Optics Communications 248 (2005) 387–394
www.elsevier.com/locate/optcom
Investigation of noncollinear QPM optical
parametric amplification based on periodically poled KTP
Zhao Baozhen, Liang Xiaoyan *, Leng Yuxin, Wang Cheng, Xu Zhizhan
Shanghai Institute of Optics and Fine Mechanics, The Chinese Academy of Sciences, PO Box 800-211, Shanghai 201800, China
Received 11 July 2004; received in revised form 29 October 2004; accepted 15 December 2004
Abstract
The properties of noncollinear optical parametric amplification based on quasi-phase matching of periodically poled
KTP are investigated theoretically. Our numerical simulation focuses on the gain spectrum of dependence upon
noncollinear angle, crystal temperature and crystal angle. At the optimal noncollinear angle and grating period with
fixed temperature, there exists a broadest gain bandwidth about 130 nm at signal wavelength of 800 nm. The deviation
from optimal noncollinear angle can be compensated by accurately tuning the crystal angle or temperature with a fixed
grating period for phase matching.
Ó 2004 Elsevier B.V. All rights reserved.
PACS: 42.65.Y; 42.65.R
Keywords: Optical parametric amplification; Femtosecond pulse; Quasi-phase matching
1. Introduction
Application of optical parametric amplification
(OPA) to chirped pulse amplification (CPA) was
first proposed and demonstrated by Dubietis
et al. [1], and this technology was defined as optical
parametric chirped pulse amplification (OPCPA).
Later, Ross et al. [2] analyzed the properties of
broad bandwidth OPA and applied this attractive
*
Corresponding author. Tel.: +862169918526; fax:
+862169918800.
E-mail address: [email protected] (L. Xiaoyan).
technique to amplification of ultrashort pulses for
high power output. Compared with CPA, OPCPA
technology has many advantages, such as high
gain with broad bandwidth, high signal-to-noise
contrast ratio and small B integral. Successful
OPCPA systems have been mainly demonstrated
at 800 nm [3,4] and 1 lm [5–7], replacing regenerative amplifiers or multi-pass preamplifiers of
CPA, using BBO, LBO and KDP nonlinear
optical crystals. The most intensive and shortest
output has reached 16.7 TW/120 fs [8] near 1064
nm. And the highest OPCPA conversion efficiency
has reached 29% [9].
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.optcom.2004.12.033
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Z. Baozhen et al. / Optics Communications 248 (2005) 387–394
Compared with those birefringence crystals,
quasi-phase matching materials [periodically
poled KTP (PPKTP), PPLN, and so on] can
substantially improve parametric gain properties
[10–12]. Firstly, the highest effective nonlinear
coefficients could be realized through quasi-phase
matching (QPM) technology. Secondly, it eliminates the limitation on the interaction length
associated with spatial walk-off by permitting
noncritical phase matching. Two of particular
ways to realizing broad bandwidth gain in
OPA are near-collinear geometry at degenerate
point and noncollinear geometry away from
degeneracy. Recently, broadband amplifications
of OPCPA with significant optical gain have
been achieved in near-collinear geometry using
PPLN and PPKTP [13–15]. Noncollinear OPO
with PPKTP was demonstrated by Smilgevicius
et al. [16] to extend the tuning range in contrast
with collinear OPO, but noncollinear geometry
OPA with QPM materials for broadband amplification has not been studied. Compared with
PPLN, PPKTP exhibits higher damage threshold, weaker photorefractive effect and lower
coercive fields which allow the fabrication of
thicker samples [17]. Therefore, PPKTP is more
suitable for generating higher energy in OPCPA
system.
In this paper, the properties of noncollinear
optical parametric amplification (NOPA) based
on PPKTP crystal in type-0 phase matching geometry are investigated theoretically with the signal
pulse centered at 800 nm and the pump pulse at
532 nm. For PPKTP with a fixed temperature,
our expressions are very useful in selecting the
proper grating period and noncollinear angle so
as to get a good performance. The properties of
gain spectrum with the change of crystal temperature or crystal angle for phase matching are simulated numerically with a given grating period.
Better gain spectrum can be obtained by tuning
the crystal temperature and the crystal angle,
respectively.
Currently the QPM gratings can be engineered
freely to satisfy phase matching condition and
the nanosecond 532 nm laser is a commercial
pump source. Therefore, the QPM NOPA geometry we design here to amplify signal beam centered
at 800 nm has great potential to replace the regenerative amplification of traditional CPA system for
ultrashort pulse output.
2. Theory of noncollinear quasi-phase matched
OPA
In the condition of type-0 phase matching, all
the interacting waves are polarized along z-axis
and propagate along x-axis of the crystal in order
to utilize the largest nonlinear coefficient d33 = 16.9
pm/V of PPKTP. The effective nonlinear coefficient is [18]
d eff ¼
2
d 33 sinðmpDÞ:
mp
ð1Þ
The duty factor D is given as D = l/K, where l is the
length of a reversed domain and K is the grating
period of the reversal. The effective nonlinear coefficient with quasi-phase matching is the largest for
the first-order process (m = 1) with a 50% duty
circle. In this case
2
d Q ¼ d eff ¼ d 33 :
p
The grating vector is
kg ¼
2p
:
K
ð2Þ
ð3Þ
Since OPA is a typical three-wave coupled nonlinear process, conservation of energy and momentum is required, that means,
hwp ¼ hws þ hwi ;
~
ks þ ~
ki þ ~
kg;
kp ¼ ~
ð4Þ
where the subscripts p, s and i refer to the pump,
signal and idler lights, respectively.
Here let us discuss the noncollinear geometry:
the grating vector is along x-axis as usual; pump
wave propagates along x-axis; and signal wave
propagates in x–y plane and keeps a small angle
with pump light, as shown in Fig. 1. Angle h between ks and kp is defined as noncollinear angle
and the angle between ki and kp is defined as u.
The fundamental expressions in phase matching
condition for the noncollinear three-wave mixing
are easily derived
Z. Baozhen et al. / Optics Communications 248 (2005) 387–394
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k 2g þ k 2p 2 cosðwÞk g k p ;
1 k g sinðwÞ
c ¼ sin
;
k pg
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k i ¼ k 2s þ k 2pg 2 cosðh cÞk s k pg :
k pg ¼
ki
ϕ
kp
x
kg
ks
Fig. 1. Geometry of the noncollinear phase matching in x–y
plane.
1=kp ¼ 1=ks þ 1=ki ;
k p ¼ k g þ k s cos h þ k i cos u;
ð5Þ
k s sin h ¼ k i sin u;
k g ¼ k p k s cos h qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k 2i k 2s sin2 h:
ð6Þ
It is obvious that the grating period is determined
exclusively by noncollinear angle h when the pump
and signal wavelength are given.
In the practical application, it is very difficult to
tune noncollinear angle h accurately with fixed
grating period, but the crystal angle can be tuned
accurately. Therefore, rotating the crystal angle
in x–y plane finely is unavoidable to get accurate
phase matching. The geometry after rotating the
crystal angle is shown in Fig. 2.
Subtracted vector kg from vector kp, we get vector kpg. Angle w between kg and kp is assumed as
crystal angle and the angle between kp and kpg is
c, and clockwise angles w and c (referring to the
direction of kp) are taken as positive. From Fig.
2, the equations in phase matching condition are
derived as,
x
ki
kg
γ
kp
kpg
ks
Fig. 2. Geometry of the noncollinear phase matching after
rotating crystal angle in x–y plane.
ð7Þ
According to the Sellmeier equations of KTP
crystal [19,20] and Eq. (6), a cluster of phase
matching curves with different grating period are
plotted as shown in Fig. 3. Because any possible
broad gain spectrum only occurs around the positions where the slopes of curves are infinite [21],
from Fig. 3 it shows that the broad gain spectrum
centered at near 800 nm exists when grating period
is around 7.90 lm, correspondingly the phase
matching noncollinear angle is near 4.70°. When
the grating period is larger, the centre of gain spectrum shifts to longer wavelength and the phase
matching noncollinear angle becomes smaller.
Therefore, an optimal period and noncollinear angle exist with a broad gain bandwidth for different
signal wavelength. And a tunable seed beam with
broad spectrum can be amplified at certain optimal grating period and noncollinear angle.
Due to a broad gain bandwidth in OPCPA
system, gain spectrum of signal beam is very
important; the properties of gain spectrum are
very useful to optimize OPA. In next part we will
discuss the gain spectrum of NOPA using PPKTP
in detail.
From left to right Λ=8.20,8.10,8.00,7.90,7.85,7.80µm
1300
Signal / idle wave length (nm)
y
y
389
1200
1100
1000
900
800
700
3.5
4
4.5
5
Noncollinear angle: θ (deg)
5.5
Fig. 3. Phase matching curves with different grating period
K(kp = 532 nm) at fixed temperature (T = 58.9 °C).
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Z. Baozhen et al. / Optics Communications 248 (2005) 387–394
The gain intensity of the amplified signal beam
can be obtained by using the analytical solution
of the coupled wave equations in the slowly varying
envelope approximation and assuming no significant pump depletion. The group-velocity mismatching (GVM) can be neglected in the case
that pulse durations of interacting waves are of
nanoseconds. The gain intensity (G) is given [22] by
2
such as grating period K, noncollinear angle h and
crystal temperature T. By numerical simulations
we will get a series of optimal values which correspond to maximal gain bandwidth. Besides that,
the compensation of unavoidable error of h is considered by rotating crystal angle or tuning temperature for phase matching. The parameters used in
below simulation are given here. The pump intensity at 532 nm is 40 MW/cm2 and a 10 mm length
of PPKTP is used, and the signal wavelength is
centered at 800 nm.
2
G ¼ 1 þ ðnLÞ ðsinh B=BÞ ;
ð8Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
where
n ¼ 4pd eff I p =2e0 np ns ni cks ki ; B ¼
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
ðnLÞ ðDkL=2Þ , and L is the crystal length, n
is the effective gain coefficient, deff is the effective
nonlinear coefficient, and Ip is the pump intensity.
Since the grating period of PPKTP for OPA is designed according to pump wavelength and central
wavelength of signal with the noncollinear geometry shown in Figs. 1 and 2, the phase mismatching
Dk can be defined as [3]
ni ðks Þ nio ðkso Þ
Dkðks Þ ¼ jD~
kðks Þj ¼ 2p
;
ð9Þ
ki ðks Þ kio ðkso Þ
3.1. Gain spectrum corresponding to Fig. 1
Here, we discuss the phase matching curve and
gain spectrum with the change of noncollinear angle at fixed temperature 58.9 °C in the condition of
Fig. 1. As shown in Fig. 4(a), for different noncollinear angles both the grating period and gain
bandwidth are calculated when QPM condition is
satisfied. With the increase of noncollinear angle,
the grating period decreases monotonously. The
maximal gain bandwidth of 130.6 nm (FWHM) is
achieved at noncollinear angle h = 4.71° which is
thought as optimal noncollinear angle, with the
corresponding grating period K = 7.90 lm. This is
consistent with the result shown in Fig. 3. When
noncollinear angle deviates from 4.71°, the gain
bandwidth reduces quickly. The corresponding
gain spectrum for some different noncollinear angles is shown in Fig. 4(b). When the noncollinear
angle is larger than 4.71°, the gain spectrum
where kio and kso are the ideal phase matched idler
and signal wavelength, respectively. For the different signal wavelength, we can get the idler wavelength from Eq. (5).
3. Numerical simulation
Based on above expressions, we will analyze the
gain spectrum of dependence upon several factors
1400
90
8.0
60
7.9
30
7.8
4.4
4.5
4.6
4.7
4.8
4.9
Noncollinear angle: θ (deg)
Gain intensity (a.u.)
Gain bandwith (nm)
8.1
0
4.3
(a)
T=58.9degree
120
Grating period Λ (µm)
8.2
140
θ=4.68°
θ=4.71°
θ=4.74°
θ=4.77°
1200
1000
800
600
400
200
0
7.7
5
(b)
750
800
850
900
950
1000
Wavelength (nm)
Fig. 4. OPA in phase matching condition at T = 58.9 °C (kp = 532 nm). (a) Dependence of gain bandwidth and grating period upon
noncollinear angle h; (b) gain spectrum at given noncollinear angle h (h = 4.68°, 4.71°, 4.74°, 4.77°).
Z. Baozhen et al. / Optics Communications 248 (2005) 387–394
becomes narrow, and the gain spectrum does not
split. When the noncollinear angle is smaller than
4.71°, the gain spectrum extends, but splits near
central wavelength, which results in the decrease
of gain bandwidth; and the gain spectrum is highly
modulated and asymmetric, which results in highly
modulated and asymmetric amplified signal spectrum. From these results we know that the gain
bandwidth is sensitive to noncollinear angle, so in
experiment it is very important to keep the accurate
noncollinear angle to get maximal gain bandwidth.
3.2. Spectral properties with the change of crystal
angle or temperature
5
130
4
120
3
1
100
0
90
-1
80
-2
70
-3
60
-4
50
4.5
(a)
2
110
4.55
4.6
4.65
4.7
4.75
Noncollinear angle:θ (deg)
angle is at 4.65°, 4.71° and 4.75°, gain spectrum
has a little dip at the central wavelength and the
gain bandwidth keeps large, as shown in Fig.
5(b). However, when the noncollinear angle deviates far away from 4.71° (at 4.80° or 4.60°), the
gain centre is concave more; and the gain spectrum
is highly modulated and asymmetric. This is induced due to a larger phase mismatch around
the point where gain dips. For a given grating period and temperature, when the noncollinear angle
has a little deviation of 0.1° from optimal noncollinear angle, a better gain spectrum can be
achieved by tuning the crystal angle for 2.5°.
This result is very useful to decrease the complexity of alignment of optical system in experiment.
With the grating period of PPKTP K = 7.90
lm, the phase matching crystal temperature and
gain bandwidth with the change of noncollinear
angle is shown in Fig. 6(a). And the gain spectrum
with some different noncollinear angles is shown in
Fig. 6(b). It demonstrates that the phase matching
condition can always be satisfied by reducing temperature with the increase of noncollinear angle
(not far away from 4.71°). When the noncollinear
angle is above 4.71°, the gain bandwidth becomes
narrow and crystal temperature decreases, the gain
spectrum does not split. But when the noncollinear
angle is below 4.71°, the gain bandwidth becomes
narrow and crystal temperature increases, and the
gain spectrum splits and is highly modulated and
asymmetric, which is disadvantageous to OPA.
Consequently, for a given grating period, when
1400
Gain intensity (a.u.)
140
Crystal angle:ψ (deg)
Gain bandwidth (nm)
In experiment, the noncollinear angle is usually
difficult to be tuned accurately, which induces
phase mismatch and reduces the gain bandwidth,
but the crystal angle and crystal temperature can
be tuned accurately. Therefore, the compensation
of error from noncollinear angle is realized by tuning the crystal angle or temperature accurately.
According to above formulas, when the grating
period K is 7.90 lm and temperature is fixed at
58.9 °C, the phase matching crystal angle and gain
bandwidth versus the noncollinear angle can be
calculated, as shown in Fig. 5(a). It shows that
with the different noncollinear angles, the phase
matching condition always can be satisfied by tuning the crystal angle. The gain bandwidth keeps
almost 130 nm when the noncollinear angle is between 4.644° and 4.765°. When the noncollinear
391
θ=4.60°
θ=4.65°
θ=4.71°
θ=4.75°
θ=4.80°
1200
1000
800
600
400
200
-5
4.8 4.83
0
(b)
750
800
850
900
950
1000
Wavelength (nm)
Fig. 5. OPA in phase matching at K = 7.90 lm and T = 58.9 °C. (a) Dependence of gain bandwidth and crystal angle on noncollinear
angle; (b) gain spectrum with different noncollinear angle.
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Z. Baozhen et al. / Optics Communications 248 (2005) 387–394
130
90
120
80
110
70
100
60
90
50
80
70
40
60
30
50
4.67 4.68
(a)
4.7
4.72
4.74
4.76
Gain intensity (a.u.)
100
Temperature (deg)
Gain bandwidth (nm)
1400
140
θ=4.69°
θ=4.71°
θ=4.73°
θ=4.75°
θ=4.77°
1200
1000
800
600
400
200
0
20
4.78
750
800
850
900
950
1000
Wavelength (nm)
(b)
Noncollinear angleθ: (deg)
Fig. 6. OPA in phase matching at K = 7.90 lm. (a) Dependence of gain bandwidth and crystal temperature on noncollinear angle;
(b) gain spectrum with different noncollinear angle.
quickly, and the gain spectrum is highly modulated
and asymmetric. The corresponding gain spectrum
is shown in Fig. 7(b). When the temperature is below 57.8 °C, there has large gain dip around 775
nm; when the temperature is above 59.3 °C, the
gain spectrum dips around 850 nm. These gain dips
are aroused due to large phase mismatch around
775 or 850 nm. Since the temperature bandwidth
is only about 1.5 °C to keep gain bandwidth about
130 nm, it is important to control the precision of
crystal temperature in experiment.
the noncollinear angle is lightly larger than 4.71°, a
smooth phase matching gain spectrum can be realized through tuning crystal temperature.
3.3. Temperature bandwidth
For a fixed noncollinear angle and grating period, deviations of the temperature from the optimal
value also cause the reduction of gain bandwidth.
Formula (8) is used to determine the temperature
bandwidth with K = 7.90 lm and h = 4.71°. The
gain bandwidth and gain spectrum with different
crystal temperature are shown in Fig. 7. From
Fig. 7(a), it shows that the gain bandwidth is almost invariable between 57.8 and 59.3 °C, and
the widest gain bandwidth is 130.7 nm. However,
when the temperature is below 57.8 °C or above
59.3 °C, the gain bandwidth becomes narrow
4. Discussion
For noncollinear PPKTP–OPA works at central wavelength of 800 nm pumped at 532 nm, an
optimal noncollinear angle of 4.71° exists when
1400
140
T=54.9°C
T=56.9°C
T=58.9°C
T=60.9°C
120
100
80
60
40
20
(a)
Gain intensity (a.u.)
Gain bandwidth (nm)
1200
1000
800
600
400
200
54
56
58
Temperature (°C)
60
0
62
(b)
750
800
850
900
950
Wavelength (nm)
Fig. 7. The gain bandwidth and gain spectrum at K = 7.90 lm and h = 4.71° for temperature tuning. (a) Dependence of gain
bandwidth upon crystal temperature; (b) gain spectrum with different crystal temperature.
Z. Baozhen et al. / Optics Communications 248 (2005) 387–394
the period grating is 7.90 lm at fixed temperature
of 58.9 °C in phase matching condition, where
the gain bandwidth is 130.6 nm. It can completely
support the bandwidth of sub-10 fs seed pulse.
With lower pump intensity (40 MW/cm2) the gain
of signal reaches about 1400 with a 10 mm length
of PPKTP. Considering the noncollinear angle of
4.71° between pump and signal the maximal interaction length could be 12 mm for 1 mm of beam
diameter, so in our geometry pump and signal
can interact over the entire length of PPKTP. Recently the thickness of PPKTP has reached 3 mm
[17], so our results are very useful for practical
experiment. By [24] the walk-off between pump
and idler does not affect interaction length and is
good at restraining the back-conversion effect
and improving the beam quality of signal. Besides
that, the interaction length also could be compensated for by using elliptical pump beam.
As the central wavelength of signal moves to
long wavelength, the optimal noncollinear angle
decreases and grating period increases in phase
matching as shown in Fig. 3. The optimal phase
matching noncollinear angle and grating period
can be calculated in the same way. Considering
the tunable wavelength of Ti:sapphire oscillator
around 800 nm, we also analyze the gain bandwidth at 780 and 850 nm with the same period
PPKTP (7.90 lm). The results show that by
changing the noncollinear angle and temperature
in small range, the maximal gain bandwidth can
reach about 120 nm. Therefore, the same
PPKTP can be used with noncollinear geometry
for the broadband OPA with the tunable seed
pulse around 800 nm from Ti:sapphire
oscillator.
This analysis is adaptive to different wavelength
and other QPM materials. For PPLN [23] with the
same interacting wavelength, the optimal noncollinear angle is 5.18° and grating period is 5.82
lm at fixed temperature (150 °C) in type-0 phase
matching condition, where exists a broadest gain
bandwidth of 115.4 nm. The noncollinear angle
of PPLN is larger than that of PPKTP, and the
fabricated thickness of PPLN is limited to about
0.5 mm. Therefore, PPKTP is more suitable to
generating higher energy in NOPCPA laser
system.
393
5. Conclusion
We have investigated noncollinear OPA process
in PPKTP crystal with type-0 phase matching
geometry to get a broad gain spectrum for the
application in OPCPA. By the tuning the crystal
angle or temperature near the optimal range, better gain spectrum with broad bandwidth can be
obtained easily, which can compensate for the error from noncollinear angle. Other periodical
poled crystals can also be analyzed with similar
method. These theoretical results are very useful
for designing the period of QPM crystal and selecting phase matching noncollinear angle to optimize
the optical parametric amplification used in OPCPA system in practice. This OPCPA system based
on PPKTP is a great potential to replace regenerative amplifier of CPA around 800 nm.
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