optical design of a 1024-channel free-space sorting demonstrator

Optical design of a1024-channel free-space sorting demonstrator

David T. Neilson, Simon M. Prince, Douglas A. Baillie, and Frank A. P. Tooley

We describe the optical design of a free-space interconnect system to be used for a 32 3 32 sorting system.The system uses 4f imaging relays to connect two hybrid optoelectronic–complementary metal-oxidesemiconductor chips. These relays are used to implement a perfect-shuffle interconnect necessary forthe sorting algorithm to be implemented. The relay lenses are also used with patterned mirrors andpolarizing elements to combine read beams necessary for the optoelectronic chips. Issues relating to thebasic system design and the detailed design of the lenses and optomechanics are given. © 1997 OpticalSociety of America

1. Introduction

The development of the technology to integrateoptoelectronic devices with conventional silicon elec-tronics1 provided the reality of thousands of high-bandwidth input and output pins, placed on a singlesilicon chip.2 These devices provide a potential ag-gregate optical data rate on and off a silicon chip inthe hundreds to thousands of gigabits per second.To relay these large numbers of data channels toother chips it is necessary to use free-space optics.As well as providing a one-to-one interconnection, itis also possible to use free-space optics to implementfan-out, fan-in,3 or nonlocal interconnect patterns,such as the perfect shuffle.4

To achieve high numbers of connections it is nec-essary for the optical system to image faithfully onearray onto another. Near-diffraction-limited perfor-mance is required if the small 20–40-mm modulatorand detectors required for high-speed operation andhigh-density packing are to be used. The opticalsystem can be implemented in a variety of ways withmicrolenses, more conventional compound lenses, ora combination of both. While microlenses can pro-vide compact optical systems, diffraction effects that

When this research was performed, the authors were with theDepartment of Physics, Heriot-Watt University, Edinburgh EH144AS, UK. D. T. Neilson is now with NEC Research, Princeton,New Jersey 08540. S. M. Prince is now with GEC-Marconi Avi-onics, Ltd., and D. A. Baillie is with Wavefront Optics, Edinburgh,UK.

Received 18 March 1997; revised manuscript received 8 August1997.

0003-6935y97y09243-10$10.00y0© 1997 Optical Society of America

are due to the small size of the beams impose penal-ties on larger array sizes ~.1000! and nonlocal inter-connects.5 The use of conventional lenses permitslarger interconnection space bandwidths ~.100,000!,although at the cost of physically larger optical sys-tems.

There are several ways in which such technologymight be used to enhance the performance of elec-tronics systems. One such way is to interconnectarrays of simple processing elements, sometimescalled smart pixels, which otherwise would be impos-sible. The optical system being considered in thispaper is one that performs such a function. Thearchitectural basis for the optical system, which im-plements a bitonic6 sort—an algorithm that takes atime of O~m2! to sort 2m numbers—is described indetail in Desmulliez et al.7 The implementation ofthe bitonic-sorting algorithm reported in this paperutilizes a perfect-shuffle optical interconnect,8 withthe data recirculating through the optical system.The use of optics for the interconnection permits alarge number of input and output channels from eachchip, enhancing the aggregate bandwidth, whereasthe nonlocal interconnect provided by the perfectshuffle reduces the number of iterations of the looprequired to complete the sort. There is a modifica-tion to the system described in Ref. 7 in that there areonly two smart-pixel arrays instead of four. Thismodification is shown in Fig. 1. The first or sortingarray consists of 32 3 16 exchange–bypass nodes andperforms the sort. The second or memory array con-sists of a 32 3 32 array of shift registers and holds thebits of the numbers to be sorted. The second chipalso provides the electrical input and output for thesystem. The system works by recirculating the data

10 December 1997 y Vol. 36, No. 35 y APPLIED OPTICS 9243

through the perfect shuffle and the exchange-bypassnodes until the sort is completed. The implementa-tion of the algorithm requires a perfect shuffle to beperformed for each full iteration of the loop.

In this paper we consider the optical system re-quired to interconnect two hybrid optoelectronicchips while performing an optical perfect shuffle.This requires consideration of the interaction of sev-eral different technologies. The performance of theoptoelectronic devices and the available laser powerwas used to determine the power budget. The formof the interconnect affects its efficiency, hence thepower budget. It also determines the magnificationof the optical system and restricts the options for thelayout of the optoelectronic devices. The size of theoptoelectronic chips sets the f-number and aberrationlimits for the relay lenses, while the dimensions of thearray set the field specifications.

2. System Requirements and Specifications

The basic function of the optical system is to imagetwo chips onto each other while performing a two-dimensional perfect-shuffle interconnect for a com-plete round trip of the optical system. Since theoutput devices on the chips are modulators, it is alsonecessary to illuminate them with read beams, whichmeans that there are three sets of beams going to andfrom each chip: read beams to the modulators, sig-nal beams from the modulators, and signal beams tothe detectors. To achieve the chip combination withminimum loss it was decided to use polarization- andimage-plane beam-combination techniques.9 Thelatter is achieved if patterned mirrors are put in theimage planes of the relay optics. The optical systemchosen uses large-field objective lenses in front of thehybrid chips. Between these objectives there aretwo 4f relays to allow for the beam-combination andinterconnection stages.

Fig. 1. Schematic of the sorter system with two-chip implemen-tation. The data to be sorted are loaded electrically into the mem-ory chip. The data are circulated through the perfect shuffle andthe sorting chip, which performs exchange–bypass operations.When sorting is complete the data are electrically unloaded fromthe memory chip.

9244 APPLIED OPTICS y Vol. 36, No. 35 y 10 December 1997

The system operates at 1047 nm to take advantageof the high-power diode-pumped Nd:YLF lasers avail-able at this wavelength. The modulators and detec-tors were InGaAs quantum-well devices grown onGaAs.10 The power budget for the system was basedon use of a 1-W laser. The laser has to supply theillumination light to operate two arrays of 1024 dual-rail channels. This yields a power supply of 488 mW~23.1 dBm! per channel, assuming that the power issplit equally between the arrays. The original spec-ified combination of an InGaAs detector and receivercircuit required 10 mW ~220 dBm! for 100-MHz op-eration, although the final receiver designs exceededtheir specifications,11,12 providing a total loss budgetof 216.9 dB. The optical modulation efficiency ofthe InGaAs modulator for a 5-V swing, which is thedifference between the high-state ~60%! and low-state ~30%! reflectivities, is 0.3 ~25.2 dB!, yielding apurely optical budget of 211.6 dB. Some of the lossoccurs before the modulator in the array-generationand beam-combination process and some during theinterconnect and relay process.

3. Perfect Shuffle

The perfect shuffle is a space-variant interconnect,but it has a sufficient level of symmetry to permit itsimplementation with largely space-invariant compo-nents. The implementation used in this study is avariant of the segmented 4-shuffle by Cloonan et al.4that was described in Desmulliez et al.7 It consistsof replication by use of a phase grating and overlap-ping of the copies, with only part of each copy beingkept.

This interconnection can be implemented either ina single stage with a 2 3 2 fan-out, in which case only25% of the light is used, or in two stages with 2 3 1fan-outs,7 in which 50% of the light is lost twice.A 2 3 2 fan-out phase-only grating has the samemaximum efficiency ~64yp4 5 0.657! as do twocrossed 2 3 1 binary gratings ~8yp2 5 0.811 each!,unless it is fabricated as both multilevel and nonsep-arable.3 The use of multilevel designs increases thefabrication complexity, which is likely to introduceadditional nonuniformity.13 Since the mask for theone-dimensional grating has only stripes, there areno corners to be written for the mask, and so fewerfabrication errors can be expected. The use of twoone-dimensional interconnects also allows the inter-connect to be split between the two relay stages.This splitting of the interconnect has the advantageof balancing the loss in both directions of the systemand consequently of balancing the optical power lev-els required on the modulators; thus 20% less poweris required.

The way in which two one-dimensional shift andinterlace functions can be combined to give a two-dimensional perfect shuffle is shown in Fig. 2. Thisversion of the perfect shuffle requires a unity magni-fication system in one path and a 23 magnification inthe other. A first-order layout of the two paths isshown in Fig. 3.

Space variance is used in this interconnect, but it is

in the form of the space variance of the array ofdetectors and therefore adds neither additional com-plexity nor components to the system. There arethree forms of loss associated with this interconnectoperation: there is the intrinsic loss resulting fromthe fact that the beam is fanned out to two intercon-nects, but only parts of each are used 0.5 ~23.01 dB!;there is loss deriving from the maximum efficiency ofa 2 3 1 binary grating 0.81 ~20.91 dB!; and there isloss owing to fabrication. The last comes from etch-depth errors in making the grating, which will beapproximately 1% ~20.04 dB! ~Ref. 3!, and the use of

Fig. 2. Operation of the two-stage perfect shuffle. The exampleshown is for a 4 3 4 array, numbered in hexadecimal. The part ofthe array delineated by the thick lines is selected. The magnifi-cation required for each direction is different. This space-variantselection is performed by the detector arrays and requires no ad-ditional masking stages.

Fig. 3. First-order layout of the optical system for the perfect-shuffle interconnect between the two chips. ~a! Memory to sortingnode, with unity magnification. ~b! Times 2 magnification re-quired to recover the original array size. The numbers corre-spond to the first row or column aligned with the interlacedirection. Only the used orders are shown, and the rays shownare chief rays.

antireflection coatings with 0.25% reflectivity ~20.01dB!. Thus an expected efficiency for this componentis 0.39, or a loss of 24.07 dB.

For the interconnection to be performed, it is nec-essary that the grating provide interlacing, which isa shift in spot position equal to half the array size,and also implement the correct offset such that aregular array is formed. The period P of the grat-ings is given by

P 52fl

d~n2 1 m2!1y2 , (1)

where f is the focal length of the lens l1, l is thewavelength, d is the pixel spacing, n is the number ofpixels to shift ~half the array size!, and m is thenumber of pixels to be off set. For the case shown inFig. 1 the offset would be half a pixel or m 5 0.5.The values of m used depend on the chosen positionsfor detectors within each node.

The choice of modulator and detector positions isinfluenced by the magnification in the interconnectand the use of dual-rail data representation, whichmeans that each input and output consists of twodiodes S and R. There is unity magnification in onedirection in the system, so the separation of the dual-rail windows of the modulators on the memory mustmatch that of the detector windows on the sortingnode, while the 23 magnification present in the otherdirection of the interconnect ~see Fig. 3! requires thatthe spacing of the modulator windows on the sortingnode be half the spacing of the detector windows onthe memory node. The spacing between modulatorwindows must be an integer fraction of the pixelpitch, as array generation uses a grating. Addition-ally, the array-generation grating will be of greaterefficiency if no orders are suppressed. The positionsand spacings of the modulators and detectors wereselected such that all the input and output for a givenpixel would lie within the pixel itself. All these con-straints lead to the design shown in Fig. 4, with in-terlaced detectors for the sorting node.

The effective channel separation of the sortingnode is only 45 mm, or m 5 45y180 5 0.25. The

Fig. 4. Layout of the pixels: Each pixel is 180 m 3 180 m, andthe channels are dual rail, as indicated by the S and R windows.The sorting node has two inputs ~D! and two outputs ~M! and formsa 32 3 16 array of pixels. The memory has only one input andoutput, forming a 32 3 32 array.


memory-channel spacing of 180 mm and the magni-fication mean that m 5 180y~2 3 180! 5 0.5. There-fore, for f 5 30 mm, l 5 1047 nm, d 5 180 mm, andn 5 16, the periods are 21.802 and 21.810 mm. Be-cause of the limitations of mask writing, the periodwas 21.8 mm. The difference between the ideal andactual grating periods ~quantization error! givesmaximum spot-position errors of 0.29 and 1.24 mm,respectively, at the edges of the field.

4. Field and Aperture Specification

The lenses in the system work at two f-numbers anddifferent fields of view ~FOV’s! as a result of the mag-nification in one path. However, for minimizing thenumber of different lenses used the objective and allthe relay lenses are the same design, with a focallength f. A lens of focal length f divided by 2 is ahalf-size version of the other lens, since this arrange-ment retains some of the advantages of a symmetri-cal optical system for reducing aberrations.

The FOV of the lenses was specified as 11 mm fulldiagonal, which corresponds to up to a 7.78 mm 37.78 mm active area on a chip. The actual field to beused in the system corresponds to a 32 3 32 array of180 mm 3 180 mm pixels, or 8.14 mm full diagonal.~The larger field allows for upgrading the system tolarger array sizes.!

For determining the f-number of the system, boththe size of the optoelectronic devices and the amountof aberration in the optical system must be consid-ered. The optoelectronic devices, both modulatorsand detectors, are less than 35 mm in diameter:Small devices minimize capacitance, which permitshigher-speed operation. The diameter ~1ye2! of theGaussian beam waist is related to the wavelengthand f-number by d0 5 4yp l fy#. When calculatingthe beam size it is the encircled energy that is impor-tant, since this represents the effectiveness of cou-pling light to the detector. The encircled energydiameter dP for the PyP0 fraction is given by dP0

[email protected] ln~PyP0 2 1!#1y2, which for 99% encircledenergy gives dP0

5 1.52d0 5 1.93 l fy#.The effect of aberration on the spot size has also to

be considered.The simplest aberration to consider is that of defo-

cus. For a Gaussian beam the effect of defocus Dz isto increase the beam size, according to

dP 5 dP0@1 1 ~DzyzR!2#1y2. (2)

If this defocus is considered in terms of the opticalpath difference ~OPD!, it is found that, at one Ray-leigh range defocus, the peak-to-valley OPD is 1y~2p!waves and the rms OPD is 0.046.14 The 99%encircled-energy beam size can then be considered interms of the level of aberration as given by

dP 5 1.93l fy#@1 1 ~wyw0!2#1y2. (3)

The rms wave-front error caused by defocus is w, andw0 5 0.046.

In practice, the compound lenses in this system arelimited by third-order astigmatism arising from tilts


and decenters of elements. Astigmatism can be con-sidered a relative defocus of the tangential ~T! andsagittal ~S! axes. When astigmatism is dominant,the minimum spot size occurs at a point halfwaybetween the minimum for either the S or T direction.The resulting rms wave-front value of w0 for the caseof astigmatism is =2 times larger than for defocus at0.066, which was close to the mean value of w0 5 0.07found in Ref. 15 for a similar lens. This mean valueis the same as the conventional Rayleigh quarter-wave system condition.10 Thus a lens meeting thiscondition ~a rms OPD of 0.07 waves! will have anencircled-energy diameter =2 times larger than thediffraction limit.

For the condition of 99% encircled energy into a35-mm detector and a lens meeting the Rayleigh cri-terion at 1047 nm, the required f-number for thesystem is fy12.2. When the presence of the relaylenses acting as a 23 telescope in the perfect shuffleis considered, this is reduced to fy6.1. To allow forerrors in the spot positions of 65 mm at the detectorplane, it is necessary to make the focused beam 10mm smaller than the windows, and the maximumf-number is reduced to fy4.3. It was therefore de-cided to design an fy4 lens for the system.

The lenses were to be used with array-generationand interconnect gratings, so they had to have an f 2sin u distortion. For ensuring correct registration ofthe spot positions the effective focal length had to becorrect to 1 in 2000.

Since the lenses were to operate as relays, it wasdesirable to keep them close to telecentric. Since thesystem uses a recirculating architecture and the timeof flight between the chips affects the operation speedof the system, the goal was to make the system ascompact as possible.

5. Design of the Lens

The choice of starting point for the design has a sig-nificant effect on the ultimate design, so some carewas put into this. There are many four-element de-signs that have been considered for this kind of ap-plication.16 There is one form that has been found towork well for a range of optical interconnection ap-plications from fy1.5 with an 8° full field17 through tofy4 at a 16° full field,18 with other variants of field andf-number.19,20 The form of these lenses is an adap-tation of the Petzval-type lens, with an external stop,a positive element, a meniscus element, a positiveelement, and a biconcave element in succession be-fore the image plane. The last element acts as afield flattener, while the meniscus element is used tocontrol the other aberrations, especially astigmatism.The meniscus element constitutes one of the majorrestrictions on this form of lens since it often becomesa thick, near-concentric element and often is in con-tact with the first element. When examining thelens required for the sorting system, other designswere considered, including one developed by Brixnerand Klein21 in which the meniscus element is the firstelement after the stop. This design can achieve thesame field and aperture specifications as the lens

developed by Barrett et al.,18 with a reduced overalllength.

There was one additional factor that influenced thedesign of the lens but did not relate directly to thesystem design. Owing to the wide range of possiblewavelengths that might be used for optical intercon-nections, specifically 790–1050 nm, it was considereduseful to design a lens that would work well acrosssuch a range. It was not intended that it would beused for more than one wavelength at a time, so thedesign did not have to be an achromat. Its front andback working distances and effective focal lengthcould vary with the wavelength, but its imaging prop-erties had to be maintained. The correction thatmust be achieved is that of achromatizing aberra-tions, such as spherical, astigmatic and distorted,although not the first-order parameters.

From an analysis of the limitations of such lenses15

it was considered that an effective focal length of 30mm would be practical, which set the FOV at 20.7°full field. It was decided to use the form of lensdescribed in Ref. 18, scaled to the focal length above,with the meniscus element split by a plano surface asthe starting point for optimization design. The me-niscus element was split because, in all the previousdesigns, it was controlling much of the astigmatism,which is one of the major limitations of these lenses.Splitting it gives some additional freedom to the de-sign.

This lens would not work well at other wavelengthssince the positive elements are high-dispersion flintglass ~SF6!. To reduce the chromatic variation ofthe aberrations of these elements while maintainingperformance it is necessary to use high-index ~n ;1.7! glasses with lower dispersion ~V . 50!. Theglasses that best match this requirement are thelanthanum-based glasses. The relative propertiesof different types of glass change depending on thespectral region considered,22 and these glasses areparticularly attractive for the near IR, since they are20% less dispersive in the 0.7–1.0-mm ~rst spectral-line! range than an equivalent so-called normal glasswith the same FdC line Abbe number, as indicated inTable 1. Their disadvantage is that, apart fromLaF2, they have a significantly higher cost and aremore likely to stain during manufacture. They areall suitable for use near an image plane owing to alow bubble count, but their sensitivity to acid makesthem less suitable as external elements of an assem-bly. On the basis of cost and availability the designwas limited to using only LaF2 from these glasses.

For the final design, which is listed in Table 2 andshown in Fig. 5, it was found that two elements ofLaF2 were sufficient. These elements provide muchof the positive power of the lens, so the high indexreduces the curvature, hence the aberrations inducedby these elements, while the low dispersion mini-mizes the chromatic variation of the aberrations.The performance of the lens at 850 and 1047 nm isshown in Fig. 6. For 850-nm performance there isvirtually no third-order astigmatism, although thereis some coma and higher-order astigmatism. The

field curvature is such that it matches the defocusrequired on axis to balance the residual sphericalaberration. At 1047 nm there is a small amount ofthird-order astigmatism. Balancing contributionsfrom third- and higher-order distortion controls thedistortion to f 2 sin u, to within 0.025% at all fieldsand wavelengths.

6. Tolerancing the Lens

For all reasonable manufacturing tolerance levels theperformance of the lens is determined by the preci-

Table 1. Dispersion of Glasses in the Near IR ~0.7–1.0 mm! Showingthat the Lanthanum-Based Glasses Are Less Dispersive than

Normal Glassesa

Glass

nnn.VVVF-d-C

~Visible!

nnn.VVVr-s-t

~0.7–1.0mm! VrstyVFdC

Cost Relativeto BK7

~Number ofTimes More!

Normal glassesSF56A 785.261 762.357 0.731 4FK5 487.704 481.967 0.728 3

Lanthanum glassesLaF2 744.447 731.753 0.594 6LaFN7 750.350 732.605 0.579 20LaF22A 782.372 765.651 0.571 20LaSFN30 803.464 789.751 0.617 28

aThe r, s, and t spectral lines are 706.5, 852.1, and 1014 nm,respectively. The glasses LaFN7, LaF22A, and LaSFN30 wereconsidered during design but were not used in the lens. Theyillustrate the difference in dispersion from more normal glasses ofthe lanthanum-based glasses in this spectral region.

Table 2. Final Design of the Five-Element Relay Lensa

Surface Radius Thickness Material

Stop 0.000 15.7331 36.510 9.600 SF56A2 234.680 0.7683 223.476 6.640 FK54 28.800 16.975 49.310 5.347 LaF26 240.946 1.4207 19.470 6.660 LaF28 54.537 2.0659 259.600 1.334 FK5

10 12.950 5.601Image 0.000 0.000

aAll dimensions are in millimeters. The positions of the stopand the image plane are given for 1047 nm. At 850 nm these are15.296 mm and 5.341 mm, respectively.

Fig. 5. Final design for the 30-mm effective focal-length lens.


sion to which it is manufactured and not the residualaberrations of the design; therefore tolerancing is acritical part of the design process. The goal was toachieve the required system performance while min-imizing the cost; therefore all the tolerances werekept to levels at or below that which optical shopsconsider normal precision.23,24 The tolerance rangesused for this lens are specified in Table 3. Withthese tolerances it was estimated by use of CODEV

tolerancing routines25 that this lens would have a

Fig. 6. Ray-analysis curves for the 30-mm effective focal-lengthlens at f4 at ~a! 1047 nm and ~b! 850 nm. The front and backworking distances are different in each case. All units are inmillimeters except for the distortion, which is given in the percentdifference from the design target of the sine.


performance of 0.042 waves rms at 1047 nm and0.051 waves rms at 850 nm, with fy4 and a 7.7-mmfield, when manufactured. ~These values corre-spond to the same physical optical path-length differ-ence at these two wavelengths.! These values aresignificantly below the diffraction limit, but the sys-tem will use multiple lens passes and it is the accu-mulated aberration that needs to be close to thediffraction limit.

These tolerances were sufficient for control of thedistortion, but control of the effective focal length wasa significant issue. The required focal-length con-trol to achieve 1-mm spot-position errors is 1 part in2000. It should be noted that the typical specifica-tion of the variation in the refractive index of theglass alone would result in more error than this. Totighten the tolerances to ensure that the focal lengthwould be correct is impractical; instead, an adjust-ment of one of the air spaces in the lens is used. Itwas determined that adjustment in focal length couldbe achieved by a 670-mm change in the spacing be-tween the last two elements ~E4 and E5!.

The design of the barrel, shown in Fig. 7, has self-centering elements to reduce the amount of work inassembly. Since a self-centering barrel designworks well with only up to three elements,26 it wasdecided to use this method for elements 1, 3, and 4and to center element 2 in a subcell, since it requiresthe most accurate alignment ~61 arc min!. The final

Table 3. Tolerances for the Surfaces, Elements, and Spacing of the30-mm Focal-Length Lens

Item Tolerance

Index of refraction 60.001Abbe number 60.8%Lens thickness 60.1 mmRadii of curvature 60.02 mm to 60.10 mmFringes

Spherical 4Irregular 1

Diameter 10y20.1 mmAir spaces 60.01 mmDecentration of element 60.02 mmElement tilt 61 arc min to 64 arc min

Fig. 7. Lens barrel design for the 30-mm lens. A thin spacer ringis used to adjust the axial position of the last element to control thefocal length. The second element is adjusted and glued into itscell before insertion into the barrel.

Fig. 8. Basic optical layout showing schematically the route of the light for each beam direction: ~a! from the memory chip to the sortingnode and ~b! from the sorting node to the memory chip in the optical system. The aperture stop size in the system shown in ~a! is 3.75mm throughout. In the system shown in ~b! it is 7.5 mm until after the relay lenses that act as the 23 telescope, when it is effectivelyreduced to 3.75 mm. Axial rays are shown.

element is mounted without affecting the otherlenses to enable easy access to the spacer ring used tocontrol the focal length.

The transmission of this lens is also important be-cause of the multiple passes. For the high-indexglasses SF56A ~n 5 1.755! and LaF2 ~n 5 1.726! asingle-layer MgF2 coating would give a .99.75%transmission per surface. For the two low-indexlenses this coating would give a 98.4% transmissionper surface. If this coating were used, the lenseswould have a transmission including absorption ofonly 91.6%. This was unacceptable since, after theseven passes required, it would represent a 22.67-dBloss. Instead, on the FK5 elements a two-layernarrow-band coating was specified, with a transmis-sion of .99.5%, which yields 95.6% transmission perassembly or a seven-pass loss of 21.37 dB.

7. System Layout

The two optical systems shown in Fig. 3 have to becombined. Additionally, the generation and inser-

tion of the read beams for the modulators is neces-sary. Each hybrid chip has three sets of beamsgoing to and from it: the read beams to the modu-lators, the modulated beams, and the beams to thedetectors. Since these beams cannot simply be com-bined, patterned mirrors were used at the interme-diate image plane that is present in the relays tocombine the read beams and the beams to the detec-tors. Polarization was used to separate the modu-lated beams from the read beams. The resultingoptical scheme is shown in Fig. 8, with the two opticalpaths—from the memory chip to the sorting nodechip and its return—shown schematically. In thememory-to-sorting-node system the aperture stop is3.75 mm, so only the 15-mm focal-length lens oper-ates at fy4, with the rest of the relay including theillumination of the modulators operating at fy8. Forthe other direction the system has a 7.5-mm aperturestop until after the 23 magnification, so the modula-tors are illuminated at fy4 and the detectors at fy8.

Polarizing beam splitters ~PBS’s! are required for


Fig. 9. Top-plate layout: The hybrid optoelectronic chips are at each end ~memory to the left and sorting to the right!, supported fromthe lower plate. Light enters the system through the two holes marked A.

beam combination in the system. Unlike conven-tional PBS’s that work over approximately 0.5°,they have to work over a significant FOV. Theactive area of the memory chip, 5.8 mm 3 5.8 mm,gives an effective angular range18 for the cube of65.6°. The increased angular range can be ob-tained by sacrifice of wide-wavelength performancesince this system is monochromatic. Although thecontrast is not critical to the performance of thesystem, a high routed fraction of light is, and toachieve a 99.5% routed fraction a contrast of 200:1is required. These values are similar in specifica-tion to those PBS’s described in Ref. 18. The cubeswere 10 mm, and the glass was chosen to be SF10~n 5 1.702! to reduce the angular range on thecoating to 63.3° and to make antireflection coatingwith MgF2 acceptable ~99.7%!. The effect of errorsin rotation of the quarter-wave plates is small, witha 61° error corresponding to a loss at the beamsplitter of the order of 0.1%.

The array generators are even-order-missing grat-ings27 to permit control of the zero-order signal, andnonseparable designs are used to ensure high effi-ciency. For the memory chip, since the device isdual rail, the 32 3 32 array of nodes gives an array of32 3 64 windows on a 180 mm 3 90 mm pitch. Thiscorresponds to a grating with 349 mm 3 698 mmperiods, with no orders suppressed other than theeven orders suppressed by symmetry. The sortingnode, being a 16 3 32 array of nodes with two dual-rail outputs per node, requires a grating with a 16 3

128 array of spots on a 180 mm 3 45 mm pitch, yield-ing a 2:1 rectangular array. The period in this caseis 349 mm 3 1396 mm.

Binary phase-level gratings were chosen becausethey would be simpler to manufacture and have lessnonuniformity than multilevel gratings.13 The ef-fect of nonuniformity is to reduce the effective signallevel, with local nonuniformities being particularlydetrimental to dual-rail operation.28 Such a binarynonseparable grating is 75% efficient, with a 2% non-uniformity. Errors in etch depth typically result in1% of the light being in the zero order and thus lost.If both surfaces are antireflection coated, there is aFresnel reflection loss of 0.25% per surface. Thisgives an overall efficiency for the component of 71.6%total ~21.45 dB!.

The patterned mirrors required for beam combina-tion were stripes, 90 mm wide at a 180-mm pitch.The mirrors were deposited gold, which has a .95%reflectivity at the system wavelength.

A ray-trace tolerance analysis of the optical sys-tem shown in Fig. 9 was conducted for the opticalpaths shown in Fig. 8 to determine the spot sizes ateach of the optical device planes. The f-number,wave-front error, and resultant spot size are listedin Table 4. This analysis indicates that, with a65-mm misalignment tolerance on the spot posi-tion, all the modulators and detectors can be lessthan 35 mm in diameter and still achieve a 99%energy collection.

Table 4. Results of a Tolerance Analysis for the Optical Paths Used in the System @Figs. 8~a! and 8~b!#a

System Path Illuminated Device f-Numberrms Wave-Front

Error of Path

99% EncircledSpot Size

~mm!

SNb to memory Modulator ~SN! 4 0.025 8.6Fig. 8~a! Detector ~M!c 8 0.069 22.7Memory to SN Modulator ~M! 8 0.040 18.6Fig. 8~b! Detector ~SN! 8 0.051 20.0

aThe f-number of the beam at the indicated device and the expected rms wave-front error, with the manufacturing errors of the lensesaccounted for, and the resulting spot sizes were calculated by use of Eq. ~2!.

bSN, sorting node.cM, memory.


Fig. 10. Picture of the assembled optical system showing the upper plate with the optical interconnection and the lower plate with thelaser, beam-shaping, and viewing optics. PCB, printed circuit board.

8. Optomechanics

Since the lens system requires a common axis of sym-metry, it was decided to construct the system by use ofa slot-plate system similar to that described in Ref. 29.There were, however, several modifications to this con-cept. The plate was made of glass-filled nylon to re-duce the mass and provide a material that was easierto machine. Since this material is not as hard as thesteel used previously, it is possible to form the slots asV grooves. Owing to the ease of machining of thismaterial, both sides of the groove are cut with a V-shaped tool. Since only one edge of the tool can per-form the final cut of the slot, the entire V is effectivelybeing cut as a single surface. This has the advantagethat the height of the optical axis is determined by theheight of the tool, and the uniformity of the axis heightacross a plate is simply the uniformity of the control ofthe height of the cutting tool and is independent of theflatness of the plate. The accuracy is then a functionof the quality of the milling-machine table and typi-cally is ,10 mm. This method of forming the slot isnot limited to V grooves, with other cross sections pos-sible. One such possibility would be to cut grooveswith a radius of curvature, where the radius is onlyslightly larger than the cell diameter to reduce thestress on the contact point.

The optical system was formed from two plates, asshown in Fig. 10, with the one shown in detail in Fig.9 mounted kinematically on top of another. Thelower plate was used to mount the Nd:YLF laser. Italso contained the beam-expansion and power-distribution optics. The optoelectronic chips weremounted on printed circuit boards and held on cus-tom five-axis positioners mounted from the lower

plate. These positioners are used for gross align-ment ~.100 mm! of the chips, and Risley beam-steering prisms were included for fine adjustment ofthe spot positions to ensure correct registration of thebeam arrays on the chips and the patterned mirrors.

To enable alignment of the arrays of beams, cam-eras were mounted on the lower plate. These cam-eras can be used to observe the optoelectronic-deviceplanes by rotation of the quarter-wave plates. Thealignment process consists of first aligning the pat-terned mirrors to the modulators then aligning theinput-beam array to the modulators for each of thetwo chips. Then the outputs of the modulators mustbe aligned through the interconnect to the detectorsof the other array. Since the patterned mirrors havealready been aligned to the modulators, they pose noadditional problem in aligning to the detectors.

9. Conclusions

We have described the design process for the opticalsystem for a 32 3 32 optical sorter. A new design ofa diffraction-limited lens with a large FOV ~20.8°! foruse in optical interconnection applications has beendescribed. The presence of the perfect shuffle isshown to introduce complexities into the optical de-sign and spacing of the windows of the optoelectronicchips. The use of patterned mirrors to reduce thebeam-combination loss increases the complexity ofthe system and the number of lens passes, but theanalysis of the spot sizes at the device planes indi-cates that the optoelectronic-device size can still beless than the 35-mm-diameter target set. The break-down of the losses from the various components in thesystem is summarized in Table 5, and the total loss,


while significant at 28.22 dB, is within the powerbudget of 211.2 dB set for the system.

The authors acknowledge George Smith for the me-chanical drawings of the optomechanics and Marc Des-mulliez for discussions about the interconnect. Thisstudy forms part of the Scottish Collaborative Initia-tive in Optoelectronic Sciences funded by the UK En-gineering and Physical Sciences Research Council.

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Table 5. Breakdown of Transmission and Losses of the Componentsin the Design of the Optical System

Component Transmission Loss ~dB!

Array generation 0.716 21.45Relay lenses 0.9557 21.37PBS surface coatings 0.9957 20.15PBS antireflection coatings 0.99714 20.18Interconnect gratings 0.39 24.07Quarter-wave plates rotation 0.9997 20.04

With antireflection coating 0.99514 20.30Risley prisms 0.99512 20.24Patterned mirrors 0.95 20.22

With antireflection coating 0.9952 20.04Beam-expansion optics 0.9954 20.08Mirrors 0.9954 20.08

Total 0.147 28.22


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optical design of a 1024-channel free-space sorting demonstrator

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