Article

High Kerr nonlinearity of water in THz spectral range

Abstract and Figures

The values of the nonlinear refractive index coefficient for various materials in the terahertz frequency range exceed the ones in both visible and NIR ranges by several orders of magnitude. This allows to create nonlinear switches, modulators, systems requiring lower control energies in the terahertz frequency range. We report the direct measurement of the nonlinear refractive index coefficient of liquid water by using the Z-scan method with broadband pulsed THz beam. Our experimental result shows that nonlinear refractive index coefficient in water is positive and can be as large as 7×10 ⁻¹⁰ cm ² /W in the THz frequency range, which exceeds the values for the visible and NIR ranges by 6 orders of magnitude. To estimate n2, we use the theoretical model that takes into account ionic vibrational contribution to the third-order susceptibility. We show that the origins of the nonlinearity observed are the anharmonicity of molecular vibrations. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Content may be subject to copyright.
High Kerr nonlinearity of water in THz spectral
range
ANTO N N. TC Y P K I N ,1,* MAKSIM V. MELNIK,1MA R IA O. ZHU KOVA ,1
IRINA O. VO R O N T S OVA,1SERGEY E. PUTILIN,1
SERGEI A. KO Z L OV,1AND XI-CH E N G ZH A N G 1,2
1
International Laboratory of Femtosecond Optics and Femtotechnologies, ITMO University, St. Petersburg
197101, Russia
2The Institute of Optics, University of Rochester, Rochester, NY 14627, USA
*tsypkinan@corp.ifmo.ru
Abstract:
The values of the nonlinear refractive index coefficient for various materials in the
terahertz frequency range exceed the ones in both visible and NIR ranges by several orders of
magnitude. This allows to create nonlinear switches, modulators, systems requiring lower control
energies in the terahertz frequency range. We report the direct measurement of the nonlinear
refractive index coefficient of liquid water by using the Z-scan method with broadband pulsed
THz beam. Our experimental result shows that nonlinear refractive index coefficient in water
is positive and can be as large as 7
×
10
10
cm
2
/W in the THz frequency range, which exceeds
the values for the visible and NIR ranges by 6 orders of magnitude. To estimate
n2
, we use
the theoretical model that takes into account ionic vibrational contribution to the third-order
susceptibility. We show that the origins of the nonlinearity observed are the anharmonicity of
molecular vibrations.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) frequency range is finding more and more applications in different fields
of fundamental research [1] and a variety of everyday applications such as nondestructive
spectroscopy [2] and imaging [3], communications [4, 5] and ultrafast control [6] as well as
biomedicine [7]. Recent advances in research have brought high intensity broadband sources of
THz radiation into play [8]. These perspectives have already been shown for highly intensive
THz pulses generated from organic crystals with peak intensity
Ipea k
1.1
×
10
13
W/cm
2
[9].
The exploration of matter nonlinearities in THz frequency range can open new directions for
devices and systems development, components and instrumentation operation.
Despite the growing interest to this issue, the observations of nonlinearities in THz frequency
range were carried out without using direct measurements of material properties in most cases.
The latter ones can be nonlinearity and dispersion in the wave propagation, nonlinear optical
response caused by intense ultrashort THz pulses [10], absorption bleaching by means of pump-
probe technique [11,12], nonlinear free-carrier response [13, 14], field-induced transparency [15],
spin response [16], giant cross phase modulation and THz-induced spectral broadening of
femtosecond pulses [17], or quadratic THz optical nonlinearities by measuring the quadratic THz
Kerr effect [18].
The most important parameter characterizing the nonlinearity of the material response in
the field of intense waves is the coefficient of its nonlinear refractive index, usually denoted as
n2
. In the first report of such kind of measurements [19] silicon was tested by the use of the
open aperture Z-scan technique. Originally, it was predicted theoretically [20] that the nonlinear
refractive index coefficient for various materials in the THz frequency range exceeds the ones
in both visible and NIR ranges by several orders of magnitude. Then this fact was proven
Vol. 27, No. 8 | 15 Apr 2019 | OPTICS EXPRESS 10419
#354766
https://doi.org/10.1364/OE.27.010419
© 2019
Received 2 Jan 2019; revised 13 Mar 2019; accepted 17 Mar 2019; published 1 Apr 2019
experimentally by the Z-scan method [21,22]. Also, estimates of the liquid nitrogen
n2
were
made on the basis of a change in the rotation angle of the THz pulse polarization ellipse [23].
However, in these works only indirect estimations of n2were made.
Until recently, the study of water in the THz frequency range has been considered impossible
due to its large absorption. The broadband THz wave generation from a water film [24,25] was
experimentally demonstrated and opened a new field of interest. In this article, we present the
direct measurement of water nonlinear refractive index coefficient for the broadband pulsed THz
radiation with the conventional Z-scan method. Since the Z-scan method can be utilized for
plane-parallel samples only, we use flat water jet. We demonstrate that the nonlinear refractive
index coefficient exceeds its visible and NIR ranges’ values by 6 orders of magnitude [26–29].
2. Experiment and analytical model
Figure 1(a) illustrates an experimental setup for measuring the nonlinear refractive index (
n2
)
of a flat liquid jet with THz pulses. We use TERA-AX (Avesta Project) as a source of THz
radiation. In this system generation of the THz radiation is based on the optical rectification
of femtosecond pulses in a lithium niobate crystal [30]. The generator TERA-AX is pumped
using a femtosecond laser system (duration 30 fs, pulse energy 2.2 mJ, repetition rate 1 kHz,
central wavelength 800 nm). The THz pulse energy is 400 nJ, the pulse duration is 1 ps (Fig.
1(b)) and the spectrum width 0.1–2.5 THz (Fig. 1(c)). The measurement of the THz electric
field was held by the conventional electro-optical detection system. The THz radiation intensity
is controlled by reducing the femtosecond pump beam intensity.The pump intensity variation
during the THz generation leads to a change in the divergence of the terahertz beam and also
influences the terahertz central position [31]. In our experiment, we use the parabolic mirror with
a focal length of 25 mm to collimate the THz radiation generated from LiNbO
3
crystal. Next,
when adjusting the experimental setup, we ensure that the THz beam of 25.4 mm in diameter
obtained at the output of the TERA-AX is collimated at all femtosecond pump energies and it’s
optical axis passes through the center of the PM1 parabolic mirror. Pulsed THz radiation is
focused and collimated by two parabolic mirrors (PM1 and PM2) with a focal length of 12.5
mm. The spatial size of the THz radiation at the output of the generator is 25.4 mm. Caustic
diameter is 1 mm (FWHM). In order to get a higher intensity in the waist, we use a short-focus
parabolic mirror with a large NA. Such a geometry allows us to get the radiation peak intensity
in the caustic of the THz beam 0.5
×
10
8
W/cm
2
. Flat water jet (jet) is moved along the caustic
area from -4 mm to 4 mm using a motorized linear translator, the restriction on the displacement
is determined by the jet width and the focusing geometry of the THz radiation (see Fig. 1(a)
insert). The polarization of the THz radiation is vertical. In this experiment we used distilled
water which does not contain any substances as medium. The water jet has a thickness of 0.1 mm
and is oriented along the normal to the incident radiation. The jet is obtained using the nozzle
which combines the compressed-tube nozzle and two razor blades [32]. This design forms a flat
water surface with a laminar flow. The optical path of the THz pulse passes through the center
of the jet area of a constant thickness. Due to the use of the pump, water is released under the
pressure. The hydroaccumulator in the system of water supply allows to reduce the pulsations
associated with the operation of the water pump significantly. The THz radiation is collimated by
the parabolic mirror PM2 and focused by the lens (L) on the Golay cell (GC). For the closed
aperture geometry the aperture (A) is moved in the beam (closed position). The synchronization
is performed using the mechanical modulator (M) located between the lens and the Golay cell.
When the jet is moved along the
z
axis through the focal region of the THz radiation, the average
power of the latter is measured using open and closed aperture.
Despite the fact the experimental setup implies nonparaxial radiation, as was shown in [33] for
pulses from a small number of oscillations, the differences between the paraxial and nonparaxial
modes are negligible. Figure 2 shows Z-scan curves for the water jet measured with open Fig.
Vol. 27, No. 8 | 15 Apr 2019 | OPTICS EXPRESS 10420
Fig. 1. (a) The experimental setup for measuring the nonlinear refractive index (
n2
) of a
liquid jet in the THz spectral range. Two parabolic mirrors (PM1 and PM2) with a focal
length of 12.5 mm form the caustics area where the water jet (jet) is scanned along the z axis.
The synchronization is performed using the mechanical modulator (M) located between the
lens and the Golay cell (GC). The aperture (A) is moved from open to closed position to
change the geometry of Z-scan from open to closed aperture. Insert - Geometrical position
of the jet moved along the z axis relative to the THz radiation. The temporal waveform (b)
and its spectrum (c) of the THz pulse generated by the TERA-AX system.
2(a) and closed 2(b) aperture for different values of the THz radiation energy. Each line is
averaged over 50 measurements. Figure 2(a) shows the water bleaching by around 2% which
is caused by the THz radiation pump energy growth by 2 orders. For
n2
determination we use
experimental data with the closed aperture (Fig. 2(b)).
Usually, the Z-scan technique is strictly valid only for quasi-monochromatic radiation. However,
it is also widely used in the case of femtosecond pulsed radiation that possesses a broad
spectrum [34]. As seen from Fig. 2(b), moving the jet along the z axis leads to a noticeable
change of the measured intensity of the THz beam, which is a distinguishing feature of Z-scan
curves obtained by the known method [35]. It is caused by different divergences of the radiation
at various positions of the water jet in the caustic, where a nonlinear Kerr lens is induced by the
THz radiation field. In view of this we use standard formulas [35
37] to evaluate n
2
of water
according to the results of our measurements shown in Fig. 2(b):
n2=
T
0.406Iin ×2λ
2πLα(1S)0.25 (1)
where
T
= 0.013 (Fig. 2(b)) is the difference between the maximum and minimum transmission,
S
is the linear transmission of the aperture,
Lα
=
α1
[1-
exp(−αL)
] is the effective interaction
Vol. 27, No. 8 | 15 Apr 2019 | OPTICS EXPRESS 10421
length,
L
is the sample thickness,
α
is the absorption coefficient (
α
= 100 cm
1
),
λ
is the
wavelength, and
Iin
is the input radiation intensity. The linear transmission of the aperture
is 2%, which allows to maximize the sensitivity of the measurement method but reduces the
signal-to-noise ratio. The radiation wavelength was chosen to be
λ0
= 0.4 mm (
ν0
= 0.75 THz).
It corresponds to the maximum of the generation spectrum of the THz radiation (see Fig. 1(b)).
The result of the evaluation calculated by Eq. (1) gives the value n2= 7×1010 cm2/W.
Fig. 2. Z-scan curves for a 0.1 mm thick water jet measured with open (a) and closed (b)
aperture for different THz radiation energy values of 4 nJ, 40 nJ and 400 nJ.
T = 0.013 is
the differential of the Z-scan curve measured with the closed aperture of radius 1.5 mm.
To illustrate the correctness of using Eq. (1) for the calculation of the nonlinear refractive index
coefficient in the case of the broadband THz radiation, we compare the experimental data with
the analytical Z-scan curve for monochromatic radiation (Fig. 3) calculated by the equation [35]:
T(z)=+
−∞ PT(∆Φ0(t))dt
S+
−∞ Pi(t)dt
(2)
where
Pi
(t)=
πw2
0I0(t)/2
is the instantaneous input power (within the sample),
S
=1-
exp(−
2
r2
a/w2
a)
is the aperture linear transmittance; the transmitted power through the aperture gives
PT(∆Φ0(t)) =c0N0πra
0
a|Ea(r,t)|2r dr (3)
where
Ea(r,t)=E(z,r=0,t)exp(−αL/2) ×
+
m=0
[iφ0(z,t)]m
m!
wm0
wm
exp(r2
w2
mikr 2
2Rm
+iQm)(4)
and E(z,r=0,t)=E0si n(2πν0t)w0/w(z),φ0(z,t)=∆Φ0(t)/(1+z2/z2
0),∆Φ0(t)=kn0(t)L.
The following values are used in these equations: absorption coefficient
α
= 100 cm
1
, sample
length
L
= 0.1 mm, central frequency of the radiation
ν0
= 0.75 THz (
λ0
= 0.4 mm), beam waist
radius
w0
= 0.5 mm, aperture radius
ra
= 1.5 mm, radius of the THz beam
wa
= 12.5 mm,
intensity of the THz beam in caustic
I0
= 0.5
×
10
8
W/cm
2
, nonlinear refractive index coefficient
n2= 7×1010 cm2/W. This value of n2was obtained in the experiment previously.
As can be seen, the experimental Z-scan curve for broadband THz radiation agrees with the
analytical Z-scan curve for the monochromatic radiation well.
Vol. 27, No. 8 | 15 Apr 2019 | OPTICS EXPRESS 10422
Fig. 3. Comparison of the experimental results of the closed aperture measurement of
Z-scan method for the pulsed broadband THz radiation for the water jet 0.1 mm thick with
an analytical Z-scan curve for monochromatic radiation with the wavelength of 0.4 mm. The
analytical curve was calculated using Eq. (2).
3. Theoretical estimate of the nonlinear refractive index coefficient
We estimate the nonlinear refractive index coefficient
n2
of liquid water through the use of a
recent theoretical treatment [20]. This treatment ascribes the THz nonlinearities in media to a
vibrational response that is orders of magnitude larger than typical electronic responses. This
model assumes that the nature of the nonlinearity of the water refractive index in the experiment
is not caused by the thermal expansion of the substance (as well as by its density change). This
expansion process is inertial. The initial cause of low-inertia nonlinearity of the refractive index
measured and the subsequent inertial thermal expansion of the substance is the anharmonicity of
molecular vibrations. We make use of Eq. (55) of reference [20], which applies to the situation
where the THz frequency
ω0
is much smaller than the fundamental vibrational frequency resulting
in absorption peak
λ
= 3
µ
m (
ω
100 THz) [38]. For our experiment this condition is well
satisfied, as
ω0/
2
π
is approximately 0.75 THz and
ω/
2
π
is 15.9 THz. This equation takes the
form:
¯n2=¯n(1)
2
+¯n(2)
2
=
3a2
1m2ω4α2
T
32n0π2q2N2k2
Bn2
0139
32πNn0}ωn2
012(5)
We evaluate this expression through the use of the following values:
a1
is the lattice constant; for
our estimations in case of liquid we use the water molecule diameter 2.8
×
10
8
cm [39],
m
=
1.6
×
10
24
g is the reduced mass of the vibrational mode,
αT
= 0.2
×
10
3
(
)
1
is the thermal
expansion coefficient [40]. The parameter
q
is the effective charge of the chemical bond; for
simplicity, we take this quantity to be the electron charge.
N
is the number density of vibrational
units. We calculate this value as the ratio between specific gravity of water equal to 1 and the
total mass of H
2
O molecule equal to the weight of molecule (1
×
2 + 16) times amu (1.67
×
10
24
).
It results in
N
= 3.3
×
10
22
in 1 cm
3
. We take the refractive index as
n0
= 2.3 which is the averaged
refractive index in 0.3–1.0 THz region [41]. Using these values, we find that the predicted value
of n2for water in the low-frequency limit is n2= 5×1010 cm2/W.
4. Summary
In conclusion we have experimentally demonstrated the possibility of direct measurement of the
nonlinear refractive index coefficient
n2
of water in the THz frequency range. Z-scan curves
obtained for broadband THz radiation experimentally are in good agreement with the analytical
model of the method for monochromatic radiation. The value of the nonlinear refractive index
Vol. 27, No. 8 | 15 Apr 2019 | OPTICS EXPRESS 10423
coefficient of water calculated from the experiment is
n2
= 7
×
10
10
cm
2
/W, which is 6 orders of
magnitude higher than for the visible and IR ranges [26
29] where
n2
has the magnitude of 10
16
cm
2
/W. These results demonstrate the high cubic nonlinearity of water in the THz frequency
range and confirm a recent theoretical prediction [20] that the ionic vibrational contribution to the
third-order susceptibility renders THz nonlinearities much larger than typical optical-frequency
nonlinearities. Therefore, in terms of applications, our demonstration opens up new perspectives
for studying various materials in the THz frequency range. Nonlinear optics, in its turn, finds
applications in the creation of light modulators, transistors, switchers and others in this spectral
range.
Funding
Russian Foundation of Basic Research (RFBR) (19-02-00154). X.-C. Zhang acknowledges
support from U.S. Army Research Office (W911NF-17-1-0428). In addition, S.E. Putilin
acknowledges support from the Government of the Russian Federation (project 3.9041.2017/7.8).
References
1.
S. Baierl, M. Hohenleutner, T. Kampfrath, A. Zvezdin, A. Kimel, R. Huber, and R. Mikhaylovskiy, “Nonlinear spin
control by terahertz-driven anisotropy fields,” Nature Photon. 10, 715–718 (2016).
2.
J. Dong, A. Locquet, M. Melis, and D. Citrin, “Global mapping of stratigraphy of an old-master painting using
sparsity-based terahertz reflectometry,” Sci. Rep. 7, 15098 (2017).
3.
K. J. Kaltenecker, A. Tuniz, S. C. Fleming, A. Argyros, B. T. Kuhlmey, M. Walther, and B. M. Fischer, “Ultrabroadband
perfect imaging in terahertz wire media using single-cycle pulses,” Optica 3, 458–464 (2016).
4.
T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,
Nature Photon. 10, 371–379 (2016).
5.
Y. V. Grachev, X. Liu, S. E. Putilin, A. N. Tsypkin, V. G. Bespalov, S. A. Kozlov, and X.-C. Zhang, “Wireless data
transmission method using pulsed thz sliced spectral supercontinuum,” IEEE Photonics Technol. Lett.
30
, 103–106
(2018).
6.
P. Bowlan, J. Bowlan, S. A. Trugman, R. V. Aguilar, J. Qi, X. Liu, J. Furdyna, M. Dobrowolska, A. J. Taylor,
D. A. Yarotski, and R. P. Prasankumar, “Probing and controlling terahertz-driven structural dynamics with surface
sensitivity,” Optica 4, 383–387 (2017).
7.
O. Smolyanskaya, I. Schelkanova, M. Kulya, E. Odlyanitskiy, I. Goryachev, A. Tcypkin, Y. V. Grachev, Y. G. Toropova,
and V. Tuchin, “Glycerol dehydration of native and diabetic animal tissues studied by thz-tds and nmr methods,
Biomed. Opt. Express 9, 1198–1215 (2018).
8. X. C. Zhang, A. Shkurinov, and Y. Zhang, “Extreme terahertz science,” Nature Photon. 11, 16–18 (2017).
9.
M. Shalaby and C. P. Hauri, “Demonstration of a low-frequency three-dimensional terahertz bullet with extreme
brightness,” Nat. Commun. 6, 5976 (2015).
10.
P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Nonlinear terahertz response of n-type
gaas,” Phys. Rev. Lett. 96, 187402 (2006).
11.
J. Hebling, M. C. Hoffmann, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Observation of nonequilibrium carrier
distribution in ge, si, and gaas by terahertz pump–terahertz probe measurements,” Phys. Rev. B 81, 035201 (2010).
12.
M. C. Hoffmann, J. Hebling, H. Y. Hwang, K.-L. Yeh, and K. A. Nelson, “Thz-pump/thz-probe spectroscopy of
semiconductors at high field strengths,” J. Opt. Soc. Am. B 26, A29–A34 (2009).
13.
G. Sharma, I. Al-Naib, H. Hafez, R. Morandotti, D. Cooke, and T. Ozaki, “Carrier density dependence of the
nonlinear absorption of intense thz radiation in gaas,” Opt. Express 20, 18016–18024 (2012).
14.
D. Turchinovich, J. M. Hvam, and M. C. Hoffmann, “Self-phase modulation of a single-cycle terahertz pulse by
nonlinear free-carrier response in a semiconductor,” Phys. Rev. B 85, 201304 (2012).
15.
S. Li, G. Kumar, and T. E. Murphy, “Terahertz nonlinear conduction and absorption saturation in silicon waveguides,”
Optica 2, 553–557 (2015).
16.
S. Baierl, J. H. Mentink, M. Hohenleutner, L. Braun, T.-M. Do, C. Lange, A. Sell, M. Fiebig, G. Woltersdorf,
T. Kampfrath, and R. Huber, “Terahertz-driven nonlinear spin response of antiferromagnetic nickel oxide,” Phys. Rev.
Lett. 117, 197201 (2016).
17.
C. Vicario, M. Shalaby, and C. P. Hauri, “Subcycle extreme nonlinearities in gap induced by an ultrastrong terahertz
field,” Phys. Rev. Lett. 118, 083901 (2017).
18.
S. Lin, S. Yu, and D. Talbayev, “Measurement of quadratic terahertz optical nonlinearities using second-harmonic
lock-in detection,” Phys. Rev. Appl. 10, 044007 (2018).
19.
G. Kaur, P. Han, and X. Zhang, “Terahertz induced nonlinear effects in doped silicon observed by open-aperture
z-scan,” in “Infrared Millimeter and Terahertz Waves (IRMMW-THz), 2010 35th International Conference on,”
(IEEE, 2010), pp. 1–2.
Vol. 27, No. 8 | 15 Apr 2019 | OPTICS EXPRESS 10424
20.
K. Dolgaleva, D. V. Materikina, R. W. Boyd, and S. A. Kozlov, “Prediction of an extremely large nonlinear refractive
index for crystals at terahertz frequencies,” Phys. Rev. A 92, 023809 (2015).
21.
A. Woldegeorgis, T. Kurihara, B. Beleites, J. Bossert, R. Grosse, G. G. Paulus, F. Ronneberger, and A. Gopal, “Thz
induced nonlinear effects in materials at intensities above 26 gw/cm 2,” J. Infrared Millim. Terahertz Waves
39
,
667–680 (2018).
22.
A. Tcypkin, S. Putilin, M. Kulya, M. Melnik, A. Drozdov, V. Bespalov, X.-C. Zhang, R. Boyd, and S. Kozlov,
“Experimental estimate of the nonlinear refractive index of crystalline znse in the terahertz spectral range,” Bull. Russ.
Acad. Sci.: Phys. 82, 1547–1549 (2018).
23.
A. V. Balakin, S. V. Garnov, V. A. Makarov, N. A. Kuzechkin, P. A. Obraztsov, P. M. Solyankin, A. P. Shkurinov, and
Y. Zhu, “"terhune-like" transformation of the terahertz polarization ellipse "mutually induced" by three-wave joint
propagation in liquid,” Opt. Lett. 43, 4406–4409 (2018).
24.
Q. Jin, Y. E, K. Williams, J. Dai, and X.-C. Zhang, “Observation of broadband terahertz wave generation from liquid
water,” Appl. Phys. Lett. 111, 071103 (2017).
25.
Y. E, Q. Jin, A. Tcypkin, and X.-C. Zhang, “Terahertz wave generation from liquid water films via laser-induced
breakdown,” Appl. Phys. Lett. 113, 181103 (2018).
26.
M. Paillette, “Recherches expérimentales sur les effets kerr induits par une onde lumineuse,” Ann. Phys.-Paris
14
,
671–712 (1969).
27.
W. L. Smith, P. Liu, and N. Bloembergen, “Superbroadening in h 2 o and d 2 o by self-focused picosecond pulses
from a yalg: Nd laser,” Phys. Rev. A 15, 2396–2403 (1977).
28. P. Ho and R. Alfano, “Optical kerr effect in liquids,” Phys. Rev. A 20, 2170 (1979).
29. R. W. Boyd, Nonlinear optics (Elsevier, 2003).
30.
K. Yang, P. Richards, and Y. Shen, “Generation of far-infrared radiation by picosecond light pulses in linbo3,” Appl.
Phys. Lett. 19, 320–323 (1971).
31.
C. Lombosi, G. Polonyi, M. Mechler, Z. Ollmann, J. Hebling, and J. A. Fulop, “Nonlinear distortion of intense THz
beams,” New J. Phys. 17, 083041 (2015).
32.
A. Watanabe, H. Saito, Y. Ishida, M. Nakamoto, and T. Yajima, “A new nozzle producing ultrathin liquid sheets for
femtosecond pulse dye lasers,” Opt. Commun. 71, 301–304 (1989).
33.
D. A. Kislin, M. A. Knyazev, Y. A. Shpolyanskii, and S. A. Kozlov, “Self-action of nonparaxial few-cycle optical
waves in dielectric media,” JETP Letters 107, 753–760 (2018).
34.
X. Zheng, R. Chen, G. Shi, J. Zhang, Z. Xu, X. Cheng, and T. Jiang, “Characterization of nonlinear properties of
black phosphorus nanoplatelets with femtosecond pulsed z-scan measurements,” Opt. Lett. 40, 3480–3483 (2015).
35.
M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical
nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
36.
M. Yin, H. Li, S. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single z-scan method,”
Appl. Phys. B 70, 587–591 (2000).
37.
Y. Cheung and S. Gayen, “Optical nonlinearities of tea studied by z-scan and four-wave mixing techniques,” J. Opt.
Soc. Am. B 11, 636–643 (1994).
38.
G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-
µ
m wavelength region,” Appl. Opt.
12, 555–563 (1973).
39.
P. Schatzberg, “Molecular diameter of water from solubility and diffusion measurements,” J. Phys. Chem.
71
,
4569–4570 (1967).
40. G. Kell, “Precise representation of volume properties of water at one atmosphere,” JCED 12, 66–69 (1967).
41.
L. Thrane, R. H. Jacobsen, P. U. Jepsen, and S. Keiding, “Thz reflection spectroscopy of liquid water,” Chem. Phys.
Lett. 240, 330–333 (1995).
Vol. 27, No. 8 | 15 Apr 2019 | OPTICS EXPRESS 10425
... where 0 is the absorption coefficient of the material at equilibrium introduced previously, I is the source intensity, and NL is the non-linear term. It has been demonstrated before 11,12,16 that liquid water at a temperature close to 21 °C displays a sizeable non-linear absorption at 1 THz, i.e., NL(21 °C)-80 cm/GW. The cascaded anharmonic effect introduced by the Kozlov group 11,12 was shown to scale with the thermal expansivity (see Figure 4 in ref. 12 ) that, in turn, vanishes at the temperature of 4 °C in liquid water 18 . ...
... It has been demonstrated before 11,12,16 that liquid water at a temperature close to 21 °C displays a sizeable non-linear absorption at 1 THz, i.e., NL(21 °C)-80 cm/GW. The cascaded anharmonic effect introduced by the Kozlov group 11,12 was shown to scale with the thermal expansivity (see Figure 4 in ref. 12 ) that, in turn, vanishes at the temperature of 4 °C in liquid water 18 . For this reason, we expected to detect a smaller THz non-linearity at 4 °C than at 21 °C in pure water. ...
... The transmission described by eq.3 becomes independent of the THz intensity when the argument of the second exponential is negligible, i.e., when NL·I·d/20. As demonstrated before 11,12,16 , the maximum THz intensity used here is enough to induce a large non-linear response in water at 21 °C. For example, by substituting in eq.2 the values NL(21 °C)-80 cm/GW and I=1.07 GW/cm 2 , the non-linear drop of the absorption coefficient is about -86 cm -1 , which is almost half of the absorption coefficient at equilibrium. ...
Preprint
Full-text available
Liquid water is one of the most studied substances, yet many of its properties are difficult to rationalize. The uniqueness of water is rooted in the dynamic network of hydrogen-bonded molecules that rearranges within about one picosecond. Terahertz fields oscillate on a picosecond timescale and are inherently suited to study water. Recent advances in non-linear terahertz spectroscopy have revealed large signals from liquid water, which have been interpreted with different, sometimes competing, theoretical models. Here we show that the non-linear response of liquid water at ~1 THz is similar at 21 {\deg}C and 4 {\deg}C, thus suggesting that the most appropriate microscopic models should depend weakly on temperature.
... The utilization of Kerr nonlinearity in the context of polarisation-structured light field has also been reported (Wen et al. 2019). Moreover, study of Kerr-type nonlinear refractive in the THz spectral range (Tcypkin et al. 2019) has also been added to literature. Thus, the investigations on the effect of Kerr type nonlinearity have been attracting the researchers and scientists and they have been making various novel contributions to the literature in this area. ...
Article
Full-text available
In this paper, we present the coupling characteristics of single-mode dispersion-shifted and dispersion-flattened fibers directional couplers both in presence as well as in absence of Kerr nonlinearity. In this regard, we apply the simple power series expression for the fundamental mode for each kind of fiber as developed by Chebyshev formalism. In order to obtain the coupling parameters in the nonlinear region, method of iteration is used to obtain the convergent values of cladding decay parameter and the normalised power series coefficients in nonlinear region. The concerned evaluation involves little computation but our results match excellently with the exact results obtainable by rigorous methods. Thus, our method can be considered as a simple alternative to the existing complex methods found in literature. So, this simple method will prove user friendly to the technologists working with such devices in the field of Kerr-type nonlinear photonics.
Article
Generation of terahertz (THz) wave from air plasma induced by femtosecond laser pulses with a single central frequency (the so-called "single-color") is one of the fundamental interactions between light and matter, and is also the basis of subsequent pumping schemes using two- or multi-color laser fields. Recently, more states of media beyond gas (e.g., atomic cluster and liquid) via photo-ionization have brought new experimental observations of THz radiation, which can no longer be simply attributed to the mainstream model of the transition-Cherenkov radiation (TCR), thus making the whole picture unclear. Here, we revisited the mechanism of this dynamic process in a new view of the traveling-wave antenna (TWA) model. By successfully reproducing the reported far-field THz radiation profiles from various plasma filament arrangements, the wide applicability of the TWA theory has been revealed. On the other hand in the microscopic view, we investigated the plasma oscillation during filamentation aiming at further bridging the plasma filament and the antenna. Accordingly, THz-plasma resonance has been theoretically and experimentally demonstrated as the elementary THz emitter, paving the way towards fully understanding this important single-color plasma based THz source.
Article
Full-text available
High-intensity optical radiation propagation in a transparent dielectric medium causes the phenomena of pulse self-action and radiation generation at triple frequencies due to the cubic nonlinearity of the medium. However, quadratic nonlinear effects usually outshine the cubic ones in anisotropic nonlinear crystals. In this work, we demonstrate that for certain experimental parameters the nonlinear effect of the third order can be stronger than the second order one in the MgO:LiNbO3 crystal for terahertz frequency range. We experimentally and theoretically show that this effect can lead to the significant modification of the classical phenomenon of radiation generation at triple frequencies in the case when the pulse represents only one complete oscillation of the optical field. The experiment demonstrated that the phenomenon of generation of radiation at triple frequencies with respect to the frequency of the maximum spectral density in a nonlinear medium of the pulse disappears, and it is replaced by the generation of radiation at quadruple frequencies. The analysis confirms that this effect is based on the asymmetry and large width of the initial spectrum of such extremely short pulses in terms of the number of oscillations.
Article
The soliton-like mode for highly efficient generation of terahertz radiation in a quadratically nonlinear medium by means of optical pulses with tilted wave fronts is investigated. For optical and terahertz pulses, a system of the Zakharov–Boussinesq type equations describing the process of generation at arbitrary angles of the tilt of wave fronts is derived. Various cases of the soliton generation are analyzed. It is shown that the tilt of wave fronts is fundamental for the formation of the optical-terahertz solitons of a new type, which we call dispersionless solitons.
Conference Paper
A detailed analysis of the applicability limits the z-scan method exhibit when employed for THz radiation is conducted. THz pulses feature critically wide spectrum and ultrashort duration, which leads to a significant decrease in the accuracy of the results obtained by z-scan method. The work presents the estimations of the z-scan method accuracy obtained through the comparison of the results of the numerical simulations of the method and analytically calculated values. The focus of the analysis was laid on dispersion, diffraction, and nonlinearity effects contributions.
Article
Full-text available
A modification of the Z-scan technique for measuring nonlinear refractive index n2 in the terahertz spectral region is proposed. Measurements are made at a broadband terahertz radiation intensity of 0.8 × 10⁹ W cm⁻². Coefficient n2 = 2.5 × 10⁻¹¹ cm² W⁻¹ is estimated for semiconductor crystalline ZnSe.
Article
Full-text available
We present a method to measure quadratic terahertz optical nonlinearities in terahertz time-domain spectroscopy. We use a rotating linear polarizer (a polarizing chopper) to modulate the amplitude of the incident terahertz pulse train. We use phase-sensitive lock-in detection at the fundamental and the second harmonic of the modulation frequency to separate the materials’ responses that are linear and quadratic in a terahertz electric field. We demonstrate this method by measuring the quadratic terahertz Kerr effect in the presence of the much stronger linear electro-optic effect in the (110) GaP crystal. We propose that the method can be used to detect terahertz second-harmonic generation in noncentrosymmetric media in time-domain spectroscopy, with broad potential applications in nonlinear terahertz photonics and related technology.
Article
Full-text available
Nonlinear refractive index and absorption coefficient are measured for common semiconductor material such as silicon and organic molecule such as lactose in the terahertz (THz) spectral regime extending from 0.1 to 3 THz. Terahertz pulses with field strengths in excess of 4.4 MV/cm have been employed. Transmittance and the transmitted spectrum were measured with Z-scan and single shot noncollinear electro-optic pump-probe techniques. The THz-induced change in the refractive index (Δn) shows frequency-dependence and a maximum change of \(-~0.128\) at 1.37 THz in lactose and up to \(+~0.169\) at 0.15 THz in silicon was measured for a peak incident THz intensity of 26 GW/cm². Furthermore, the refractive index variation shows a quadratic dependence on the incident THz field, implying the dominance of third-order nonlinearity.
Article
Full-text available
The optical clearing method has been widely used for different spectral ranges where it provides tissue transparency. In this work, we observed the enhanced penetration of the terahertz waves inside biological samples (skin, kidney, and cornea) treated with glycerol solutions inducing changes of optical and dielectric properties. It was supported by the observed trend of free-to-bound water ratio measured by the nuclear magnetic resonance (NMR) method. The terahertz clearing efficiency was found to be less for diabetic samples than for normal ones. Results of the numerical simulation proved that pulse deformation is due to bigger penetration depth caused by the reduction of absorption and refraction at optical clearing.
Article
Full-text available
The process by which art paintings are produced typically involves the successive applications of preparatory and paint layers to a canvas or other support; however, there is an absence of nondestructive modalities to provide a global mapping of the stratigraphy, information that is crucial for evaluation of its authenticity and attribution, for insights into historical or artist-specific techniques, as well as for conservation. We demonstrate sparsity-based terahertz reflectometry can be applied to extract a detailed 3D mapping of the layer structure of the 17th century easel painting Madonna in Preghiera by the workshop of Giovanni Battista Salvi da Sassoferrato, in which the structure of the canvas support, the ground, imprimatura, underpainting, pictorial, and varnish layers are identified quantitatively. In addition, a hitherto unidentified restoration of the varnish has been found. Our approach unlocks the full promise of terahertz reflectometry to provide a global and detailed account of an easel painting’s stratigraphy by exploiting the sparse deconvolution, without which terahertz reflectometry in the past has only provided a meager tool for the characterization of paintings with paint-layer thicknesses smaller than 50 μm. The proposed modality can also be employed across a broad range of applications in nondestructive testing and biomedical imaging.
Article
Understanding the physics of terahertz (THz) wave generation from water is essential for developing liquid THz sources. This letter reports detailed experimental measurements of THz wave emission by focusing intense laser pulses onto water films. The simulation based on a ponderomotive force-induced dipole is supported by the observation of the THz intensity dependence on the laser incidence angle. This work provides fundamental insights into the THz wave generation process in water and an alternative perspective for studying laser-induced breakdown in liquids.
Article
In this Letter, we show experimentally for the first time, to the best of our knowledge, the possibility to observe the effect of polarization mutual action of three elliptically polarized waves, with one of them at terahertz frequency, when they propagate in the isotropic nonlinear medium. When three light pulses are propagated at frequencies ω, 2ω, and ω THz through liquid nitrogen, we observed the rotation of the ellipse main axis and the ellipticity change. We have shown that this effect is very well described theoretically in the framework of a physical approach analogous to the self-rotation of the polarization ellipse first described in 1964 by Maker et al., but expanded for the case of multi-frequency interaction.
Article
A mathematical model of evolution of the space–time spectra of nonparaxial few-cycle optical waves in isotropic dielectric media with an arbitrary dispersion of the refractive index and the inertialess third-order nonlinearity has been discussed. It has been shown that, at the self-focusing of a wave single-cycle at the input to a nonlinear medium into an optical filament with transverse dimensions comparable with the central radiation wavelength, the strength of the increased longitudinal component of its electric field can become larger than the initial longitudinal component by a factor of 7 and can be 18% of the transverse component of the input wave field. Errors of the calculations of the self-action of radiation with superwide time and spatial spectra within simplified mathematical models have been estimated.
Article
A method of ultrafast wireless information transmission using spectrum-sliced supercontinuum (SC) along the THz frequency range is presented in this manuscript. The THz spectrum-sliced SC was formed by femtosecond optical pulses doubled in a Michelson interferometer before being input onto a MgO:LiNbO3 THz generator. Two THz pulses generated by femtosecond pulses within a MgO:LiNbO3 crystal provided the spectrum-sliced SC in the spectral domain, which was recorded by an electro-optical detection system. The transmission rate in this method is determined by the bandwidth of the THz spectrum, the number of spectral lines in the SC, and the pulse repetition rate. We have demonstrated a SC containing 31 spectral lines with 23 GHz spacing within the range from 0.04 to 0.75 THz. The signal with encoded information was successfully transmitted over 2.4 meters in free-space.
Article
Bulk liquid water is a strong absorber in the terahertz (THz) frequency range, due to which liquid water has historically been sworn off as a source for THz radiation. Here, we experimentally demonstrate the generation of broadband THz waves from liquid water excited by femtosecond laser pulses. Our measurements reveal the critical dependence of the THz field upon the relative position between the water film and the focal point of the laser beam. The THz radiation from liquid water shows distinct characteristics when compared with the THz radiation from air plasmas with single color optical excitation. First, the THz field is maximized with the laser beam of longer pulse durations. In addition, the p-polarized component of the emitted THz waves will be influenced by the polarization of the optical excitation beam. It is also shown that the energy of the THz radiation is linearly dependent on the excitation pulse energy.