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 [3–5]. 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 [6–8]. 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