Optics and Photonics Journal, 2012, 2, 260-264
http://dx.doi.org/10.4236/opj.2012.24031 Published Online December 2012 (http://www.SciRP.org/journal/opj)
Phase-Matching and Parametric Conversion for the
Mid-Infrared in As2S3 Waveguides
Qi Chen, Xin Wang, Christi Madsen
Department of Electrical & Computer Engineering, Texas A&M University, College Station, USA
Received September 7, 2012; revised October 5, 2012; accepted October 17, 2012
ABSTRACT
We illustrate two As2S3 waveguide designs for four-wave mixing, which can generate 3.03 μm mid-infrared light from
a 1.55 μm near-infrared signal source and a 2.05 μm pump source. Through simulations, we verify that four-wave mix-
ing phase-matching efficiencies up to 100% can be achieved using dispersion engineering to maintain the dispersion at
2.05 μm near to zero. The best conversion efficiency is –10 dB. When the waveguide length is 1 cm, the parametric
conversion bandwidth is 1525 nm. We also evaluated the shift of 100% phase-matching efficiency wavelengths based
upon fabrication tolerances.
Keywords: As2S3; Mid-Infrared; Phase-Matching; Four-Wave Mixing
1. Introduction
Four-wave mixing (FWM) is a third-order nonlinear
process. In degenerate FWM, if the phase-matching con-
dition is met, two pump photons and a signal photon can
generate an idler photon. In mid-infrared (Mid-IR) region,
the vast majority of gaseous chemical substances exhibit
fundamental vibrational absorption bands, and the ab-
sorption of light provides a nearly universal means for
their detection [1]. The high sensitivity and capability of
non-intrusive in-situ detection make it ideal for trace gas
detection.
Recently, although many papers have been published
on FWM in silicon waveguides for both near-infrared
(near-IR) [2-9] and mid-IR [10,11] and in chalcogenide
waveguides for near-IR [12-14], the parametric conver-
sion by FWM for mid-IR in chalcogenide waveguides
has not been demonstrated yet. In addition, the applica-
tions silicon waveguides cannot be utilized over 2.5 μm
wavelength region due to the strong absorption from the
substrate material, silicon dioxide (SiO2). On the contrary,
lithium niobate (LiNbO3), as a widely-used optical mate-
rial, has very high transmission over the wavelength
range from 0.42 to 5.2 μm and exhibits excellent electro-
optic, nonlinear and piezoelectric properties. Therefore, it
is a good substrate material for mid-IR integrated optics
up to 5 μm.
Chalcogenide glasses have been investigated as an al-
ternative platform for nonlinear signal processing [15].
They are a set of amorphous materials which show good
transparency and low loss for both 1.3 μm - 1.55 μm tele-
communication windows and into the mid-IR region.
Arsenic tri-sulfide (As2S3) is very popular among them
by its low two photon absorption (TPA) coefficient,
which makes it ideal for nonlinear optics. Magnesium
fluoride (MgF2), which has wide transmission range (0.2
μm - 7 μm) into the mid-IR, is a good candidate for clad-
ding material because of its lower refractive index.
Magnesium fluoride (MgF2), which has wide transmis-
sion range (0.2 μm - 7 μm) at mid-IR, is a good candidate
for cladding material because of its ruggedness and dura-
bility. It also keeps the potential of optical tuning by
adding electrodes on it.
In this paper, we report two As2S3 waveguide designs,
which have near zero dispersion at a pump wavelength of
2.05 μm and satisfy the phase-matching condition at a
signal wavelength of 1.55 μm. The corresponding idler
wavelength is 3.03 μm which is a common operation
wavelength for trace gas sensors [16]. The FWM phase-
matching efficiency can be as high as 100%. Through
simulations, we verify that the parametric conversion
efficiency is –10 dB for pump power intensity of 0.1
GW/cm2. Under the same intensities, our results are 20
dB better than the parametric conversion efficiency of
silicon waveguides.
2. Dispersion Engineering
To satisfy the phase-matching condition, dispersion en-
gineering is required. In the first place, we have to main-
tain the very low dispersion at the pump wavelength by
varying the waveguide dimensions. To achieve high effi-
C
opyright © 2012 SciRes. OPJ

Q. CHEN ET AL. 261
cient FWM, it is also necessary to tune the 100% phase-
matching efficiency at signal wavelength by changing
cladding thickness. Figures 1(a) and (b) show that the
structures of As2S3 waveguide with and without MgF2
top cladding. The reason to simulate different designs is
to evaluate the influence of MgF2 on conversion band-
width.
The resulting dispersion curves for the fundamental
TE mode are demonstrated in Figure 2. All simulations
are from Fimmwave, a commercial software by Photo
Design Inc. When the waveguide width is 1.4 μm and the
height is 1.7 μm with 0.18 μm MgF2 cladding on top of it,
the dispersion at 2.05 μm is 1.2 ps/nm/km which is very
close to zero; when the waveguide width is 1.5 μm and
the height is 1.685 μm without a cladding material, the
zero dispersion wavelength is exactly 2.05 μm.
3. Phase-Matching Condition and FWM
Phase-Matching Efficiency
FWM is a nonlinear phase-matched process resulting
from the near-instantaneous third-order susceptibility, χ(3)
[17]. For degenerate FWM, the relationship of the three
wavelengths can be described as:
121
ips


 (2)
Figure 1. (a) As2S3 waveguide with MgF2 cladding (b)
without cladding.
Figure 2. Dispersion curves for two As2S3 waveguide de-
signs.
where λi, λp and λs are idler, pump and signal wavelengths.
The FWM phase-matching efficiency depends on how
well the phase-matching condition is satisfied:
where ns, ni and np are effective indices of signal, idler
and pump wavelengths; Pp is pump power.
2π22
p
si
p
si p
n
nn P


 

  


(2)
2
2π
peff
n
A
  (3)
γ is nonlinearity coefficient. Aeff is effective mode area
for the pump, which are 1.84 μm2 and 1.99 μm2 for the
structures with and without MgF2 cladding, respectively.
If the phase-matching condition is achieved, the FWM
efficiency can be very high. It is described by the fol-
lowing formula in [18]:


0
0
2
2
20
22 2
0
sin 2
14e
1e
L
L
L















 




(4)
where α0 is the waveguide propagation loss at 2.05 μm.
We use a value of 0.33 dB/cm from our previous work
[19]. Since TPA coefficient of As2S3 is very small, the
nonlinear loss due to it can be neglected. L is the length
of As2S3 waveguide, 4 cm.
Figure 3 shows the phase-matching curves for the two
As2S3 waveguide designs. The phase-matching condition
is met at 1.55 μm, 3.03 μm and the region near the pump
wavelength, which means that the FWM phase-matching
efficiency, depicted in Figure 4, can be as high as 100%
at these wavelengths for both designs. In wavelength
regions near 1.55 and 3.03 μm, the FWHM of the struc-
ture without cladding is 25 nm, which is 9 nm wider than
that of structure with MgF2 cladding on top.
4. Coupled Equation and Parametric
Conversion Efficiency
FWM can be described by the following coupled differ-
ential equations [20]:



2
22
2
i22
exp i
s
s
ip
pi
A
s
A
AA
z
AA z






A
(5)



2
22
2
i22
exp i
i
ispi
ps
A
A
AAA
z
AA z






(6)



222
i22
2expi
p
p
is
isp
A
p
A
AA
z
AAA z






A
(7)

Q. CHEN ET AL. 262
(a)
(b)
(c)
Figure 3. (a) Phase mismatch curves as a function of signal
wavelength; (b) Phase mismatch around 1.55 μm and (c)
3.03 μm.
Figure 4. FWM phase-matching efficiency as a function of
signal wavelength.
where Ap, As and Ai denote the complex electric field
amplitude of pump, signal and idler wavelengths, re-
spectively. An improved understanding can be obtained
by considering a strong pump and a weak signal incident
such that the pump remains undepleted during the FWM
process [20]. Therefore, the coupled differential equa-
tions can be solved by an analytic method. The para-
metric conversion efficiency is described by:

2
sinh
p
i
P
Gg
g

e
ff
L






 (9)
where g is parametric gain and Leff is the effective As2S3
waveguide length for nonlinear process. They can be
expressed by:


22
2
p
gP  
For simulation purposes, the pump power intensity
coupled into the As2S3 waveguide are chosen to be 0.1
GW/cm2 and 0.01 GW/cm2, respectively. The parametric
conversion

0
0
1exp
eff
L
L



 (10)
efficiency Gi is shown in Figure 5. When L is 4 cm, Gi is
–10 dB and –30 dB for each pump power intensity. Un-
der the same intensities, our results are 20 dB better than
the parametric conversion efficiency of silicon wave-
guides in [21]. The remarkable improvement is mainly
due to the 100% FWM phase-matching efficiency η2.
5. Fabrication Tolerance
In addition to the high nonlinearity, chalcogenide glass
exhibits photosensitivity, too [22]. We have studied the
photodarkening effect of As2S3 in a hybrid Mach-
Zehnder interferometer [23]. A uniform exposure to

Q. CHEN ET AL. 263
intensive green light can increase As2S3 refractive index
by 1% [5], which can change the phase-matching condi-
tion of the As2S3 waveguides. It provides the tuning abil-
ity after traditional photolithography.
Figure 6 shows that the FWM phase-matching effi-
ciency curves for the design with MgF2 cladding when
the refractive index of As2S3, waveguide width or height
is changed. These cases may happen during fabrication.
The changes shift the 100% phase-matching efficiency
wavelengths, which are summarized in Table 1.
Figure 7 demonstrates the parametric conversion effi-
ciency curves corresponding to the different As2S3
waveguide lengths for 0.1 GW/cm2 pump power inten-
sity. Due to the length dependence of phase-matching
(LΔκ), the conversion bandwidth increases with the de-
creasing waveguide length. When L is 1 cm (Leff = 0.96
cm), the conversion bandwidth is 1525 nm corresponding
to –21 dB parametric conversion efficiency. The flat
curve indicates that we can achieve continuously tunable
Figure 5. Parametric conversion efficiency as a function of
signal wavelength.
Figure 6. FWM phase-mismatch efficiency as a function of
signal wavelength.
Table 1. 100% FWM phase-matching efficiency wavelengths
for different fabrication tolerances.
Fabrication
tolerances
100% FWM
phase-matching
efficiency wavelength (μm)
Idler wave
length (μm)
1% refractive index
increasing of As2S3 1.418 3.698
5% waveguide width
increasing 1.555 3.007
5% waveguide height
increasing 1.486 3.304
5% cladding height
increasing 1.554 3.013
Figure 7. Parametric conversion efficiency as a function of
signal wavelength.
FWM between the near-IR and mid-IR.
6. Conclusion
In this paper, we presented mid-IR FWM simulations for
As2S3 waveguides, which can generate 3.03 μm mid-IR
light by a 1.55 μm near-IR signal source and a 2.05 μm
pump source. The FWM phase-matching efficiency at
1.55 μm is up to 100% for the designs with and with-
out MgF2 cladding. For 0.1 GW/cm2 pump power
intensity, the best parametric conversion efficiency at
3.03 μm is –10 dB, which is 20 dB better than the results
in silicon waveguides in [21]. The largest conversion
bandwidth of 1525 nm is achieved when the waveguide
length is 1 cm. In addition, we simulated the 100% FWM
phase-matching efficiency shift for various fabrication
variations.
7. Acknowledgements
This material is based upon work supported by the
National Science Foundation under grant No. EEC-
0540832.

Q. CHEN ET AL. 264
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