Abstract: Microring resonators are an interesting device to build integrated optical interconnects, but their asymmetric loss behavior could limit the scalability of classical optical interconnects. We present new interconnects able to increase scalability with limited complexity

Bianco, Andrea

Cuda, Davide

Garrich, M.

Gaudino, Roberto

Gavilanes, G.

Giaccone, Paolo

Neri, Fabio

English

A. Bianco

D. Cuda

M. Garrich

R. Gaudino

G. Gavilanes

P. Giaccone

F. Neri

Crossref

Optical interconnection architectures based on microring resonators

PORTO Publications Open Repository TOrino

Optical Interconnection Architectures based on Microring Resonators
A. Bianco1, D. Cuda1, M. Garrich2, R. Gaudino1, G. Gavilanes1, P. Giaccone1, F. Neri1
1: Politecnico di Torino, B ﬁrstname.lastname@polito.it – 2: Universitat Polite`cnica de Catalunya
Abstract: Microring resonators are an interesting de-
vice to build integrated optical interconnects, but their
asymmetric loss behavior could limit the scalability of
classical optical interconnects. We present new inter-
connects able to increase scalability with limited com-
plexity.
Keywords: optical interconnects, microring resonators
1. Introduction
The need to carry petabytes of information in high-
performance computing systems, and recent break-
throughs in CMOS-compatible silicon photonic are
boosting the penetration of optical technologies into in-
terconnection systems. Promising for optical switch-
ing are silicon microring resonators, small foot-print de-
vices that have been used for ﬁltering, delaying or mod-
ulating optical signals. In this papera we ﬁrst describe
some Switching Elements (SE) based on microring res-
onators. Second, we highlight scalability and com-
plexity limitations of two classical interconnects using
microring-based SEs as building blocks. Finally, we
propose new hybrid architectures to improve the scala-
bility of microring-based optical interconnects.
2. Microring-based switching elements
Fig 1a illustrates a simple structure of a 1x2 microring-
based SE (called 1B-SE). Optical signals entering the
input port can be deﬂected either to the drop port, when
the ring is properly tuned to the input signal wavelength
(for instance by carrier injection [1]), or to the through
port in the normal non-tuned ring state. This 1B-SE
presents an asymmetric behavior: experimental mea-
surements [2] show that input signals coupled into the
ring suffer larger power losses (due to the propagation
inside the ring and the ring-waveguide coupling) than
signals routed to the through port. This will also lead
to a larger coherent (in-band) crosstalk cumulation in
an optical interconnect made of several SEs. Fig. 1b
depicts an implementation of a basic 2x2 SE (called
2B-SE) based on two 1B-SEs jointly controlled to pro-
vide two switching states: the bar state (in1→out1,
in2→out2) and the cross state (in1→out2, in2→out1).
Each ring deﬂects (lets pass) the corresponding optical
input signal to the drop (through) port of the respective
1B-SE when the 2B-SE is conﬁgured in the bar (cross)
state. Hence, 2B-SE exhibits an asymmetric behavior
too: power losses are higher in the bar state, whereas
they are negligible in the cross state [3]. In general,
we say that microring-based SEs present a High-Loss
State (HLS) and a Low-Loss State (LLS). Fig. 1c shows
the newly proposed 2x2 Mirrored-SE (called 2M-SE).
By cross-connecting input ports, the 2M-SE swaps HLS
and LSS with respect to 2B-SE: the bar conﬁguration,
aThis work was partially supported by the BONE project, a Net-
work of Excellence funded by the European Commission within the 7th
Framework Programme.
corresponding to (in1→out1, in2→out2) is now real-
ized by setting up the internal 2x2 SE in the cross
state, whereas the cross state (in1→out2, in2→out1)
is achieved with an internal bar state.
(a) 1x2 Basic SE (b) 2x2 Basic SE (c) 2x2 Mirrored SE
Fig. 1: Elementary microring-based switching elements
3. Interconnection Architectures
We now study larger (i.e., with more ports) intercon-
nects built as compositions of the above described SEs.
For maximum scalability, we aim at minimizing the max-
imum number of SEs in HLS (either the drop port for a
1B-SE, the bar-state for a 2B-SE, or the cross-state for
a 2M-SE) crossed by optical signals for every possible
input/output connection. We denote by XC the max-
imum number of SEs conﬁgured in HLS that an input
signal must cross in the optical interconnect.
Fig. 2a shows a 4x4 crossbar, based on 1B-SEs; col-
umn waveguides are the inputs and row waveguides
are the outputs. The crossbar exhibits the best scalabil-
ity performance, since each input can be connected to
any output crossing a single HLS SE (hence XC = 1).
Despite its optimal scalability performance, the cross-
bar shows a high complexity, assessed in terms of num-
ber of microrings, equal to N2. As a consequence, it
exhibits a large footprint and requires controlling a large
number of SEs.
(a) 4x4 microring-based crossbar (b) 8x8 Benes network
Fig. 2: Interconnection networks considered
The deﬁnition of non-blocking networks less complex
than the crossbar naturally leads to multistage inter-
connects, among which we consider here the Benes
network. Benes networks exhibit several advantages,
such as a straightforward recursive construction rule,
a simple routing and re-arranging algorithm and es-
pecially, a complexity (number of crosspoints) asymp-
totically close to the minimum. Fig. 2b shows a 8x8
Benes network. A N × N Benes network permits any
one-to-one interconnection between inputs and outputs
using a number of stages (columns of SEs) equal to
S = 2 log2 N − 1, each stage including N/2 2x2 SEs.
Hence, the complexity of a N×N Benes network scales
as Θ(2N log2 N), as each 2x2 SE includes 2 rings. De-
spite this complexity reduction, XC = S for worst-case
9781-4244-3856-3/09/$25.00 ©2009 IEEE
Authorized licensed use limited to: Politecnico di Torino. Downloaded on November 9, 2009 at 12:09 from IEEE Xplore.  Restrictions apply. 
paths in a Benes network. Thus, classical multistage
architectures don’t scale to large port counts because
their physical impairments grow with the network depth
S.
(a) Mirrored architecture (b) Plane Selector
Fig. 3: Mirrored architecture and plane selector
To improve scalability of multistage networks (i.e., to
reduce XC) we present here the mirroring technique
and the new Hybrid Benes-Crossbar (HBC) architec-
ture. The main idea behind the mirroring technique
can be illustrated through Fig. 3a. Onto two differ-
ent spatial planes, we build two interconnection net-
works which are topologically indistinguishable. On
the normal plane we build an interconnection architec-
ture based on 2B-SEs, whereas on the mirrored plane
we deploy the same interconnection network exploiting
2M-SEs. All inputs connect to both planes by means of
the plane selector depicted in Fig. 3b (which requires
one extra HLS SE). Each output collects information
from the two planes by means of a coupler (at a negligi-
ble impairments cost with respect to a ring). Exploiting
the 2M-SE property of swapping HLS and LLS, all the
input/output connections that would cross K ≥ S/2+ 1
HLS 2B-SEs in the normal plane can now be routed
on the mirrored plane, actually crossing (S − K) HLS
2M-SEs. Thus, by using the mirroring technique, XC
reduces to S/2+1 instead of S as in the original single-
plane architectures.
The HBC solution instead combines the crossbar
and the Benes network, and is based on the obser-
vation that a N × N Benes network is made of two
edge stages of SEs connected to two (N/2) × (N/2)
non-blocking networks in the middle stage. These
non-blocking networks are usually Benes networks as
well. However, being crossbars non-blocking and opti-
mal in terms of scalability, they can be employed in the
middle stage of a multistage network and then inter-
connected according to the Benes pattern using edge
stages composed by 2x2 SEs. In Fig. 4, four 4x4 cross-
bars are used as middle stages to build a 16x16 in-
terconnect. These crossbars are ﬁrstly employed as
building blocks for two 8x8 networks (shaded in Fig. 4),
which are then interconnected to build the 16x16 net-
work. The HBC complexity CHBC(N,m) scales as
Θ
(
2N log2
N
m
+ Nm
)
, where 2 ≤ m ≤ N is the size
of the inner crossbars used in the middle stage (m = 4
in Fig. 4). Note that, when m = 2 or m = N , the
HBC architecture degenerates into a Benes or a cross-
bar network, respectively. Hence, differently from a
Benes network, the HBC architecture is always feasi-
ble (by adapting m to the maximum acceptable XC),
and presents a constructive rule depending on N and
XC: m can be derived from XC ≤ 2 log2 Nm +1. When
mirroring is applied to the HBC architecture (M-HBC),
it is possible to show that mM-HBC = 2m2HBC/N with re-
spect to the single plane solution for a given value of
XC, and that its complexity scales as CM-HBC(N,m) =
Θ
(
2
(
CHBC(N, 2
m2
N
) + N
))
.
Fig. 4: Hybrid Benes-Crossbar (HBC) network
102
103
104
105
24 25 26 27 28 29 210 211
Co
m
pl
ex
ity
 (#
of 
rin
gs
)
N (# of ports)
XBAR (XC=1)
HBC XC=6
M-HBC XC=6
HBC XC=12
M-HBC XC=12
Benes XC=12
M-Benes XC=12
104
105
106
107
108
210 211 212 213 214 215 216
Fig. 5: Complexity and scalability for crossbar, Benes and
hybrid Benes-crossbar networks
4. Complexity and scalability
Fig. 5 shows the complexity for the crossbar, the Benes
and the HBC networks varying their number of in-
put/output ports N . We considered both single plane
(identiﬁed by the continuous lines) and mirrored ar-
chitectures (identiﬁed by the “M-” preﬁxes and by the
dashed lines). In addition, we consider XC = 6 and
XC = 12 to illustrate two feasibility conditions charac-
terized by a maximum of allowed number of crossed
HLS SEs which is either quite low or rather high, re-
spectively. m in HBC networks is chosen as to achieve
the given XC. The larger ﬁgure refers to “small” in-
terconnects (N ranging from 24 to 211), whereas the
smaller ﬁgure refers to “large” systems (N ranging from
210 to 216). The Benes network (only shown for XC =
12) exhibits the lower complexity but also the poorest
scalability performance. Exploiting mirroring, the maxi-
mum size of a feasible Benes increases from N to N2
for a given XC. The HBC architecture is always fea-
sible; indeed, appropriately dimensioning m, XC can
be upper bounded to 2 log2
N
m
+ 1. Regarding HBC,
mirrored solutions lead to larger complexity for smaller
interconnects, whereas mirroring becomes complexity-
advantageous when the interconnect size increases.
Fig. 5 shows only the M-HBC architectures compliant
with the feasibility condition mM-HBC ≥ 2. Note that, the
smaller XC, the smaller the size of the HBC intercon-
nect for which mirroring becomes complexity-effective.
References
1 C. Li, A.W. Poon, CLEO 2007, Paper JThD115
2 B.G. Lee et al., IEEE Photonic T. L., Vol. 20, Iss. 10, pp.
767-769, May 2008
3 B.G. Lee et al., ECOC 2008, Paper Tu.3.C.3
9781-4244-3856-3/09/$25.00 ©2009 IEEE
Authorized licensed use limited to: Politecnico di Torino. Downloaded on November 9, 2009 at 12:09 from IEEE Xplore.  Restrictions apply. 


IEEE Authorized licensed use limited to: Politecnico di Torino. Downloaded on

Optical Interconnection Architectures based on Microring Resonators

BIANCO, ANDREA

CUDA, DAVIDE

GARRICH ALABARCE, MIQUEL

GAUDINO, ROBERTO

GAVILANES CASTILLO, GUIDO ALEJANDRO

GIACCONE, PAOLO

NERI, Fabio

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

05 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEOptical Interconnection Architectures based on Microring Resonators / A. BIANCO; D. CUDA; M. GARRICH; R.GAUDINO; G. GAVILANES; P. GIACCONE; F. NERI. - STAMPA. - (2009), pp. 1-2. ((Intervento presentato al convegnoPhotonics in Switching (PS 2009) tenutosi a Pisa, Italy nel Sept. 2009.OriginalOptical Interconnection Architectures based on Microring ResonatorsPublisher:PublishedDOI:10.1109/PS.2009.5307809Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2285600 since:IEEEOptical Interconnection Architectures based on Microring ResonatorsA. Bianco1, D. Cuda1, M. Garrich2, R. Gaudino1, G. Gavilanes1, P. Giaccone1, F. Neri11: Politecnico di Torino, B firstname.lastname@polito.it – 2: Universitat Polite`cnica de CatalunyaAbstract: Microring resonators are an interesting de-vice to build integrated optical interconnects, but theirasymmetric loss behavior could limit the scalability ofclassical optical interconnects. We present new inter-connects able to increase scalability with limited com-plexity.Keywords: optical interconnects, microring resonators1. IntroductionThe need to carry petabytes of information in high-performance computing systems, and recent break-throughs in CMOS-compatible silicon photonic areboosting the penetration of optical technologies into in-terconnection systems. Promising for optical switch-ing are silicon microring resonators, small foot-print de-vices that have been used for filtering, delaying or mod-ulating optical signals. In this papera we first describesome Switching Elements (SE) based on microring res-onators. Second, we highlight scalability and com-plexity limitations of two classical interconnects usingmicroring-based SEs as building blocks. Finally, wepropose new hybrid architectures to improve the scala-bility of microring-based optical interconnects.2. Microring-based switching elementsFig 1a illustrates a simple structure of a 1x2 microring-based SE (called 1B-SE). Optical signals entering theinput port can be deflected either to the drop port, whenthe ring is properly tuned to the input signal wavelength(for instance by carrier injection [1]), or to the throughport in the normal non-tuned ring state. This 1B-SEpresents an asymmetric behavior: experimental mea-surements [2] show that input signals coupled into thering suffer larger power losses (due to the propagationinside the ring and the ring-waveguide coupling) thansignals routed to the through port. This will also leadto a larger coherent (in-band) crosstalk cumulation inan optical interconnect made of several SEs. Fig. 1bdepicts an implementation of a basic 2x2 SE (called2B-SE) based on two 1B-SEs jointly controlled to pro-vide two switching states: the bar state (in1→out1,in2→out2) and the cross state (in1→out2, in2→out1).Each ring deflects (lets pass) the corresponding opticalinput signal to the drop (through) port of the respective1B-SE when the 2B-SE is configured in the bar (cross)state. Hence, 2B-SE exhibits an asymmetric behaviortoo: power losses are higher in the bar state, whereasthey are negligible in the cross state [3]. In general,we say that microring-based SEs present a High-LossState (HLS) and a Low-Loss State (LLS). Fig. 1c showsthe newly proposed 2x2 Mirrored-SE (called 2M-SE).By cross-connecting input ports, the 2M-SE swaps HLSand LSS with respect to 2B-SE: the bar configuration,aThis work was partially supported by the BONE project, a Net-work of Excellence funded by the European Commission within the 7thFramework Programme.corresponding to (in1→out1, in2→out2) is now real-ized by setting up the internal 2x2 SE in the crossstate, whereas the cross state (in1→out2, in2→out1)is achieved with an internal bar state.(a) 1x2 Basic SE (b) 2x2 Basic SE (c) 2x2 Mirrored SEFig. 1: Elementary microring-based switching elements3. Interconnection ArchitecturesWe now study larger (i.e., with more ports) intercon-nects built as compositions of the above described SEs.For maximum scalability, we aim at minimizing the max-imum number of SEs in HLS (either the drop port for a1B-SE, the bar-state for a 2B-SE, or the cross-state fora 2M-SE) crossed by optical signals for every possibleinput/output connection. We denote by XC the max-imum number of SEs configured in HLS that an inputsignal must cross in the optical interconnect.Fig. 2a shows a 4x4 crossbar, based on 1B-SEs; col-umn waveguides are the inputs and row waveguidesare the outputs. The crossbar exhibits the best scalabil-ity performance, since each input can be connected toany output crossing a single HLS SE (hence XC = 1).Despite its optimal scalability performance, the cross-bar shows a high complexity, assessed in terms of num-ber of microrings, equal to N2. As a consequence, itexhibits a large footprint and requires controlling a largenumber of SEs.(a) 4x4 microring-based crossbar (b) 8x8 Benes networkFig. 2: Interconnection networks consideredThe definition of non-blocking networks less complexthan the crossbar naturally leads to multistage inter-connects, among which we consider here the Benesnetwork. Benes networks exhibit several advantages,such as a straightforward recursive construction rule,a simple routing and re-arranging algorithm and es-pecially, a complexity (number of crosspoints) asymp-totically close to the minimum. Fig. 2b shows a 8x8Benes network. A N × N Benes network permits anyone-to-one interconnection between inputs and outputsusing a number of stages (columns of SEs) equal toS = 2 log2 N − 1, each stage including N/2 2x2 SEs.Hence, the complexity of a N×N Benes network scalesas Θ(2N log2 N), as each 2x2 SE includes 2 rings. De-spite this complexity reduction, XC = S for worst-case9781-4244-3856-3/09/$25.00 ©2009 IEEEAuthorized licensed use limited to: Politecnico di Torino. Downloaded on November 9, 2009 at 12:09 from IEEE Xplore.  Restrictions apply. paths in a Benes network. Thus, classical multistagearchitectures don’t scale to large port counts becausetheir physical impairments grow with the network depthS.(a) Mirrored architecture (b) Plane SelectorFig. 3: Mirrored architecture and plane selectorTo improve scalability of multistage networks (i.e., toreduce XC) we present here the mirroring techniqueand the new Hybrid Benes-Crossbar (HBC) architec-ture. The main idea behind the mirroring techniquecan be illustrated through Fig. 3a. Onto two differ-ent spatial planes, we build two interconnection net-works which are topologically indistinguishable. Onthe normal plane we build an interconnection architec-ture based on 2B-SEs, whereas on the mirrored planewe deploy the same interconnection network exploiting2M-SEs. All inputs connect to both planes by means ofthe plane selector depicted in Fig. 3b (which requiresone extra HLS SE). Each output collects informationfrom the two planes by means of a coupler (at a negligi-ble impairments cost with respect to a ring). Exploitingthe 2M-SE property of swapping HLS and LLS, all theinput/output connections that would cross K ≥ S/2+ 1HLS 2B-SEs in the normal plane can now be routedon the mirrored plane, actually crossing (S − K) HLS2M-SEs. Thus, by using the mirroring technique, XCreduces to S/2+1 instead of S as in the original single-plane architectures.The HBC solution instead combines the crossbarand the Benes network, and is based on the obser-vation that a N × N Benes network is made of twoedge stages of SEs connected to two (N/2) × (N/2)non-blocking networks in the middle stage. Thesenon-blocking networks are usually Benes networks aswell. However, being crossbars non-blocking and opti-mal in terms of scalability, they can be employed in themiddle stage of a multistage network and then inter-connected according to the Benes pattern using edgestages composed by 2x2 SEs. In Fig. 4, four 4x4 cross-bars are used as middle stages to build a 16x16 in-terconnect. These crossbars are firstly employed asbuilding blocks for two 8x8 networks (shaded in Fig. 4),which are then interconnected to build the 16x16 net-work. The HBC complexity CHBC(N,m) scales asΘ(2N log2Nm+ Nm), where 2 ≤ m ≤ N is the sizeof the inner crossbars used in the middle stage (m = 4in Fig. 4). Note that, when m = 2 or m = N , theHBC architecture degenerates into a Benes or a cross-bar network, respectively. Hence, differently from aBenes network, the HBC architecture is always feasi-ble (by adapting m to the maximum acceptable XC),and presents a constructive rule depending on N andXC: m can be derived from XC ≤ 2 log2 Nm +1. Whenmirroring is applied to the HBC architecture (M-HBC),it is possible to show that mM-HBC = 2m2HBC/N with re-spect to the single plane solution for a given value ofXC, and that its complexity scales as CM-HBC(N,m) =Θ(2(CHBC(N, 2m2N) + N)).Fig. 4: Hybrid Benes-Crossbar (HBC) network10210310410524 25 26 27 28 29 210 211Complexity (#of rings)N (# of ports)XBAR (XC=1)HBC XC=6M-HBC XC=6HBC XC=12M-HBC XC=12Benes XC=12M-Benes XC=12104105106107108210 211 212 213 214 215 216Fig. 5: Complexity and scalability for crossbar, Benes andhybrid Benes-crossbar networks4. Complexity and scalabilityFig. 5 shows the complexity for the crossbar, the Benesand the HBC networks varying their number of in-put/output ports N . We considered both single plane(identified by the continuous lines) and mirrored ar-chitectures (identified by the “M-” prefixes and by thedashed lines). In addition, we consider XC = 6 andXC = 12 to illustrate two feasibility conditions charac-terized by a maximum of allowed number of crossedHLS SEs which is either quite low or rather high, re-spectively. m in HBC networks is chosen as to achievethe given XC. The larger figure refers to “small” in-terconnects (N ranging from 24 to 211), whereas thesmaller figure refers to “large” systems (N ranging from210 to 216). The Benes network (only shown for XC =12) exhibits the lower complexity but also the poorestscalability performance. Exploiting mirroring, the maxi-mum size of a feasible Benes increases from N to N2for a given XC. The HBC architecture is always fea-sible; indeed, appropriately dimensioning m, XC canbe upper bounded to 2 log2Nm+ 1. Regarding HBC,mirrored solutions lead to larger complexity for smallerinterconnects, whereas mirroring becomes complexity-advantageous when the interconnect size increases.Fig. 5 shows only the M-HBC architectures compliantwith the feasibility condition mM-HBC ≥ 2. Note that, thesmaller XC, the smaller the size of the HBC intercon-nect for which mirroring becomes complexity-effective.References1 C. Li, A.W. Poon, CLEO 2007, Paper JThD1152 B.G. Lee et al., IEEE Photonic T. L., Vol. 20, Iss. 10, pp.767-769, May 20083 B.G. Lee et al., ECOC 2008, Paper Tu.3.C.39781-4244-3856-3/09/$25.00 ©2009 IEEEAuthorized licensed use limited to: Politecnico di Torino. Downloaded on November 9, 2009 at 12:09 from IEEE Xplore.  Restrictions apply. 

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.6294

Optical Interconnection Architectures based on Microring Resonators

Abstract

Similar works

Full text

Available Versions

Crossref

PORTO Publications Open Repository TOrino

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)