Detection of Broadband Terahertz Waves with a Laser-Induced Plasma in Gases
Jianming Dai, Xu Xie, and X.-C. Zhang*
Center for Terahertz Research, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
(Received 25 April 2006; published 8 September 2006)
We report the experimental results and theoretical analysis of broadband detection of terahertz (THz)
waves via electric-field-induced second-harmonic generation in laser-induced air plasma with ultrashort
laser pulses. By introducing the second-harmonic component of the white light in the laser-induced
plasma as a local oscillator, coherent detection of broadband THz waves with ambient air is demonstrated
for the first time. Our results show that, depending on the probe intensity, detection of THz waves in air
can be categorized as incoherent, hybrid, and coherent detection. Coherent detection is achieved only
when the tunnel ionization process dominates in gases.
DOI: 10.1103/PhysRevLett.97.103903PACS numbers: 42.65.?k, 52.38.?r
Coherent detection with a simultaneous measurement of
the amplitude and phase of a pulsed terahertz (THz) wave
is the basis of time-domain spectroscopy (TDS), which has
become one of the most active spectroscopic methods in
the physics and material science communities . It pro-
vides dynamic properties of various dielectric materials
over the frequency range from 0.1 to 10 THz, which was
previously considered to be a difficult-to-access range. For
example, the unique features of this coherent and time-
resolved method provided direct measurement of dynamic
formation of Drude model in photoexcited Coulomb
dressed free carriers . Commonly used coherent detec-
tors for detecting THz waves in the THz TDS are photo-
conductive dipole antennas and electro-optic crystals [3,4].
However, their bandwidth is limited by the carrier lifetime
in semiconducting photoconductors and phonon absorp-
tion in electro-optic crystals.
In this Letter, we present theoretical analysis and ex-
perimental demonstration of both incoherent and coherent
detection of broadband THz waves using gases as the
sensor medium through a third-order nonlinear optical
process with femtosecond (fs) laser pulses. We demon-
strate that the field-induced second harmonic from the
nonlinear optical interaction in the air offers time-resolved
measurement of pulsed THz waves. By using the white
light from the laser-induced plasma as the local oscillator
(LO), the detection could be coherent. Furthermore, by
increasing the probe beam intensity, the detection changes
from incoherent detection at lower intensities to coherent
detection at higher intensities. Correspondingly, the laser-
induced ionization of the gas changes from multiphoton
ionization (MI)totunnel ionization (TI),which isindicated
by the Keldysh parameter ? [5,6].
Gases, especially ionized gases, have been demonstrated
to generate intense THz waves through laser-induced pon-
deromotive forces , Lorentz forces , and third-order
nonlinear optical processes [9–12]. Similar to the electro-
optic detection of THz waves in nonlinear crystals by
second-order optical nonlinearity, THz waves can be de-
tected by third-order optical nonlinearity. Ambient air,
with a composition of about 78% nitrogen, exhibits re-
markable performance for the generation and detection of
THz waves with fs laser pulses.
Experimentally, a Ti:sapphire amplifier, generating
800 nm, 120 fs, 800 ?J pulses at a repetition rate of
1 kHz, is used. The laser beam is split into two beams.
One beam is used to generate THz waves, and the other is
used to detect the THz waves. Figure 1 schematically
illustrates this all-optical process for the generation and
detection of THz waves using air as the emitter and sensor.
First, the fundamental (!) beam and its SH (2!), after
passing through a 100 ?m thick type-I beta barium borate
(BBO) crystal, are focused in air to produce plasma . An
/2 wave plate
120 fs, 800 µJ
800 nm, 1 kHz
THz wave is generated by mixing the ! pump beam and its
SH (from a type-I BBO crystal) at the first air plasma point. The
first parabolic mirror collimates the THz beam. A high-
resistivity silicon wafer blocks the residual 800 and 400 nm
beams. The second parabolic mirror focuses the collimated THz
beam. A ?=2 wave plate controls the polarization of the probe
beam. The THz wave is detected by measuring the time-resolved
SH signal produced by mixing the ! beam and the THz field at
the second plasma point.
Schematic diagram of the experimental setup. The
PRL 97, 103903 (2006)
8 SEPTEMBER 2006
© 2006 The American Physical Society
intense, highly directional, broadband THz wave is gener-
ated through four-wave mixing [11,12]. Detailed experi-
mental results regarding the nonlinear process for the THz
wave generation in air plasma are demonstrated in our
previous publication , and references therein. To detect
the THz waves in air,the THz wave and the probe beam are
focused at the same point, with estimated focal spots of
about 0.8 mm and 24 ?m in diameter, respectively. The
THz-field-induced second harmonic (TFISH) is detected
by a photomultiplier tube.
We measured time-resolved TFISH signals at different
probe intensities. To eliminate the water vapor absorption,
the entire THz system is purged with nitrogen gas. As the
probe intensity increases from 9:2 ? 1012
1015W=cm2while the THz field is kept the same, the
detected SH signal increases accordingly while the wave-
form is kept the same with a unipolar feature until the
probe intensity reaches ?1:8 ? 1014W=cm2. Above this
intensity level, the waveform begins to change, and espe-
cially above 3:3 ? 1014W=cm2, the measured SH wave-
form starts to change from the unipolar shape to bipolar.
Figure 2 shows a typical unipolar waveform of incoherent
measurement (upper), a bipolar waveform of coherent
measurement (lower), and a waveform between them
(middle), with their offsets shifted for clarity. When the
probe intensity is over ?5:5 ? 1014W=cm2, the SH wave-
forms are nearly identical to those detected by the ZnTe
crystal, indicating the coherent detection of the THz
In the reciprocal process of four-wave rectification, the
general physical concept of TFISH in third-order nonline-
arity [14,15] can be understood as:
to 1:0 ?
where ??3?is the third-order susceptibility of air, and E is
the electric field component associated with the optical
field or THz field. Since Esignal
the measured SH is proportional to the intensity of the THz
wave: I2!/ ITHz. The phase information is lost; therefore,
the measurement is incoherent.
When the SH LO contribution ELO
analysis, the total SH intensity in the time average values
over one period of E-field oscillation has the form:
/ ETHz, the intensity of
2!is included into the
I2!/ ?E2!?2? ?Esignal
where ’ is the phase difference between the Esignal
generated from the laser-induced air plasma through self-
phase modulation and self-steepening, and it depends on
plasma density, especially in the transition from ambient
air to ionized air, and, accordingly, the LO should have a
well-defined threshold. Equation (2) can be written as:
2!. The LO ELO
2!is contributed from the white light
I2!/ ???3?I!?2ITHz? ?ELO
The first term is proportional to the intensity of the THz
wave. With a zero or a weak LO (small ELO
is dominant, leading to I2!/ ITHz. The second term is the
dc contribution from the LO and can be filtered out through
the use of a lock-in amplifier by modulating the THz beam.
The third term is the interference term, which is propor-
tional to ETHz. This term provides the basis of coherent
detection. With the above approximations, Eq. (3) can be
simplified to the form:
2!), the first term
I2!/ ???3?I!?2ITHz? 2??3?I!ELO
Equation (4) is obtained from the plane-wave approxima-
tion. It should be pointed out that ??3?could be probe
intensity dependent, especially when the probe intensity
approaches the plasma threshold. A constant ’ is a good
approximation because we experimentally proved that, in
our setup, the only source for the SH LO is the 2!
component of the white light, which has a fixed phase
relationship with the ! beam when the probe energy is
Equation (4) predicts that I2!/ ITHzwithout a LO or
I2!/ ETHzwith a strong LO. With probe intensity less
than the air ionization threshold, the LO ELO
and the total SH is dominated by the first term in Eq. (4);
therefore, the measured I2!is unipolar, and the detection is
incoherent. With the probe intensity much higher than the
plasma threshold, the second term dominates. I2!is pro-
portional to the THz electric field with a bipolar waveform,
and the detection is coherent. The measured I2!wave-
forms at three different probe intensities indicated in
Fig. 2 qualitatively agree well with the predication in
9.2 x 10
4.6 x 10
1.8 x 10
SH Signal I2ω (a.u.)
measured with a gas sensor at three different estimated probe
1:8 ? 1014W=cm2
(middle), and 9:2 ? 1014W=cm2(lower), respectively. The
waveform offsets are shifted for clarity.
Typical time-resolved SH waveforms (solid lines)
4:6 ? 1014W=cm2
PRL 97, 103903 (2006)
8 SEPTEMBER 2006
To verify the LO ELO
different probe intensities, we measured the dc term
blocking the THz beam. Figure 3 plots the intensity of total
SH LO (ILO
log scale. The SH LO does not become significant until the
probe intensity reaches ?1:8 ? 1014W=cm2. After that,
the intensity of SH LO increases dramatically with the
probe intensity. When the probe intensity reaches over
?5:5 ? 1014W=cm2, the increase of the LO intensity
slows down with an average slope of ?1:5.
2!and its contribution following
2!?2in Eq. (3) by modulating the probe beam while
2!) versus the estimated probe intensity on a log-
To identify these different processes, we indicate the
Keldysh parameter ? at different probe intensities in
Fig. 3. Meanwhile, we define three different detection
regimes, i.e., incoherent, hybrid, and coherent detection,
SH Signal (a.u.)
using nitrogen gas as the sensor and the corresponding THz
spectrum obtained from the discrete Fourier transform of the
THz waveform. The waveform, measured by a field-induced-
second-harmonic signal I2!in air, shows the coherent nature
which measures both the amplitude and phase of THz pulses.
Detected THz waveform in the time domain (inset)
12345 6 7 8 9 10
1 1 0.9 0.8 0.70.6 0.50.4
SH Local Oscillator Intensity I2ω
Probe Intensity (10
γ γ γ γ
log scale (solid dots). The local oscillator intensity becomes
significant after the probe intensity is greater than 1:8 ?
1014W=cm2. The corresponding Keldysh parameters ? are
indicated on the upper axis. The entire probe intensity range is
divided into three subranges, which are experimentally defined
as incoherent, hybrid, and coherent detection, respectively, with
two vertical dashed-dotted lines.
Local oscillator intensity ILO
2!vs probe intensity in log-
Probe Intensity (1014 W/cm2)
0.51.0 1.5 2.0
THz field: ~4.8 kV/cm
Peak SH Signal I2(a.u.)
Probe Intensity (10
Peak SH Signal (a.u.)
Incoherent detection: I2ω ITHz
~1.8 x 10
Peak SH Signal I2ω (a.u.)
THz Intensity ITHz (10
~16 x 10
Coherent detection: I2ω ETHz
Peak SH Signal I2ω (a.u.)
THz Field ETHz (kV/cm)
intensity I!(solid dots). When the probe intensity is below the
plasma threshold ( ? 1:8 ? 1014W=cm2), the data fit well to a
quadratic function (solid line). (b) Measured I2!versus the THz
intensity ITHz when the probe intensity is fixed at 1:8 ?
1014W=cm2(solid dots). The solid line is a linear fit.
(c) Measured I2!versus THz electric field strength ETHzwhen
the probe intensity is fixed at ?16 ? 1014W=cm2(solid dots).
The solid line is a linear fit. Note that shorter focal lengths of the
parabolic mirror and probe focal lens are used to increase the
dynamic range of the measurement.
(a) Measured SH intensity I2!versus the probe beam
PRL 97, 103903 (2006)
8 SEPTEMBER 2006
according to the waveforms obtained at different probe
intensities. The boundary between incoherent and hybrid
detection is reasonably located around the white light
plasma threshold. The defined boundary between hybrid
and coherent detection is close to the transition condition
between MI and TI, i.e., ? ? 1=2, which was previously
required to be ? ? 1 by Keldysh theory and modified to
? < 1=2 for the TI in the fs region . The plasma for-
mation directly gives rise to a change of the refractive
index and causes a spectral broadening towards the blue
side of the pump frequency . The intensity of the
400 nm component of white light increases due to the
further spectral broadening towards the blue as the plasma
density increases. Apparently, the fast increase of SH LO
in the hybrid detection region is due to MI, which cannot
yield very strong plasma because of the fs pulse duration.
In MI, the SH component (LO) of the white light increases
very fast so that the second term in Eq. (4) increases much
faster than the first term until TI dominates, at which point
the LO becomes very strong and the second term in Eq. (4)
dominates. In other words, only when TI dominates the
process can the total LO be strong enough to lead to
The highest dynamic range of the coherent detection
demonstrated is over 103, with a lock-in time constant of
0.3 s. Figure 4 plots a typical spectrum and its waveform
(inset) with the air-breakdown-coherent detection whenthe
THz wave is generated and detected in nitrogen gas. In
Fig. 4, we observed dips at 0.5 and 3.25 THz. At this
moment, we cannot identify the origin of dips. However,
the dips shift slightly and even disappear with different
Figure 5(a) shows a quadric dependence of the peak SH
signal on probe intensity when it is below ?1:8 ?
1014W=cm2while the THz field is kept at ?4:8 kV=cm;
when the probe intensity is over 1:8 ? 1014W=cm2, the
variation of the peak SH signal with probe intensity be-
comes complicated due to the simultaneous existence of
incoherent and coherent detection. Figure 5(b) shows a
linear dependence of peak SH signals on the THz intensity
when the probe intensity is fixed at ?1:8 ? 1014W=cm2.
Figures5(a) and5(b)verified thevalidity ofthe firstterm in
Eq. (4) for incoherent detection. In the case of coherent
detection, we need to verify I2!/ ETHz, i.e., the second
term in Eq. (4). To ensure that the probe beam has enough
intensity at the focal spot while maintaining adequate
dynamic range in the pump beam, we reduced the focal
lengths of the probe lens and the parabolic mirror near the
probe and fixed the probe intensity at ?16 ? 1014W=cm2.
Figure 5(c) plots I2!versus ETHz, with a linear relationship
between I2!and ETHz. The results agree well with Eq. (4).
In conclusion, we report the first demonstration of
broadband THz wave detection through third-order non-
linear optical processes using gases as the sensor. Our
results show that, when the probe intensity is below the
white light plasma threshold, the detection is completely
incoherent; above the threshold, but when the ionization is
dominated by multiphoton processes, both incoherent and
coherent detection exist simultaneously; we defined this
case as hybrid detection; when the probe intensity is well
above the threshold, TI dominates the process, and the
detection is coherent. We proposed that coherent detection
using gases as the sensor medium is achieved only when
the TI process dominates. The demonstration offers great
flexibility in the choice of sensing location, since air is one
of the most readily available resources in free space. This
all-air, all-optical approach could send optical beams to
generate and detect THz waves locally, utilizing a lower
attenuation at the visible range ( < 0:01 dB=km) in ambi-
ent air. Air-breakdown-coherent detection will enable THz
wave remote sensing and spectroscopy, which was previ-
ously considered impossible.
We acknowledge J. Xu, N. Karpowicz, H. Zhong, and
T. Yuan for informative discussion. This work is partially
supported by the Army Research Office, the Office of
Naval Research, and the National Science Foundation.
*Electronic address: email@example.com
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