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PROCEEDINGS OF SPIE

SPIEDigitalLibrary.org/conference-proceedings-of-spie

Terahertz wave transmission and

reflection characteristics in plasma

Geng, Xingning, Xu, Degang, Li, Jining, Chen, Kai, He,

Yixin, et al.

Xingning Geng, Degang Xu, Jining Li, Kai Chen, Yixin He, Jianquan Yao,

"Terahertz wave transmission and reflection characteristics in plasma," Proc.

SPIE 11196, Infrared, Millimeter-Wave, and Terahertz Technologies VI,

111961T (17 December 2019); doi: 10.1117/12.2538833

Event: SPIE/COS Photonics Asia, 2019, Hangzhou, China

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Terahertz wave transmission and reﬂection characteristics in

plasma

Xingning Genga,b, Degang Xu*a,b , Jining Lia,b, Kai Chena,b , Yixin Hea,b, and Jianquan Yaoa,b

aSchool of Precision Instrument and Opto electronics Engineering, Institute of Laser and

Optoelectronics, Tianjin University, Tianjin 300072, China

bKey Laboratory of Opto-electronics Information Technology (Ministry of Education), Tianjin

University, Tianjin 300072, China

ABSTRACT

After entering the near space, a layer of plasma sheath is formed outside the hypersonic vehicles due to the high-

temperature and high-pressure environment. The plasma sheath, which characteristic frequency is similar to

microwave, will cause serious impediment to communication signal. This phenomenon is known as the blackout

problem. With the rapid development of aerospace industry, plasma sheath blackout has become an urgent

problem to be solved. Current research shows that increasing the frequency of electromagnetic wave higher

than the plasma characteristic frequency can eﬀectively reduce the shielding eﬀect of plasma. The frequency of

terahertz (THz) wave is much higher than microwave, it can propagate through plasma sheath, which provides

an eﬀective method to solve the problem of plasma sheath. In this paper, a theoretical model of plasma is

established, and the transmission properties of THz wave in plasma is simulated using scattering matrix method.

Then a kind of plasma jet is produced in laboratory environment according to dielectric barrier discharge.

And the experiments of a broadband THz source and THz time-domain spectrum transmission in this kind

of plasma and a 2.52 THz wave reﬂection imaging of target under plasma shelter are carried out respectively.

The transmittance increases with frequency under 0.5 THz and becomes stable at 100% over 0.5 THz, and the

result of experiments and simulation are in good agreement. Both theory and experiments show that THz wave

has good penetration in plasma jet and can detect targets behind plasma, and this study will lay a theoretical

foundation for solving the plasma blackout problem of hypersonic vehicle in near space.

Keywords: Terahertz wave, plasma, transmission, reﬂection

1. INTRODUCTION

When vehicles ﬂying at hypersonic speeds in near space, the produced plasma sheath will cause the interruption

of communication signals and the failure of radar tracking[1,2]. The main solution to the blackout problem is to

record the main information when the communication of the aircraft is interrupted, then continue to communicate

after the vehicle leaves the blackout area. This method only avoids the inﬂuence of blackout, but does not reduce

the transmission loss and cannot carry out real-time communication. The real-time communication and tracking

are of great importance. Therefore, a new method is urgently needed for real-time communication. And the key

to solve this problem is to study the interaction between electromagnetic wave and plasma.

Many researches have been made on the interaction between electromagnetic wave and plasma. In 1970s,

researchers of project RAM of NASA studied the interaction between microwave and plasma, put forward several

theoretical methods to reduce the blackout problem, and carried out corresponding reentry ﬂight experiments

[3]. Sazhin et al. approximated the propagation of diﬀerent types of electromagnetic waves in weakly relativistic

plasma, and discussed the possible application in the diagnosis of magnetospheric parameters [4]. Nowakowska et

al. studied the characteristics of electromagnetic waves propagating along dense plasma ﬁlaments at atmospheric

pressure in the microwave frequency range, and gave the numerical results of phase and attenuation coeﬃcient

dependence on plasma parameters [5]. Based on the continuous boundary conditions of electromagnetic waves in

Further author information: (Send correspondence to Degang Xu)

Degang Xu: E-mail: xudegang@tju.edu.cn

Infrared, Millimeter-Wave, and Terahertz Technologies VI, edited by Cunlin Zhang,

Xi-Cheng Zhang, Masahiko Tani, Proc. of SPIE Vol. 11196, 111961T · © 2019 SPIE

CCC code: 0277-786X/19/$21 · doi: 10.1117/12.2538833

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one-dimensional plasma photonic crystals, the relationship between dispersion and transmission are investigated

by He et al. [6].

Terahertz (THz) wave generally refers to the electromagnetic wave in the frequency range of 0.1 THz-10

THz, which is between microwave and infrared ray in the electromagnetic spectrum. In recent years, with the

development of THz wave generation and detection technology, this wave band has attracted more attentions.

THz technology has also been widely used in more and more ﬁelds, such as THz radar, THz communication,

THz security, THz quality inspection, THz bioimaging and so on [7–10]. The interaction between THz wave and

plasma has also been paid more attention. Tian et al. studied the absorption coeﬃcients of THz waves in plasma

with diﬀerent collision frequencies, and found that the inhomogeneous collision frequencies could accelerate the

decrease of absorption spectra [11]. Wang et al. used the propagation matrix method to study the propagation

of THz wave in a stratiﬁed dielectric plate containing dust plasma. And the dispersion of conductors and dust

plasma were calculated [12]. The relationship between THz wave propagation characteristics in the reentry

plasma sheath and the angle of attack of the vehicle are discussed by Yuan et al. through a three-dimensional

numerical model [13].

However, most of the theoretical and experimental researches focus on low-frequency THz band [14–17]. The

high frequency THz band is far away from the plasma oscillation frequency and it has advantages on transmission

loss and imaging resolution. Therefore, it is necessary to study the transmission characteristics of THz wave with

higher frequency in plasma theoretically and experimentally. In this paper, an approximate theoretical model

of inhomogeneous plasma sheath is established based on the scattering matrix method, and the propagation

characteristics of 0.1-10THz THz wave in plasma are calculated. Furthermore, a plasma jet is generated by

dielectric barrier discharge. The transmittance of THz time-domain spectroscopy system and broadband THz

source system in plasma are measured, and the reﬂection imaging experiments of 2.52THz THz wave penetrating

plasma shielding target are carried out respectively. Both theoretical and experimental results show that THz

wave has good penetration in plasma. This study may contribute to the application of THz wave in plasma

blackout problem of hypersonic vehicle in near space.

2. THEORETICAL SIMULATION

The scattering matrix method (SMM) divides the continuous inhomogeneous dielectric into several layers and

each layer is assumed homogeneous, the propagation characteristics of electromagnet wave in the whole dielectrics

can be solved through the transmission matrix of each layer [18]. The plasma sheath distribution around the

hypersonic vehicles can be regarded as Gauss distribution, which is

ne(z) = nemaxexp[δ1(z−z0)2] (z1≤z≤z0)

nemaxexp[ −δ2(z−z0)2] (z0≤z≤z2),(1)

where nemax is the maximum plasma density, zis the vertical distance from the to the vehicle surface, z0is

the segmentation point of the Gauss function, δ1and δ2are constants describing the segmentation of the Gauss

function. z2−z1is the plasma thickness.

The SMM stratiﬁcation of Gauss distribution plasma is shown in Fig. 1In this calculation, the plasma is

divided into 10 layers, and the layers are uniformly distributed according to thickness.

The plasma frequency is deﬁned as ωp=qω2

pe +ω2

pi, where ωpe and ωpi are the oscillation frequencies of

plasma electrons and ions, which can be expressed as ωpe =qnee2

ε0meand ωpi =qnie2

ε0mi.neand niare electron

and ion densities of plasma, respectively, and ne=ni.ε0= 8.85 ×10−12F/m is the permittivity of vacuum,

me= 1.67 ×10−27kg is electron mass, miis ion mass,e= 1.6×10−19 C is electron charge.

For mimeand ωpe ωpi ,the plasma frequency can be simpliﬁed as

ωp,m ≈ωpe,m =sne,me2

ε0me

,(2)

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Fig. 1. SMM stratiﬁcation of Gauss distribution plasma.

where εris the relative permittivity of plasma medium, in each layer it can be expressed as

ε(m)

r= 1 −ω2

p,m

ω2+ν2

en

−jνen

ω

ω2

p,m

ω2+ν2

en

,(3)

where ωis the angular frequency of electromagnetic wave,νen= 2πfen is the collision frequency between electrons

and neutral particles, in plasma it is also called plasma collision frequency. The wave number in plasma is

k(m)=k0qε(m)

r, and k0=ω/c is the wave number in vacuum.

The scattering matrix of m-th layer can be expressed as

Sm= e−jk(m)dmej k(m)dm

k(m)e−jk(m)dm−k(m)ej k(m)dm!−1 e−jk(m−1) dmejk(m−1)dm

k(m−1) e−jk(m−1) dm−k(m−1) ejk(m−1) dm!.(4)

Assuming Ais the total reﬂection coeﬃcient and Dis the total transmission coeﬃcient, Bmand Cmare the

transmission coeﬃcient and the reﬂection coeﬃcient of the m-th layer. To match the boundary condition at

z= 0, we can get

B1

C1=S1A

1,(5)

where

S1=1

2k(1) k(1) −k(0) k(1) +k(0)

k(1) +k(0) k(1) −k(0) .(6)

Similarly, to match the boundary condition at z=dn+1 , we can get

Bn

Cn=Vp·D, (7)

where

Vp=1

2k(n) k(n)+k(n+1)ej(k(n)−k(n+1) )dp

k(n)−k(n+1)e−j(k(n)+k(n+1) )dp!.(8)

From the above equations, we can get

SgA

1=Vp·D, (9)

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where Sgis the total scattering matrix, and

Sg= 2

Y

m=n

Sm!S1.(10)

Sgcan be transformed as

A

D=−(Sg1−Vp)−1·Sg2,(11)

then Aand Dcan be solved, and the reﬂectance, transmittance and absorbance are

R=|A|2

T=|D|2

Q= 1 −R−T

(12)

When the plasma collision frequency fen = 0.1×1012Hz, plasma thickness d=10cm, the maximum electron

density nemax = 1018m−3, the propagation of 0.1-10THz THz wave is shown in Fig. 2. As shown in Fig. 2,

Fig. 2. Propagation characteristics of THz wave in plasma. (a)Transmittance; (b)Reﬂectance; (c)Absorbance.

with the increasing of THz wave frequency, the transmittance increases, while the reﬂectance and absorbance

decreases. This is because when the THz wave frequency increases, the electrons in plasma cannot respond to

the rapid changing electric ﬁeld in time, which resulting in less interaction between electrons and THz wave,

and more energy can pass through the plasma. In the low frequency range below 1 THz, the transmittance

increases rapidly. At 0.1 THz, the transmittance is 69.96%; and at 1 THz, the transmittance is 99.3%. At above

1 THz, the transmittance becomes stable. The reﬂectance is expressed by decibel scale. Because of the multiple

reﬂection of electromagnetic wave at the plasma boundary, the reﬂectance oscillates periodically. The oscillation

period is k=nπ/d, in this condition, the period is 0.15 THz. The absorbance of THz wave mainly varies with

the transmittance. Because the high frequency THz wave can almost pass through the plasma, the absorbance

is close to 0. From the propagation characteristics, it can be concluded that THz wave can penetrate the plasma

sheath, which provides an important method to solve the problem of near space communication blackout.

3. EXPERIMENT

3.1 Plasma jet generation

According to the principle of dielectric barrier discharge, an atmospheric pressure plasma jet is generated. [19]

the generator is composed of a high voltage power supply, a quartz tube and an air supply device, which is shown

in Fig. 3(a). The inner diameter of quartz tube is 6 mm, the thickness of tube wall is 1 mm. The copper ring

electrode is wrapped near the oriﬁce of quartz tube. A high voltage power supply with voltage of 10 kV and

frequency of 15 kHz is applied to the electrode, and neon is injected into the quartz tube as the ionized gas. The

plasma jet with about 20 mm long and 3 mm maximum width is produced, as shown in Fig. 3(b). Unlike the

traditional dielectric barrier discharge which conﬁnes the plasma in the discharge gap, this plasma producing

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method separates the plasma from the high voltage electrode, which increases the security. The research teams

at Eindhoven University of Technology measured the radial distribution of this kind of plasma jet with diﬀerent

gases, and found that the density is around 1018 −1019m−3and decreases from the center of the oriﬁce to the

surrounding area, which is similar to the Gauss distribution [20,21].

Fig. 3. Dielectric barrier discharge. (a) device structure; (b) plasma jet.

3.2 Transmission characteristics of THz wave in plasma jet

The transmission characteristics of THz wave in plasma are measured by the THz time-domain spectroscopy

(THz-TDS) and the broadband THz radiation source system [22]. The THz-TDS system is shown in Fig. 4.

After passing through the beam splitter, a beam of femtosecond laser passes through the delay line and enters

the THz emitter, which has a photoconductive antenna structure. By applying voltage to the antenna, the THz

pulse will be radiated when the carriers are excited. The THz pulse is focused on the sample through an oﬀ-axis

parabolic mirror, and then carries the sample information into the THz detector. Another beam, as detection

light, arrives at the detector at the same time with THz wave to realize the control of the detector.

The broadband THz radiation source system is shown in Fig. 5. The Nd:YAG laser generates 1064 nm laser,

which passes through a KTP crystal to enter the optical parameter oscillation (OPO) system composed of two

KTP crystals. One KTP crystal is ﬁxed and the other is placed on an adjustable oscillator to control the angle of

parameter oscillation, so as to achieve dual-wavelength output. Two beams with similar wavelength pass through

the DAST crystal to generate THz wave based on diﬀerence frequency. The output THz wave is received by

the THz detector after passing through the plasma. The transmission of THz wave in plasma is obtained by

comparing the received signal without plasma.

The results of THz-TDS and broadband THz source transmittance measurements are shown in Fig. 6(a) and

(b). According to the parameters measured by THz-TDS [23], the average plasma density in this paper is about

3.7×1018m−3. The theoretical results based on the plasma density are also shown in Fig. 6(a) and (b). It can

be seen that the transmittance measured by THz-TDS increases with the increase of frequency in the frequency

range below 0.5 THz, and gradually stabilizes at about 100% above 0.5 THz, which is basically consistent with

the simulation results. And the transmittance measured by the broadband THz source system is basically stable

at about 99.5%. Compared with the results of THz-TDS, the results of broadband THz sources diﬀer greatly

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Fig. 4. THz-TDS transmittance measurement system.

Fig. 5. Broadband THz source transmittance measurement system.

from the theoretical results, which is due to the low radiation power as well as low signal-to-noise ratio of the

system. Besides, the broadband source system is placed in an open laboratory environment, the atmospheric

loss is not negligible, while the THz-TDS system is continuously ﬁlled with dry air, so the measurement error is

relatively small.

3.3 Target reﬂection imaging of THz wave

A continuous wave THz imaging system is used to perform THz wave penetration through plasma and reﬂection

imaging of target. The experimental device is shown in Fig. 7.Optically pumped CW CO2laser is used as the light

source. The output THz frequency is 2.52 THz. The output signal is modulated by a 50 Hz chopper to satisfy

the response characteristics of the detector.In order to reduce the image noise caused by weak power ﬂuctuation,

the signal is divided into reference light and signal light by line grating. The reference light is detected by Golay

cell. The signal light penetrates the plasma through a confocal system consisting of oﬀ-axis proﬁlers and focuses

on the target.The signal light is also detectedby Golay Cell. Objects are placed on a computer-controlled scanner

and two-dimensional images are obtained. The size of the plasma is larger than that of the spot, which can shield

the spot.The target material used is metal sphere and screw.Because THz wave can not penetrate metal, the

detector can receive the signal reﬂected by metal. According to theoretical simulation, the transmittance of 2.52

THz wave in plasma is over 98%. In this band, THz wave can penetrate plasma with less loss.

Reﬂection images are shown in Fig. 8. It can be seen that the image of screw can basically show the outline

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Fig. 6. The transmittance measurements results. (a) THz-TDS system; (b) broadband THz source system.

Fig. 7. THz wave reﬂection imaging system.

while the image of sphere has a small area of high reﬂection. Due to the diﬀerent thickness and roughness of the

targets surface, the irregular scattering of the targets surface results in the distortion of the image. The surface

of the sphere is much smoother and only a small fraction of the reﬂected THz wave is accepted. These results

show that THz wave has good abilities in blackout active imaging detection.

4. CONCLUSION

In this paper, the theoretical model of inhomogeneous plasma is established by scattering matrix method, and the

propagation characteristics of THz wave in plasma at 0.1-10 THz waveband are simulated and calculated. The

results show that with the increasing of THz wave frequency, the transmittance increases while the reﬂectance and

absorbance decrease. In the low frequency range, the transmittance increases rapidly. And in the high frequency

range the transmittance tends to be stabilized at 100%. Due to the multiple reﬂection of electromagnetic wave

at the plasma boundary, the reﬂectance oscillates periodically, Besides, according to the principle of dielectric

barrier discharge, an inhomogeneous plasma jet is generated. The THz-TDS system and the broadband THz

source system are utilized to measure the transmission of THz wave in plasma, and a 2.52 THz CO2laser is used

to carry out the target reﬂection experiment of THz wave. The experimental results show that the transmittance

of THz wave in plasma jet in laboratory environment is over 98%, and the reﬂection imaging is not aﬀected by

plasma sheltering. Both theory and experiment show that THz wave, especially high frequency THz wave,

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Fig. 8. Targets and THz wave reﬂection images. (a) sphere; (b) screw; (c) reﬂection image of the sphere; (d) reﬂection

image of the screw.

has good penetration to plasma, which provides an eﬀective method to solve the plasma blackout problem of

hypersonic vehicle in near space.

ACKNOWLEDGMENTS

This work is supported by the Equipment Pre-Research Foundation (No. 6140415010202) and the National

Natural Science Foundation of China (No. 61705162).

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