were 4 mm and 2 mm, respectively. The polarizations of two pumping lasers were set to be parallel by using an air-space zero-order half-wave plate (HWP). An off-axis parabolic mirror was used to collect and collimate the forward propagation of the THz pulse emitted by the air plasma. The THz pulse energy was characterized by a Golay cell detector (GC-1P, Tydex Inc.), which was equipped with a 6-mm diameter high-density polyethylene input window. Note that in order to detect the THz pulses using the Golay cell, the femtosecond laser beam output from the laser systems was modulated by a chopper with a frequency of 15 Hz. Four pieces of 2-mm-thick Teflon plates were placed behind the filament to block the femtosecond laser and the stray light, which guaranteed that only the THz radiation can be detected by the Golay cell. Furthermore, the first-order autocorrelation of the THz pulse was measured by using a homemade Fourier spectrometer based on a Michelson interferometer as shown in Figure 1. The spectrum of the THz pulse was obtained by Fourier transforming the autocorrelation trace.
Another beam passed through a 100 μm thick type-I beta barium borate (BBO) crystal. The generated SH pulse () was implemented as the probe of a shadow-graphic setup . In detail, the SH beam propagated through the plasma zone perpendicularly. The plasma was imaged by a lens with a focal length of 50 mm onto a CMOS camera (DCC1240C-HQ, Thorlabs Inc.). A band-pass filter (ZBPA400, Asahi Spectra Inc.), which has a high within the spectral range of 390 nm-410 nm, was used to prevent FL and most of the supercontinuum from entering the CMOS camera.
The time delays among , , and were adjusted by two translation stages (PT1-Z8, Thorlabs Inc.). The delay time between and is indicated as Δt1 and Δt2 refer to the delay time between and . When or , lagged behind or , respectively.
3.1. Experimental Results
In Figure 2(a), the generated THz efficiency as a function of in the experiment is shown as the black solid line. Note that the single pulse energies of pump light and infrared light are 0.5 mJ and 0.3 mJ before the focusing lenses L1 and L2, respectively. It could be clearly seen that the THz energy has a maximum value near zero delay. The highest energy of the THz wave measured by the Golay cell detector is 188 nJ, and the corresponding THz conversion efficiency is 0.0235%. The THz waveform autocorrelation trace and the corresponding THz spectrum for are depicted in Figure 2(b).
Besides, the recorded shadowgraphs of the filament are shown in Figures 3(a)–3(c) for at different values of . Worth mentioning that when , there is no temporal overlap between and as indicated in Figure 2(a). It could be seen that as increases, the filament becomes longer, which is mainly associated with the propagation of the fundamental pulse in air. However, the filament does not change significantly when is greater than 5000 fs, because the fundamental pulse has exceeded the filamentation zone. The shadowgraphs with different for fs were recorded to retrieve the variation of plasma density inside the filament. As an example shown in Figure 3(d), when is about zero, the absorption of the probe light after passing through the filament becomes weaker, and the filament becomes longer toward the lens.
3.2. Numerical Simulations
The plasma density was then deduced according to the absorption coefficient as the follows : where denotes the mean diameter of the filament, and represent the probe laser intensities before and after passing through the plasma. , κ, , ε,, τ, , , , , , and correspond to the probe beam light frequency, the imaginary part of the refractive index of the air, the light speed in vacuum, the dielectric function, the real part of the dielectric function, the imaginary part of the dielectric function, the plasma frequency, the scattering time , the charge of electron, the electron’s mass, the permittivity in vacuum, and the free electron density of plasma, respectively. Similar to the shading method, the filament fluorescence with different time delays was obtained during the experiment. When and 400 fs, Normalized fluorescence intensity distribution along the diameter of the filament is shown in Figure 4(a), and the full width at half maximum of the fluorescence intensity is almost the same. In addition, the diameters of the filaments with different time delays are basically the same, as shown in Figure 4(b). Therefore, the same diameter (d) can be substituted into the calculation.
Hence, the calculated free density at different is shown in Figure 3(e). In addition, the evolution of on-axis plasma density at , which corresponds to the center of the filament, is highlighted in Figure 2(a) as the red dash-dotted line. Clearly, the plasma density on the filament has a minimum value when , which is surprisingly opposite to the trend of THz generation efficiency shown in Figure 2(a).
Conventionally, THz wave generation by femtosecond laser filamentation could be explained by a photocurrent model . In this scheme, the combined TCL field can be expressed as , where and point to the amplitudes of the FL and the infrared light fields, respectively, and are the angular frequency of the FL and the infrared light, and 𝜃 denotes the initial relative phase between two fields. The ionization rate (per molecule) could be given by the static tunneling (ST) ionization model in the form: where is the atomic frequency unit and represents the atomic field of the ground state electron in a hydrogen atom. The yielded free electron density is maximum when is near zero, which is contrary to our experimental results .
The contradiction might be attributed to the reduced ionization by the 1600 nm laser induced by the resonance between the excited states. Though the influence of Rydberg states on multiphoton ionization remains unclear, previous studies have demonstrated that the intermediate states during ionization can trap excited electrons [17, 24]. Since nitrogen molecules dominate in the air, we focus on the electronic energy levels of nitrogen molecule which have been calculated based on the hybrid functional B3LYP and triple-zeta basis set aug-cc-pvtz [25, 26]. The electronic energy levels below are displayed in Figure 5. Note that 15.6 eV corresponds to the ionization energy of the nitrogen molecule.
In the case of dual-color field, the electron from HOMO is excited by 800 nm and 1600 nm photons shown in Figure 6. Since the energy of 1600 nm photon is 0.78 eV and the vibration energy of nitrogen is around 0.2 eV, resonance induced by 1600 nm photon is probable to occur when the electronic energy gap is around 0.78 ± 0.2 eV. Moreover, by analyzing the energy level, it is noted that the energy difference between HOMO and LUMO+7 is 15.47 eV. The value approximates the sum of seven 800 nm photons and six 1600 nm photons. Therefore, the electron can be excited to LUMO+7 orbital during ionization. Besides, the energy gap between LUMO+6 and LUMO+7 is 0.59 eV, implying that the resonance between the two levels can be induced by a 1600 nm laser and electron may be trapped, as shown in Figure 5. Thus, the decrease of the plasma density at zero delay might be attributed to the electron trapping by the excited states.
Since the two incident beams are Gaussian in the time domain, the experimentally measured plasma densities versus in Figure 2(a) can be fitted and expressed as where τ is the fitting parameter, about 85 fs. In order to understand the anti-correlation between the THz wave generation efficiency and plasma density, the underlying dynamic of THz wave generation has been studied according to the photocurrent model. The resulting transverse electron current can be written as where denotes the initial instant of the ionization process, dNe(t’) represents the density of free electrons produced by the laser field in the interval between t’ and t’ + dt’, and υ(t,t’) refers to the drift velocity of those electrons at t. By substituting the experimental parameters such as laser center wavelength and electric field amplitude into Equation (4), the relative THz radiation intensities versus could be calculated.
However, since the conventional photocurrent model has failed in the explanation of the THz generation in our experiment, the description of the ionization dynamic, namely, ST model, has been replaced by an empirical model in the current work. The empirical model is modified on the basis of the traditional photocurrent model, the final plasma density obtained by the ST model at different time delays is replaced by the experimentally measured plasma density, and then the terahertz intensity is calculated by inversion. The resulted THz pulse energy is demonstrated in Figure 2(a) as the blue dashed line, which agrees well with the experimental outcome.
Furthermore, the temporal variation of when fs and 32.7 fs are highlighted in Figure 6(a). It is essential to emphasize that the net current determines the energy of the generated THz pulse in the framework of the photocurrent model [11, 12]. Figure 6(a) indicates that depends on , namely, the temporal delay between the fundamental laser pulse and the infrared laser pulse, strongly. Hence, the variation of with respect to is also depicted in Figure 6(b). The oscillation period of the is about 2.67 fs; however, due to the limitation of the translation stage precision during the experiment, only the envelope curve of the terahertz intensity can be obtained. Figure 6(b) implies that though the maximum free electron density inside the filament has minimum value when was small, might reach the peak value, leading to the highest THz pulse energy. It should be attributed to the dominant role of the free electron acceleration by the laser pulse inside a filament according to Equation (4).
In conclusion, the collinear propagations of 1600 nm light and 800 nm light with different time delays are focused to form a filament in air. The free electron density inside the filament and the emitted THz pulse energy have been found anti-correlated, which contradicts the common sense of the community. The decrease of the plasma density at zero delay can be attributed to the electron trapping by the excited states. On the other hand, the drifting velocity accelerated by the two-color laser field has been confirmed to play a dominant role during the THz pulse generation process. The experiment results indicated the failure of the convention photocurrent model, which describes the ionization rate by using the static field model. In contrast, wavelength-dependent ionization model has to be taken into account. The results of the present work arouse the attention of the revisiting of the underlying dynamics of the THz generation by two-color laser filamentation, which has been paid broad research attention in the field of intensity THz wave generation.
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this article.
Z. Q. Yu, L. Sun, and W. W. Liu performed the experiments. N. Zhang, J. X. Wang, and P. F. Qi performed the simulations and analyzed the data. L. J. Guo and H. Misawa contributed to the revision of this paper. Q. Sun and W. W. Liu proposed the original idea and supervised the project. Z. Q. Yu and L. Sun contributed equally to this work.
This study was supported by the National Key R&D Program of China (2018YFB0504400), the National Natural Science Foundation of China (12061131010 and 12074198), the Russian Science Foundation (21-49-00023), and the Natural Science Foundation of Tianjin Municipality (20JCYBJCO1040).
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