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Journal ArticleDOI

Design of efficient single stage chirped pulse difference frequency generation at 7 {\mu}m driven by a dual wavelength Ti:sapphire laser

04 Nov 2013-arXiv: Optics-

Abstract: We present a design for a high-energy single stage mid-IR difference frequency generation adapted to a two-color Ti:sapphire amplifier system. The optimized mixing process is based on chirped pulse difference frequency generation (CP-DFG), allowing for a higher conversion efficiency, larger bandwidth and reduced two photon absorption losses. The numerical start-to-end simulations include stretching, chirped pulse difference frequency generation and pulse compression. Realistic design parameters for commercially available non linear crystals (GaSe, AgGaS2, LiInSe2, LiGaSe2) are considered. Compared to conventional un-chirped DFG directly pumped by Ti:sapphire technology we report a threefold increase of the quantum efficiency. Our CP-DFG scheme provides up to 340 {\mu}J pulse energy directly at 7.2 {\mu}m when pumped with 3 mJ and supports a bandwidth of up to 350 nm. The resulting 240 fs mid-IR pulses are inherently phase stable.

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Design of efficient single-stage chirped pulse difference frequency
generation at 7 lm, driven by a dual wavelength Ti:sapphire laser
Christian Erny
Christoph P. Hauri
Received: 19 December 2013 / Accepted: 13 April 2014 / Published online: 30 April 2014
Ó The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract We present simulations for a design of a high-
energy single-stage mid-IR difference frequency genera-
tion adapted to a two-color Ti:sapphire amplifier system.
The optimized mixing process is based on chirped pulse
difference frequency generation (CP-DFG), allowing for a
higher conversion efficiency and reduced two-photon
absorption losses. The numerical start-to-end simulations
include stretching, chirped pulse difference frequency
generation and pulse compression. Realistic design
parameters for commercially available nonlinear crystals
(GaSe, AgGaS
2
, LiInSe
2
, LiGaSe
2
) are considered. Com-
pared with conventional unchirped DFG directly pumped
by Ti:sapphire technology, we predict a threefold increase
in the quantum efficiency. Our CP-DFG scheme provides
up to 340 lJ pulse energy directly at 7.2 lm when pumped
with 8 mJ and supports a bandwidth of up to 350 nm. The
resulting 240 fs mid-IR pulses are inherently phase stable.
1 Introduction
Intense laser pulses, tunable in the mid-infrared wavelength
range (3–20 lm), are interesting for numerous applica-
tions, ranging from investigations of the fingerprint spectral
region and semiconductors [1, 2] to the scaling of high-
order harmonic generation toward the water window and
beyond [35]. A prominent approach for accessing this
wavelength range is based on a multistage white-light
seeded optical parametric amplifier (OPA) system, driven
by a femtosecond Ti:sapphire laser system. While such
BBO-based OPA stages typically provide tunable output
between 1.3 and 2.6 lm, the longer wavelength range
(3–20 lm) is typically accessed by an additional difference
frequency generation (DFG) stage [68]. For such tunable
systems, the typical conversion efficiency between the
near-IR and the IR is rather small (&1 %), with a corre-
sponding quantum efficiency (QE) of &10 %. The energy
stability is limited by the multiple nonlinear conversion
stages and the pulses are not intrinsically CEP stable for
signal and idler mixing.
In the past, several DFG approaches based on AgGaS
2
(AGS) and GaSe (GS) have been presented. Throughout
those efforts transform-limited (TL) or unchirped femto-
second pulses were used. Due to the high intensities and the
subsequently strong TPA, only a low DFG efficiency could
be achieved, which limited the generated output power
significantly. Even though the applied laser systems pro-
vided pulse energies at 800 nm comparable to our system,
the generated output energy between 7 and 10 lm was not
exceeding 8 lJ with AGS [9, 10], corresponding to a pump
to idler QE of 3.7 %. In GS, up to 0.6 lJ has been pro-
duced between 10 and 20 lm (QE = 3.4 %) [11].
In this paper, we present a different approach based on a
single-stage, high-energy difference frequency generation,
using chirped phase matching [12] between two intense
laser pulses with different colors from a common Ti:sap-
phire amplifier source (Fig. 1).
The scheme offers several advantages over DFG by
unchirped pulses and the above-mentioned multistage OPA
approach. It has the potential to provide increased energy
C. Erny (&) C. P. Hauri
Paul Scherrer Institute (PSI), SwissFEL, 5232 Villigen,
Switzerland
e-mail: christian.erny@psi.ch
C. P. Hauri
e-mail: christoph.hauri@psi.ch
C. Erny C. P. Hauri
Ecole Polytechnique Federale de Lausanne, 1015 Lausanne,
Switzerland
123
Appl. Phys. B (2014) 117:379–387
DOI 10.1007/s00340-014-5846-6

stability, a simpler experimental setup, directly carrier
envelope phase (CEP) stable [13, 14] mid-IR output pulses,
an increased phase-matching bandwidth, as well as an
increased interaction length and thus higher conversion
efficiency. In particular, the chirped input pulses signifi-
cantly reduce the impact of two-photon absorption (TPA)
due to lower input intensity compared with the unchirped
case.
Our investigation is motivated by recent progress in
Ti:sapphire amplifier technology which is now capable to
deliver synchronously a pair of intense pulses, which are
easily tunable around their central wavelengths [15].
Thanks to the advancement of intra-cavity acousto-optic
pulse shaping [16] in the regenerative amplifier, tunable
two and more color operation up to 20 mJ at 100 Hz rep-
etition rate has been demonstrated by our group [15]. The
large wavelength separation (up to 90 nm) between the two
pulses makes this source well suited for a single-stage
direct DFG offering to cover a spectral range between 7
and 30 lm. The two colors can be separated by a suitable
spectral beam splitter and sent into individual compressors.
The polarization of the pump beam is controlled after the
compressors. And the two chirped pulses are then recom-
bined with a second mirror.
To our best knowledge, DFG with chirped input pulses
from a Ti:sapphire laser has not been investigated up to
present. DFG with chirped pulses offers the potential for
significantly reduced TPA effect and offers thus higher
output energies. We performed start-to-end simulations for
chirped pulse difference frequency generation (CP-DFG)
under realistic conditions, based on the above-mentioned
two-color Ti:sapphire laser system. This includes chirping,
nonlinear wave mixing, including two-photon absorption
and subsequent pulse compression. The principal goal was
to find the pump power, the amount of chirp, the crystal
thickness, the beam size, and the compression scheme for
broadband and efficient DFG. We predict that by CP-DFG
a quantum efficiency of up to 60 % can be achieved while
maintaining a large bandwidth. This exceeds largely the
quantum efficiency of previous experimental implementa-
tions and of the conventional multistage OPA approach.
We show that the generated pulses can be compressed
close to the transform limit by direct bulk material
compressing.
We have structured this paper the following way. In the
first part (Sect. 2), we discuss the simulation procedure
necessary to optimize the parameter set and give an over-
view of the required nonlinear crystals. In the following
sections, we make a comparison of the performance of
DFG by transform-limited pulses (TL-DFG) and chirped
pulses (CP-DFG) and demonstrate the expected perfor-
mance improvement. Later we give an example for a
realistic experimental realization (Sect. 5), including a
simple compression scheme, based on bulk Germanium
(Sect. 6). In the last section (Sect. 7), we give insight in the
mixing process and we discuss the effects allowing CP-
DFG to be three times more efficient than TL-DFG,
showing that only a minor part of the improvement is
related to the reduced losses. The major part comes from
the fact that we can design the input beam parameters such
that more photons are contributing to the mixing process
and that the gain can be tailored such that the input photons
are converted to the mid-infrared before they are absorbed
by TPA.
2 Simulation and optimization
In recent years, many new materials have been developed
for the application in the mid-IR wavelength range. Some
of them have even been used for nonlinear mixing schemes
[17], but most of them are still under development. For our
wavelength mixing scheme suitable are the nonlinear
materials AgGaS
2
(AGS), GaSe (GS), LiInSe
2
(LISe), and
LiGaSe
2
(LGSe) [18]. AGS and GS are well established,
but show high TPA. LISe and LGSe have a significantly
smaller TPA coefficient, but also a lower nonlinear coef-
ficient. All four materials have reasonably low absorption
at 800 nm as well as at 7.2 lm and above (Table 1). To our
best knowledge, these are the only nonlinear materials
currently commercially available and suitable for our
mixing scheme.
Fig. 1 CP-DFG mixing scheme
for dual-color Ti:sapphire laser
amplifier system. Splitting and
recombination of signal and
pump are done by dielectric
band-pass mirrors
380 C. Erny, C. P. Hauri
123

The main mixing parameters for the four nonlinear
crystals are summarized in Table 1. For our studies, we
have selected the phase-matching type providing the
highest d
eff
and bandwidth. We did only take into account
collinear phase matching in the crystallographic planes.
As driving source for our DFG mixing, a dual wave-
length Ti:sapphire laser system is considered, operating at
760 nm (pump, TL 53 fs) and 850 nm (signal, TL 66 fs)
(Fig. 1), with a full width at half maximum (FWHM)
bandwidth of 16 nm for both pulses and a repetition rate of
100 Hz. We are assuming Gaussian input pulses. The given
maximum wavelength separation of 90 nm allows gener-
ating mid-IR radiation at 7.2 lm (idler). By reducing the
wavelength separation between pump and signal, the idler
could be tuned to longer wavelengths, but this is not the
subject of this paper. Compared with the simulated QE for
the presented mixing scheme, we expect the QE to scale
with the coupling coefficient j = d
eff
2
/(n
1
n
2
n
3
k
1
k
2
k
3
)[19].
All simulations in this paper have been performed with a
nonlinear propagation code by Arisholm [20]. The same
code has been used successfully to model optical nonlinear
interaction, e.g., optical parametric chirped pulse amplifiers
(OPCPA [21] ) at 800 nm [22] and 3.5 lm[23]. It
numerically solves the equations for second-order nonlin-
ear frequency mixing of full three-dimensional beams in an
arbitrary birefringent crystal and takes into account the
effects of depletion, diffraction, walk-off, and TPA.
For a given nonlinear crystal, the presented optimization
problem is multidimensional, where both, the nonlinear
gain and the TPA losses are driven by the total input
intensity of pump and signal. Thus, the aim of our simu-
lation was to find for each total input intensity pump chirp,
ratio between pump and signal chirp, crystal length, and
pump and signal energy. In a crystal, when TPA is not
taken into account, the damage threshold and available
seed energy define the mixing conditions. In our case, we
are not limited by the signal energy, but little is known
about the damage threshold. Our calculations are thus
covering the intensity range where we expect the damage
limit. To take into account that any parameter modification
might have an impact on the other parameters, we have
applied the procedure as illustrated by Fig. 2.
This has been done through 1D simulations in the plane-
wave approximation. For comparison, we have set the 1/e
2
beam radius for pump and signal to 5 mm for all crystals,
all though LGSe is currently only available with 5 mm
diameter. Diffraction effects on the mixing process can
thus be neglected.
To reduce the parameter space, we have set initially the
chirp ratio between pump and signal to a fixed factor
according to chirp-assisted group-velocity matching [12].
The largest bandwidth in the TPA free case is expected for
the following pump to signal chirp ratio:
A
1
¼ 1
n
g;pump
n
g;signal
n
g;idler
n
g;signal
¼
GDD
pump
GDD
signal
; ð1Þ
where GDD is the Group Delay Dispersion and n
g
is the
group-velocity index. The chirp ratio A
2
between signal
and idler is then given by
A
2
¼ 1 A
1
¼
GDD
signal
GDD
idler
: ð2Þ
As TPA is depending on the spectral intensity, in the
stretched pulse case, it appears as an additional spectral
loss component, thus competing with the gain through
phase matching. We therefore had to retrieve the optimized
value for A
1
from our simulation. There is no longer a
single chirp ratio that gives the best performance over the
whole intensity range. We have therefore defined the fol-
lowing figure of merit (FOM)
Table 1 Main properties of nonlinear crystal for DFG between 760 nm (pump) and 850 (signal) to 7.2 lm (idler)
GS AGS LISe LGSe
Point group
62 m
42 m
mm
2
mm
2
Type (idler ? signal ? pump) oo ? eoo? eeo? eeo? e
Plane xy xy
h,u phase-matching angle (°) 20.6 51.4 49.9 42.4
d
eff
/(pm/V) 50.45 13.5 11.9 8
Nonlinear coupling constant j (pm/V)
2
/lm
2
25.2 1.5 1.6 1.3
Phase-matching bandwidth (nm)/(THz) 359/2.09 358/2.08 205/1.19 181/1.05
Two-photon absorption b (cm/GW) 6 [28]4[29] 0.6 [30] \0.07 [30]
Transparency (lm) 0.62–20
*
[31] 0.48–11.4
[32] 0.72–10.4
[33] 0.37–13.2
à
[34]
700–900 nm absorption coefficient (cm
-1
) \0.3 [35] 0.01 [35]n.a. n.a.
Idler absorption coefficient (cm
-1
) \0.07 [35] \0.04 [36]n.a. n.a.
Phase-matching type and plane have been chosen to maximize d
eff
and bandwidth. The nonlinear coupling constant is given by j
2
= d
eff
2
/
(n
1
n
2
n
3
k
1
k
2
k
3
). The transparency range is given at
a ¼ 1cm
1
,
à
a ¼ 5cm
1
, and
*
‘0’ transmittance level
Design of efficient single-stage chirped pulse difference frequency generation at 7 lm 381
123

FOM ¼
E Dk
I
: ð3Þ
This value depends on the idler pulse energy (E), its
spectral FWHM bandwidth (Dk), and the total pump and
signal intensity (I). For further optimization, FOM is
evaluated at a fixed intensity. Normally, the damage
threshold would be a reasonable choice, but since it is
unknown, we have defined a critical intensity based on the
assumption that energy dissipation through TPA is the
dominating limiting effect. Since only little data on the
subject are available, we have based our definition on the
earlier experimental implementation of DFG by com-
pressed pulses by Xia et al. [13]. We have estimated in
their experiment a 75 % loss of input energy in AGS due to
TPA, an absorbed fluence of &3.8 mJ/cm
2
, without dam-
age in the crystal.
1
Based on their observation, we have defined the critical
intensity where the loss fluence is 3.8 mJ/cm
2
for all
investigated materials. Compared with the value from
chirp-assisted group-velocity matching [12], the FOM
optimum chirp factor is pushed to a higher value due to TPA
(Table 2). Besides of this, the pump and signal pulses have
the same sign in chirp, while the generated idler has the
opposite chirp. In this article, we are only treating the case
of positively chirped pump and signal, since the negatively
chirped idler can be compressed by bulk materials.
To restrict the parameter range, we limited the maxi-
mum pump chirp to B3 ps depending on the nonlinear
crystal considered (Fig. 3d). Typical pulse durations for the
high intensities are between 1 and 2 ps. For lower inten-
sities, the curves become divergent. The introduced chirp
limitation prevents this asymptotic behavior.
On the basis of the above-found parameter sets for the
critical intensity, the crystal length has been optimized
through 3D simulations for no back conversions and then
used for the second loop. In a final step, we have performed
a pump to signal intensity ratio optimization for maximum
FOM.
We also considered a strong contribution from the cross-
TPA terms originating from the absorption of the signal
Fig. 2 Flowchart of
multidimensional optimization
procedure
Table 2 Parameter for optimum CP-DFG estimated from simulation
Material Crystal
length
(mm)
Optimum
chirp
factor
Chirp
factor
from
GVM
Intensity
ratio
signal/
pump
Figure
of
merit
GS 1 1.35 1.25 0.48 12.8
AGS 2 1.30 1.25 0.82 13.7
LISe 3 1.17 1.17 0.38 14.7
LGSe 2 1.35 1.13 0.29 6.5
1
We have verified this experimentally for GaSe. By focusing a 4 mJ,
50 fs laser beam to 3.3 mm beam radius onto a 1 mm thick GaSe
sample we measured an absorption of 3.3 mJ and a heating of the
sample of 6 °C. We could not observe any damage.
382 C. Erny, C. P. Hauri
123

induced by an intense pump and vice versa. Unfortunately,
little is known about these coefficients, but as a reasonable
upper limit approximation, we have taken the diagonal
coefficient values, corrected by a factor of 2 to take the
weak wave retardation into account [24].
Other parasitic processes (e.g., thermo optic effect and
linear absorption) are neglected. We have estimated the
impact of nonlinear refractive index based on data avail-
able for similar nonlinear materials. For example, for sili-
con waveguides [25] and AgGaSe
2
[26, 27], TPA
coefficient and nonlinear refractive index are available. For
both materials, the TPA coefficient is ranging between 1
and 10 cm/GW and the corresponding nonlinear refractive
index 3 9 10
-5
–6 9 10
-5
cm
2
/GW for 1.5 lm wave-
length. We assumed similar values for GS and AGS. A
nonlinear refractive index of up to 10 9 10
-5
cm
2
/GW did
not show a significant impact according to our simulations.
For each total (pump plus signal) input intensity, this
resulted in a set of total input energy (Fig. 3a), pump chirp
(Fig. 3b), pump to signal chirp factor, absorption (Fig. 3c),
pump to signal intensity ratio, and crystal length (Table 2)
for the optimized CP-DFG.
3 TL-DFG and its limitations
As a benchmark, we first calculated conventional DFG
with TL pump and signal and for different DFG crystal
types in dependence of the total input intensity. The cal-
culation shows that even at high intensities up to 80 GW/
cm
2
and with a total input energy of 4 mJ not more than
40 lJ output can be achieved at a wavelength of 7.2 lm
(Fig. 4a). This is in-line with the reported results [9, 10]. In
TL-DFG, the main limiting factor for a larger conversion
into the idler is the high loss through TPA and the group-
velocity mismatch. This loss increases rapidly even at low
intensities (i.e., a few GW/cm
2
) and surpass 80 % for
intensities above 40 GW/cm
2
(LISe, AGS, and GS)
(Fig. 4b).
This large and detrimental impact of TPA in the mixing
process can only be controlled by reducing the input
intensity, which does not correct for the group-velocity
mismatch in the TL case. However, CP-DFG can control
both effects.
4 Chirped pulse DFG
We illustrate the potential of CP-DFG by presenting first
the optimized achievements against the TL case (Fig. 5).
By inducing the ideal chirp (Fig. 3) to both pump and
signal, the output energy can be increased by an order of
magnitude, while reducing the input intensity. The FWHM
bandwidth is also enhanced by CP-DFG (Fig. 5c, d). It can
be observed that the output energy scales linearly with the
input intensity. The sharp edge around 5 GW/cm
2
is due to
our chirp limitation. Here, significantly longer pump and
idler pulses would be required to maintain the linear
behavior. On the high-intensity side, GS shows a saturation
behavior. The strong nonlinear coefficient leads to back
conversion, which could be prevented by a shorter crystal.
The best performance in terms of conversion efficiency
can thus be expected for the newer Li-based materials,
while GS and AGS support larger gain bandwidth.
To get more realistic estimation for experimental
implementation, we have performed the simulation for the
Fig. 3 Parameter set for
optimized CP-DFG (a) and
(b) in dependence of the total
(pump and signal) intensity.
a Total required input energy
for a 10-mm-diameter nonlinear
crystal for GS (blue triangles),
AGS (red squares), LISe (black
dots), and LGSe (purple
diamonds), b required pump
chirp value for maximum output
energy, c resulting total input
absorption, and d average input
pulse duration. The chirp of the
signal is related to the pump
chirp by the chirp factor from
Table 2
Design of efficient single-stage chirped pulse difference frequency generation at 7 lm 383
123

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