Research on Terahertz Generation Based on Cherenkov-Type
Difference Frequency
Zhiming Rao and Chao Li
College of Physics and Communication Electronics, Jiangxi Normal University, Jiangxi, China
Keywords: Terahertz Wave, Difference Frequency Generation, Cherenkov Effect.
Abstract: In this paper, we report a new method of highly efficient terahertz generation based on Cherenkov-type cavity
phase matching cascade difference frequency. The influence of different temperature, crystal length, pump
light inversion times and reflectivity on the power conversion efficiency of terahertz wave emitted along
Cherenkov angle is analyzed. Our theoretical calculation shows that the highest terahertz photon conversion
efficiency reach to 443.6%. Compared with the cavity phase matching technology, the Cherenkov effect
introduced in the preparation of terahertz sources is a new idea, which is expected to develop efficient
terahertz sources.
1 INTRODUCTION
Terahertz wave is an electromagnetic wave with a
wavelength ranging from 0.03 to 3 mm. It contains
rich physical and chemical information when
interacting with substances. In recent years, terahertz
sources have been widely used in radar, medical
diagnosis, safety inspection, broadband
communication, electromagnetic weapons, non-
destructive testing and other fields (Wang R-H.
Tanoto). Among many methods of generating
terahertz source wave, nonlinear optical method has
the advantages of wide tuning, compact structure, no
threshold and easy realization, which has attracted
more and more attention (He Y-Ravi K).Using two
infrared lasers with similar wavelengths to conduct
frequency difference in nonlinear crystals is a
common method to obtain terahertz wave radiation
sources. As early as 1965, since the birth of the laser,
Zernike and Berman (F. Zernike, 1965) have started
to use neodymium glass lasers to conduct frequency
difference through quartz crystals to obtain terahertz
wave output with a frequency of 3 THz (100 µ m), but
the output efficiency at that time was extremely low.
In 2005, S.Y. Tochisky et al. used a CO
2
laser with a
pulse width of 250 ps to conduct non-collinear
frequency difference on GaAs crystal (S. Y.
Tochitsky, 2005).In 2007, they used a CO
2
laser with
a pulse width of 200 ns to conduct non-collinear
differential frequency on GaAs crystals at room
temperature, and obtained terahertz wave output in
the range of 0.5-3.0 THz, with a peak power of 2 kW
(S. Y. Tochitsky, 2007) .In 2008, Stokes light and anti
Stokes light were detected in the experiment,
confirming the cascade process (Schaar J E, 2008).In
2011, the team of Tianjin University pumped the
periodically inverted GaAs crystal by picosecond
pulse, generated narrowband THz wave by
differential frequency technology, and analyzed the
coupling distance of pump light in GaAs crystal and
the data under different parameters of the optimal
inversion period length of nonlinear crystal (Zhang
Chengguo, 2011).In 2011, Vodopyanov K. L. et al.
used 11 and 15 layers of GaAs chips to form a "period
reversal chip stack", and achieved terahertz wave
output with an average power of 200 μw in the ring
resonator v (Vodopyanov K L, 2011).In 2015,
Kyosuke Saito et al. described a method for efficient
terahertz generation, which uses the total reflection of
the laser at both ends of the sheet Fabry Perot (F-P)
microcavity to compensate for phase mismatch,
known as "cavity phase matching" (CPM) (SAITO K,
2015).
In recent years, the Cherenkov phase matching
method in terahertz radiation sources has been
proposed. Cherenkov phase matching has high
conversion efficiency and wide tuning, which can
automatically realize phase matching and effectively
overcome the frequency difference of nonlinear
crystals in optical and terahertz bands. The phase
matching condition satisfies any angle of the pump
light path (P. A. Cherenkov, 1934). Koji Suizu et al.
demonstrated the generation of Cherenkov type
280
Rao, Z. and Li, C.
Research on Terahertz Generation Based on Cherenkov-Type Difference Frequency.
DOI: 10.5220/0012281300003807
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 2nd International Seminar on Artificial Intelligence, Networking and Information Technology (ANIT 2023), pages 280-284
ISBN: 978-989-758-677-4
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
terahertz wave using organic DAST crystal and Si
prism coupler prism coupling (Suizu K, 2021). In
2012, Karun et al. reported the method of generating
terahertz radiation using dual-wavelength quantum
cascade lasers (QCL) based on Cherenkov phase
matching at room temperature (Vijayraghavan K,
2012). At present, the method of realizing terahertz
wave source based on Cherenkov phase matching
needs to be further explored, and there is still much
room for development of this method to generate
terahertz radiation (Juntao Huang, 2019).
This paper studies the process of generating
efficient terahertz wave by cavity phase matching
difference frequency of GaAs cavity based on
Cherenkov-type. The angle between the generated
terahertz wave direction and the cavity phase
matching generated terahertz wave direction is
Cherenkov angle. The formula of power conversion
efficiency of terahertz wave emitted along Cherenkov
angle is obtained through calculation. Considering
the influence of temperature, pump inversion times,
crystal length and reflectivity, terahertz photon
conversion efficiency is compared by numerical
simulations. The terahertz source prepared by this
method is simple and efficient, and will have great
application prospects.
2 CASCADE FREQUENCY
DIFFERENCE PRINCIPLE OF
CHERENKOV EFFECT
CAVITY PHASE MATCHING
The frequency difference process is influenced by
many factors. Such as working conditions, working
temperature, pump photon energy, and crystal body
growth technology, etc. The schematic diagram of
cascade frequency difference method is shown in the
figure 1.
Fig. 1. Schematic of cascade DFG.
The cascade process includes Stokes light and anti
Stokes light. High-frequency pump light ω
is
consumed while low-frequency pump light ω
interaction is amplified to generate terahertz photons
frequencyω
. This process is called Stokes process,
which will generate Stokes light. The amplified low-
frequency pump light ω
acts as the high-frequency
pump light of the second differential frequency, and
it interacts with the terahertz photon differential
frequency to produce the low-frequency pump light
ω
in the second differential frequency process. By
analogy, the cascade frequency difference process
can generate multiple terahertz photons. At the same
time, the anti Stokes process consumes terahertz
photons to generate high-frequency pump light ω
.
Each Stokes process will produce terahertz photons,
while the anti Stokes process will also consume
terahertz photons. However, the anti Stokes process
is always weaker than the Stokes process, which
eventually leads to the generation of terahertz waves.
Cherenkov phase matching is a method with high
energy output efficiency and wide tunability. The
phase matching conditions during the Cherenkov
phase matching process automatically meet any angle
of the pump laser path. The structure diagram of THz
wave generation based on Cherenkov effect cavity
phase matching cascade differential frequency is
shown in Fig. 2.
Fig. 2. Schematic of terahertz generation by cascade DFG
based on Cherenkov effect CPM.
F1 and F2 are two optical dielectric mirrors, and M
is the working medium. The collinear pump light
frequency ω
and ω
enter the cavity from the left
cavity mirror F1, and performs cascade differential
frequency through M to generate terahertz wave and
propagate to the right cavity mirror F2.In this paper,
Cherenkov angle θ
is introduced based on the
principle of Cherenkov effect cavity phase matching
cascade frequency difference.
3 THEORETICAL ANALYSIS OF
TERAHERTZ CONVERSION
EFFICIENCY
Terahertz wave generated by cascade frequency
difference is accumulated and emitted in the direction
of angle θ
and automatically meets the phase
matching condition.The three wave coupling
equation as follow (Zhi-ming Rao, 2011).
=
ω
ε
E
E
e
(
∆
)
(1)
Research on Terahertz Generation Based on Cherenkov-Type Difference Frequency
281
=
ω
ε
E
E
∗
e
(
∆
)
(2)
=
ω
ε
E
E
∗
e
(
∆
)
(3)
Effective nonlinear coeficient d
as follow
(
Z.D.Xie, 2011),
d
=d∙sin (
π
)/(
π
) (4)
Where c is the speed of light，E
，E
，E
a r e
electric field intensity of pump light frequency ω
and ω
, and THz wave respectively.d is the second-
order nonlinear coefficient of the nonlinear working
medium M , l
is Coherent length，ε
is vacuum
dielectric constant，n
，n
，n
are refractive index
on working medium M of pump light frequency ω
and ω
, and THz wave respectively.
Cherenkov angle θ
meets the conditions
(Juntao Huang, 2019),
cosθ
=
λ
(
)
π
(5)
where nT is the refractive index in the THz range
and λT is the wavelength of the THz wave in the DFG
process.
When there is no cascade, consider the destructive
interference between the pump light outside the left
side cavity. The pump energy is expected to be
retained in the cavity by considering the destructive
interference that can be expressed by (Shijia Z, 2020):
R
E
−
T
E
=0 (6)
R
E
−
T
E
=0 (7)
Where, E
and E
are the amplitudes of the two
pump beams outside the cavity respectively. Rj and
Tj (j = 1,2) are, respectively, the reflectances and
transmittances of F1 for the two pump lasers. n1and
n2 are the refractive index of crystal in the cavity for
frequency ω
and ω
, respectively. n01 and n02 are,
respectively, the refractive index of frequency ω
and ω
in the air. According to wave equation,
∇
E
+(k
)E
=
ε
(2ε
d
E
e
(
ω
)
.E
e
(
ω
)
) (8)
Replace E
with,
E
=E
.e
(Δ
)
(9)
Phase mismatch Δk
is given by,
Δk
=k
−k
−k
∙ cosθ
−
π
. (10)
Amplitude E
of THz wave generated by
difference frequency as follow,
E
=−
μ
ε
ω
(Δ)
∙E
E
(11)
According to the boundary conditions observed in
the waveguide propagation process,
E
+E
=−(E
+E
)
E
e
+E
e
=−
R
(E
e
+E
e
)
. (12)
Where, k
=k
−k
，
E
=−
μ
ε
ω
(Δ
)
∙E
E
∙
∆
∆
∆
(
)
.
(13)
Terahertz photon conversion efficiency η
as
follow,
η
=
. (14)
η
=
(
π
)
ε
λ
(
)
θ
. (15)
When cascading effects generation, the horizontal
forward propagation amplitude E
of the terahertz
wave generated by the n-order connected differential
frequency as follow,
E
=−
μ
ε
ω
(Δ
)
∙E
E
∙
∆
∆
∆
(
)
. (16)
Phase mismatch Δk
is given by,
Δk
=k
−k
−k
∙cosθ
−
π
. (17)
Horizontal forward propagation amplitude of all
cascaded THz waves is as follow,
E
=E
+⋯+E
. (18)
When cascading effects occur, n-order terahertz
photon power conversion efficiency η
is given by,
η
=η
+⋯η
. (19)
4 FACTORS EFFECTING
CONVERSION EFFICIENCY
The calculated results show that two CO2 laser lines
(9.5524μm(9P(20), λ
), 9.7937μm(9P(46), λ
))
can approximately meet Eqs.(19) when k
L≈14π.
For two pump powers P
=P
=100kW , and
A= 1mm
, the change curve of terahertz photon
conversion efficiency under different parameters is as
follows.
4.1 The Influence of Environment
Temperature for the Conversion
Efficiency
The refractive index of working medium GaAs is
given by (Skauli T, 2003)：
n
(
λ
)
=b+
g
b
− λ
+
g
b
− λ
+
g
b
− λ
where ΔT = T−22 °C indicates the deviation of
the actual temperature to the room temperature as
used in the calculations above, and parameter values
of GaAs dispersion equation is shown on table 1.
ANIT 2023 - The International Seminar on Artificial Intelligence, Networking and Information Technology
282
Table 1: parameter values of GaAs dispersion equation.
The effect of changing temperature on the power
conversion efficiency is illustrated in Fig. 3.
Fig. 3. Relationship between terahertz photon conversion
efficiency and temperature.
It can be seen from Fig. 3 that with the increase
of temperature, the terahertz photon conversion
efficiency of the 10-order and 15-order couplets first
increased and then gradually decreased, and the gap
gradually narrowed. The 15-order couplets reached
the maximum value of 443.6% at 22
℃ , while the
terahertz photon conversion efficiency of the 15th
class couplets without Cherenkov was only 382.5%.
4.2 The Influence of Crystal Length for
the Conversion Efficiency
The relationship between terahertz photon conversion
efficiency and crystal length is shown in Fig. 4. The
crystal length variation range is 700-800
μm. It can
be seen from Fig. 4 that as the crystal length increases,
the terahertz photon conversion efficiency increases
to the highest point and then decreases. In this range,
the maximum terahertz photon conversion efficiency
of the 15-order junction can reach 443.6%. At this
time, the crystal length is 758
μm. The maximum
terahertz photon conversion efficiency of the 15-
order junction without Cherenkov is 384.3%. The
highest terahertz photon conversion efficiency is
81.3% when there is no cascade, and the 15 order
cascade has increased 4.5 times compared with the
cascade.
Fig. 4. Relationship between terahertz photon conversion
efficiency and crystal length
5 CONCLUSION
In this paper, the process of generating high
efficiency terahertz by using Cherenkov based GaAs
cavity phase matching cascaded differential
frequency is theoretically analyzed, and the principle
of cavity phase matching based on Cherenkov is
introduced. The two pumping beams frequency ω
and ω
act nonlinearly in the cavity, and each
Stokes process will generate terahertz photons.
ACKNOWLEDGMENTS
This work was financially supported by nation nature
science fund of China, grant number 62065008.
REFERENCES
Wang R, Deng B, Qin Y, et al. Bistatic Terahertz Radar
Azimuth-Elevation Imaging Based on Compressed
Sensing. IEEE Transactions on Terahertz Science &
Technology, 2017, 4(6):702-713.
Kai-Erik Peiponen, Prince Bawuah, Mousumi Chakraborty,
Mikko Juuti, J. Axel Zeitler, Jarkko Ketolainen.
Estimation of Young’s modulus of pharmaceutical
tablet obtained by terahertz time-delay measurement,
International Journal of Pharmaceutics, 2015, 489:
100-105.
Liu. W, Li. C, Sun. ZY, Zhang, QY. Fang. GY, Three-
dimensional sparse image reconstruction for terahertz
surface layer holography with random step frequency,
Optics Letters, 2015, 40(14):3384-3387.
N. V. Vvedenskii, A. L. Korytin, V. A. Kostin, A. A.
Murzanev, A. A. Silaev, and A. N. Stepanov. Two-color
Research on Terahertz Generation Based on Cherenkov-Type Difference Frequency
283
Laser-plasma generation of terahertz radiation using a
frequency-tunable half harmonic of a femtosecond
pulse. Physical Review Letters, 2014, 112: 055004.
Atsushi Nakanishi, Shohei Hayashi, Hiroshi Satozono and
Kazuue Fujita. Spectroscopic Imaging with an Ultra-
Broadband (1–4 THz) Compact Terahertz Difference-
Frequency Generation Source. Electronics, 2021, 10,
336.
Nemec. H, Zajac. V, Kuzel. P, Maly. P, Gutsch. S, Hiller. D,
Zacharias. M, Charge transport in silicon nanocrystal
superlattices in the terahertz regime. Phys. Rev. B, 2015,
91:195443.
R.A. Motiyenko, B. Tercero, J. Cernicharo, L. Margul.
Rotational spectrum of formamide up to 1 THz and first
ISM detection of its vibrational state. Astronomy and
Astrophysics, 2012, 548:A71.
H. Tanoto, J.H. Teng, Q.Y. Wu, et al. Greatly enhanced
continuous-wave terahertz emission by nano-electrodes
in a photoconductive photomixer. Nature Photonics,
2012, 6: 121-126.
He Y, Wang Y, Xu D , et al. High-energy and ultra-wideband
tunable terahertz source with DAST crystal via
difference frequency generation. Applied Physics B,
2018, 124(1):16.
Liu P, Zhang X, Chao Y, et al. Widely tunable and
monochromatic terahertz difference frequency
generation with organic.crystal 2-(3-(4-hydroxystyryl)-
5, 5-dime-thylcyclohex-2-enylidene) malononitrile.
Applied Physics Letters, 2016, 108(1): 621-629.
Ravi K, Schimpf D N, Franz X. Kärtner. Pulse sequences
for efficient multi-cycle terahertz generation in
periodically poled lithium niobate. Optics Express,
2016, 24(22):25582.
F. Zernike, P. R. Berman. Generation of Far Infrared as a
Difference Frequency. Phys. Rev. Lett., 1965, 15(26):
999-1004
S.Y.Tochitsky, J.E.Ralph, C.Sung, et al. Generation of
megawatt-power terahertz pulses by noncollinear
difference-frequency mixing in GaAs. J. Appl. Phys.,
2005, 98(2): 26101
S. Y. Tochitsky, C. Sung, S. E. Trubnick, et al. High-power
tunable, 0.5-3 THz radiation source based on nonlinear
difference frequency mixing of CO
2
laser lines. J. Opt.
Soc. Am. B, 2007, 24(9): 2509-2516
Schaar J E,Vodopyanov K L,Kuo P S,et al. Terahertz
Sources Based on Intracavity Parametric Down-
Conversion in Quasi-Phase-Matched Gallium Arsenide.
IEEE Journal of Selected Topics in Quantum
Electronics, 2008, 14(2): 354-362.
Zhang Chengguo, Study on terahertz radiation generated by
optical difference frequency (D) Tianjin University,
2011
Vodopyanov K L, Hurlbut W C, Kozlov V G, Photonic THz
generation in GaAs via resonantly enhanced intracavity
multispectral mixing (J). Appl.Phys. Lett.2011, 99,
041104
SAITO K, TANABE T, OYAMA Y. Cascaded terahertz-
wave generation efficiency in excess of the Manley–
Rowe limit using a cavity phase-matched optical
parametric oscillator. Journal of the Optical Society of
America B, 2015, 32(4): 617-621.
P. A. Cherenkov. Visible glow of pure liquids under γ-
irradiation. Dokl. Akad. Nauk SSSR 1934, 2, 451.
Suizu K, Shibuya T, Uchida H, et al. Prism-coupled
Cherenkov phase-matched terahertz wave generation
using a DAST crystal. Optics Express, 2010,
18(4):3338-3344.
Vijayraghavan K, Adams R W, Vizbaras A, et al. Terahertz
sources based on Cherenkov difference-frequency
generation in quantum cascade laser (J). Appl.Phys. Lett.
2012, 100, 2511044
Juntao Huang, Zhiming Rao, Fangsen Xie. Cascaded DFG
via quasi-phase matching with Cherenkov-type PPLN
for highly efficient terahertz generation, Optics Express,
2019, 27(12):17199-17208.
Zhi-ming Rao, Xin-bing Wang, Yan-Zhao Lu, et al. Two
Schemes for Generating Efficient Terahertz Waves in
Nonlinear Optical Crystals with a Mid-Infrared CO2
Laser(J).Chin. Phys. Lett., 2011, 28(7).176-179
Z. D. Xie, X. J. Liu, Y. H. Liu, et al. Cavity phase matching
via an optical parametric oscillator consisting of a
dielectric nonlinear crystal sheet (J). Physical Review
Letters, 2011, 106(8):083901.
Shijia Z, Zhiming R, Wenjiang T, et al. A cascaded
difference frequency generation method combined with
cavity phase matching and quasi phase matching for
high-efficiency terahertz generation (J). Laser Physics,
2020, 30: 115401.
Skauli T, Kuo P S, Vodopyanov K L, et al. Improved
dispersion relations for GaAs and applications to
nonlinear optics (J). Journal of Applied Physics, 2003,
94(10): 6447-6455.
ANIT 2023 - The International Seminar on Artificial Intelligence, Networking and Information Technology
284
