Investigation on terahertz generation from zinc-blende crystal waveguide at polariton resonance

Abstract

Terahertz (THz) wave generation from zinc-blende crystal waveguide, such as GaAs, InP, ZnTe and CdTe, at polariton resonance region (PRR) with a transverse pumping geometry is investigated. It is shown that by using grating vector of periodically inverted crystal, THz wave can be efficiently generated by difference frequency generation (DFG) with a transverse pumping geometry. Parametric gain coefficients in the low-loss limit and absorption coefficients of THz wave during DFG process in the vicinity of PRR are analyzed. The frequency tuning characteristics of THz wave via varying wavelength of difference frequency waves and poling period of periodically inverted crystal are numerically analyzed.

Full text

RESEARCH ARTICLE
Investigation on terahertz generation from zinc-blende crystal
waveguide at polariton resonance
Zhongyang Li
1
•Mengtao Wang
1
•Silei Wang
1
•Pibin Bing
1
•Sheng Yuan
1
Received: 17 March 2017 / Accepted: 27 November 2018
ÓThe Optical Society of India 2018
Abstract Terahertz (THz) wave generation from zinc-
blende crystal waveguide, such as GaAs, InP, ZnTe and
CdTe, at polariton resonance region (PRR) with a trans-
verse pumping geometry is investigated. It is shown that by
using grating vector of periodically inverted crystal, THz
wave can be efficiently generated by difference frequency
generation (DFG) with a transverse pumping geometry.
Parametric gain coefficients in the low-loss limit and
absorption coefficients of THz wave during DFG process in
the vicinity of PRR are analyzed. The frequency tuning
characteristics of THz wave via varying wavelength of
difference frequency waves and poling period of periodi-
cally inverted crystal are numerically analyzed.
Keywords Terahertz wave Difference frequency
generation Zinc-blende crystal Transverse pumping
geometry
Introduction
In the research of modern terahertz (THz) optoelectronics,
monochromatic THz sources play an important role in
high-resolution THz applications, such as environmental
gas monitoring, high-density and high-speed wireless
communications [1–4]. Difference frequency generation
(DFG) with two closely spaced laser frequencies x1and x2
in second-order nonlinear optics crystals is one of the
promising processes for efficient monochromatic THz
wave output in the wide frequency tuning range and room
temperature operation [5,6]. THz wave generation based
on DFG has been intensively researched [7–9]. Unfortu-
nately, the maximum frequencies generated by these optics
processes are limited to 7 THz [10]. Moreover, the output
power of THz wave with high frequency is extremely low.
Such limitations on output frequencies and power are
caused by the dramatically increased absorption of the
nonlinear materials in the vicinity of polariton resonance
region (PRR). However, at the same time, polariton reso-
nances can induce giant second-order nonlinearities. The
giant second-order nonlinearities in the vicinity of PRR can
be exploited to extend the output frequencies and enhance
the output power of THz wave [11]. In the vicinity of PRR
for THz wave generation, the crucial point for efficient
THz wave generation is to minimize the path of THz wave
in the crystal. A transverse pumping geometry can over-
come this problem [12–14]. The optical beams propagate
close to crystal lateral surface, and THz wave radiates from
the crystal surface and propagates perpendicular to the
direction of the optical beams. The absorption loss is
minimized because the THz wave is generated from the
crystal surface.
A frequently employed material for DFG is the nonlin-
ear optical crystal MgO:LiNbO
3
, because of its relatively
large second-order nonlinear optical coefficient
(d
33
= 25.0 pm/V at 1064 nm) and its wide transparency
range [15]. However, DFG from zinc-blende-type semi-
conductors, such as GaP, GaAs and CdTe, is advantageous
in obtaining an intense THz wave since their second-order
nonlinear optical coefficients are several times larger than
that of MgO:LiNbO
3
.d
36
of GaAs, GaP and CdTe is
170 pm/V, 70.6 pm/V and 109 pm/V at 1064 nm, respec-
tively [16,17]. In addition, their absorption coefficients in
&Zhongyang Li
thzwave@163.com
1
College of Electric Power, North China University of Water
Resources and Electric Power, Zhengzhou 450045, Henan,
China
123
J Opt
https://doi.org/10.1007/s12596-018-0500-z

the THz frequency region are about ten times smaller than
that of MgO:LiNbO
3
[18].
In this paper, we explore THz wave generation from
zinc-blende crystals, such as GaAs, InP, ZnTe and CdTe
with a transverse pumping geometry. Parametric gain
coefficient in the low-loss limit of THz wave during DFG
process in the vicinity of PRR is analyzed. We investigate
the frequency tuning characteristics of THz wave via
varying wavelength of optical waves and poling period of
periodically inverted crystal.
Theoretical model
The schematic drawing of a surface-emitted DFG from
zinc-blende crystal waveguide with a transverse pumping
geometry is presented in Fig. 1. Two input optical waves
k1and k2at the frequencies of x1and x2in the infrared
(IR) domain are propagating collinear along the x-axis in a
zinc-blende crystal waveguide. The waveguide is achieved
by periodically switching the orientation between 111½and

1

1

1½, achievable through the epitaxial growth of zinc-
blende crystals on an orientation-patterned substrate
[19,20]. A THz wave is emitted due to the oscillating
nonlinear polarization at the difference frequency between
the two input waves. The radiation angle hbetween
directions of the optical and THz wave propagation is
determined by the refractive index of optical waves and
THz wave in the crystal, and the poling period of period-
ically inverted crystal,
cos h¼KIR
KTHz
;ð1Þ
where KTHz ¼xTHznTHz =cis the wave vector of THz
wave, nTHz is the refractive index at xTHz frequency; KIR ¼
n1x1=cn2x2=c2p=K;where Kis the poling period of
periodically inverted crystal, n1and n2are the refractive
indices at optical wavelengths k1and k2at x1and x2
frequencies, respectively. THz wave can be generated in a
direction perpendicular to the optical wave propagations if
KIR equals to zero.
The parametric gain coefficient g0in the low-loss limit
during DFG processes in cgs units can be determined by
the following expression [21]:
g2
0¼pxTHzx2
2c3n1n2nTHz
Ik1d0
EþSx2
0d0
Q
x2
0x2
THz
!
2
ð2Þ
aTHz ¼2xTHz
cIm e1þSx2
0
x2
0x2
THz ixTHzC

1
2
ð3Þ
where aTHz is absorption coefficient in THz region, and x0,
Sand Cdenote eigen frequency, oscillator strength of the
polariton mode and the bandwidth of the phonon mode in
the zinc-blende crystal, respectively. Ik1is the power
density of the optical wave with wavelength k1.d0
Eand d0
Q
are nonlinear coefficients related to pure parametric (sec-
ond order) and Raman (third order) scattering processes,
respectively. The relationship between d0
Eand d0
Qis [21].
d0
EþSd0
Q¼rn4
1ð4Þ
where ris the electro-optic coefficient. In this paper, the
data for GaAs, InP, ZnTe and CdTe are taken from refer-
ences [16,22,23].
Parametric gain characteristics
GaAs, InP, ZnTe and CdTe have infrared- and Raman-
active transverse optical (TO) phonon modes at the fre-
quencies of 269 cm
-1
, 304 cm
-1
, 179 cm
-1
and
141 cm
-1
, respectively. The TO phonon modes are useful
for efficient THz wave generation because of the largest
parametric gain in the vicinity of PRR, as shown in Fig. 2.
From the figure, we find that the central frequencies of PRR
are 4.23 THz, 5.37 THz, 8.07 THz and 9.12 THz, corre-
sponding to CdTe, ZnTe, GaAs and InP, respectively. As
THz wave frequencies approach PRR, the parametric gain
coefficient g0sharply reaches a maximum value ([10
5
cm
-1
) and the absorption coefficient aTHz intensively
increases to 10
4
cm
-1
. Such dramatic enhancements of
parametric gain coefficients can be exploited for improving
the output powers and extending the frequency bands of
THz waves if using a transverse pumping geometry to
minimize the propagation path of THz wave within the
crystal. As discussed above, output frequencies of THz
wave from 4.23 THz to 9.12 THz can be efficiently real-
ized in the vicinity of PRR by using CdTe, ZnTe, GaAs and
InP with a transverse pumping geometry.
1
λ
2
λ
THz
YZ
X
Zinc blende crystal
Λ
Fig. 1 Schematic diagram of a surface-emitted DFG from zinc-
blende crystal waveguide with a transverse pumping geometry
J Opt
123

Frequency tuning characteristics
According to Eq. (1), the frequencies of the THz wave can
be tuned by varying poling period Kand wavelength of
optical waves k1and k2. Figure 3shows the tuning char-
acteristics as a function of optical wavelength k1ranging
from 0.75 to 2.5 lm. From the figure, we find that the
frequencies of THz wave are rapidly and smoothly
increased with the increase in wavelength k1. In Fig. 3a,
THz wave with frequencies ranging from 5.65 to 8.88 THz
can be obtained from GaAs crystal as K¼10 lm. The
central frequency of PRR corresponds to k1¼1:22 lm.
Similarly, THz wave with frequencies ranging from 8.25 to
9.62 THz, from 4.71 to 5.76 THz and from 3.22 to
7.29 THz can be obtained from InP, ZnTe and CdTe
crystals as K¼10 lm, K¼20 lm and K¼15 lm,
respectively. The central frequency of PRR corresponds to
k1¼1:08 lm, k1¼1:13 lm and k1¼0:8lm, respec-
tively. THz wave generated from PRR can be realized by
tuning the wavelength k1.
The frequencies of THz wave as a function of poling
period Kas k1¼1:064 lm are depicted in Fig. 4. From the
figure, we find that widely tunable THz wave can be
obtained by varying poling period K. From the figure, we
find that the frequencies of THz wave are rapidly and
smoothly decreased with the increase in poling period K.
As shown in Fig. 4a, b, THz wave with frequencies ranging
from 9.5 to 1.6 THz and from 11.3 to 1.9 THz can be
obtained from GaAs and InP crystals as Kchanges from 8
to 48 lm, respectively. The central frequencies of PRR
correspond to K¼9:4lm and K¼9:9lm, respectively.
As shown in Fig. 4c, d, THz wave with frequencies ranging
from 10.5 to 2.1 THz and from 9.4 to 1.88 THz can be
obtained from ZnTe and CdTe crystals as Kchanges from
10 to 50 lm, respectively. The central frequencies of PRR
correspond to K¼19:7lm and K¼22:1lm, respec-
tively. THz wave generated from PRR can realized by
tuning the poling period K.
Compared with other works in which THz wave gen-
erations are far from PRR to avoid intensive absorption, the
theoretical model proposed in this letter can exploit dra-
matic enhancement of parametric gain in the vicinity of
PRR with a transverse pumping geometry. The theoretical
model proposed in this work is useful to other materials
with crystal birefringence properties, such as LiNbO
3
,
LiTaO
3
and KTA, in which polaritons are both infrared
active and Raman active. The theoretical model is also
useful to semiconductor optical waveguide with modal
birefringence properties. By utilizing modal birefringence
6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
10
100
1000
10000
100000
Coefficient (cm
-1
)
THz frequency (THz)
gain
absorption PRR
6 7 8 9 10 11 12
10
100
1000
10000
100000
Coefficient (cm
-1
)
THz frequency (THz)
gain
absorption PRR
4.0 4.5 5.0 5.5 6.0 6.5 7.0
10
100
1000
10000
100000
Coefficient (cm
-1
)
THz frequency (THz)
gain
absorption PRR
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
1
10
100
1000
10000
100000
Coefficient (cm
-1
)
THz frequency (THz)
gain
absorption PRR
(c) (d)
(a) (b)
Fig. 2 Parametric gain coefficient in the low-loss limit g0and absorption coefficient aTHz versus THz wave frequency at room temperature.
k1¼1:064 lm, Ik1¼100 MW=cm2.aGaAs, bInP, cZnTe, dCdTe
J Opt
123

0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
THz
λ
2
Wavelength of λ
1
(μm)
THz frequency (THz)
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
Wavelength of
λ2
(μm)
PRR
0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
8.25
8.50
8.75
9.00
9.25
9.50
9.75
THz
λ
2
Wavelength of λ
1
(μm)
THz frequency (THz)
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
Wavelength of λ2
(μm)
PRR
0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
4.6
4.8
5.0
5.2
5.4
5.6
5.8
THz
λ
2
Wavelength of λ
1
(μm)
THz frequency (THz)
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
Wavelength of
λ
2
(μm)
PRR
0.75
1.00 1.25 1.50 1.75 2.00 2.25 2.50
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
THz
λ
2
Wavelength of
λ
1
(μ
m)
THz frequency (THz)
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
Wavelength of λ
2
(
μm)
PRR
(d)
(a) (b)
(c)
Fig. 3 THz wave frequencies versus the wavelength of optical wave k1.aGaAs, K¼10 lm, bInP, K¼10 lm, cZnTe, K¼20 lm, dCdTe,
K¼15 lm
8 12162024283236404448
0
1
2
3
4
5
6
7
8
9
10
THz
λ
2
Poling period of GaAs (µm)
THz frequency (THz)
1.065
1.070
1.075
1.080
1.085
1.090
1.095
1.100
1.105
Wavelength of
λ
2
(μm)
PRR
8 12162024283236404448
0
1
2
3
4
5
6
7
8
9
10
11
12
THz
λ
2
Poling period of InP (µm)
THz frequency (THz)
1.065
1.070
1.075
1.080
1.085
1.090
1.095
1.100
1.105
1.110
1.115
Wavelength of
λ
2
(μm)
PRR
10
15 20 25 30 35 40 45 50
2
3
4
5
6
7
8
9
10
11
12
THz
λ
2
Poling period of ZnTe (µm)
THz frequency (THz)
1.070
1.075
1.080
1.085
1.090
1.095
1.100
1.105
1.110
Wavelength of
λ
2
(μm)
PRR
10 15 20 25 30 35 40 45 50
0
1
2
3
4
5
6
7
8
9
10
THz
λ
2
Poling period of CdTe (µm)
THz frequency (THz)
1.070
1.075
1.080
1.085
1.090
1.095
1.100
1.105
Wavelength of
λ
2
(μm)
PRR
(c) (d)
(a) (b)
Fig. 4 THz wave frequencies versus the poling period K,k1¼1:064 lm. aGaAs, bInP, cZnTe, dCdTe
J Opt
123

of fundamental TE and TM modes in planar waveguide,
the absorption at PRR can be efficiently reduced [24].
Conclusion
We explore THz wave generation at PRR of zinc-blende
crystal waveguide by DFG with a transverse pumping
geometry. It is shown that by using grating vector of
periodically inverted crystal, THz wave can be efficiently
generated by DFG in the vicinity of PRR. Dramatic
enhancement of parametric gain coefficients in the vicinity
of PRR can be exploited for improving the output power
and extending the frequency bands of THz wave by using a
transverse pumping geometry to minimize the propagation
path of THz wave within the crystal. THz wave generated
from PRR can be realized by tuning the wavelength k1and
poling period K.
Acknowledgements This work was supported by the National Nat-
ural Science Foundation of China (61201101, 61601183 and
61205003); the Natural Science Foundation of Henan Province
(162300410190); the Program for Innovative Talents (in Science and
Technology) in University of Henan Province (18HASTIT023); the
Young Backbone Teachers in University of Henan Province
(2014GGJS-065) and the Program for Innovative Research Team (in
Science and Technology) in University of Henan Province
(16IRTSTHN017).
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