sensors

Article
Measurement and Control of Radially Polarized THz Radiation
from DC-Biased Laser Plasma Filaments in Air
Bonan Han 1,2 , Yanping Chen 1,2, *, Tianhao Xia 1,2 , Linzheng Wang 1,2 , Chen Wang 1,2 and Zhengming Sheng 1,2,3

1 Key Laboratory for Laser Plasmas (Ministry of Education), School of Physics and Astronomy,
Shanghai Jiao Tong University, Shanghai 200240, China; hbn0528@sjtu.edu.cn (B.H.);
xth1996@sjtu.edu.cn (T.X.); linzhengwangsjtu@sjtu.edu.cn (L.W.); w_chen@sjtu.edu.cn (C.W.);
zmsheng@sjtu.edu.cn (Z.S.)
2 Collaborative Innovation Center of IFSA, Shanghai Jiao Tong University, Shanghai 200240, China
3 Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
* Correspondence: yanping.chen@sjtu.edu.cn

Abstract: Detection and manipulation of radially polarized terahertz (THz) radiation is essential for
many applications. A new measurement scheme is proposed for the diagnosis of radially polarized
THz radiation from a longitudinal dc-biased plasma filament, by introducing a movable metal mask.
The amplitude and spectrum of the radially polarized THz beam was measured with a <110>-cut
ZnTe crystal, where the THz beam pattern was modulated by the mask. Based on this measurement
scheme, it was demonstrated that the amplitude and spectrum of the radially polarized THz radiation
from the longitudinal dc-biased filament could be manipulated by controlling the strength and the
location of the dc-biased field.

Keywords: terahertz radiation; laser plasmas; radial polarization; longitudinal dc-biased electric field

Citation: Han, B.; Chen, Y.; Xia, T.;

Wang, L.; Wang, C.; Sheng, Z.
1. Introduction
Measurement and Control of Radially Radially polarized terahertz (THz) radiation is a special THz vector beam whose
Polarized THz Radiation from polarization direction is along the radial direction in the beam cross section [1]. Longitudinal
DC-Biased Laser Plasma Filaments in THz electric fields can be formed by tightly focusing radially polarized terahertz radiation,
Air. Sensors 2022, 22, 5231. https:// which have important applications in electron acceleration [2], optical tweezers [3], THz
doi.org/10.3390/s22145231 imaging [4], etc. In recent years, many research groups have proposed a variety of methods
Academic Editor: Simone Borri to generate radially polarized THz radiation. Ryo et al. generated radially and azimuthally
polarized THz beams by piecing together nonlinear crystals [5]. Cliffe et al. used a radially
Received: 29 May 2022 biased photoconductive antenna to generate a longitudinal THz electric field up to 2 kV/cm
Accepted: 11 July 2022
after focusing [6]. Using segmented waveplates, linearly polarized THz radiation can be
Published: 13 July 2022
converted to radially polarized THz radiation [2,7]. Additionally, strong radially polarized
Publisher’s Note: MDPI stays neutral broadband THz radiation can be generated in accelerator-based light sources through
with regard to jurisdictional claims in coherent diffraction and transition radiation [8,9]. D’Amico et al. generated radially
published maps and institutional affil- polarized THz radiation from laser plasmas [10]. Later, Liu et al. increased the intensity of
iations. this THz radiation by an order of magnitude by introducing an external electric field to
laser plasmas [11].
Recently, THz radiation from laser plasmas has attracted broad interest due to its high
damage threshold and ultrabroad spectral bandwidth, compared with other methods [12–18].
Copyright: © 2022 by the authors.
However, effective characterization of the radially polarized THz radiation from laser
Licensee MDPI, Basel, Switzerland.
plasmas is still challenging. Heterodyne detectors have been used for the measurement
This article is an open access article
of radially polarized THz at specific frequencies [10,11,18]. Rizaev et al. discussed the
distributed under the terms and
spectral distributions of radially polarized THz radiation from DC-biased laser plasmas by
conditions of the Creative Commons
Attribution (CC BY) license (https://
using a bolometer with THz filters [16]. Fukuda et al. measured the angular distribution of
creativecommons.org/licenses/by/
radially polarized THz by calibrated diode detectors with sensitive bands at 0.14 THz to
4.0/).
0.33 THz [14]. The above methods can obtain the intensity and spatial distribution of the

Sensors 2022, 22, 5231. https://doi.org/10.3390/s22145231 https://www.mdpi.com/journal/sensors

Sensors 2022, 22, 5231 2 of 11

radially polarized terahertz wave, but the electric field and the corresponding spectrum of
this THz signal cannot be obtained. The waveform of the longitudinal THz electric field
formed by focusing the radially polarized THz emission has been demonstrated by using
<100>-cut GaP or ZnTe crystal [16,19], whose signal-to-noise ratio is much lower than the
measurement of the linearly polarized THz signal with a <110>-cut ZnTe crystal. Following
this, some research groups divided the emitted radially polarized THz beam into four
pieces with a sectorial mask, and measured the waveform of this THz signal piece-by-piece
with a <110>-cut ZnTe crystal [19,20]. However, with this method, alignment is not easy
because the resultant THz signal is very sensitive to the transverse position of the sectorial
mask with respect to the THz beam profile.
In this paper, a new method is proposed for the measurement of radially polarized THz
radiation from a plasma filament with a longitudinally oriented external electric field. The
waveform and corresponding spectrum of the radially polarized THz pulse from a plasma
filament can be distinguished and obtained by electro–optic (EO) sampling technique with
a <110>-cut ZnTe crystal, by modulating the THz beam pattern with a movable metal
mask. Based on this measurement scheme, it will be demonstrated that the amplitude and
spectrum of the radially polarized THz radiation from a longitudinally dc-biased filament
can be manipulated by control of the amplitude and the location of the external electric field,
respectively. This paper is organized as follows. In Section 2, the detection method for the
radially polarized THz radiation is presented. In Section 3, the experimental result based
on the measurement scheme is shown. Based on the experimental result, the THz spatial
distribution is analyzed by the transition-Cherenkov radiation principle. In Section 4, the
radially polarized THz radiation is manipulated by adjusting the external electric field.
Finally, a summary is given in Section 5.

2. Detection Methods
THz radiation from plasma filaments with an external electric field can be either
radially polarized (with a longitudinally oriented dc-bias) [11] or linearly polarized (with a
transversely-oriented dc-bias) [21]. When the THz radiation is collected and focused, the
polarization of the radially polarized THz components will become longitudinal at the focal
plane (Figure 1a), while the polarization of the linearly polarized THz components is in the
transverse direction at the focal plane (Figure 1b). Detection of the linearly polarized THz
radiation often uses an electro–optic sampling technique with a <110>-cut ZnTe crystal [22].
For a longitudinal THz electric field, however, it will not change the refractive index of the
ZnTe crystal in the (110) plane. Therefore, the longitudinal THz components at the focal
plane (as Ez in
Sensors 2022, 22, x FOR PEER
Figure 1a), which originated from the radially polarized THz components,
REVIEW 3 of 1
cannot be directly measured by electro–optic sampling with a <110>-cut ZnTe crystal, for
normal incidence.

Figure 1. The directions of the electric fields at the focal plane originating from (a) radially polarized
Figure 1. The directions of the electric fields at the focal plane originating from (a) radially polarized
THz waves, and (b) linearly polarized THz waves.
THz waves, and (b) linearly polarized THz waves.
Sensors 2022, 22, 5231 3 of 11

To measure the waveforms of the radially polarized and linearly polarized THz
radiation from plasma filaments at the same time, we introduced a rectangular metal plate
in front of the focusing optics as a mask to block part of the THz radiation, as shown in
Figure 2. As the lower edge of the mask moves from the top to the bottom of the THz
beam pattern, the residual THz radiation with radial polarization will occur transversely
polarized THz components, Ey , at the focal plane (as Ey in Figure 2a) while the residual
THz radiation with linear polarization retains its polarization. Thus, the waveforms of the
radially polarized
Figure 1. THz radiation
The directions canfields
of the electric be obtained by plane
at the focal measuring the THz
originating fromcomponents, Ey , at
(a) radially polarized
THz
the waves,
focal andwith
plane (b) linearly
a metalpolarized
mask and THz waves.
a <110>-cut ZnTe crystal.

Figure 2. Side view (a), and front view (b), of the schematic diagram for beam shielding with a
Figure 2. Side view (a), and front view (b), of the schematic diagram for beam shielding with a
rectangular metal
rectangular mask.
metal mask.

To determine the spatial distribution of the THz radiation from plasma filaments, we
To determine the spatial distribution of the THz radiation from plasma filaments, we
first placed the metal mask so as to completely block the THz beam pattern. Then the mask
first placed the metal mask so as to completely block the THz beam pattern. Then the mask
was moved upwards along the y-axis until the THz signal started to appear. This particular
was moved upwards along the y-axis until the THz signal started to appear. This particu-
location of the lower edge of the mask was defined as y = 0, corresponding to a lower edge
lar location of the lower edge of the mask was defined as y = 0, corresponding to a lower
of the THz beam pattern, as shown in Figure 3a. As the mask was moved further upwards,
edge of the THz beam pattern, as shown in Figure 3a. As the mask was moved further
the distance between the lower edge of the mask and the location y = 0 was defined as d,
upwards, the distance between the lower edge of the mask and the location y = 0 was
which had close correlation to the THz signal arriving at the detector. When the THz signal
defined as d, which had close correlation to the THz signal arriving at the detector. When
remained constant while the mask was moved upwards, the location of the lower edge
ofthe
theTHz
masksignal remained
was defined as constant while the mask
y = L (corresponding was moved
to upper edge ofupwards,
the THz beamthe location
pattern).of
the lower
Thus, edge roughly
we could of the mask was defined
determine as y = L (corresponding
the boundary of the THz beam to upper
patternedge
by of the THz
scanning
beam pattern). Thus, we could roughly determine the boundary of
the metal mask across the whole THz beam profile in y direction. In the measurement, the THz beam pattern
we
by scanning the metal mask across the whole THz beam profile in y direction.
could obtain the horizontally polarized and the vertically polarized THz electric fields In the meas-
at
urement,
the we could
focal plane obtainthe
by rotating theangles
horizontally polarized
of a half-wave and(HWP)
plate the vertically polarized
and a ZnTe THz
crystal in elec-
the
tric fields at sampling
electro–optic the focal plane
system by [21,23].
rotatingHere,
the angles of a half-wave
we defined plate (HWP)
the horizontally and and a ZnTe
vertically
crystal inTHz
polarized the electro–optic sampling
signals as Exlower system
and Eylower [21,23].
(Figure 3a),Here, we defined
respectively. Whenthe horizontally
d was changed and
𝑙𝑜𝑤𝑒𝑟 𝑙𝑜𝑤𝑒𝑟
vertically polarized THz signals as 𝐸 𝑥 and 𝐸
from 0 to L, the horizontal and the vertical components of the linearly polarized THz signal d
𝑦 (Figure 3a), respectively. When
was changed
became from the
larger with 0 toincrease
L, the horizontal
in d. Forandthe the vertical
radially components
polarized of the linearly
THz beam, however, polar-
its
vertical components increased from zero to a maximum, when d changed from 0 tobeam,
ized THz signal became larger with the increase in d. For the radially polarized THz L/2.
For d larger than L/2, the THz signals from the upper half of the radially polarized THz
beam (with inversed polarization) canceled the THz signals from the lower half, leading to
a decrease in total THz vertical components at the focal plane. Meanwhile, the horizontal
THz components from a radially polarized THz beam remained at zero when moving
the mask vertically (along the y-axis) because the horizontal THz components from the
left half and the right half of this THz beam canceled each other at the focal plane. In
order to improve the accuracy of our experiment, being certain that radially polarized
THz radiation had been measured, we also measured the THz radiation by moving the
metal mask in the opposite direction, as shown in Figure 3b. After blocking the whole
 the horizontal THz components from a radially polarized THz beam remained at zero
when moving the mask vertically (along the y-axis) because the horizontal THz compo-
nents from the left half and the right half of this THz beam canceled each other at the focal
plane. In order to improve the accuracy of our experiment, being certain that radially po-
Sensors 2022, 22, 5231 4 of 11
larized THz radiation had been measured, we also measured the THz radiation by moving
the metal mask in the opposite direction, as shown in Figure 3b. After blocking the whole
THz beam pattern with the mask, we slowly moved the mask downwards. In the same
THz beam pattern with the mask, we slowly moved the mask downwards. In the same
way, the boundary of the THz beam pattern could be decided when the upper edge of the
way, the boundary of the THz beam pattern could be decided when the upper edge of the
mask was locatedmask
at z =was
L (corresponding to upper edge
located at z = L (corresponding to of the edge
upper THz ofbeam pattern)
the THz beamand z = and z = 0
pattern)
0 (corresponding(corresponding
to lower edgetooflowerthe THz beam pattern). In this case, d was defined as
edge of the THz beam pattern). In this case, d was defined as the
the distance between the between
distance upper edge of theedge
the upper THzof beam
the THzpattern and theand
beam pattern upper edgeedge
the upper of the
of the mask,
mask, while the horizontally polarized
while the horizontally and theand
polarized vertically polarized
the vertically THz THz
polarized signals were
signals de-defined as
were
𝑢𝑝𝑝𝑒𝑟 upper
𝑢𝑝𝑝𝑒𝑟 upper
fined as 𝐸𝑥 Ex𝐸𝑦 and, respectively.
and Ey , respectively.

Figure 3. Determination the boundary of the THz beam pattern by moving a metal mask upwards
Figure 3. Determination the boundary of the THz beam pattern by moving a metal mask upwards
(a), and downwards (b).
(a), and downwards (b).
3. Results
3. Results The experimental setup for the generation and the detection of the THz radiation from
laser-induced air plasmas is sketched in Figure 4. An 800 nm, 40 fs, 2 mJ laser was divided
The experimental setup for the generation and the detection of the THz radiation
by a beam splitter (BS) into a pump beam and a probe beam. The pump beam was focused
from laser-induced air plasmas is sketched in Figure 4. An 800 nm, 40 fs, 2 mJ laser was
by a convex lens with 50 cm focal length to produce a 1 cm long laser filament in air. Two
divided by a beam splitter
copper (BS) into
electrodes a pump
(with beam
a hole in theand a probe
center beam.
of each The
copper pump
plate) beam
with was of 5 cm
a diameter
focused by a convex lens with 50 cm focal length to produce a 1 cm long laser filament
were set on both sides of the filament, forming a longitudinally oriented external in electric
air. Two copper electrodes
field along (with a hole The
the filament. in the centerbetween
distance of eachthe
copper plate) plates
two copper with awasdiameter
around 1 cm and
of 5 cm were set ontheboth sides
voltage of the
applied to filament, forming
the plates could a longitudinally
be varied from 0 to 10 oriented external
kV. Thereafter, THz radiation
electric field along the filament. The distance between the two copper plates was around mirrors
from the longitudinally dc-biased filament was collected by two off-axis parabolic
(OAP)applied
1 cm and the voltage with focal
tolength of 10 cm
the plates and be
could measured
variedby electro–optic
from sampling
0 to 10 kV. technique with a
Thereafter,
<110>-cut ZnTe crystal. The diameters of the off-axis parabolic mirrors were both 50 mm,
THz radiation from the longitudinally dc-biased filament was collected by two off-axis
and they could collect THz radiation at an angle of up to 15 degrees from axis z. A silicon
parabolic mirrors (OAP) with focal length of 10 cm and measured by electro–optic sam-
wafer was placed between the two off-axis parabolic mirrors to separate the THz beam from
pling technique with a <110>-cut
the pump beam. ZnTe crystal. metal
A rectangular The diameters
mask, whichof the off-axis
could parabolic
be moved mir-y-axis, was
along the
rors were both 50placed
mm, and they could collect THz radiation at an angle of up to 15 degrees
just after the silicon wafer to control the THz beam pattern that reached the detector.
Figure 5 shows the evolution of the measured THz waveforms when scanning the
metal mask upwards (along the y-axis). Exlower and Eylower correspond to the measured THz
waveforms of the horizontally polarized THz components and the vertically polarized
THz components when moving the metal mask downwards (Figure 5a,b), respectively.
Each vertical line relates to a THz waveform obtained at a specified d. The signals with
d = 0 were obtained when the THz radiation was completely blocked by the metal mask.
Sensors 2022, 22, 5231 5 of 11

The radially polarized THz beam was centrosymmetric about the center of the THz beam
pattern, so the left half and the right half of the THz beam canceled each other in the
horizontal polarization at the focal plane when the mask was moved along the vertical
direction (parallel to the y-axis). As a result, the radially polarized THz radiation did
not contribute to the measured horizontally polarized THz components, Exlower . As the
external electric field along the filament was not perfectly longitudinally oriented, the
measured Exlower corresponded to the horizontal components of the linearly polarized THz
radiation from the filament with a transversely oriented external electric field [21]. In this
case, the measured Exlower increased with an increase in d, as shown in Figure 5a. As for
the vertically polarized THz components, Eylower , however, the measured waveforms were
contributed by both the radially polarized THz radiation and the linearly polarized THz
radiation. As the polarity of the radially polarized THz beam was opposite between the
Sensors 2022, 22, x FOR PEER REVIEW 5 of 12
lower
upper and lower halves, the measured vertically polarized THz components, E y , had a
decreasing tendency at d > 25 mm, as shown in Figure 5b. When the mask was completely
removed (d = 50 mm in Figure 5b), the measured Eylower only corresponded to the vertical
from axis z. A silicon wafer was placed between the two off-axis parabolic mirrors to sep-
components of the linearly polarized THz radiation from the filament with a transversely
arate the THz beam from the pump beam. A rectangular metal mask, which could be
oriented external
moved along electric field,
the y-axis, was because the
placed just THz
after thesignals from to
silicon wafer the upper
control thehalf
THzofbeam
the radially
polarized THz beam canceled those
pattern that reached the detector. from the lower half.

Sensors 2022, 22, x FOR PEERFigure 4. Schematic

Figure
REVIEW diagram
4. Schematic for
diagram forthe
theexperimental setup:
experimental setup: HWP,
HWP, half-wave
half-wave plate; plate; QWP, 6quarter-wave
QWP, quarter-wave
of 12
plate;Wollaston
plate; WP, WP, Wollaston prism;
prism; PD,PD, photodiode detector.
photodiode detector.

Figure 5 shows the evolution of the measured THz waveforms when scanning the
metal mask upwards (along the y-axis). 𝐸𝑥𝑙𝑜𝑤𝑒𝑟 and 𝐸𝑦𝑙𝑜𝑤𝑒𝑟 correspond to the measured
THz waveforms of the horizontally polarized THz components and the vertically polar-
ized THz components when moving the metal mask downwards (Figure 5a,b), respec-
tively. Each vertical line relates to a THz waveform obtained at a specified d. The signals
with 𝑑 = 0 were obtained when the THz radiation was completely blocked by the metal
mask. The radially polarized THz beam was centrosymmetric about the center of the THz
beam pattern, so the left half and the right half of the THz beam canceled each other in the
horizontal polarization at the focal plane when the mask was moved along the vertical
direction (parallel to the y-axis). As a result, the radially polarized THz radiation did not
contribute to the measured horizontally polarized THz components, 𝐸𝑥𝑙𝑜𝑤𝑒𝑟 . As the exter-
nal electric field along the filament was not perfectly longitudinally oriented, the meas-
ured 𝐸𝑥𝑙𝑜𝑤𝑒𝑟 corresponded to the horizontal components of the linearly polarized THz ra-
diation from the filament with a transversely oriented external electric field [21]. In this
case, the measured 𝐸𝑥𝑙𝑜𝑤𝑒𝑟 increased with an increase in d, as shown in Figure 5a. As for
the vertically polarized THz components, 𝐸𝑦𝑙𝑜𝑤𝑒𝑟 , however, the measured waveforms were
contributed by both the radially polarized THz radiation and the linearly polarized THz
radiation. As the polarity of the radially polarized THz beam was opposite between the
Figureupper
Figure and
5. Measured lower
5. Measured halves,
THzTHz the measured
radiation
radiationfrom verticallyfilament
from a dc-biased
dc-biased polarized
filamentwithTHz
with components,
a longitudinal
a longitudinal 𝐸𝑦𝑙𝑜𝑤𝑒𝑟
external , had electric
external
electric
𝑙𝑜𝑤𝑒𝑟
afield
field along along
decreasing the
the𝑙𝑜𝑤𝑒𝑟 filament:(a)
tendency
filament: (a)
athorizontally
𝑑 > 25 mm,
horizontally polarized component
as shown
polarized (𝐸𝑥 5b.);When
incomponent
Figure (b)lower
(E x
vertically
the
); polarized
mask
(b) was
vertically com-
com-polarized
ponent (𝐸
pletely removed
𝑦
lower ). (d = 50 mm in Figure 5b), the measured 𝐸 𝑙𝑜𝑤𝑒𝑟 only corresponded to the
component (Ey ). 𝑦
vertical components of the linearly polarized THz radiation from the filament with a
As mentioned
transversely oriented above, not only
external a radially
electric polarized
field, because theTHz
THzbeam,
signals but
fromalsothe
a linearly
upper halfpo-
larized THz beam were generated in our experiment when
of the radially polarized THz beam canceled those from the lower half. applying a longitudinally ori-
ented dc-bias to the filament. This was due to a slight deviation in the direction the dc-
bias with respect to the propagation direction of the laser beam, which induced a trans-
verse component of the external electric field to the plasma filament responsible for the
Sensors 2022, 22, 5231 6 of 11

As mentioned above, not only a radially polarized THz beam, but also a linearly
polarized THz beam were generated in our experiment when applying a longitudinally
oriented dc-bias to the filament. This was due to a slight deviation in the direction the dc-
bias with respect to the propagation direction of the laser beam, which induced a transverse
component of the external electric field to the plasma filament responsible for the generation
of the linearly polarized THz beam [22]. We will now discuss how to distinguish the THz
signals for the radially polarized THz beam from those for the linearly polarized THz beam.
In Figure 5b, the measured THz signal Eylower involves vertical components from both a
linearly polarized THz beam and a radially polarized THz beam. In order to obtain the
radially polarized THz signal, we need to subtract the linearly polarized THz component
from Eylower . The measured THz signal Exlower only involves horizontal components from
a linearly polarized THz beam. Thus, from the measured horizontal THz components in
Figure 5a, we can obtain the ratio between the THz electric field obtained with the mask
located at d Exlower (d) and the THz electric field obtained without the mask (located at
L = 50 mm) Exlower ( L) as:
αlower (d) = Exlower (d)/Exlower ( L). (1)
For the linearly polarized THz beam, the vertical THz components should have the
same relation to the mask location d. Therefore, it can be derived that:

αlower (d) = Elin

lower lower
(d)/Elin ( L ), (2)
lower ( d ) is the electric field of the linearly polarized THz beam when the mask is
where Elin
located at position d. In Figure 5b, the measured THz signal Eylower ( L) only corresponds to
the vertical components of the linearly polarized THz beam, as the vertical components
from the upper half and lower half of the radially polarized THz beam cancel each other.
Thus, the vertical components of the linearly polarized THz beam with the mask located at
d, denoted as Ey,linlower ( d ), can be derived as:

lower
Ey,lin (d) = Eylower ( L)·αlower (d). (3)

lower ( d ),
and then, the vertical components of the radially polarized THz beam, denoted as Ey,rad
can be derived as:
lower ( d ) = Elower ( d ) − Elower ( d )
Ey,rad y y,lin
(4)
= Eylower (d) − Eylower ( L)· Exlower (d)/Exlower ( L).
In this way, we can obtain the waveform and the one dimensional spatial distribution
of the vertical components of the radially polarized THz beam. In the same way, the radially
polarized THz signal can be obtained by scanning the mask downwards as:
upper upper upper upper upper
Ey,rad (d) = Ey (d) − Ey ( L)· Ex (d)/Ex ( L ). (5)

Based on Equations (1)–(5), the vertical components of the radially polarized THz beam
when scanning the mask upwards and downwards, are shown in Figure 6a,b, respectively.
The measured radially polarized THz signal reaches its maximum when the mask blocks
lower ( L/2) and Eupper ( L/2)), while it goes back to
exactly half of the THz beam pattern (Ey,rad y,rad
lower ( L ) and E upper
zero when the mask is completely removed (Ey,rad y,rad ( L )). The waveform of the
upper
vertical components from the upper half of the radially polarized THz beam Ey,rad ( L/2)
has opposite polarity compared with that from the lower half of the radially polarized THz
lower ( L/2) (as shown in Figure 6c) while their corresponding spectra remain the
beam Ey,rad
same (as shown in Figure 6d). All these behaviors match well with the characteristic of a
radially polarized THz beam. Therefore, based on our method, the signal for a radially
polarized THz beam can be well distinguished from the measured THz signals with other
polarizations (a linear polarization in this experiment).
 𝑢𝑝𝑝𝑒𝑟
beam 𝐸𝑦,𝑟𝑎𝑑 (𝐿/2) has opposite polarity compared with that from the lower half of the
𝑙𝑜𝑤𝑒𝑟 (𝐿/2)
radially polarized THz beam 𝐸𝑦,𝑟𝑎𝑑 (as shown in Figure 6c) while their correspond-
ing spectra remain the same (as shown in Figure 6d). All these behaviors match well with
the characteristic of a radially polarized THz beam. Therefore, based on our method, the
Sensors 2022, 22, 5231 signal for a radially polarized THz beam can be well distinguished from the measured 7 of 11
THz signals with other polarizations (a linear polarization in this experiment).

Verticalcomponents
Figure6.6.Vertical
Figure components of of
thethe radially
radially polarized
polarized THzTHzbeam beam
whenwhen scanning
scanning the upwards
the mask mask up-
𝑙𝑜𝑤𝑒𝑟(E lower ( d )) (a), and downwards 𝑢𝑝𝑝𝑒𝑟 upper
wards
( 𝐸𝑦,𝑟𝑎𝑑 (𝑑)) (a), and downwards (𝐸𝑦,𝑟𝑎𝑑 (𝑑))
y,rad (E ( d ) ) (b); (c,d) are, respectively, the waveforms
y,rad(b); (c,d) are, respectively, the waveforms and the andcor-
the
𝑙𝑜𝑤𝑒𝑟
lower upper
𝑢𝑝𝑝𝑒𝑟
responding
corresponding spectra of 𝐸of
spectra (𝐿/2)
Ey,rad
𝑦,𝑟𝑎𝑑 and
( L/2 𝐸𝑦,𝑟𝑎𝑑
) and (𝐿/2).
Ey,rad ( L/2).

Based on
Based onthe
themeasurement,
measurement, we wecan
canalso
alsoanalyze
analyzethethespatial
spatialdistribution
distributionof
ofthe
theradially
radially
polarized THz
polarized THz radiation
radiationfrom
fromthe
the longitudinally
longitudinallydc-biased
dc-biasedfilament.
filament.AAfocused
focusedfemtosec-
femtosec-
ond laser
ond laser will
will induce
induce plasmas
plasmas in in air
air and
and form
form aa long
long laser
laser filament
filament due
due to
to an
an interplay
interplay
between the Kerr-focusing effect and the plasma-defocusing effect. Inside the filament,
the laser-induced ponderomotive force will drive the electrons to produce longitudinal
oscillations, which can be regarded as a dipole-like charge current, jzw (ω ), oriented along
the filament [10]. When the filament is applied by an external electric field, Eext , with its
orientation parallel to the filament, the electrons ionized by the laser will also be driven by
the external electric field to form a current, jze (ω ), which is proportional to the amplitude of
the external electric field [11]. Consequently, the total longitudinal electron current can be
expressed as jz (ω ) = jzw (ω ) + jze (ω ). The dipole moving at the light velocity will generate
a Cherenkov-like THz radiation with the spatial distribution of its energy spectral density
denoted as [18]:

d2 W | jz (ω )|2 ρ40 sin2 θ

 
2 Lω
= sin (1 − cosθ ) , (6)
dωdΩ 4πε 0 c (1 − cosθ )2 2c

where ω is the frequency of the radiation, θ is the radiation angle with respect to the laser
propagation axis, ε 0 and c are the dielectric constant and the speed of the light in vacuum,
respectively, and ρ0 and L are the radius and length of the filament, respectively. Based on
Equation (6), considering the Fourier spectrum of the measured Ey,radlower ( L/2) as j ( ω ), the
z
energy distribution of the observed radially polarized THz radiation from a longitudinally
dc-biased filament can be simulated, as shown in Figure 7a. The corresponding spatial
distribution of the THz amplitude and its vertical components are shown in Figures 7b
and 7c, respectively. The diameters of the off-axis parabolic mirrors used in the experiment
were 50 mm, so we only considered the THz signals within the spatial limit of these mirrors
 respectively, and 𝜌0 and 𝐿 are the radius and length of the filament, respectively. Based
𝑙𝑜𝑤𝑒𝑟
on Equation (6), considering the Fourier spectrum of the measured 𝐸𝑦,𝑟𝑎𝑑 (𝐿/2) as 𝑗𝑧 (𝜔),
the energy distribution of the observed radially polarized THz radiation from a longitu-
dinally dc-biased filament can be simulated, as shown in Figure 7a. The corresponding
Sensors 2022, 22, 5231 spatial distribution of the THz amplitude and its vertical components are shown in Figure 8 of 11
7b and Figure 7c, respectively. The diameters of the off-axis parabolic mirrors used in the
experiment were 50 mm, so we only considered the THz signals within the spatial limit
ofinthese mirrors in the
the simulation. Thesimulation.
red and blue The red in
colors and
theblue
THzcolors
beam in the THz
pattern beam 7c
in Figure pattern in
represent
Figure 7c represent
the upper and the the upper
lower andofthe
halves thelower halves
vertical of the vertical
components of thecomponents of the ra-
radially polarized THz
dially
radiation possessing opposite polarities. If we introduce the mask method to thisthe
polarized THz radiation possessing opposite polarities. If we introduce mask
simulated
method to this simulated
beam pattern, we could beam
obtainpattern,
the THzwe could obtain
amplitude as a the THz amplitude
function of d (definedas ainfunction
Figure 3),
ofasd the
(defined in Figure 3), as the solid curve in Figure 7d. It is notable that
solid curve in Figure 7d. It is notable that the simulated result well agrees the simulated
with the
result well agrees
experimental with the experimental observations.
observations.

Figure
Figure 7. 7. Spatial
Spatial distribution
distribution of of
(a)(a)
thethe energy
energy density,
density, (b)(b) the
the field
field amplitude,
amplitude, and
and (c)(c) the
the vertical
vertical
components
components of of
thethe
THzTHz radiation
radiation fromfrom a longitudinally
a longitudinally dc-biased
dc-biased filament.
filament. (d) Simulation
(d) Simulation and
and ex-
perimental results for THz amplitude as a function of
experimental results for THz amplitude as a function of d. d.

4. Manipulation of the Radially Polarized THz Radiation

Based on the above mask method, the amplitude of the radially polarized THz radia-
tion can be manipulated by adjusting the amplitude of the longitudinal external electric
field. Figure 8 shows the measured waveforms and the corresponding Fourier spectra
of the radially polarized THz radiation from the longitudinally dc-biased filament as the
external electric field changes. When the amplitude of the external electric field increased
from 2 kV/cm to 10 kV/cm, the amplitude of the radially polarized THz radiation in-
creased linearly with respect to the amplitude of the external electric field, while the peak
frequency of the THz spectrum was almost fixed around 0.2 THz. The THz peak frequency
from the dc-biased filament was lower than the peak frequency of THz radiation from
the filament without external electric field (0 kV/cm) because the external electric field
can only influence electrons in the outer layer of the filament with a thin thickness due
to the Debye shielding effect. When there is no external electric field, however, the THz
signal emits from the whole filament, including the central region of the filament with
relatively higher plasma density compared with the outer layer. Therefore, the frequency
of the THz radiation without the external q electric field was much higher, according to
ne e 2
the relation for plasma frequency ω p = me ε 0 , where ne is the plasma density, e is the
charge of the electron, me is the electron mass, and ε 0 is the dielectric constant in vacuum,
respectively [11].
 only influence electrons in the outer layer of the filament with a thin thickness due to the
Debye shielding effect. When there is no external electric field, however, the THz signal
emits from the whole filament, including the central region of the filament with relatively
higher plasma density compared with the outer layer. Therefore, the frequency of the THz
radiation without the external electric field was much higher, according to the relation for
𝑛𝑒 𝑒 2
Sensors 2022, 22, 5231 plasma frequency 𝜔𝑝 = √ , where 𝑛𝑒 is the plasma density, 𝑒 is the charge of the elec- 9 of 11
𝑚𝑒 𝜀0
tron, 𝑚𝑒 is the electron mass, and 𝜀0 is the dielectric constant in vacuum, respectively [11].

Figure 8. (a) Measured waveforms, and (b) corresponding spectra, of the radially polarized THz
Figure 8. (a) Measured waveforms, and (b) corresponding spectra, of the radially polarized THz
radiations when the external electric field changes from 0 to 10 kV/cm.
radiations when the external electric field changes from 0 to 10 kV/cm.
With this longitudinally dc-biased filament, we could also slightly manipulate the
With
peakthis longitudinally
frequency of the radiallydc-biased
polarized THz filament,
radiation,we could
except also
for its slightly
amplitude. In amanipulate
long the
peak frequency of thethe
plasma filament, radially polarized
plasma density alongTHz radiation,
the filament is not except for itsWe
homogeneous. amplitude.
extended In a long
plasmathe length ofthe
filament, the plasma
filament to 2 cm byalong
density increasing
the the laser energy
filament is notto homogeneous.
4 mJ. Figure 9 shows We extended
the spectra of the radially polarized THz radiation when moving the electrodes longitu-
the length of the filament to 2 cm by increasing the laser energy to 4 mJ. Figure 9 shows the
dinally along the filament. The THz spectrum marked with dz = 0 mm was measured when
spectrathe
of location
the radially
of the polarized THz
left piece of the radiation
electrodes waswhen moving the
at the beginning electrodes
of the longitudinally
filament, while
along the
the filament.
THz spectrum The THz with
marked spectrum marked
dz = 10 mm with dzwhen
was measured = 0 the
mmlocation
was measured
of the elec- when the
locationtrodes
of thewasleft
changed
piecebyof10themmelectrodes
towards the wastailingatofthe
the beginning
filament. It was of notable that the while the
the filament,
radially polarized THz radiation from the beginning of the filament was comparably
THz spectrum marked with dz = 10 mm was measured when the location of the electrodes
lower than that from the tailing of the filament. This could be interpreted by the fact that
Sensors 2022, 22, x FOR PEER REVIEWwas changed by 10 mm towards the tailing of the filament. It was notable that
the plasma density was a little bit higher at the location of the geometric focus. By thisthe radially
10 of 12
polarized THz radiation from the beginning of the filament was comparably lower than
that from the tailing of the filament. This could be interpreted by the fact that the plasma
density was
technique, a little
we could bit higher
smoothly tuneatthe
thepeak
location of the
frequency ofgeometric
the radiallyfocus. By this
polarized THz technique,
sig- we
nal from 0.17 THz to 0.21 THz.
could smoothly tune the peak frequency of the radially polarized THz signal from 0.17 THz
to 0.21 THz.

Figure
Figure 9. 9. Normalized
Normalized spectra
spectra of radially
of radially polarized
polarized THz radiation
THz radiation from a dc-biased
from a dc-biased filament when
filament when
the
the location
location of the
of the electrodes
electrodes moves moves from
from the the beginning
beginning to theoftailing
to the tailing of the The
the filament. filament. The external
external
electric field
electric is 10
field is kV/cm. The distance
10 kV/cm. from the
The distance beginning
from of the filament
the beginning of the to the electrodes
filament to the is defined is defined
electrodes
as dz, as shown in the figure.
as dz , as shown in the figure.
5. Conclusions
We demonstrated the diagnosis of the radially polarized THz radiation from a longi-
tudinal dc-biased laser plasma filament by introducing a movable metal mask. The am-
plitude and spectrum of the radially polarized THz beam was measured with a <110>-cut
Sensors 2022, 22, 5231 10 of 11

5. Conclusions
We demonstrated the diagnosis of the radially polarized THz radiation from a longitu-
dinal dc-biased laser plasma filament by introducing a movable metal mask. The amplitude
and spectrum of the radially polarized THz beam was measured with a <110>-cut ZnTe
crystal by modulating the THz beam pattern with the mask. Meanwhile, the linearly
polarized components of the THz radiation from this dc-biased filament could be well
distinguished from the THz pulses withradial polarization. The measured 1-D spatial distri-
bution of the radially polarized THz radiation matched well with the simulation, according
to the transition-Cherenkov model. Based on the mask method, the amplitude, as well as
the spectrum of the radially polarized THz radiation, was manipulated by adjusting the
amplitude and location of the external electric field, respectively. This work provides a
new method of simultaneously measuring radially polarized and linearly polarized THz
radiation, which has wide relevance in THz applications.

Author Contributions: B.H. and Y.C. conceived the idea and designed the experiments; B.H., T.X.,
L.W. and C.W. conducted the experiments; B.H. and Y.C. wrote the paper; Z.S. generally supported
the project. All authors have read and agreed to the published version of the manuscript.
Funding: This work is supported by the National Natural Science Foundation of China (11774228,
12074250, 11991073, 11721091 and 12135009) and the Science and Technology Commission of Shanghai
Municipality (16DZ2260200).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data presented in this study are available on request from the
corresponding author.
Conflicts of Interest: The authors declare no conflict of interest.

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