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Accepted: Sep. 27, 2018

Posted: Jan. 17, 2019

Published Online: Nov. 14, 2018

The Author Email: Liangliang Zhang (zhlliang@126.com)

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Kai Kang, Liangliang Zhang, Tong Wu, Kai Li, Cunlin Zhang. Terahertz wave generation via pre-ionized air plasma[J]. Chinese Optics Letters, 2018, 16(11): 110401

## Abstract

We report the terahertz (THz) wave generation from a single-color scheme modulated by pre-ionized air plasma via an orthogonal pumping geometry. It is found that the amplitude of the THz signal generated by the pump beam tends to decrease gradually with the increase of the modulation power. We believe that the ponderomotive force plays an important role in the process of the interaction between the pump beam and the pre-ionization beam. The hydrostatic state of the electrostatic separation field caused by the modulation beam will directly affect the generation efficiency of the THz wave. Our results contribute to further understanding of the theoretical mechanism and expanding of the practical applications of THz wave generation and modulation.

## 2.1 成像原理及误差分析

Figure 1. Scheme of distributed aperture synthesis imaging system based on digital holography

The binary weight maps $BWIR(i)$ ($i=2,…,n$) are also filtered using the GDGF with the corresponding detail images $DIR(i,1)$ ($i=2,…,n$) as guidance images. Finally, weight maps of the infrared for the large-scale detail level $WIR(i)$ ($i=2,…,n$) can be obtained as $WIR(i)=GDGFr(i),λ(i)(DIR(i,1),BWIR(i)),(i=2,…,n),$where $r(i)=rg(i)$, and $λ(i)=λg(i)/10$ for the GDGF.

For the base level, the fused image $FB$ is computed as $FB=WIRBBIR+(1−WIRB)BVis,$where $BIR$ and $BVis$ are the base images of the infrared and visible, respectively, and $WIRB$ is the weight map of the infrared image for the base level.

The saliency maps of the infrared and visible images for the base levels $SIRB$ and $SVisB$ are obtained via the frequency-tuned filtering for the corresponding base images. Then, the binary weight map of the infrared $BWIRB$ is computed as $BWIRB={1if SIRB≥SVisB0otherwise.$

The binary weight map $BWIRB$ is smoothed using a Gaussian filter to fit the combination of extremely coarse-scale information. Finally, the weight map for the base level $WIRB$ is obtained as follows: $WIRB=gσb(BWIRB),$where $σb=2rsn$ for the Gaussian filtering $g()$.

In order to test the proposed FNCE method, three state-of-the-art fusion methods are selected for comparison: the guided filtering fusion (GFF) method[13], the gradient transfer fusion (GTF) method[14], and the GFCE method[7]. All the comparative methods are implemented using the public codes, where the parameters are set according to the corresponding Letters. In the FNCE method, the number of decomposition scales $n=4$, the decomposition factor $k=2$, and the initial values of the GF are $rs(1)=3$, and $λs=104$, as well as the initial values of the GDGF of $rg(1)=2$, and $λg(1)=0.05$.

It can be seen from the fusion results of the test images in Fig. 6 that the results of the FNCE method have clearer details (including edges), more salient targets, better contrast, and less noise than other methods. Close-up views for the labeled regions are presented below the images. The results of the GFF method have little detail information from the visible image and are similar than the infrared image with unclear details, as shown in Fig. 6(a). Moreover, the clouds from the infrared image are nearly lost in the “Buildings” result. For the GTF method, as shown in Fig. 6(b), although the results have the least noise, the details are unclear enough. Moreover, lots of information from the visible is lost, for example, the lights. For the GFCE method, as shown in Fig. 6(c), the bright parts (for example, the labeled building with lights) are obviously over-enhanced, and the noise in the sky is obvious in the “Buildings” result. The results of the GFCE method have obvious noise and not clear enough details (edges). Moreover, some distortions may occur due to the over enhancement in the GFCE method. For the FNCE method, as shown in Fig. 6(d), the road sign shown by the red arrow is clearest without distortions in the “Queen’s Road” result. Therefore, the proposed FNCE method is able to acquire better results for the human visual perception in night vision.

Figure 6. Fusion results of different methods for the test images.

Information entropy (IE), average gradient (AG), gradient-based fusion metric ($QG$)[15], the metric based on perceptual saliency (PS)[7], and the fusion metric based on visual information fidelity (VIFF)[16] are selected for the objective assessment. IE evaluates the amount of information contained in an image. AG indicates the degree of sharpness. $QG$ is recommended for night-vision applications[17] to evaluate the amount of edge information transferred from the source images. PS measures the saliency of perceptual information contained in an image. VIFF evaluates the image quality of the fused image in terms of human visual perception. Table 1 gives the quantitative assessments of different fusion methods on four test image pairs, and the best results are highlighted in bold. The values in Table 1 are averaged values of the four test pairs. It can be seen from Table 1 that IE, AG, PS, and VIFF all achieve the best values in the FNCE method, which means the proposed FNCE method can extract more information, have better sharpness, have more saliency information, and achieve better human visual perception. In addition, the $QG$ value of the FNCE method is in the second rank, and it means edges can be relatively better preserved via the FNCE method as well.

• #### Table 1. Quantitative Assessments of Different Methods

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#### Table 1. Quantitative Assessments of Different Methods

MethodIEAGQGPSVIFF
GFF6.60930.01000.613216.48000.4278
GTF6.32750.00610.284713.75860.2205
GFCE6.81060.01520.361219.57980.5648
FNCE6.97860.01870.602920.69760.6580

The average running time of the different methods on $640 × 480$ source images is shown in Table 2. All of the compared methods are implemented via MATLAB on a computer (Inter i5 3.40 GHz CPU, 4G RAM).

• #### Table 2. Average Running Time on 640 × 480 Images

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#### Table 2. Average Running Time on 640 × 480 Images

MethodGFFGTFGFCEFNCE
Time (s)0.5266.8331.6052.069

After the experimental comparisons, it can be seen that better human visual perception is achieved with more salient targets, better details (edges) performance, better contrast, better sharpness, and less noise in the FNCE method. Obviously, the proposed FNCE method is more effective, which will help to obtain better context enhancement for the night-vision imaging. Although the FNCE method is slightly time-consuming, it is acceptable, considering the better fused result.

In conclusion, an FNCE method is proposed. First, an adaptive brightness stretching method is proposed to enhance the visibility of the low-light-level visible image. Following this, a structure of the hybrid MSD with the GF and the GDGF is proposed for fully decomposing the enhanced source images. In addition, weight maps are obtained via a perception-based saliency detection technology at each scale.

Experimental results show that better results for night-vision context enhancement can be acquired via the proposed FNCE method. In the future, the idea of the fast GF[18] may be introduced into the simplifications of the FNCE method for practical applications. Moreover, the previous frame video image may be used as the guidance image of the current frame to reduce the delay.

The Helmholtz equation for the laser field ($E⊥$) to propagate within the plasma is expressed as $∂E⊥/∂x2+κ2E⊥=0,$where $κ$ is the wave vector. In the above formula, subscripts $e$ and $i$ represent the electron and ion, respectively. $n$ and $u$ stand for the particle density and velocity, respectively. Particles in plasma are subjected to thermal pressure $∂pe,i/∂x$, electrostatic forces, collision forces $ρiνe,i(ue−ui)$, and pondermotive forces $fNLe$, where $pe,i=ne,ikTe,i$, $k$ is Boltzmann’s constant and $Te,i$ is temperature, and $ρ$ represents the mass density. The pondermotive force of particles can be expressed as $fNLe=q24mωΔE2(x),$where $ω$ is the angular frequency of the laser and $E$ is the amplitude of the laser field. With the effect of $E$, the electron has scattered out in the direction perpendicular to the optical path and experienced the process of accelerating and decelerating in the direction of the optical path. Due to the great difference in the mass of ions and electrons, the pondermotive force received is also greatly different, which results in a strong electrostatic separation field. Then the electrons and ions speed up or decelerate in the transient electric field to form a transient current. In this model, another strong force is thermal pressure, which is caused by electrons. Absorbing the laser energy efficiently, the electron temperature rises rapidly, and produces strong thermal pressure on the two sides of the low-temperature region, pushing the electrons to move quickly to both sides. So neutrality is destroyed again and another electrostatic separation field has been created that drives the movement of ions and electrons to the regions with low electron temperatures, resulting in a powerful electromagnetic transient and eventual THz wave generation.

When the two laser beams are vertically focused at one point on the same horizontal plane, we believe that the plasma is nearly orthogonal in space to form a more complex plasma region. In this area, the pre-ionization plasma plunders parts of electrons and ions and these particles become meaningless for the generation of a THz wave. For this reason, $ρ$, $n$, and $u$ decrease so that the electric field amplitude ($E$) and the particle motion velocity, as well as the acceleration, directly reduce under the influence of the pondermotive force and the thermal pressure, which leads to the reduction of the THz wave intensity.

In our experiments, we also calculated the dependence of THz wave energy on the arrival time of the pre-ionization plasma generation pulse with respect to the pump beam. The integral over the square of the whole THz waveform gives the energy of the THz pulse. The intensity of THz radiation varies sharply with the intersection of two plasmas in the spatial and temporal domains. First, we optimize the experimental system to make the two plasmas orthogonal in space. Then a translator is placed in the modulation path to adjust the time delay. When the two beams are consistent in the time and space domains, modulation occurs, as shown in Fig. 3(a). In the early stage (0–5 ps), the pump beam arrives at the cross region prior to modulation; when adjusting the translation platform, the two beams arrive at the cross region together at 5 ps and the duration of the modulation process is 3 ps. After 8 ps, the modulation breaks away from the cross region, and the peak value begins to recover slowly. For clarity, the curves corresponding to the three representative pump beam powers of 0.4 W, 0.6 W, and 0.8 W to generate THz waves are shown.

Figure 3. (a) THz signal of three representative excitation pump powers of 0.4 W, 0.6 W, and 0.8 W in the presence of pre-formed plasma as a function of the relative time between the pump beam and the modulation beam. (b) The effect of the modulated laser intensity on the THz wave modulation depth.

Here, we define a THz wave modulation depth $M=(S1−S2)/S1$ to predict the degree of the pre-ionization suppression on the THz wave intensity, where $S1$ is the THz wave signal generated by the pump beam without pre-ionization plasma, and $S2$ is the THz wave signal when the 800 nm pre-ionization plasma is prior to the arrival of the pump beam[25]. Figure 3(b) shows the effect of the modulated laser intensity on the THz wave modulation depth. There are two orthogonal pondermotive force fields in the cross region, and changing the power of any beam will affect the THz radiation. First, when the pump beam power is constant, the stronger the modulated beam is, the more electrons become useless for THz wave generation. The weaker the intensity of the THz wave, the stronger the modulation depth. Second, when the modulation power remains constant, the stronger the pump beam power is, the more electrons become useful for THz wave generation. What is more, the greater the intensity of the THz wave, the lower the modulation depth. However, when the modulation power is less than 0.6 W, the result somewhat deviates from our theory. We believe that it is the low modulation power and the error caused by the experimental measurement that result in the indistinct discrimination.

Figure 4 shows the THz wave polarization under different modulation powers with a fixed pump power of 0.8 W. It is obvious that the THz wave polarization stays linear and its direction does not rotate with the increase of the modulation power. The results are basically consistent with the expectations of our analysis. The effect of the lateral modulation beam reduces the excitation of the longitudinal pump beam, so that some particles do not participate in the THz wave generation. It does not substantially change the general structure of the plasma, so it does not change the THz polarization.

Figure 4. THz wave polarization under different modulation powers.

In conclusion, we demonstrated that the THz wave energy modulation depth depends upon the energy of the pump pulse when a pre-ionization plasma is created by a synchronized modulation beam using an orthogonal pumping geometry. We found that the THz wave modulation depth increases as a function of the modulation beam power. When the power of the modulation beam increases, the THz wave modulation tends to be saturated. Our results contribute to further understanding of the theoretical mechanism and expanding of the practical applications of THz wave generation and modulation.

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