Main > Chinese Optics Letters >  Volume 16 >  Issue 11 >  Page 110401 > Article
Chinese Optics Letters, Vol. 16, Issue 11, 110401 (2018)

Terahertz wave generation via pre-ionized air plasma

Kai Kang1, Liangliang Zhang1,*, Tong Wu2, Kai Li3, and Cunlin Zhang1

Author Affiliations

  • 1Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, and Beijing Advanced Innovation Center for Imaging Technology, Department of Physics, Capital Normal University, Beijing 100048, China
  • 2Beijing Key Laboratory for Precision Optoelectronic Measurement Instrument and Technology, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China
  • 3Daheng New Epoch Technology Inc., Beijing 100085, China

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.

1 引言

孔径综合是提高光学成像系统分辨率的有效手段之一[1-4]。基于数字全息术的分布式孔径综合成像系统采用多个子孔径对目标进行全息探测,然后根据其空间位置对各个子孔径上的目标光复振幅进行综合,从而实现多孔径综合高分辨率成像[5-10]。这种技术具有模块化、三维成像和数字综合等优点,但是孔径综合的相位误差一般应控制在1/10波长以内[8]。系统装配误差是子孔径间相位误差的来源之一,如子孔径探测器间的相对位移、倾斜、旋转以及缩束装置的放大率误差都会引起孔径综合的相位误差,对此目前主要采用基于像清晰化的校正方法[11-13]。针对子孔径间的位移误差,Jiang等[14]研究了基于综合孔径图像质量评价及优化的数字校正方法,达到了亚像素精度。考虑到子孔径间的相对位移和旋转误差,Gunturk等[15]提出一种基于坐标系变换、多域串行迭代式的校正方法,即把在直角坐标系下较难直接处理的孔径旋转、位移等误差,通过坐标系变换(如极坐标、对数坐标系等)、傅里叶变换等方法,转化为倾斜和位移等误差,然后对各种相位误差依次采用迭代式像清晰化法进行校正。考虑到多次坐标系变换引起的数值误差以及散斑噪声对迭代式像清晰化算法收敛特性的影响[16],这种校正方法方法存在耗时长、甚至局部收敛的问题。

针对子孔径间的旋转和放大率误差,本文提出了基于子孔径目标图像配准的误差校正方法。与目前直接采用迭代式像清晰化校正方法[15]相比,本文方法不仅无需坐标系变换和迭代运算,而且可以同时校正两种误差。

2 原理和方法

2.1 成像原理及误差分析

基于数字全息术的分布式孔径综合成像系统示意图如图1所示[5,11]

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

Download full sizeView all figures

激光器发射出的相干光束被分为两束,一束光射向目标,另一束光进一步分束为各个子孔径内的本地参考光。子孔径内的光电探测器分别记录本地参考光与目标返回光的干涉信号。在数字信号处理器中,首先利用傅里叶变换等方法从干涉信号中分别复原出子孔径探测器上的目标返回光复振幅Ui,然后按照子孔径空间位置对Ui进行综合,并通过菲涅耳衍射公式计算出目标平面上的复振幅:

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+(1WIRB)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={1ifSIRBSVisB0otherwise.

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.

Download full sizeView all figures

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

    View tableView all Tables

    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

    View tableView all Tables

    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(ueui), 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.

Download full sizeView all figures

Here, we define a THz wave modulation depth M=(S1S2)/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.

Download full sizeView all figures

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.

References

[1] D. H. Auston, K. P. Cheung, P. R. Smith. Appl. Phys. Lett., 45, 284(1984).

[2] J. T. Darrow, B. B. Hu, X. C. Zhang, D. H. Auston. Opt. Lett., 15, 323(1990).

[3] N. M. Froberg, B. B. Hu, X. C. Zhang, D. H. Auston. Appl. Phys. Lett., 59, 3207(1991).

[4] A. Rice, Y. Jin, X. F. Ma, X. C. Zhang, D. Bliss, J. Larkin. Appl. Phys. Lett., 64, 1324(1994).

[5] X. Xie, J. Dai, X. C. Zhang. Phys. Rev. Lett., 96, 075005(2006).

[6] A. Mysyrowicz, B. Prade, G. Beaudin, G. Méchain, G. Patalano, J. M. Munier. Opt. Lett., 27, 1944(2002).

[7] J. Dai, X. C. Zhang. Appl. Phys. Lett., 94, 1210(2009).

[8] H. W. Du, H. Hoshina, C. Otani, K. Midorikawa. Appl. Phys. Lett., 107, 2725(2015).

[9] M. Kress, T. Löffler, S. Eden, M. Thomson, H. G. Roskos. Opt. Lett., 29, 1120(2004).

[10] T. Löffler, M. Kress, M. Thomson, H. G. Roskos. Acta Phys. Pol., 107, 99(2005).

[11] N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao. Appl. Phys. Lett., 92, 1759(2008).

[12] M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, A. Lotti. Phys. Rev. Lett., 110, 253901(2013).

[13] K. Y. Kim, A. J. Taylor, J. H. Glownia, G. Rodriguez. Nat. Photon., 2, 605(2008).

[14] X. Y. Peng, C. Li, M. Chen, T. Toncian, R. Jung, O. Willi. Appl. Phys. Lett., 94, 1120(2009).

[15] M. D. Thomson, V. Blank, H. G. Roskos. Opt. Express, 18, 23173(2010).

[16] T. I. Oh, Y. S. You, N. Jhajj, E. W. Rosenthal. Appl. Phys. Lett., 102, 1210(2013).

[17] Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, T. Suemoto. Appl. Phys. Lett., 102, 041105(2013).

[18] J. Shin, Z. Jin, T. Hosokai, R. Kodama. Asia Pacific Physics Conference(2013).

[19] J. Zhao, L. Zhang, Y. Luo, T. Wu, C. Zhang, Y. Zhao. Chin. Opt. Lett., 12, 083201(2014).

[20] H. Hamster, A. Sullivan, S. Gordon, W. White, R. W. Falcone. Phys. Rev. Lett., 71, 2725(1993).

[21] Y. Bai, J. Tang, R. Xu, P. Liu. Chin. Opt. Lett., 14, 093201(2016).

[22] W. Wang, Z. Sheng, Y. Li, L. Chen, Q. Dong, X. Lu, J. Ma, J. Zhang. Chin. Opt. Lett., 9, 110002(2011).

[23] Q. Wang, Y. Zhang, Z. Wang, J. Ding, Z. Liu, B. Hu. Chin. Opt. Lett., 14, 110201(2016).

[24] Y. E. Geints, A. M. Kabanov, A. A. Zemlyanov, E. E. Bykova, O. A. Bukin, S. S. Golik. Appl. Phys. Lett., 99, 181114(2011).

[25] T. Wu, L. Dong, S. Huang, R. Zhang, S. Zhang, H. Zhao. Appl. Phys. Lett., 112, 171106(2018).