Diffraction-grating-based (de)multiplexer using image plane transformations

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1194 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 8, NO. 6, NOVEMBER/DECEMBER 2002

Diffraction-Grating-Based (De)Multiplexer UsingImage Plane Transformations

Charles X. Yu, Member, IEEE,and David T. Neilson, Senior Member, IEEE

Abstract—We present the concept of using image plane trans-formations with free-space diffraction-grating-based multiplexers.We demonstrate two examples of a diffraction-grating-based mul-tiplexer that take advantage of image plane spatial transforma-tions. We show that the use of such spatial transformations hasunique advantages for multiplexing schemes. We also demonstrateunique system applications enabled by these multiplexers.

Index Terms—Optical fiber devices, optical image processing,wavelength division multiplexing.

I. INTRODUCTION

T HE PERFORMANCE of the wavelength multiplexer iscritical to the design and capability of optical transmission

systems. The minimum channel spacing of a practical multi-plexer defines a lower bound on the channel spacing of the densewavelength division multiplexed (DWDM) systems. The widthand shape of the passband influences the maximum data rateon a given wavelength channel. With a conventional end-to-endtransport system, there is one multiplexer (mux) and one de-multiplexer (demux) in the optical path. However, with the in-troduction of optical layer switching, there can, in principle, beseveral and varied numbers of multiplexers and demultiplexersin the optical path, thus putting greater requirements on theirpassband characteristics. While demultiplexers typically sepa-rate each optical channel onto an individual port, the use ofhierarchical demultiplexing using interleavers or banded mul-tiplexers is becoming more prevalent.

Bulk diffraction gratings can be used to separate wavelengthsand its applicability as the (de)mux in WDM lightwave sys-tems has long been recognized and demonstrated [1]–[5]. Oneof the attractive features of bulk gratings over other technolo-gies such as the arrayed waveguide grating (AWG) routers [6],[7] is the low crosstalk of bulk gratings due to their low scat-tered light. This results in very low non adjacent crosstalk whichmakes them more attractive for very large channel count sys-tems. Recently commercial multiplexers with narrow channelspacing and high port counts based on diffraction gratings arebecoming available [8]. The basic schematic of such a device isshown in Fig. 1(a). The input fiber carries multiple wavelengthsand is collimated with a lens and incident upon the grating. Thelens/grating combination transforms this input and displays thetransform at the image plane. The output fiber array is placedat the image plane and a different wavelength is coupled intoeach of the fibers in the array. The demux passbands are nec-

Manuscript received August 15, 2002; revised October 2, 2002.The authors are with Bell Labs, Lucent Technologies, Holmdel, NJ 07733

USA (e-mail: [email protected]; [email protected]).Digital Object Identifier 10.1109/JSTQE.2002.805977

(a)

(b)

(c)

Fig. 1. (a) Grating demux, transmission configuration. (b) Grating demux,reflecting configuration. (c) Functional block diagram of the (a) and (b).

essarily subject to spatial filtering in these output fibers. Thepassband to channel spacing is a function of the fill factor ofthe mode size to mode spacing. The use of conventional fiberwith a 10- m core and a 125- m pitch leads to very poorpassbands. The passbands can be significantly improved by in-creasing the fill factor of the modes. This can be achieved byreducing the spacing of the modes, increasing the mode size orboth. Spacing reduction has been achieved by using concentra-tors made using a planar lightwave technology [5] or thinnedfibers. Mode size change has been achieved by using arrays ofmicrolenses [2] to expand the mode, while keeping the fiberspacing large. These modifications change the passband widthto fill factor ratio but do not modify the passband shape. Pass-band flattening techniques which modify the mode profile canbe used to produce flatter passbands though they inevitably in-troduce loss at the center wavelength.

Typically the systems are built in a folded configuration, il-lustrated in Fig. 1(b), where the grating is reflective and the lightdouble-passes the lens. This configuration is attractive since itis generally more compact and requires fewer optical compo-nents. This allows one fiber of the fiber array to be used as theinput and the others as the output, though often the input andoutput may be separated in order to use relative motion to tunethe channel spacing.

II. I MAGE PLANE SPATIAL TRANSFORMATIONS

The unfolded and folded multiplexer shown schematically inFig. 1(a) and (b) have the same functionality. The first pass of

1077-260X/02$17.00 © 2002 IEEE

YU AND NEILSON: DIFFRACTION-GRATING-BASED (DE)MULTIPLEXER USING IMAGE PLANE TRANSFORMATIONS 1195

the lens is used to set the beam size on the grating, which willangularly disperse the light. For a grating with angular disper-sion and small angles we have

(1)

The second lens is a Fourier transform lens of focal length,which transforms the angular shift () of the grating to a lateralshift ( ) at the output plane

(2)

Thus, this system does an input to output mapping of

(3)

(4)

as summarized by the block diagram in Fig. 1(c).It can be seen that the output position inis linearly depen-

dent on the wavelength. The wavelength-dependent coupling ef-ficiency ( ) is then given by

(5)

where and are the input and output fields, respectively. Fromthis relation we can see that appropriate choice of the modefunctions can allow a range of passband widths and shapes.Since this function depends explicitly on the wavelength as amodification to the position, the way to flatten the passband isto choose modes that give uniform coupling across a range of

values. Doing so in a single-mode system requires that thesystem have loss relative to an unflattened one and, the greaterthe wavelength range over which uniform coupling occurs, thegreater the loss.

If we now consider an alternative system which usesback-to-back systems similar to that of the conventionaldemultiplexers given above. It consists of a lens and a gratingfollowed by another lens to create an image plane. This plane isthen imaged through another lens-grating system to the outputplane. This system performs a two-stage transformation

(6)

(7)

This system maps each point on the input plane to the equivalentpoint on the output plane. It has no wavelength dependence andproduces no useful demultiplexing function. However, it doeshave an intermediate plane at which the signals are separated

Fig. 2. Block diagram of the grating demux that uses optical processing.

by wavelength. If we perform some transformation at this inter-mediate image plane, we can create useful devices. If the trans-forms at this plane are

(8)

(9)

where and are arbitrary functions of , then the completesystem performs the transformation

(10)

(11)

The coupling efficiency is then given by (12), shown at thebottom of the page. These transformations mean that the cou-pling efficiency has wavelength dependence in it but the wave-length dependence is controlled not simply by the dispersion ofthe grating but by the effect of the functions and onthe dispersion. We have now also added the option of couplingthe axis to the wavelength dependence. This-axis couplingis unique for a diffraction grating since a diffraction grating isa three-dimensional (3-D) device. An AWG, for example, is atwo-dimensional device and does not have freedom in theaxis,though an axis transform is possible.

It is worth noting that and are only a subset ofthe transforms possible and in principle any image transforma-tion technique could be used to create a wide variety of func-tions. Examples of these include gain-equalizing filters whichimpose an amplitude transformation [9] and wavelength-selec-tive switches [10] which impose a linear phase transform to steerthe beams. In this paper, we will consider some of the implica-tions of the transforms listed above. For instance, we will showthat the passbands are no longer necessarily subject to the con-ventional spatial filtering. In this paper we present two examplesof the setup shown in Fig. 2. For each example, we demonstrateunique advantages of these devices and the system applicationenabled by these unique attributes.

III. EXAMPLE 1: DEMUX WITH A VERY HIGH

FIGURE-OF-MERIT

The first example is a demux with very high figure-or-merit(FOM). FOM here is defined here as the 1-dB bandwidthover the 20-dB bandwidth. Since the demux passband shown

(12)


Fig. 3. (a) Demux schematic with anf = 50-mm lens and a 600-line/mmgrating. (b) Principle of the demux: I) at the input fiber; II) at the output fibers;III) before the v-groove array; IV) after the V-groove array.

in Fig. 1 undergoes spatial filtering in the output fibers, theyhave Gaussian passbands. Flattening these Gaussian passbandsusually leads to higher insertion loss. In this section, wedemonstrate that such constraint does not exist for the demuxin Fig. 2.

Fig. 3(a) shows our experimental setup. One fiber of the fiberarray is the input waveguide, and the other fibers are the out-puts. The input light is collimated with a –mm com-pound lens and the collimated beam has a diameter of8.7 mm. The lens is an AR-coated four-element achromat withdiffraction-limited performance from 1500 to 1600 nm. It hasa 6-mm field-of-view (FOV). The grating (600 line/mm) oper-ates in Littrow configuration, which enables small polarizationdependence, high grating efficiency, and simpler alignment ofthe fiber array. The grating has a loss of1.3-dB/pass and apolarization-dependent loss (PDL) of0.5 dB/pass. With thedouble-pass configuration, its background ghost level is65dB. A quarter-wave plate is inserted before the grating so thatin the double-pass configuration it interchanges the TE and TMpolarizations and reduces the PDL of the grating. At the imageplane is the spatial transform device which consists of a spe-cial retroreflector-array (V-groove array), which creates spa-tial offsets in the direction between the different wavelengthchannels. Because of these offsets, different channels have dif-ferent foci along the direction when transformed back to theinput plane. Each of these channels is then coupled to a differentoutput fiber if the fiber spacing corresponds exactly to the off-sets created by the reflector array. This principle is illustrated inFig. 3(b). To first order, the mapping between input and outputis

(13)

for (14a)

for (14b)

where is the fiber spacing, and are the two ends ofthe designed passband, and corresponds to the middle ofthe V-groove array ( ).

Because we double-pass the grating and the spatial offsetin the image plane occurs in the direction orthogonal to the

Fig. 4. Top and side views of the retro-reflector array; note that differentoutputs have different spatial offsets.

grating axis, the sharpness of the (de)mux passband is limitedby the resolution of the lens/grating combination. Though thelens/grating also determines the system’s spatial dispersion,the demux bandwidth can still be independently controlled byvarying the width of each retroreflector. For an -mmlens and a 600-line/mm grating, the resolution is 0.2 nm. Thusif the passband width is much greater than 0.2 nm, a very highFOM can be achieved. Furthermore, the resulting demux can bechromatic-dispersion-free within the passband because everywavelength travels exactly the same path length.

To achieve those offsets, a V-groove array is assembled, asshown in Fig. 4. The assembly consists of four 90retroreflec-tors, each shifted from its neighbor. In order to match the fiberarray pitch of 127 m, the shifts are designed to be close to 63.5,127, and 63.5 m, respectively. The reflectors are diamond ma-chined individually with rms surface roughness10 nm andpeak-to-valley value 80 nm and then assembled together. Notethat in [11] the same principle has been employed to demon-strate a single-channel optical filter for multimode-fiber trans-mission. In [12], a different reflector structure has been used todemonstrate a singlemode demux. The demux in [12] does nothave high FOM and can suffer from uncanceled residual dis-persion. Moreover, its loss was not reported. Here we show thatthe required accuracy for the demux can be met for single-modefiber systems without adjusting the reflectors individually. Theresulting FOM is high and the loss is reasonable. We note thatour approach can scale to large channel counts by assembling to-gether more retroreflectors with the appropriate widths and off-sets. Since the reflectors are diamond machined on brass, theycan in principle be replicated in large quantities for very lowcost. Fig. 5 shows such a replica with gold coating. The replicais 1 in in diameter, gold-coated, and made from a polymer ma-terial.

Fig. 6 shows the measured amplitude and phase responses ofone of the channels. The amplitude is smooth except for a fewripples. The ripples are due to the imperfect surface qualities ofthe retro-reflectors. The changes in group delay across the pass-band is very small and approaches the instrumentation limit. If alinear fit is applied to those group delays (dashed line), then thefitted dispersion is 0.34 ps/nm. Fig. 7(a) shows the experimentalresults for all four channels, which covers the extended CLband. The channel spacing is23.5 nm and the loss is10 dB


Fig. 5. Polymer replica of the V-groove array. The part is 1 in in diameter.

Fig. 6. Experimental results: amplitude and phase responses of one of thechannels. RBW= 0:1 nm. The dashed line is the linearly fitted phase response.

for the two inner channels. The loss for the two outer channelsincreases but by no more than 4 dB. The amplitude responsesof the two outer channels are not uniform possibly because theretro-reflectors are tilted with respect to the grating axis. ThePDL of the device is 0.2 dB because the quarter-wave plateameliorates the grating’s PDL of 0.5 dB/pass. Taking into ac-count fresnel losses, lens-induced distortions, and grating loss,the expected total loss is 6 dB. One possible explanation for ourlarger-than-expected-loss is that the shifts between the adjacentV-grooves do not correspond exactly to the fiber spacings. Sincethe V-groove array is placed at the focal plane, any variations intheir offsets are translated, one-to-one, back to the fiber array. Toensure coupling into all the fibers, the coupling into individualfiber is not optimized. Fig. 7(b) shows the detailed structures atthe edges of the two inner channels. The FOM of these channelsis measured to be 97% and corresponds well with the theoreticalpredictions. We would like to point out that the FOM of our de-vice is independent of its insertion loss. Thus, in principle, ourdemux can have very high FOM and very low insertion loss. Thebackground crosstalk of our demux is better than50 dB.

A potential application for this device is its use as thebanding (de)mux in a banded DWDM system. In bandedDWDM, individual wavelengths are first multiplexed assubgroups, and all the subgroups are then multiplexed with abanding demux [13]. Each subgroup can be considered as a

(a)

(b)

Fig. 7. (a) Measured amplitude response for all four channels. RBW= 0:1

nm. (b) Closer inspection of the edges of the two inner channels. RBW= 0:05

nm.

band and manipulated as a unit. An example of banded DWDMis the recent triple-banded 10-Tb/s transmission experiment,which combines channels from S-, C- and L-bands [14]. Inpractical systems, the bands can range anywhere from severalnanometers in some optical add–drop nodes to several tens ofnanometers in optical repeaters. If the banding (de)mux doesnot have the needed FOM, guard bands as large as severalnanometers can become necessary between bands even ifthe optical amplifier covers the entire wavelength range. Toinvestigate the device’s merit as a banding (de)mux, we sendsingle-channel 40-Gb/s pseudorandom bit sequence(PRBS) nonreturn-to-zero (NRZ) data through it. The crossoverpoint in Fig. 7(b) is used as the reference wavelength. Thesignal wavelength from a tunable laser is first set to thisreference and then gradually tuned away from it into the flatportions of the demux and the corresponding BER at eachwavelength is measured. The results are summarized in Fig. 8.At the reference wavelength [0 GHz from the crossover pointin Fig. 7(b)], a very large power penalty has been measuredbecause the signal is located at the filter edge. However, as wetune away from the filter edge into the flatter portions of thedemux the power penalty decreases quickly. The 1-dB penalty,measured at a bit error rate (BER) 10occurs at 45-GHzoffset and there is no power penalty when the offset frequencyis 160 GHz. Detuning toward the other frequency directionleads to the same results. Therefore, when this device is usedfor 40-Gb/s NRZ system with 100-GHz spacing, no guardband will be needed if the system can tolerate a 1-dB penalty,and only two channels closest to the crossover point, one on


Fig. 8. Offset frequency versus power penalty. Zero offset (0 GHz) is definedby the crossover point in Fig. 7(b).

each side, need to be skipped if the system cannot tolerate anypenalties from the banding demux.

IV. EXAMPLE 2: 12.5 GHz SPACED (DE)MUX

The second example is a demux with narrow channel spacing.As data traffic grows, the channel spacing of a WDM networkmust become narrower to enable denser channel packing. At a10-Gb/s data rate, 25-GHz channel spacing is already commer-cially available. Therefore components with 12.5-GHz channelspacing is critical to increasing the present spectral efficiency. Inorder to accomplish this channel spacing, either the spacing be-tween the fibers in the array needs to be decreased or spatial dis-persion of the device must be increased. The fiber spacing is lim-ited to 25 m because of increased waveguide crosstalk dueto thinner cladding. At 1550 nm, the frequency of the grating islimited to 1160 lines/mm to guarantee a reasonable grating ef-ficiency ( 75%) in both polarizations. Thus for a demux shownin Fig. 1, increasing the spatial dispersion means increased di-mensions. However, a very simple processing in the image planecan increase the dispersion by a factor of 2 with negligible in-crease in the device’s dimensions.

Fig. 9(a) shows the demux schematic. A waveguide concen-trator [5] is attached to the SMF-28 fiber array to reduce the fiberspacing from 127 to 26 m. One of the waveguides serves asthe input and the other waveguides are the outputs. The beam iscollimated with an -mm lens and a plate followingthe lens eliminates the PDL. The collimated beam is incidentupon the bulk diffraction grating in Littrow configuration. Thediffraction grating is a commercial ecchelle (52 lines/mm) op-erating in the 22nd order and has a bandwidth of 30 nm centeredat 1550 nm. Grating operation in such a high order leads to highspatial dispersion, which facilitates achieving narrow channelspacing. At the image plane, a 90prism flips the wavelengthsabout the axis [Fig. 9(a), inset] such that the effective disper-sion doubles when the image goes back to the input plane [15].The input–output mapping is

(15)

(16)

The significance of the mapping is obviously a doublingof the dispersion of the system. The effect of themapping isalso significant since it means that anymotion of the input is

(a)

(b)

Fig. 9. (a) Demux schematic. Inset: wavelength is flipped at the image plane.(b) Demux characteristics for a selected wavelength range.

exactly matched by an identical movement in the output. Thus,unlike the single-pass systems, if the input and output are movedin the direction simultaneously here the coupling efficiencydoes not change. Since motion in thedirection causes smallchanges in grating dispersion, it can be used to fine tune thechannel spacing of the multiplexer.

Fig. 9(b) shows the typical demux characteristics tested withan amplified spontaneous emission (ASE) source. The fiber-to-fiber loss is on average 10 dB. This loss is due to the loss at thefiber-array/waveguide-concentrator interface (1.8 dB/pass), theloss at the diffraction grating(1.2 dB/pass), Fresnel losses andthe distortion due to the lens. The channel spacing is 12.5 GHz(0.1 nm) and the channel passbands are Gaussian-shaped with afull-width at half-maximum (FWHM) of 6.5 GHz. The demux’sPDL is 0.2 dB because the plate ameliorates the grating’sPDL of 0.7 dB/pass. The typical crosstalk from the adjacentchannel is 20 dB and the typical background crosstalk, theratio between peak transmittance and the residual light a fewchannels away from the signal channel, is better than35 dB.The center wavelength of the demux can be easily tuned overthe entire C-band by rotating the grating. To our knowledge, thisdevice demonstrates the narrowest channel spacing reported fora free space demux [17].

To show that this demux is indeed compatible with 12.5-GHzspaced DWDM networks, we performed vestigial sideband fil-tering experiments [18]–[20]. For a 10-Gb/s NRZ signal, itsdouble-sideband spectrum is 20 GHz wide. Thus, vestigial side-band modulation must be employed for the signal spectrum tofit into the 12.5-GHz grid. The grating is mechanically rotatedto match the transmitter wavelength of 1549.8 nm. The centerfrequency of the transmitter is then detuned with respect to thedemux passband. The transmitter is modulated with


(a)

(b)

Fig. 10. (a) Power penalty versus VSB frequency detuning. (b) Eye diagrams for various frequency detuning.

PRBS data, sent through the demux and detected with a pinreceiver. The back-to-back receiver sensitivity is21.9 dBm.Fig. 10(a) shows the system penalty as a function of the detuningand Fig. 10(b) shows the eye diagrams for some of the detunedfrequencies. When the detuning is less than 3 GHz, error-freeoperation (10 ) cannot be achieved for powers below our re-ceiver’s saturation level. The eye opening at 0 GHz is signifi-cantly reduced but starts to improve as the detuning increases.The best eye opening is obtained when the detuning frequencyis 4 GHz. The power penalty is 1.2 dB for4 GHz and 1.5 dBfor 4 GHz. One possible explanation for this slight asymmetryis the chirp in the modulator and/or the dispersion at the demuxedge. Fig. 11 shows the vestigial side band (VSB) spectrum afterthe mux when the offset between the center of the mux passbandand the carrier frequency is 4 GHz. The VSB spectrum is asym-metric and has a 20-dB bandwidth of 12 GHz.

We then perform an eight-channel DWDM experiment.Fig. 12(a) shows our experimental setup. Eight external cavitylaser diodes are set to have channel spacings of 12.5 GHzaround 1550 nm. Fig. 12(b) shows the optical spectra of alleight channels. The frequency errors are measured with awavelength meter to be under 2 GHz, and the variations in theoutput powers is under 3 dB. The even and odd channels arecombined into two groups using 4 1 splitters and modulatedseparately with independent PRBS data patterns. The

Fig. 11. The spectrum of the VSB (dashed line) and the DSB (dotted line)signals. The resolution bandwidth of the OSA is 0.01 nm.

even and odd groups are each splitted into four copies using 14 splitters. Each copy is sent through a different port of our

12.5-GHz-spacing optical mux. The mux not only filters outthe unwanted channels, but also acts as the VSB filter for thesignal channel. We note that in a field trial situation where eachlaser is followed by its own data modulator, the splitters are notneeded. The mux can combine the channels and accomplishVSB filtering. Thus, comparing to the standard NRZ trans-mitter, the VSB transmitter doesn’t require additional complex-


(a)

(b)

Fig. 12. (a) Experimental setup. (b) The eight channels at the fiber input.

ity. Furthermore, the same direct detection scheme applies forboth VSB signaling and the conventional double-sideband NRZsignal. A grating-based tunable filter selects a single channeland drops the other seven. The filter passband is flat-toppedwith an FWHM of 10.5 GHz and is crosstalk is better than40dB. The dispersion across its passband is minimal. This narrowbandwidth and the sharp edges of the filter allow for smallcrosstalk penalties even at very narrow channel spacings. Theselected channel is amplified and sent into a preamplified pinreceiver for BER measurement. For 10-Gb/s NRZ data with

40-dB OSNR, this receiver has a back-to-back sensitivityof 33 dBm at 10 BER. For the VSB signals, the receiversensitivity degrades from this back-to-back sensitivity by atleast 2 dB. This degradation originates from VSB filteringand the crosstalk penalties from the adjacent channels due totight channel spacing (1 dB). Fig. 13 shows the -factor andthe received power at 10 BER for all eight channels. Thefrequency offset between the laser and the filters is very criticalnot only because it determines the VSB filtering distortions andthe transmitter power, but also because the wrong offset

Fig. 13. Q-factor (square) and receiver sensitivity (triangle) for all eightchannels.

can lead to increased crosstalk from the adjacent channels. Webelieve that if external wavelength lockers were applied to thetransmitters to reduce the variations in those frequency offsetsthe and sensitivity variations amongst the channels will begreatly reduced.

V. CONCLUSION

We have presented two examples of a class of diffraction-grating-based demux that utilizes image plane transformations.In the first example, a record FOM of 97% has been achieved.The superiority of this device as a banding demux has beendemonstrated. In the second example we construct a 32-channel12.5-GHz-channel-spacing demux. We use this demux to applyVSB filtering at the 10-Gb/s transmitter and shows its compati-bility with DWDM systems. These examples and the system ap-plications they enable show that the use of image plane transfor-mations leads to unique advantages in diffraction grating baseddemux.

ACKNOWLEDGMENT

The authors would like to thank T. Zhou, S. Chandrasekhar,and L. Buhl for helping with the system testing, and M. Zirngibl,C. Doerr, and J. Ford for discussions.

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Charles X. Yu (S’96–M’98) received the B.S., M.S., and Ph.D. degrees in elec-trical engineering from the Massachusetts Institute of Technology, Cambridge,in 1995, 1996, and 2001, respectively.

During school, he held internships with Hewlett-Packard and IBM andstudied quantum noise and squeezed solitons for his doctoral dissertation. Tofurther his education after graduation, he joined Bell Labs, Lucent Technolo-gies, Holmdel, NJ, as a Member of Technical Staff in the Photonic NetworksResearch Department.

Dr. Yu is a member of Tau Beta Pi, Sigma Xi, and Eta Kappa Nu.

David T. Neilson (M’97–SM’01) received the B.Sc. and Ph.D. degrees fromHeriot-Watt University, Edinburgh, U.K., in 1990 and 1993, respectively.

He was a researcher working on Optical Interconnect systems from 1993 to1996 at Heriot-Watt University. From 1996 to 1998, he was a Visiting Scientistat NEC Research Institute, Princeton, NJ, researching applications of opticalinterconnects to computer networks. Since 1998, he has been with Bell Labs,Lucent Technologies, Holmdel, NJ, where he has been working on the applica-tion of MEMs devices to WDM systems and free-space optical crossconnects.In 2001, he became Director of the Photonic Subsystems Research Departmentof Bell Labs. He has authored more than 70 journal and conference papers andholds four U.S. patents.

Dr. Neilson is a Senior Member of the IEEE Lasers and Electro-Optics andCommunications Societies and a Member of the Optical Society of America.

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Diffraction-grating-based (de)multiplexer using image plane transformations