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http://dx.doi.org/10.1109/LPT.2015.2495230
http://hdl.handle.net/10251/79149
Institute of Electrical and Electronics Engineers (IEEE)
Brimont, ACJ.; Hu, X.; Cueff, S.; Rojo-Romeo, P.; Saint Girons, G.; Griol Barres, A.; Zanzi,
A.... (2016). Low-Loss and Compact Silicon Rib Waveguide Bends. IEEE Photonics
Technology Letters. 28(3):299-302. doi:10.1109/LPT.2015.2495230.
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Abstract—Waveguide bends support intrinsically leaky
propagation modes due to unavoidable radiation losses. It is
known that the losses of deep-etched/strip waveguide bends
increase inevitably for decreasing radius. Here, we theoretically
and experimentally demonstrate that this result is not directly
applicable to shallow-etched/rib waveguide bends. Indeed, we
show that the total losses caused by the bends reach a local
minimum value for a certain range of compact radii and rib
waveguide dimensions. Specifically, we predicted minimum
intrinsic losses <0.1 dB/90° turn within the range of 25-30µm bend
radii in a 220nm-thick and400nm-wide silicon rib waveguide with
70nm etching depth. This unexpected outcome, confirmed by
experimental evidence, is due to the opposite evolution of radiation
(bending) losses and losses caused by the coupling to lateral slab
modes (slab leakage) as a function of the bend radius, hence
creating an optimum loss region. This result may have important
implications for the design of compact and low-loss silicon
nanophotonic devices.
Index Terms—Integrated optics, silicon photonics, rib
waveguides, waveguide bends, optical design.
I. INTRODUCTION
OW-loss silicon waveguides, allowing efficient on-chip
dissemination of optical signals are the backbone of
silicon-based nanophotonics. Among the existing geometries,
rib waveguide architectures are usually chosen to leverage
industrial fabrication of advanced silicon based telecom and
datacom photonic integrated circuits (PICs) [1-2]. The reason
for this is that passive and active photonic components can
readily be patterned with a single shallow-etch step using
current complementary-metal-oxide-semiconductor (CMOS)
fabrication techniques. Indeed, a rib waveguide-based
interconnect layer decreases the complexity of the process by
ruling out potential fabrication dependent errors such as
alignment between strip/rib Si-photonic layers as well as the
extra-cost associated with additional lithography masks.
Typical rib waveguides consist of straight and bend sections
exhibiting three sources of losses:
Manuscript received XXX; revised XXX; accepted XXX. This work was
supported in part by the European STREP program “FP7-ICT-2013-11-
619456-SITOGA and “FP7-ICT-2012-10-318240 PhoxTroT”. Financial
support from TEC2012-38540 LEOMIS is also acknowledged.
A. Brimont, A. Griol, A. Zanzi and P. Sanchis are with the Nanophotonics
Technology Center, Universitat Politècnica de Valencia, Camino de Vera s/n
46022 Valencia, Spain (e-mail: abrimont@ntc.upv.es; agriol@ntc.upv.es;
anzan@ntc.upv.es; pabsanki@dcom.upv.es).
A) Propagation losses due to sidewall roughness and other
process/material dependent effects;
B) Slab leakage losses, produced by coupling to the lateral
slab and radius dependent;
C) Bending losses which are inherent to the bend and
radius dependent.
This is in contrast to strip (deep-etched) waveguides which
only suffer from two sources of losses, namely A (propagation
losses caused by sidewall roughness) and C (bending losses).
The aim of this paper is to demonstrate that the singular
refractive index distribution associated with the presence of the
slab in rib waveguides mitigates the bending losses in a certain
range of bend radii.
Although straight rib waveguide parameters are always
chosen to rule out slab leakage losses (B) by confining most of
the modal power in the ridge area, aggressive bending may
cause the confined light to leak into the slab. Additionally,
bending losses (C) rapidly increase as the bend radius becomes
smaller. Therefore, to prevent on-chip-losses from becoming
prohibitive, radii of about hundreds of microns are usually
chosen to achieve low-loss in rib waveguide bends [3]. As a
result, the footprint of integrated photonic devices featuring
these large radii rib waveguide bends may reach unacceptable
proportions for large scale PICs.
Fig. 1. Geometry of the curved rib waveguide (W = 0.4 µm, h = 0.07 µm and
t = 0.15 µm).
X. Hu, S. Cueff, P. Rojo-Romeo, G. Saint-Girons and R. Orobtchouk are
with the Institut des Nanotechnologies de Lyon (INL), CNRS UMR5270, 7
avenue Jean Capelle, INSA-Lyon, Villeurbanne 69621, France (e-mail:
xuan.hu@insa-lyon.fr; sebastien.cueff@ec-lyon.fr; pedro.rojo-romeo@ec-
lyon.fr; guillaume.saint-girons@ec-lyon.fr; regis.orobtchouk@insa-lyon.fr).
Low-loss and compact silicon rib waveguide
bends
Antoine Brimont, Xuan Hu, Sébastien Cueff, Pedro Rojo Romeo, Guillaume Saint Girons, Amadeu
Griol, Andrea Zanzi, Pablo Sanchis, Régis Orobtchouk
*
L
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It has been reported that losses can be mitigated by increasing
the etching depth in the outer side of the curvature [4].
However, such a solution requires extra dedicated technological
steps, which eventually increases the complexity and cost of the
whole fabrication process.
In this paper, we theoretically and experimentally
demonstrate that low loss rib waveguide bends can be obtained
for a specific range of bend radii without adding more
complexity to standard waveguide fabrication processes.
In the following, we present a theoretical analysis confirmed
by experimental evidence. We show that losses lower than 0.1
dB/90° turn (excluding propagation losses due to sidewall
roughness and/or process/material dependent effects) can be
obtained for a range of bend radius as small as 25 µm to 30 µm.
II. THEORY AND MODELING
Modeling of the bends is performed with a home-made finite
difference full-vectorial mode solver in cylindrical coordinates
[5]. Transparent boundaries conditions are used to accurately
calculate the leakage and bending losses introduced by the
curvature [6]. Importantly, note that the following calculations
have been performed excluding the propagation losses due to
sidewall roughness or other process/material dependent effects.
The geometry of the rib waveguide and refractive indices
used are depicted on Fig. 1. Width ,W, thickness of Si layer, t,
and height, h, of the rib waveguide are respectively 0.4, 0.15
and 0.07 µm. The refractive indices of Si and SiO
2
are set to
3.4758 and 1.4442 at λ= 1.55 µm. Calculated variations of the
losses (leakage + bending) of the quasi-TE fundamental mode
versus the bend radius is plotted in Fig. 2.
Interestingly, we observe two regimes of low-loss (<0.1 dB):
one for large bend radius (r > 200µm), and a second one for
small radius of about 25 µm. This atypical behavior implies that
one can design waveguide bends with both a small radius and
low losses.
Fig. 2. Evolution of the radiation losses (dB/90°turn) versus the radius (µm)
for the quasi-TE fundamental mode at λ = 1.55 µm.
As shown in fig. 3, the regime of low-loss reduction for small
radius occurs similarly for a wide range of waveguide widths
and heights. Interestingly, the minimum loss value (0.09
dB/90ºturn) for a radius of about 25 µm obtained for the target
waveguide geometry (70 nm etch and 400 nm waveguide
width) is a local minimum among the parameter scan range.
Fig. 3 a) Evolution of the bend radius for minimum loss and b) lowest bend loss
versus waveguide width (w) an height (h)
Radiation losses of a rib waveguide bend can be explained
via the well-known conformal mapping transformation, in
which the wave propagation equation in cylindrical coordinates
is approximated by that of a straight waveguide in Cartesian
coordinates [7-8]. The results of this conformal transformation
induce modifications in the refractive indices of the straight rib
waveguide, as reported in Fig. 4. a). As the refractive indices of
the materials increase with r, there is a threshold value r
3
above
which the effective index n
eff
of the propagating mode becomes
lower than the refractive index of the cladding. In that case, the
evanescent part of the mode becomes propagative and
introduces bending losses, as illustrated by the green arrow in
Fig. 4. b). One can notice that when the bend radius decreases,
the exponential variation of the refractive index with r implies
a faster reduction for the threshold value r
3
than r
2
, hence
inexorably increasing bending losses in dB/unit length, just as
what happens in strip waveguide bends.
Fig. 4. a) Equivalent refractive index profile (n) of a rib waveguide bend versus
radius (r) and b) schematic representation of the sources of losses in a rib bend
waveguide. Namely, bending losses (Green arrow pointing towards the outer
part of the bend, higher r values) and leakage losses produced by coupling to
the slab mode (yellow arrows). Mode profiles for c) 20, d) 30 e) 50 and f) 100
µm radii. Respective theoretical losses are 1.44, 0.0942, 0.151 and 0.299 dB/90º
bend. Modal asymmetries can be observed for more compact bend radii (20 and
30 µm).
However, it turns out that, in contrast to strip geometries, rib
waveguide bends exhibit an additional source of losses
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produced by the coupling of the mode to the lateral Si slab
(yellow arrows in Fig. 4 b)). This effect has been used for the
rejection of higher order modes in straight rib waveguides [9-
11]. In the case of a rib waveguide bend, the lateral coupling to
the slab is not symmetric: in the inner part of the bend, the
refractive index of the slab decreases, while in the outer part of
the bend the refractive index of the slab increases.
The asymmetry of the refractive index causes the maximum
field value of the mode profile to move towards the inner part
of the bend (towards the left side, Fig 4a)), therefore reducing
the radiation (bending losses) produced by the r
3
threshold
value. Moreover, the same asymmetry shifts the mode upwards,
hence contributing to further decrease losses by reducing the
coupling to the slab (leakage losses). This shift was also
observed by D. Dai and all [12] for high order modes without
any physical interpretation. Pictures of the simulated mode
profiles in bends with radii of 20, 30, 50 and 100 µm are
respectively shown in Fig. 3. c), d), e) and f).
Therefore, in contrast to their strip counterparts, rib
waveguide bends exhibit additional internal loss compensation
mechanisms. Furthermore, for a 90° turn, decreasing the radius
of curvature also implies shortening the total length (by a factor
πr/2) which reduces the total losses per bend due to the
shortened arc length. According to our numerical modeling, in
the range of curvature between 25 µm and 100 µm, all of the
above mentioned effects concur to reduce the total net loss
when the curvature is decreased.
III. EXPERIMENT
To confirm our theoretical results, we measured the bend losses
using the photonic test structures pictured in Fig.5, for different
bend radii (20, 30, 50 and 100 µm). In order to accurately
measure only bending (B) and leakage loss (C) contributions
within the bend losses, the input waveguide is split into two
arms with identical lengths of N.π.R/2. The upper output arm
contains the bends and its output power is normalized by that of
the lower arm, in order to eliminate the propagation losses
produced by sidewall roughness. This is to match our
theoretical modeling which does not include the losses due to
sidewall roughness and process/material dependent issues.
Details on the measurement method are given in [13].
Fig. 5 Silicon photonic test structures used for loss measurement of the rib
waveguide bends.
The structures have been fabricated on standard Silicon-on-
insulator (SOI) samples with a top 220 nm thick silicon layer
and a buried oxide layer (BOX) thickness of 2 µm. Silicon
waveguides were fabricated with electron beam lithography
(RAITH 150) and inductively coupled plasma-reactive ion
etching (ICP-RIE). The etch depth is 70 nm for both
waveguides and grating couplers, leaving a 150 nm thick slab.
The shallow-etched passive silicon chip is then covered with
700 nm silicon oxide using plasma-enhanced chemical vapor
deposition (PECVD) at 400ºC (Centura P5200). Experiments
were performed using a set of optical components composed of
N = 0, 16 or 32 90°-turn bends.
Fig. 6. Spectral responses of the different photonic test structures consisting of
0, 16 and 32 90° bends with respective radii of a) 20, b) 30, c) 50 and b) 100
µm.
Spectral responses of the 12 (3 test structures per bend
radius) optical test structures are given in Fig. 6 for curvature
radii of 20, 30, 50 and 100 µm. In order to extract the loss per
90º bend, a least-square linear regression versus the number of
90° turns is performed wavelength by wavelength using a
tunable laser (SANTEC TSL 210-F). Linear regression also
gives the accuracy of the measurements. The evolution of the
losses versus wavelength is plotted on Fig. 7. The bend losses
are approximately constant in the range of wavelength between
1540 to 1580 nm and equal to 0.343±0.154, 0.103±0.044,
0.157±0.0098, and 0.295±0.0021 dB/90° turn at 1.55µm for
curvature radii of 20, 30, 50 and 100 µm, respectively. Fig.8
shows the evolution of the loss per bend in a range of bend radii
between 15 and 100 µm. There is a very good agreement
between theory and measurement, without any fit parameters.
This is a clear demonstration of a low-loss regime for small
radius rib-waveguide bends.
We can notice that the measurement errors increase as the
radius decreases. This may be explained by the mode profile
mismatch at the transition between straight and bent
waveguides. Indeed, the differences in mode shape and
effective indices induce additional losses, back reflections and
interferences and hence produce oscillations in the spectral
response of the device (see Fig. 6 a)).
The deviation observed for a bend radius of 20 µm was
expected and can be explained as follows: we have considered
in our modeling a perfectly smooth waveguide (i.e. no sidewall
roughness) experiencing only the losses produced inherently by
the bending and the coupling to the slab mode. Yet again, in our
measurements, we have ruled out the propagation losses
produced by the sidewall roughness and other process/material
dependent effect by normalizing the output spectrum of rib
waveguide bends by a straight rib waveguide with the same
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length. This normalization has been performed assuming the
sidewall roughness similarly affects the losses of both straight
waveguide and waveguide bends. Our assumption is confirmed
experimentally for bend radii ranging from 30 µm to 100 µm
since a very good agreement between theoretical data and
experimental results can be observed.
However, such a normalization assumes the modal distortion
produced by the bending is small enough so that the optical
modes associated with both geometries interact similarly with
the sidewall roughness.
Fig. 7. Evolution of the bend losses versus wavelength for radii of a) 20, b) 30, c) 50 and
d) 100 µm.
Fig. 8.Evolution of the loss per bend versus the bend radius at 1.55 µm
wavelength.
Here, for smaller radii (< 20 µm), the modal distortion resulting
from this more aggressive bending increases the interaction of
the high field intensity region with the sidewall roughness
eventually causing the model to become less accurate. In other
words, the spectral normalization of the bent waveguide output
by the response of a straight waveguide is less accurate in that
range.
In conclusion, we have demonstrated that an optimal value
of the bend radius for rib waveguides, allowing low losses and
small footprint, can be obtained for the fundamental quasi-TE
mode in a wide range of waveguide widths and heights. A
physical interpretation based on the evolution of the net losses
versus radius, as well as the competition between radiation
losses and losses caused by coupling to the lateral slab has been
given. These results offer a simple solution to design compact
and low-loss nanophotonic silicon rib waveguide bends without
altering the fabrication process.
ACKNOWLEDGMENT
We thank NTC-UPVLC’s clean room staff, T. Ivanova, J.
Hurtado, L. Bellières, N. Sánchez and R. Bueno for the
fabrication of the samples.
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