Phase-Matching and Parametric Conversion for the Mid-Infrared in As<sub>2</sub>S<sub>3</sub> Waveguides

doi:10.4236/opj.2012.24031

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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

Email: [email protected]

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-

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

si p

nn P





 



 





(2)

2π

peff



 (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]:



22 2

sin 2

14e



























 









(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]:







i22

exp i

AA z













(5)







i22

exp i

ispi

AAA

AA z













(6)







222

i22

2expi

isp

AAA z













(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:



sinh















 (9)

where g is parametric gain and Leff is the effective As2S3

waveguide length for nonlinear process. They can be

expressed by:







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



1exp

eff





 (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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