Download High-efficiency light coupling in a submicrometric

High-efficiency light coupling in a submicrometric
silicon-on-insulator waveguide
Régis Orobtchouk, Abdelhalim Layadi, Hamid Gualous, Daniel Pascal, Alain Koster,
and Suzanne Laval
Light coupling into a sub-micrometer-thick waveguide is usually done through a grating coupler. Coupling efficiency is strongly enhanced by addition of a mirror above the grating. This new kind of coupler
can be designed to achieve efficiencies as great as 80%. Numerical calculations for a high-angularspread Gaussian incident beam are compared with experimental results obtained for a standard siliconon-insulator waveguide. © 2000 Optical Society of America
OCIS codes: 310.2790, 230.7390, 230.1950.
1. Introduction
Although end coupling is usually used to inject light
into integrated optical waveguides, it is not really
achievable for sub-micrometer-thick waveguides, unless high insertion losses are accepted. The grating
coupler is then a good alternative, because it can be
monolithically integrated, at any point in the optical
circuit. It can provide a good coupling efficiency regardless of the waveguide thickness. Moreover,
only one mode of the guiding structure is resonantly
excited.
The grating parameters 共period and modulation
depth兲 must be adjusted for a given waveguide structure to get the maximum coupling efficiency by
means of limiting the number of diffracted orders.
The grating period is usually chosen to get only the
first diffracted order propagating in the waveguide
and the transmitted and the reflected beams 共zero
When this research was performed, the authors were with the
Institut d’Électronique Fondamentale, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8622, Bâtiment
220, Université Paris-Sud, F-91405 Orsay cedex, France. R.
Orobtchouk is now with the Laboratoire de Physique de la Matière,
Centre Nationale de la Recherche Scientifique, Unité Mixte de
Recherche 5511, Institut National des Sciences Appliquées, Bâtitment 502, 20 Avenue A. Einstein, F-69100 Villeurbanne cedex,
France. H. Gualous is now with the Institut Génie Energétique,
Université de Franche Comté, 12 rue des Entrepreneurs, F-90000
Belfort, France. A. Koster’s e-mail address is [email protected].
Received 9 February 2000; revised manuscript received 19 June
2000.
0003-6935兾00兾05773-05$15.00兾0
© 2000 Optical Society of America
order兲 outside. Even at resonance the reflected and
the transmitted beam intensities are not zero, and
the maximum coupling efficiency is limited to ⬃40%.
This can be greatly increased by addition of a mirror
that reinjects the transmitted beam into the
waveguide, provided a phase condition is fulfilled.
Such an efficient coupler including a grating and a
mirror has been studied both theoretically and experimentally. From a theoretical point of view, coupling efficiency for an incident Gaussian beam has
been calculated following the method described by
Nevière1 and used by other authors2,3 for low angular
beam spread. In this paper we calculate the coupling efficiency for a Gaussian beam with high angular beam spread such that this could be applied to
beams issued from an optical fiber, for instance.
Experimental devices have been processed on different silicon-on-insulator 共SOI兲 substrates. SOI
applications are increasingly developed in both microelectronics and optoelectronics.4 –7 Layadi et al.
demonstrated that standard Simox substrates for microelectronics can be used to realize low-loss monomode waveguides at 1.3 ␮m, although the guiding
silicon film is only 0.2 ␮m thick.8 The coupling efficiency was measured for various incident beam
waists and compared with the calculated values.2
2. Device Description
SOI Simox is obtained by deep oxygen ion implantation in a silicon substrate and thermal annealing,
which create a buried silicon dioxide layer under a
silicon film of good crystal quality. The standard
layer thicknesses are 0.4 ␮m for the buried dioxide
and 0.2 ␮m for the silicon film. Substrates were
purchased from Soitec 共France兲. Gratings are de1 November 2000 兾 Vol. 39, No. 31 兾 APPLIED OPTICS
5773
Fig. 1. Schematic drawing of device and of spatial evolution of guided power. Coupling efficiency depends on the beam-waist value w0
with respect to the decoupling length of the coupler LC, and on the distance of the maximum of the incident beam from the grating edge.
AR, antireflection coating.
fined by holographic lithography. To get gratings
only on limited areas, local variations of the reflection
coefficient at the interface between the substrate and
the photoresist are induced at the insolation wavelength 共0.4579 ␮m兲 by means of multilayer coating9:
a silicon dioxide layer 共260 nm兲, which is removed in
the regions where gratings are to be present, followed
by an antireflection coating consisting of 90 nm of
silicon nitride and 45 nm of silicon oxide. The photoresist gratings are transferred into the silicon oxide
and nitride and in a small fraction of the silicon layer
共30 nm兲 by means of reactive ion etching. Two gratings 共0.38 ␮m period and 0.35 filling factor兲 separated
by a noncorrugated waveguide are realized: The
first enables light injection into the waveguide,
whereas the second permits light decoupling. Coupling efficiency can be evaluated in this way. A silicon dioxide passivation layer is then deposited by
plasma-enhanced chemical vapor deposition, followed by aluminium deposition above the input coupler grating to realize the mirror. The thickness of
the silicon dioxide passivation layer 共0.46 ␮m兲 was
adjusted according to the numerical simulations presented hereafter to get a high coupling efficiency. As
shown in Fig. 1, the incident light beam 共␭ ⫽ 1.3 ␮m兲
reaches the grating through the substrate. Thus a
Si3N4 antireflection coating had to be deposited on
the entrance face.
3. Calculation of the Coupling Efficiency
The method that we used is based on Nevière’s research,1 which considers a Gaussian beam incident
on an infinite grating. The incident beam is described as a superposition of infinite elementary
plane waves. In the vicinity of the resonant excita5774
APPLIED OPTICS 兾 Vol. 39, No. 31 兾 1 November 2000
tion of the guided mode the coupler response to an
incident plane wave is given by a Lorentzian function
of the incident angle, and the diffracted field can be
assimilated to the guided-mode response. The coupler response for an incident beam is obtained by
addition of the contributions of the elementary planewave spectrum and normalized to the incident intensity.
The coupling efficiency is then given by the following formula,10,11
␩共z兲 ⫽
⫻
(
冦
2kp,z⬙ 兩r共z兲兩2 ⫹
冉
冤
冉
冊
2␲
kp,z⬙
⌳
2k0 cos ⌰0
k0 sin ⌰0 ⫹ m
)
冊冧
Re关ir共z兲q*共 z兲兴
2␲
k0 sin ⌰0 ⫹ m
⌳
兰
⫹⬁
⫺⬁
冥
兩Em,y共kp,z⬘, x兲兩2dx ,
(1)
where
i. Em,y共kp,z⬘, x兲 is the complex amplitude profile of
the mth diffracted order. It corresponds to the TE0
guided mode for m ⫽ ⫺1.
ii. ⌳ is the grating period, and k0 ⫽ 共2␲兾␭兲 is the
norm of the wave vector corresponding to the mean
incidence angle ⌰0 of the Gaussian beam, where ␭ the
beam wavelength, each of them measured in air.
iii. kp,z ⫽ kp,z⬘ ⫹ ikp,z⬙ is the complex pole of the
mth diffracted order field amplitude. At resonance
Table 1. Refractive Index and Thickness of the Structure’s Various Layers
Layers
Indexes
Thicknesses 共␮m兲
Al
SiO2 共passivation兲
Si3N4
Si 共guide兲
Buried SiO2
Si
共substrate兲
Si3N4
共antireflection兲
1.3 ⫹ i14
0.2
1.45
Variable parameter
1.98
0.09
3.505
0.205
1.45
0.38
3.505
500
1.98
0.12
its real part is close to the wave vector of the guided
mode propagating under the grating; i.e., kp,z⬘ ⬇ k0
sin ⌰r ⫹ m共2␲兾⌳兲. Its imaginary part is related to
the characteristic decoupling length of the grating Lc,
which can be measured from the 1兾e value of the light
intensity decoupled outside when the guided mode
arrives on the grating used as a decoupler: kp,z⬙ ⫽
1兾2Lc.
iv. q共z兲 is the Fourier transform of the incident
field amplitude of a Gaussian beam in the local coordinates of the grating coupler12 共see Fig. 1兲, and q*
denotes the complex conjugate of q,
q共 z兲 ⫽
兰
⫹⬁
p共kz兲exp关i共kz ⫺ kp,z⬘兲z兴dkz,
(2)
⫺⬁
where
p共kz兲 ⫽ A
kz k0,z ⫹ kx k0, x
k0 kx
冋
exp ⫺
册
w02共⫺kx k0,z ⫹ kz k0, x兲2
4k02
⫹ i共kx dx ⫺ kz dz兲 ,
(3)
where w0 is the beam waist, dx and dz give the distance of the beam center from the axis origin. kx is
related to kz by kx ⫽ 共k02 ⫺ kz2兲1兾2. A is a constant
associated with the incident beam power.
v. The integral formula r共z兲 depicts the response of
the grating coupler for the diffracted 共guided兲 field:
r共z兲 ⫽ ⫺i
兰
⫹⬁
⫺⬁
p共kz兲
exp关i共kz ⫺ kp,z⬘兲z兴
dkz.
kz ⫺ kp,z⬘ ⫺ ikp,z⬙
(4)
The first factor in Eq. 共1兲 allows us to calculate the
variations of the light power injected into the
waveguide as a function of the coupler characteristic
length LC, of the beam waist w0, and of the incidence
conditions 共angle, distance between the waist and the
device surface, distance between the coupler edge and
the maximum of the incident beam兲. The second
factor is usually referred to as a coupling term FC,
which is often ignored in coupling efficiency calculations, depending on the characteristics of the whole
structure through the diffracted field profile.
Assuming that FC is equal to 1, we consider only
the first factor to optimize the coupling efficiency. In
the general case the integral equations 共2兲 and 共4兲
cannot be formally solved. For a Gaussian beam
with low beam spread and assuming that the beam
waist is on the device surface, the paraxial approximation is used to provide an analytical solution of
these two equations.2,3 This allows us to determine
the optimum resonant coupling efficiency, for a given
coupler characterized by the decoupling length LC, as
the beam parameters and position are varied. It is
found that the optimum coupling of ⬃80% is obtained
for a beam waist w0 ⫽ 1.37 LC cos ⌰r and when the
distance d between the beam center and the coupler
edge is approximately equal to LC.
For a high angular beam spread the paraxial approximation is no longer valid, so the integral equations 共2兲 and 共4兲 must be solved numerically with a
fast Fourier transform. For the highest angular
beam spread considered it appears that we obtain the
same optimum coupling conditions as calculated with
the paraxial approximation.
Let us now focus on the coupling factor FC, which
determines the global coupling efficiency. The parameters that are to be optimized are the grating
modulation depth h and the distance between the
grating and the mirror, which corresponds to the
thickness of the silicon dioxide passivation layer.
The calculation is carried out with the rigorous differential method proposed by Vincent13 and used by
Chang et al.14 For proper accounting of the metallic
mirror and the large substrate thickness, we used an
S matrix formalism,15 which avoids numerical divergence problems related to exponential terms in the
equations. As the guided power varies with the incidence angle as a Lorentzian function, an analytical
formula that directly gives the value of ⌰r is deduced
from the calculation of three points of the resonance
curve. This method is much less time consuming
than pole research in the complex plane for the determination of the effective index of the guided mode
under the grating as usually done, for example, in
Ref. 1.
The structure considered in the computation is represented in Fig. 1 and is used with m ⫽ ⫺1. The
complex refractive index 共taken from Palik16兲 and the
thickness of the various layers are given in Table 1.
Since the coupler performances are mainly determined by the decoupling length LC and the coupling
factor FC, these two parameters were calculated for
various values of the grating modulation depth as a
function of the thickness of the passivation silicon
dioxide layer.
The decoupling length LC is plotted in Fig. 2. The
length decreases when the modulation depth increases, as the grating becomes more efficient, and it
varies periodically with the silicon dioxide thickness.
It can be confirmed from Fig. 2 that the period is
determined by the optical path of the light between
1 November 2000 兾 Vol. 39, No. 31 兾 APPLIED OPTICS
5775
Fig. 4. Experimental setup. DFB, distributed feedback.
Fig. 2. Characteristic length LC of coupler versus silicon dioxide
thickness for various etching depth of grating in silicon.
the grating and the mirror. The calculated period is
0.477 ␮m, which is equal to ␭兾2n cos ⌰r, with ␭ ⫽ 1.3
␮m, n ⫽ 1.45, and ⌰r ⫽ 20°.
The corresponding coupling factor is plotted in Fig.
3. Sharp resonances are observed for thickness values of the silicon oxide layer corresponding to a ␲
phase shift for the reflected light. Between these
resonances the coupling factor is close to 1 over a
large range of the passivation layer thickness.
4. Experimental Results
The experimental setup is represented in Fig. 4.
The light source is a distributed-feedback monomode
laser diode from Hitachi, emitting at ␭ ⫽ 1.3 ␮m. Its
operating temperature is fixed by a Peltier device. A
microscope objective and several lenses with different
focal lengths allow us to get Gaussian beams whose
waists can be varied from 14 to 48 ␮m. Micropositioning elements are used to adjust the beam waists
on the input coupler. An IR camera is used to locate
the incident beam on the input coupler and to record
the decoupled light intensity emerging from the output coupler. Photodetectors measure the light in-
Fig. 3. Coupling factor FC versus silicon dioxide thickness for
various etching depth of grating in silicon.
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APPLIED OPTICS 兾 Vol. 39, No. 31 兾 1 November 2000
tensities reflected on the input coupler and decoupled
by the output grating.
The light power that is decoupled from the
waveguide decreases exponentially along the grating
with the characteristic length LC. For the sample
under consideration, with a grating etched in silicon
30 nm deep, measurements performed with the IR
camera give a value LC ⫽ 23 ␮m. This result is
coherent with the calculated value for the passivation
silica layer thickness of 0.46 ␮m 共Fig. 2兲. The coupling factor is then equal to 0.97 共Fig. 3兲, which allows
for a coupling efficiency of 78% for an optimum beamwaist value of 30 ␮m.
The reflected power on the input coupler was measured as a function of the incidence angle for various
beam-waist values. Results are plotted in Fig. 5.
The difference between the power measured off resonance and at resonance corresponds to the injected
light power. Once it is normalized to the incident
power, it gives the coupling efficiency. The experimental values ␩exp are compared with the theoretical
ones in Table 2.
The maximum coupling efficiency is theoretically
obtained for a 30-␮m waist, and the experimental
results are in qualitative agreement with the calculated ones. Nevertheless, the measured values are
smaller than the theoretical ones, in particular for
Fig. 5. Measured values of device reflectivity as a function of
incidence angle for various incident beam-waist values.
Table 2. Comparison of the Experimental and Theoretical Values of the
Coupling Efficiency for Various Beam Waists
Waist w0 共␮m兲
Measured Coupling
Efficiency ␩exp 共%兲
Theoretical Coupling
Efficiency ␩th 共%兲
48
24
21
17
14
51
57
36
28
28
73.1
76.9
75.5
71.9
67.6
2.
3.
4.
5.
the smallest waists. These results are consistent
with the limitations of the one-dimensional model of
divergence we used. Stronger diverging beams 共as
issued from an optical fiber兲 will impose a twodimensional model. Further optimization of the
coupler realization could lead to coupling efficiencies
still closer to the theoretical limit, which is ⬃80%.
The curves in Fig. 5 also show that the angular
acceptance of such a coupler is ⬃1 deg, which permits
easy alignment.
6.
7.
8.
9.
5. Conclusion
We have demonstrated that high coupling efficiency
is achieved by addition of a mirror above a conventional grating coupler. Nearly 60% of the incident
light has been coupled into a sub-micrometer-thick
SOI waveguide, with a strongly angular beam-spread
Gaussian beam. The experimental results are coherent with the calculations. The latter take into
account the case of strongly angular beam-spread
Gaussian beams and predict, with the employed onedimensional model of divergence, coupling efficiencies as great as 80%.
The authors acknowledge the contribution of B.
Abécassis and C. Gousset for realization of the device.
This study was supported by Centre National
d’Etudes des Télécommunications—France Telecom
contract 931B140.
10.
11.
12.
13.
14.
15.
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