Auto-routing algorithm for field-programmable photonic gate arrays

AITOR LÓPEZ,1,* DANIEL PÉREZ,1,2

PROMETHEUS DASMAHAPATRA,1,2 AND

JOSÉ CAPMANY1,2

1ITEAM Research Institute, Universitat Politècnica de València, Camino de Vera s/n 46022 Valencia, Spain 2iPronics Programmable Photonics S.L., Camino de Vera s/n 46022 Valencia, Spain *ailoher@iteam.upv.es

Abstract: Programmable multipurpose photonic integrated circuits require software routines to make use of their flexible operation as desired. In this work, we propose and demonstrate the use of a modified tree-search algorithm to automatically determine the optimum optical path in a field-programmable photonic gate array (FPPGA), based on end-user specifications, circuit architecture and imperfections in the realized FPPGA arising, for example, from fabrication variations. In such a scenario, the proposed algorithm only requires the hardware topology and the location of the connections of the FPPGA defining the optical path to be programmed. The routine is able to optimize the path over multiple and competing objectives like the overall length, accumulated loss and power consumption. In addition, should any region of the circuit suffer from any potential damage that may affect the device performance, this algorithm is also able to provide basic self-healing and fault-tolerance capabilities by supplying alternative paths through the photonic arrangement.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Photonic Integration combines multiple optical components on a chip to enable optical signal processing while maintaining a low-form factor. It has mostly been utilized in the form of Application Specific Photonic Integrated Circuits (ASPICs), where each circuit is designed and optimized to perform a particular functionality. As with electronic integrated circuits, the non-recurring engineering costs including custom mask tooling, design hours, custom packaging and specific process developments reduce the cost effectiveness for moderate volume applications. Although Photonic Integrated Circuits (PICs) have been proven successful for a myriad of applications in the literature, only a few like transceivers and data centres have shown enough volume fabrication to compensate the cost overhead [1]. Similar to electronics, a solution leading to mass production and subsequent cost reduction for PIC manufacturing, multi-project wafers are fabrication runs where different designs from different users are combined on the same wafer providing cost sharing [2-4]. However, their time-to-market becomes limited by the design processes and by large development periods to minimum of 12-24 months per design-fab-packaging-test iteration, depending on the chip complexity [5].

In the quest to enable cost-effective and programmable photonic-driven solutions, field programmable photonic arrays (FPPGAs) have recently emerged as a new solution to achieve general-purpose functionality and flexible operation [6]. The design of such devices is based on a generic PIC hardware comprising a set of reconfigurable processing blocks and a core of photonic actuators and beamsplitters that are programmed by the user, enabling their use across a wide variety of optical signal processing functionalities [7,8]. The FPPGA core can be employed to program optical components such as optical splitters, combiners, couplers, routers, delay lines, optical filters, beamformer networks and multiport interferometers [7-9], as well as to route on-demand using High-performance Building Blocks (HPBBs). HPBBs are

components thto the circuit aby using ring

Very receintegration defactors, some power consuinterfacing duconfigurationmoderate numoperation calisuch arrangem

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ctionality lity filters e a few. w higher y several rtion loss, electrical

ontrol and ited to a automated tion when

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modulators nario, the olling the is highly

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labelled

working in d EF. The rst circuit

incorporates the formation of an optical resonator (in blue). This scenario requires an automated routine to build up the interconnection and the programmable waveguides for the structures programmed in the FPPGA core. To address this problem, we explore the use of auto-routing algorithms to find the optimum configuration of a waveguide mesh arrangement for different features. The reported solution, following our previous work done in [12], is inspired by the modification of Dijkstra’s algorithm [13], widely used in many different research fields such as IP traffic engineering [14], artificial intelligence [15] and even for classical FPGA routing [16-18]. In addition, we demonstrate that the use of the algorithm leads to unprecedented self-healing and fault-tolerant capabilities of the PIC, where given a set of damaged areas of the circuit, the algorithm is able to find alternative sub-optimal paths through the photonic arrangement. Before concluding the paper, we discuss about the application scenarios and constrains of the proposed solution.

2. Definitions of the photonic circuit and the method

Fig. 1 illustrates a hexagonal FPPGA core. This PIC performs two main tasks: First, it provides the dynamic connections between high-performance photonic building blocks connected to each optical port and the optical I/Os at the optical interface. Secondly, it enables the synthesis of optical delay lines, beamsplitters and combiners, and phase actuators by means of software programming each programmable unit cell or Tunable Basic Unit (TBU). When combined, these building blocks are employed to build-up more complex optical processing circuits. With the aim to enable the automatic reconfiguration and programming of each TBU to configure optical connections and delay lines, we apply a control routine inspired by shortest-path evaluation techniques. Before discussing the algorithm in more depth, we define first the key concepts in graph theory and their adaptation to waveguide mesh-based photonic integrated circuits.

• Graphs, the fundamental objects in graph theory, are systems of nodes connected in pairs by edges. In this work, the nodes are the physical optical ports of the TBUs and the edges represent the connections between the TBU ports.

• Weights are numerical values assigned to each graph edge. The overall weight of any path inside the graph (i.e., the route traversed with or without repeated nodes and consequently edges) will be given by the sum of the weights of the edges within such path. In this work, the weights are defined as the performance parameter to be optimized during the creation of the optical connection or delay line.

The fundaments of shortest-path evaluations consist of searching the shortest route between two nodes through a weighted graph with the purpose of finding the route that accumulates the least weight [19]. In addition, the proposed method should avoid a brute-force search of every possibility to ensure scalability. The method proposed in this work features a couple of differences with respect to the basic Dijkstra’s algorithm, the most common example in this family of algorithms.

Fig. 2 (a-c) illustrate the graphical representation of a 7-cell hexagonal mesh containing 30 TBUs. In this case, a balanced Mach-Zehnder interferometer (MZI) is used to form the TBU [7]. Each TBU has a phase actuator attached to each of its arms, allowing the independent tuning of both its power splitting ratio and phase, as shown in Fig. 2(d). Hence, by modifying each TBU configuration we can alter the full scattering matrix of the waveguide mesh arrangement, and therefore, allow the synthesis of a wide range of photonic structures. Each of its isolated optical nodes corresponds to an actual different input/output optical connection between TBUs.

In order to develop, apply and illustrate the performance of this auto-routing algorithm, we need to define and name our graph nodes (optical nodes), and edges (optical connections using TBUs). To do so, we name each cell and create an additional set of imaginary cells at the circuit perimeter, as illustrated in Fig. 2(a) by the dashed cells I1-I12 (where ‘I’ stands for ‘imaginary’). In addition, we name each inner vertex at each cell as v1-6, and each of the 30

TBU as HXX. port number,

With theobserved in Ftransmission This TD is ainsertion loss tunable coupl(BUD) [7]. Fpurposes, theparameter duritself the optimthis distributio

Fig. 2. (a) numbered frclockwise animaginary ceand green re(c) internal cfrom one noexperimentalPower consuimplementinarms.

After definpropagates thrport, as in claof additionalconsecutivelyelement. Secoif they force astates during ton running undestination povalues as give

Finally, we narespectively.

ese definitions,Fig. 2(c). Nexdistance (TD)

a weighted sum(IL), the powe

ler length and Fig. 2(d) summe weights can ring the optimimum path withon of weights

Graph representaom top to bottom nd hereinafter refeell (x={1, 2, …,12espectively, (b) noconnections of the ode to another. (dl figures of merit uumption, BUD: B

ng a TBU, whose

ning such distarough the rema

assical tree-seal constraints: y, as this is notondly, the pathsany of its constthe synthesis ontil a fixed nuort. Then, the en by equation

ame the edges a

, the representxt, in order to

to each edge m of the TBUer consumptionthe arc length

marizes severasimply add u

ization processh respect to an{ci}, as desired

TDxy = c1 · IL

ation of a 30 TBUand from left to r

erred to as C(/I)xv2}) in which the n

ode representation TBU where TD:

d) Illustration of under use in this w

Basic Unit Delay, phase imbalance

ance for every aining ones by rch algorithm First, light c

t physically pos are only disctituting TBUs

of any specific umber of TBUroutine selects(1).

as TDio, where

tation of the o apply the alg

connecting twU’s main figuren (Pc) and its bof the access

al of these FoMup to 1 and res. Hence, the ny combinationd:

+ c2 · BUL + c

U waveguide mesright. Graph nodesvy, where Cx or Ix

node is located. Twwhere vy denotes

Transmission distathe eight possibl

work as input for tBUL: Basic Unitis created by an i

TBU, a shorteaccumulating implementatio

cannot propagossible withouarded if they gto be (simultaninterferometri

U paths, defines the optimum

e i,o represent t

graph of a singorithm, we cwo optical nodes of merit (F

basic unit lengtwaveguides, aM for TBU H

reflect the impproposed algo

n of these attrib

c3 · Pc + …

sh. TBUs, actual s within each hexa represents the acwo light path exam

s its position insidtance stands for thle TDs of TBU the algorithm, whet Length. (e) Schindependent, therm

est path with theach TD prior

ons. However, gate through ut it being recigo through the neously) in twoc circuit. Inste

ed as an inputm path based o

the input and th

ngle TBU cancan define a wdes in the arraFoM), which cth (BUL) the suand the basic uH11. For normportance givenorithm is able tbutes by only

and imaginary ceagonal cell are numctual (x={1, 2, …mples are marked de of it (y={1, 2, e weight or cost toH11 along with ere IL: Insertion l

hematic example omal tuning of each

he input node ar to reaching deit is subject tothe same TBrculated by ansame node twoo different tran

ead, the algoritht argument, reaon the accumu

the output

n also be weight or angement. can be its um of the unit delay malization n to each to find by changing

(1)

ells are mbered

…,7}) or in blue …,6}), o travel several oss, Pc: of MZI h of its

as the root estination

o a couple BU twice n external o times or nsmission hm keeps aches the

ulated TD

A proposed pseudocode to achieve this task can be found below. As a preliminary step, we index all the TDs from our proposed graphs. This aids in implementing the aforementioned constraint whereby a path cannot traverse through a TBU twice consecutively, thus leading to greatly expedited process. The algorithm starts by creating the graph framework from this ordered list of nodes and TDs and by setting the accumulated distance from initial node to itself as zero and to all the others as infinity. From then on, a shortest path tree with the input port as root propagates through the remaining ones in the graph by accumulating each TD prior to reaching the destination port. Similar to original Dijkstra’s implementation, the paths that go through the same node more than one time during the process are discarded and the rest are stored inside the ‘paths’ variable. Once the destination port has been reached, the resulting path is stored in ‘pathsDest’ variable and the process keeps running until a fixed number of paths defined in ‘max_paths’ variable also arrives to the destination. A potential issue arising from this implementation is that the number of paths stored in ‘paths’ variable would increase exponentially after each iteration, leading to equally large computational times while dealing with the synthesis of larger delay lines. A recommended alternative to overcome such a problem consists on implementing the same protocol for both source and destination ports of the path to be synthesized and store each path emerging from the intersection of both branches in ‘pathsDest’ (provided that the same set of aforementioned constraints are also met), hence preventing the path trees from both nodes to expand to greater extents.

To demonstrate the behaviour, we implemented the algorithm in Python and apply it to several application cases, as described in the next section. We run all the experiments using a desktop, 4-core, 3.60 GHz processor.

requires initialNode, destNode, listOfTDs procedure findShortPath (initialNode, destNode, listOfTDs)

% initialNode: Initial node of the synthesized path % destNode: Destination node of the synthesized path % listOfTDs: set of TDs of each TBU in the graph (load architecture) set currentNode as initialNode set paths, pathsDest equal to empty list add currentNode inside paths % We now have a first path containing ‘currentNode’ set max_paths setNodes() % Mark all graph nodes unvisited and store them setDistances() % Set the accumulated distance to zero for the initial node and to

infinity for all the others while length(pathsDest) < max_paths do for path in paths currentNode = path[last] % We take the last element of ‘path’ TD(currentNode, prior TBU node), TD(currentNode, opposite TBU input node) = ∞ % To avoid backpropagation of light in next iteration for neighbour in neighbourList do % ‘neighbourList’ contains all nodes in the vicinity of ‘currentNode’

if TD(currentNode, neighbour) != ∞ accumulate TDs from currentNode to neighbour, make a copy of path and add neighbour inside it

if neighbour appears twice in path remove path from paths

if neighbour == destNode add {path, accumulated ID} inside pathsDest break

3. Results

In this section, we will demonstrate the performance of the auto-routing algorithm using two hexagonal waveguide meshes of different sizes: a 7-cell and an 18-cell configuration,

containing 30delay lines aapplication of

3.1 Synthes

In our first exTBUs; i.e., c1

vertices in thdifferent optisetting ‘max_we are rulingwith respect telapsed time in Fig. 3. In ppath between as discussed synthesis of ais not permitte

Table 1. Reoptimized

# I/O

1 I12v1 →

I1v4 → I

2 C1v1 →

C4v3 →

3 I10v6 →

I3v3 → I

4 I7v2 → I

I8v6 → I

5 C1v4 →

C2v2 →

Fig. 3. Synt

Secondly, those synthesknow in advaDue to fabricconditions im

0 and 81 TBUand optical cof our algorithm

is of optical d

xperiment, we c1 = c3 = 0, c2 =he graph (optimized optical

_paths’ to 1 to g out the possito other FoM.after nine inde

particular, note nodes C1v4 anat the end of

an optical looped both physic

esults obtainedwith respect to

I1v4 [I12v1,C

I12v1 [I1v4,C

C4v3

C1v1

I3v3 [I10v6,C

I10v6 [I3v3,C

I8v6 [I7v

I7v2 [I8v

C2v2

C1v4

thesis of optical de

we changed tized paths thatance the requircation induced

mplying that th

Us, respectivelyonnections in

m to the synthes

delay lines

consider the op= 1. In other wical nodes). Upaths (in bothstop the proce

ibility of findin The results cependent execu

how Fig.3(c) nd C2v2 (or vicf previous sec consisting of ally and by the

from the syntho the number of

Obt

C7v4,C7v5,C7v6,C

C1v1,C1v2,C3v5,C4

[C1v1,C1v2

[C4v3,C4v2

C6v3,C6v4,C7v1,C

C2v6,C2v1,C2v2,C4

v2,C5v5,C5v6,C5v1

v6,C3v3,C6v6,C4v3

[C1v4,C2v1,C2v6

[C2v2,C2v3,C2v4

elay lines #1 (a), #

the values of tt minimize powred driving powd phase errorse electrical po

y. First, we wisuch arrange

sis of optical in

ptimum path wwords, we try tUnder this assuh directions) iess as soon as ng other pathsan be found inutions of the aillustrates a cle

ce versa) couldction, the forw5 TBUs, as ba

e algorithm.

hesis of 5 differecrossed TBUs

ained path

C4v3,C4v2,C3v5,C

4v2,C4v3,C7v6,C7

2,C3v5,C4v2,C4v3

2,C3v5,C1v2,C1v1

C4v4,C4v5,C2v2,C

4v5,C4v4,C7v1,C6

1,C4v4,C4v3,C6v6

3,C4v4,C5v1,C5v6

6,C2v5,C2v4,C2v3

4,C2v5,C2v6,C2v1

3 (b) and #5 (c) fr

the coefficientswer consumptiower to set eachs, each TBU

ower required t

ill deal with thements. Afterwnterferometers.

with respect to tto find the shoumption, we in the waveguthe first path

s with the samn Table 1, tog

algorithm for eear example of

d be traversed tward propagatiackwards prop

ent delay lines ain a 30-TBU sm

C1v2,C1v1,I1v4]

7v5,C7v4,I12v1]

3]

1]

C2v1,C2v6,I3v3]

6v4,C6v3,I10v6]

6,C3v3,I8v6]

6,C5v5,I7v2]

3,C2v2]

1,C1v4]

rom Table 1 in a 30

s to c1 = c2 = on. Before starh individual Tis in a randoto set them to

he formation owards, we ex

the number of ortest path betwsimulated a to

uide mesh of 3is retrieved. T

me length but ogether with theeach path synthf a case where through C2v1, ion of light foagation inside

and interconnecmall waveguide m

# TBUs

Avdura

9 0

9 0

4 0

4 0

9 0

9 0

8 0

8 0

6 0

6 0

0-TBU waveguide

0, c3 = 1 to srting, we woul

TBU to cross/bom state under

cross or bar i

of optical xtend the

traversed ween two otal of 5 30 TBUs

Therefore, optimized e average hesis, and

a shorter however,

forces the the TBU

ctions mesh.

verage ation (s)

0.056

0.054

0.034

0.038

0.054

0.051

0.053

0.050

0.049

0.048

e mesh.

search for ld need to bar states. r passive is equally

random. Suchresponse of ecriterion to tillustrated in Fwe can obtainresistance– oflarge-scale wa

Fig. 4. Re-sto power con

Next, we overall IL of individual TBsign will be ppotential fabraverage IL of

Here we cself-healing oTo demonstraalternative pamalfunction (results in its lan overall IL indeed not so and 0.47 dB. 0.16 s. Owinmeshes can blocal impairm

Fig. 5. DemH10 (a), a sub

This auto-rousame time, le

h values have every phase athe same opticFig. 4. Comparn power consuf 45.08%, 30.1aveguide mesh

synthesis of opticansumption.

study the optf the optical roBU from a trupositive) with ication error a

f 0.15 with the can illustrate onor fault-toleranate this behavioath between no(which in realitlosses to be -2of 2.82 dB anfar away fromThe average eg to this featu

be sustained owments, very muc

monstration of self-b-optimum path ca

uting algorithmeading to the c

been obtainedctuator and Tcal ports as ering the power umption impro12% and 20.35h arrangements

al circuits from Fig

timization of oute, thus haviuncated Gaussi

mean 0.59 ans reported in [same standard ne of the main nt capabilities tor, Fig. 5 showodes C2v1 and ty can, for exa0 dB. After ap

nd 1.01 dB for m the ones befoelapsed time takure, the functiowing to its tolch unlike the c

f-healing capabilityan be reconfigured

m also supportscreation of mu

d by means oBU [9]. If we

employed in Frequired by th

ovements –assu5%, respectivels.

g. 2 using our auto

the 30-TBU wing c2 = c3 = ian random vand a standard 9]. We then redeviation for evirtues of this to any multipu

ws a scenario wC4v2. Here, T

ample, arise fropplying the algboth IL distrib

ore applying exken by the rouonality of proglerance for fabase of an ASPI

y in a 30-TBU wavd through H11, H16

s the synthesis ulti-in, multi-ou

of a basic route run the algoFig. 3 we obthe path in Fig. 3uming that all ly. This capab

o-routing algorithm

waveguide me0, c1 = 1. We

ariable distribudeviation of 0

epeated our simeach TBU as realgorithm: its

urpose waveguwhere our algoTBU H10 is siom an error dugorithm, we obbutions, respecxtra H10 malfunutine was in bogrammable PI

brication errorsIC.

veguide mesh. Aftand H21 (b).

of more than ut systems suc

tine to charactorithm, under tain different 3 and the path heaters have

ility can be es

m optimizing with

esh with respee define the ILution (to satisf0.05 to accounmulation consideported in [20]potential use to

uide mesh arraorithm is able timulated to repuring fabricatiobtain solutions ctively. Such vnction, which woth cases in theC based on ws and regardle

ter a malfunction i

one optical pach as the one

terize the this new paths, as in Fig. 4, the same

ssential in

respect

ect to the L of each fy that its nt for any dering an ]. o provide

angement. to find an present a

on) which featuring

values are were 1.84 e order of

waveguide ss of any

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ath at the shown in

Fig. 1. To do all the TDs cconstituting Tnew structure6(a) and Fig. which we synfrom those opedges would algorithm.

Fig. 6. ConsecuInputs and outp

In order arrangement wcell hexagonaactual cells, idesign.

Fig. 7. Grapfrom top to bNodes nume

Followingpath with respwhose results

so, we first foccorresponding TBUs to infinites while maint6(b). Looking

nthesize each inptical paths wbecome unusa

utive synthesis of mputs are numbered

to explore thewe applied it tal waveguide mit also includes

ph representation bottom and from lration follows the

g again the propect to the nums can be observ

cus on the syntto the oppositty. Once finishaining the prevat both results

ndividual elemwhose inputs anable for the res

multiple delay linefollowing the ord

e behavior ofto an alternativ

mesh under stus 20 imaginary

of a larger wavegleft to right. Graphsame criteria than

cedure describmber of traverved in Table 2

thesis of the fire transmission

hed, we can runvious ones, ass, we observe h

ment. As a rule nd outputs layst of the paths

s at a time in a 30-der in which their c

f the algorithmve circuit. Thedy can be founy cells that sur

guide mesh. TBUsh nodes within eacn in Fig. 2.

bed in Section rsed cells to sy2 and Fig. 8. T

rst structure ann states and din the algorithm

s illustrated in how these willof thumb, it w

y closer, so thas waiting to be

-TBU waveguide mcorresponding opti

m in a large-e graph represend in Fig. 7. Thrround them as

s, actual and imagich hexagonal cell

2, we start by ynthesize severThis time, the a

nd, once finisheirections for eam sequentially the example f

l depend on thewill be preferab

at a smaller nue synthesized

mesh in two differical paths were syn

scale waveguientation of thehis time, aparts in the previo

inary cells are numare numbered cloc

searching the ral optical conaverage durati

ed, we set ach of its to create

from Fig. e order in le to start umber of using the

rent orders. nthesized.

ide mesh e new 18-t from the ous graph

mbered ckwise.

optimum nnections, ion of ten

independent ethe process to

Table 2

# I/O

1 I1v2 →

I20v2 →

2 I8v6 →

I13v4 →

3 C3v6 →

C16v2 →

4 C9v4 →

C10v2 →

5 C2v5 →

C8v6 →

Fig. 8. Syntmesh.

Moreoveralgorithm usin0.59 dB with can be observobserve the opwe repeat sucH71 –with saoptimization rwhich can be 13.34 dB. Hosmall mesh. Tlength paths t

experiments, sco stop when the

2. Results obtainrespect to the

O

→ I20v2 [I1v

→ I1v2 [I20v

→ I13v4 [I8v6,

→ I8v6 [I13v

→ C16v2 [C

→ C3v6 [C1

→ C10v2 [C

→ C9v4

→ C8v6

→ C2v5

thesis of optical d

, we also demng this larger a standard dev

ved in Fig. 9. ptimum path bh experiment caid malfunctioroutine with reobserved on t

owever, the elaThis is becauseo find a solutio

cales up to a fee first result wa

ned from the synumber of cros

B

v2,I6v5,C1v2,I8v5,C13v5,C14v2,C

v2,I19v5,C18v2,C1

C9v6,C5v3,C5v,I8v5,C5v2,C5v3,C

C14v5,I1

v4,I13v3,I13v2,C14

C9v6,C5vC3v6,C3v5,C3v4,C7

C12v4,

6v2,C16v1,C12v4,CC2v4

C9v4,C13v1,C13v2,

[C10v2,C9v5,C9v

[C2v5,C2v4,C

[C8v6,C5v3,C

elay lines #1 (a) a

monstrate the mesh. This timviation of 0.05On the extrem

between nodes considering a mon increasing espect to the ovthe right hand apsed time (aroe we were forceon, which did n

ew seconds foras retrieved.

ynthesis of 5 difssed TBUs in ou

est Path

C5v2,C5v3,C9v6,C17v5,C18v2,I19v5,I

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and #3 (b) from Ta

self-healing ame we conside5 and a larger me right and leI7v6 and I16v4,

malfunction in each of thei

verall loss, the side of the sam

ound 35 s) to aed to run the anot cross any o

r larger delay

fferent delay linur large wavegu

C9v5,C10v2, I20v2] C10v2,C9v5, I1v2] C10v3,C14v6,

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,C5v4,C6v1,

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able 2 in the propo

and fault-tolerered them to fenumber of dam

eft hand corne, featuring an oTBUs H14, H15

ir IL to 20 algorithm retu

me figure, withachieve this tasalgorithm up toof the damaged

lines. Again, w

es optimized wuide mesh.

# TBUs

Avedurat

14 0.7

14 0.6

12 0.5

12 0.5

10 0.5

10 0.5

6 0.1

6 0.2

5 0.1

5 0.1

osed 81-TBU wav

rant capabilitieeature an averamaged TBUs, r of the imageoverall IL of 8.5, H32, H41, H51

dB– and perurns an alternah an accumulask is longer thao the search of d TBUs.

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ith

rage ion (s)

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veguide

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ative path, ated IL of an for the 22-TBU-

Fig. 9.

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Fig. 10. Synthe

Finally, oor delay modinterferometri

3.2 Synthes

Most interfermirrors with periodic respoalso be appliethe simplified

Demonstration of

h this subsectiothe 81-TBU w

ved in Fig. 10,BUs each. We

BUs facilitates mpering betwee

he time spent each.

esis of multiple delfollowing the or

one could find difying the TDic structures, as

is of interfero

rometric structdelay lines o

onse frequencyed as a sub-roud place_and_r

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on by demonstwaveguide me, where we shoe expect that di

the synthesis en them. The e

in each indiv

lay lines at a time der in which their

the optimum vD expression. T

s described in t

ometric structu

tures are combof specific lengy or free spectrutine for the auoute routines

fault-tolerant capab

trating the samesh such as weow the combinisposing of broof a larger numelapsed time tovidual path syn

in a 81-TBU wavecorresponding op

value of a delayThis capabilitythe following s

ures

binations of ogth. This leng

ral range (FSR)utomated confreported in [2

ability in an 81-TB

me multi-in, mue did for the smned synthesis ooader waveguidmber of opticao finish the pr

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ay line with a sy is essential fsection.

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BU waveguide mes

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plitters, combidifference imp

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From thearchitecture tarchitecture isof different leone of the Moverall IL of remaining pohalt the proceto appear (feawe aim to ch(ORRs) we wacting as TCselements are t

Fig. 11 iinterferometrion the cavity ms as can beemployed usin[7,9,21], canaccommodate

Fig. 11. Synalgorithm. CTBU ORR (CROW) (f).

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ponding to anaring responsibthe optimizatio

atios (ER) is automatic me

o cross or bar ste initial parameto be synthess defined by twength. In this c

MZI’s arms usithe device. Afrts of the TCs

ess as soon as aaturing lower Iharacterize oth

would only nees, along with ththe base for moillustrates the uic structures inlength to be ob

e seen in Tableng all their po

n be employee crossings of a

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(d), a 12-TBU O.

Fig. 12 illustratared to those ob

uplers and thenn the ports o

no fully automThe current appn intermediatebilities in the syon of the splibeyond the

echanisms for tate). eter requiremesized. For inswo tunable coucase, we can firing the TBUs,fterwards, we ps to find a patha first candidatIL or power coher structures, d to run the pr

he same terminore complex phuse of our alg

n a waveguide btained by the e 1. Also noterts. This TBU d both for i

a delay line or i

interferometric cip left: a 2-TBU M

ORR (e) and a 6-

tes the synthesibtained in Fig.

n the auto-rouof the tunable

mated demonstrproach requiree software comynthesis of sucitting and comscope of thisestablishing o

nts, the processtance, for theplers or combirst run the algo which functioperform a secoh length matchte comes up or onsumption, fo

such as Sagnrocess once beation protocol,hotonic circuitsgorithm to syn

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ircuits in our smaMZI (a), an 8-TBU

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wait longer foor instance, as nac filters or etween the avai, as originally ps [22].

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circuits workinwith itself.

all waveguide mesMZI (b), a 6-TBU

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order to minie algorithm betted FSR. We cor more suitablshown in Sectoptical ring rilable ports of proposed in [2

al different wehich as alwaystask was in thed H16 in Fig. wn as TBU reng in parallel

sh using our auto-U Sagnac filter (c)nator optical wav

rcuits using theme after ten ind

this paper lay lines.

he tunable the user, user and

d in [7,8]. arbitrary

vides and gure each

e filtering MZI, the ical paths ath across imize the tween the can either le options tion 2). If esonators

f the TBU 1]. These

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-routing ), a 10-veguide

e 81-TBU dependent

trials to synth18.546 s for t11(c). This is double of thconsiderably result was retfrom source n

Fig. 12. Syrouting algorfilter (c).

Note how arrangement. arrangements synthesis of sAlthough, thetime, one canprogram a sec

4. Discuss

The algorinterconnectioits tunable baelapsed time ooptimization tto a hexagonasynthesis of oloss. The sambe employed t

hesize each is the 14-TBU OR

not only becae previous onlarger. As in

trieved. Companode only (arou

ynthesis of several rithm. Clockwise

several of the A recent e

can support several circuitse proposed algon fix the TBUcond circuit to

sion

rithm presenteons and delay lsic units –suchof a few secondtopology has aal waveguide moptimized opti

me idea proposeto optimize mu

significantly lRR of Fig. 11(

ause the numbene, but also bprevious scenaring the elapsund 10-15 min)

interferometric cirfrom top left: a 10

structures fromexperimental multiple opera

s working in paorithm can onlUs employed coexist.

ed in this worlines in a FPPGh as the IL, theds. During the

also been publimesh arrangemical interconneed in this presenultiple key perf

larger: 0.797 s(b) and 0.598 ser of componenbecause the synarios, we stopsed time to the), the improvem

rcuits in our large 0-TBU MZI (a), a

m Fig. 10 occudemonstration

ations at the sarallel with croly work on onby one circuit

rk supports opGA core with r power consumpreparation ofshed [24]. In th

ment topology aects between thnt contributionformance param

s for the 10-TBs for the 14-TBnts of this newynthesized patpped the procee one it takes ment is evident

waveguide mesh a 14-TBU ORR (b

upy separate ren confirms tsame time throsstalk values

ne single interft and launch

ptimum self-corespect to the mmption and its f this manuscrihat contributio

and demonstrathe mesh portsn of multiple tameters simulta

BU MZI of FBU Sagnac filtw mesh is moreth differences ess as soon asto perform thet.

using the proposeb) and a 14-TBU

egions of the wthat waveguidrough the simubetter than 24

ferometric struca second algo

onfiguration omain figures ofbasic unit leng

ipt, another graon, a graph is ates its applicatis with respect arget optimizataneously. More

ig. 11(a), er of Fig. e than the

are also s the first e process

ed auto-Sagnac

waveguide de mesh ultaneous

4 dB [23]. cture at a orithm to

of optical f merit of gth– in an aph-based associated ion to the to power

tion could eover, our

contribution propose the application of auto-routing techniques for the synthesis of delay lines in interferometric circuits and multiple input-multiple output circuit topologies. As an illustrative example, Fig. 1 shows a FPPGA architecture where the algorithm is applied to self-configure a full electro-optical circuit and a pure optical processing engine, simultaneously. Considering the required future work missing in current demonstrations, including this one, there are some features and routines that need to be developed to exploit the flexibility inherent in the FPPGA architecture and general-purpose waveguide mesh arrangements in general. In particular, the programming of a large number of simultaneous paths might be addressed with solutions beyond the sequential application of the algorithm. Future work should address these considerations and provide benchmarking efficiency metrics.

As mentioned in Section 2 and 3, the presented routine requires certain information prior to its execution. First, we need to load the full circuit architecture in the shape of a graph. Then, we specify the features to be optimized and the location of the input and output ports that delimit the optical interconnection. As covered in the text for the case of optical filter synthesis, one can feed the periodic frequency of the filter as well, and the algorithm will make the translation. For the case where the IL is being optimized, only optical power monitors placed at the external perimeter are required. In other words, there is no need for characterizing or monitoring the individual IL of each TBU to run the algorithm as long as the delay line to be synthesized connects two input/output ports of the waveguide mesh, as it only considers the accumulated IL of the overall path. For the case where the delay lines or internal interconnections are not connected to the perimeter, for instance to program an interferometric circuit, the algorithm requires the knowledge of each individual TBU IL values. This issue can be addressed either with internal TBU monitoring or by means of periodic pre-characterization routines. To ensure the scalability of the circuit and avoid monitoring system overhead the latter solution is preferred. Pre-characterization routines can be implemented by building up a linear system of equations describing a number of optical interconnections greater than the number of existing TBUs. It should also be noted that a pre-characterization of the power splitting ratio as a function of the applied electrical power is also required as this is the enabler which helps in setting the paths as per desire and hence, achieving the (re-)configuration setting.

Regarding the scalability, we have compared two circuit sizes and different optical interconnection lengths. Clearly, longer interconnections have required longer execution times arising from the nature of the algorithm itself. If finding an optimum path with respect to other feature is not necessary, early stopping conditions could be implemented to speed up the progress to some extent. When it comes to implementing simple optical delay lines (optical interconnections constrained by the number of TBUs), scaling up the size of the mesh does not provide significant delays to the process –which, depending on their length, usually lasts in the order of a few seconds. The proposed algorithm can be applied for self-configuration and circuit programming in any arbitrary waveguide mesh arrangement architecture, either geometrical or flattened lattices that allows a higher integration density [10]. Several of these mesh topologies along with their corresponding graph representations appear in Fig. 13. An exciting area of research will deal with the application of the proposed algorithm and its combination with advanced optimization methods, to reduce the number of variables to be optimized and achieve better convergence rates [10].

Fig. 13. Severamesh, (b) triangu

5. Conclus

This work prcore through overall accumelements or/afabricated wafor different cgeneral-purpodemonstrated programmablcapabilities tarrangements fundamental circuits.

Funding

The authors aADG-741415Valenciana Fexcellency awfor World Clapara caracteri

Disclosures

Authors decla

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