Enhanced optical Kerr nonlinearity of graphene/Sihybrid
waveguide
Cite as: Appl. Phys. Lett. 114, 071104 (2019); doi:
10.1063/1.5064832Submitted: 9 October 2018 . Accepted: 5 February
2019 .Published Online: 19 February 2019
Qi Feng,1 Hui Cong,1 Bin Zhang,1,2 Wenqi Wei,1,2,3 Yueyin
Liang,1,2 Shaobo Fang,1,2 Ting Wang,1,a)
and Jianjun Zhang1,b)
AFFILIATIONS1Institute of Physics, Chinese Academy of Sciences,
Beijing 100190, People’s Republic of China2School of Physical
Sciences, University of Chinese Academy of Sciences, Beijing
100190, China3School of Physics and Technology, Wuhan University,
Wuhan 430072, China
a)Electronic mail: [email protected])Electronic mail:
[email protected]
ABSTRACT
In this work, we experimentally study the optical Kerr
nonlinearities of graphene/Si hybrid waveguides with enhanced
self-phasemodulation. In the case of CMOS compatible materials for
nonlinear optical signal processing, Si and silicon nitride
waveguideshave been extensively investigated over the past decade.
However, Si waveguides exhibit strong two-photon absorption (TPA)
attelecommunication wavelengths, which leads to a significant
reduction of the nonlinear figure-of-merit (FOM). In contrast, a
sili-con nitride based material system usually suppresses the TPA
but simultaneously leads to the reduction of Kerr nonlinearity
byone order of magnitude. Here, we introduce a graphene/Si hybrid
waveguide, which maintains the optical properties and
CMOScompatibility of Si waveguides, while enhancing the Kerr
nonlinearity, by transferring over to the top of the waveguides.
The gra-phene/Si waveguides are measured to have an enhanced
nonlinear parameter of 510W�1 m�1, compared with that of the Si
wave-guide of 150W�1 m�1. An enhanced nonlinear FOM of 2.4860.25
has been achieved, which is four times larger than that of the
Siwaveguide of 0.660.1. This work reveals the potential application
of graphene/Si hybrid waveguides with high Kerr nonlinearityand FOM
for nonlinear all-optical signal processing.
Published under license by AIP Publishing.
https://doi.org/10.1063/1.5064832
Optical nonlinear effects in CMOS-compatible integratedoptical
devices are of great significance as they can be explored torealize
a variety of functionalities ranging from all-optical
signalprocessing to light generation.1–5 A silicon-on-insulator
(SOI) hasbeen regarded as a popular platform for ultra-dense
on-chip inte-gration of photonic and electronic circuitry due to
its compatibil-ity with CMOS fabrication. In addition, the
nonlinear opticalproperties of siliconwaveguides are also heavily
explored over thepast decade, such as stimulated Raman scattering,
Raman amplifi-cation, self-phase modulation (SPM), four-wave
mixing, andsuper-continuum generation.2,6–9 However, the existence
of two-photon-absorption (TPA) at telecom wavelengths
(around1550nm) in the Si platform leads to a strong degradation in
thevalue of the nonlinear figure-of-merit (FOM). TPA increases
thephoton loss in the process and generates carriers
subsequentlyproducing usually undesired free-carrier absorption
(FCA) andfree-carrier dispersion (FCD).TPA and FCA generally cause
optical
losses, which in turn lower the peak power inside the
waveguideand therefore reduce the conversion efficiency of the
optical non-linear process.10,11 In addition, non-negligible
single-photonabsorption (SPA) should be taken into consideration
not only atvery low power levels but also at moderate
powers.12,13
There are other promising platforms such as chalcogenideglass
and AlGaAs, which possess high nonlinearity and low TPA,but highly
challenging fabrication processes limit their usage inCMOS
compatible applications.14,15 Furthermore, CMOS com-patible
platforms such as Si3N4 and Hydex glass exhibit low TPAat telecom
wavelengths, thus efficiently reducing the nonlinearloss as well as
linear loss; however, their nonlinear refractiveindex is
approximately one order of magnitude smaller than thatof
silicon.16,17 Therefore, the best way to fulfill the requirementof
silicon nonlinear photonics is to integrate themwithmaterialswith a
high Kerr coefficient while keeping the silicon platformfor its
economic advantages.
Appl. Phys. Lett. 114, 071104 (2019); doi: 10.1063/1.5064832
114, 071104-1
Published under license by AIP Publishing
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PinPout
¼ 2ImðcÞLeffeaLPin þ eaL; (1)
where Im(c) ¼ bTPA/(2Aeff) is the imaginary part of the c,
nonlin-ear coefficient due to TPA, bTPA, is the two-photon
absorptioncoefficient, Leff is the effective length reduced by the
linearpropagation loss through Leff ¼ ð1� e�aLÞ=a, L is the
physicallength, a¼3.5dB/cm is the linear propagation loss, and
Aeff(�0.16 lm2) is the effective mode area of waveguide. Thus, Eq.
(1)discloses a linear relation between the ratio Pin/Pout and
themeasured input power Pin with the slope being proportional tothe
nonlinear coefficient bTPA. The TPA coefficients bTPA for bothSi
waveguides and G/Si hybrid waveguides can be extractedwith similar
values of 0.5cm/GW.
We calculated the case where a Gaussian-shape laser pulseis
coupled into the Si waveguide and G/Si hybrid waveguide. Byusing
the nonlinear Schr€odinger equation (NLSE) with the split-step
Fourier method, the on-chip SPM process can be simulatedwith the
following equation:33
@A@z¼ � 1
2aAþ i
X10
m¼2
imbmm!
@mA@smþ icjAj2A� r
2ð1þ ilÞNcA; (2)
where A(z, t) is the slowly varying temporal envelope along
thelength z of a nonlinear medium, c¼x0n2/cAeff is the
nonlinearparameter, x0 is the optical frequency, bm is them-th
order dis-persion coefficient, n2 is the nonlinear Kerr
coefficient, r is thefree carrier absorption coefficient, l is the
free carrier disper-sion coefficient, and Nc is the free carrier
density. Nc can beobtained by solving
@Nc@t¼ bTPA
2�hxjAj4
A2eff�Nc
sc; (3)
where sc is the effective lifetime of free carriers with an
esti-mated value of 0.5ns.10 Noting that pulse width T0 < sc,
the scterm can be ignored as carriers do not have enough time
torecombine over the pulse duration. The pulse dynamics are
gov-erned by the interplay of SPM and dispersion whose
relativestrengths can be determined by several characteristic
lengths,namely, the GVD, defined as LD ¼ T2o=jb2j, and the
nonlinearlength, defined as LNL ¼ 1=cPin.
Here, the nonlinear length LNL and the dispersion lengthLD, are
calculated to be 0.65mm and 19.26mm, respectively.Given that LD is
much longer and LNL is much shorter than thewaveguide length
(3.5mm) for both Si and G/Si hybrid wave-guides, the pulse dynamics
will be dominated by the third-ordernonlinearity rather than the
dispersion.
As shown in Fig. 5, the simulated spectra have relativelygood
agreement with our experimental results under variousinput
energies. The extracted n2 value of the G/Si hybrid wave-guide is
here calculated to be 2� 10�17 m2/W, which is threetimes larger
than that of the Si waveguide. Furthermore, the cal-culated
nonlinear parameter c is about 510W�1m�1. In contrast,the
calculated n2 and nonlinear parameter c of the Si waveguideare 6�
10�18 m2/Wand 150W�1m�1, respectively.
The nonlinear figure-of-merit can be defined as FOM¼n2/(kbTPA),
which is a measure of the optical nonlinear efficiency of
the medium when both the nonlinear refractive index and
non-linear loss mechanisms are accounted for.35–37 In addition,
itprovides a useful dimensionless measurement of the suitabilityof
the material for nonlinear switching. In this work, nonlinearFOM of
the bare Si waveguide is �0.660.1 at 1.55lm, insuffi-cient for
optical switching applications, while the FOM of the G/Si hybrid
waveguide is calculated to be approximately 2.48,which is higher
than that reported in Si (0.83),6 SiGe (0.26),38 andhydrogenated
amorphous-Si (0.66)39,40 waveguides.
In addition, for those platforms which possess low or
negli-gible TPA in the telecom region, another figure of
merit,c�Leff,max, is more suitable. It provides a metric for
comparisonbetween nonlinear waveguides, where the acquired
nonlinearphase scales linearly with the incident peak power.
Leff,max¼ 1/ais the maximum effective length achievable in a
waveguide witha loss coefficient of a, and c is the nonlinear
parameter. The fig-ures of merit c�Leff,max for Hydex glass41
(loss¼0.06dB cm�1and c � 0.22W�1m�1) and ultra-low-loss silicon
nitride42(loss¼0.5dB cm�1 and c � 1W�1m�1) are calculated to be
0.16and 0.087W�1, respectively. For the G/Si waveguides used inthis
work, c�Leff,max¼ 1.98W�1, which suggests that nonlinearwaveguide
devices implemented on this platform are able toachieve 10 times
more nonlinear phase shift than ultra-low-lossplatforms at the same
peak power level. Furthermore, the fieldstrength interaction
between the silicon waveguide and gra-phene would be enhanced as
the silicon waveguide changes to220nm in height due to the much
higher electric field distribu-tion, and this would further enhance
the nonlinear behavior. Thesignificant improvement in both the
optical Kerr nonlinearityand nonlinear FOM inG/Si raises the
prospect to provide a trulypractical and viable platform for
nonlinear photonic applicationsin the telecommunication wavelength
window. This reveals thatthe incorporation of single layer graphene
can be employed toincrease the nonlinear performance of
silicon-based waveguidesin all-optical signal processing.
In summary, enhancement of third-order nonlinearity inthe G/Si
hybrid waveguide has been studied here by self-phasemodulation
experiments, and enhanced spectrum broadening
FIG. 5. Experimentally measured and numerically calculated
spectra of the outputpicosecond pulse propagating along G/Si hybrid
waveguides for various coupledpulse energies, denoted by solid and
dashed curves, respectively.
Applied Physics Letters ARTICLE scitation.org/journal/apl
Appl. Phys. Lett. 114, 071104 (2019); doi: 10.1063/1.5064832
114, 071104-4
Published under license by AIP Publishing
https://scitation.org/journal/apl
has been observed in the G/Si hybrid waveguide. Although
thedecorated graphene exhibits a relatively weak evanescent
fieldsin such a structure, three times larger Kerr nonlinearity is
stillachieved on the G/Si hybrid waveguide with an overall
opticalnonlinear parameter of 510W�1/m, higher than that of the
sili-con waveguide of 150W�1/m. The FOM has been improved aswell
from 0.660.1 to 2.48 compared with that of the Si wave-guide. The
FOM for comparison with those platforms withoutTPA and G/Si hybrid
waveguides is able to achieve 10 timesmore nonlinear phase at the
same peak power level. This workprovides an insight that on-chip
integration of graphene withCMOS-compatible silicon platform
enables the realization ofdevices that possess many all-optical
functions at telecommuni-cationwavelength.
The authors acknowledge the graphene transfer processby Dr. F.
G. Yan from the Institute of Semiconductors, ChineseAcademy of
Sciences in China. Financial support was providedby the National
Natural Science Foundation of China (GrantNos. 11504415, 11434010,
11574356, 61635011, 11804382, and61804177), the Ministry of Science
and Technology (MOST)of People’s Republic of China (2016YFA0300600
and2016YFA0301700), and the Key Research Program of
FrontierSciences, CAS (Grant No. QYZDB-SSW-JSC009).
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114, 071104-5
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