LOW CROSSTALK DEVICES FOR WAVELENGTH-ROUTED HETWORKS.
`
`M.J. Robes* (now'), F.P. Payne*, P. Dainty', T.J. Ball' and W.A. Crossland*.
`
`Abstract: OVer the last year, bo1odyne beat noise and bandwidth narrowing due to filter concatenation have been
`identified as 1ajor probleJS for large wavelength-routed networks. These probleJS will beco1e 1ore acute and will
`interact at the design stage, as wavelength channel spacings are decreased and as the channel bit rate is increased,
`leading to the reguire•ent for devices with high fractional bandwidth per channel and with very low (<-50 dB)
`crosstalk. lie explore the funduental lilits to crosstalk in optical routing co1ponents, and propose new design
`concepts for wavelength delultiplexers/Jultiplexers and space switches that have the potential to 1eet these strict
`perfonance reguirewts.
`
`1 Introduction.
`
`Wavelength division Jultiplexing (Iiiii) is an attractive
`technique for providing the high aggregate capacities
`into optical routing nodes because, with appropriate
`network design, the routing can be transparent to the
`bit-rate per channel and to the transport 1ecbaniS1
`(PDB/SDB/ATH) , and the routing does not reguire any fon
`of synchronisation between channels [ 1]. In the next
`section we outline two of the current ujor probleJS in
`wavelength-routed networks, and describe bow
`these
`probleJS lead to the deland for wavelength-routing
`devices with high fractional bandwidth per channel and
`very low crosstalk, typically - 50 dB. The purpose of
`the work presented in this paper was to investigate the
`design of wavelength-routing co1ponents with such
`properties.
`
`It is an ai1 of the POETS project to investigate free-space
`iapleJentations of optical routing, based on the use of
`fixed and dynuic holographic co1ponents. In the context
`of a colloquiUJ on guided-wave devices, we were interested
`in answering the following questions: what sort of
`crosstalk (and bandwidth) perfonance light we be able
`to achieve with holographic
`(free-space) optical
`co1ponents, bow does the likely crosstalk perfonance
`of
`the holographic devices co1pare with
`that of
`guided-wave devices, and bow can we take advantage of
`recent advances in 1icroengineering techniques [ 2], and
`exploit the potential for 2-D fan-out with free-space
`optics, in order to design co1pact devices.
`
`even for switches with infinite extinction ratio. For
`'free-space' optical switching we
`show
`that
`the
`'background' crosstalk uy be suppressed by exploiting
`the coupling behaviour of Gaussian bealS into single-Jode
`fibres.
`
`In section 4 we present a new holographic i1ple1entation
`for optical switching with spatial light 1odulators,
`that bas been designed to eli1inate the crosstalk fro•
`higher diffraction orders. In section 5 we show that
`guided-wave wavelength deJultiplexing and reJultiplexing
`devices are unlikely to provide the colbination of high
`fractional bandwidth and low crosstalk that will be
`required in wavelength-routed networks. lie also discuss
`the probleJS that arise for a blazed-grating wavelength
`de1ul tiplexer when narrow channel spacings are reguired.
`Finally, in section 6 we present a new design of wavelength
`deJultiplexer, designed to overco1e the probleJS of a
`blazed grating approach.
`
`2 Current problas in wavelength-routed networks.
`
`one of the first applications of optical routing is
`likely to be an evolutionary one: not a fully transparent
`optical network but a transparent optical transport
`layer, overlaid on the electronic transport layer (3,4].
`The function of the optical crossconnects would be to
`route high capacity
`tande1 traffic, bypassing the
`electronics, and 'adding (dropping)' the lower capacity
`channels and the originating (teninating) traffic fro•
`(to) an electronic cross-connect. The function of a liDII
`crossconnect is to set up se1i -penanent routes for each
`wavelength channel: this uy be achieved with three
`optical stages: a wavelength detultiplexer on every input
`fibre,
`followed by a reconfigurable space-switch,
`followed by a wavelength Jultiplexer on everv ""~-- ·
`fibre (figure 1).
`
`In section 3 we discuss bow the various choices Jade
`during the design of a space-switch will influence the
`final crosstalk, and co1pare the funda1ental li1i ts to
`the crosstalk in guided-wave and free-space optical
`switching: we predict that for se1iconductor integrated
`guided-wave devices there is a 'background' level of
`As a result of recent de1onstrator projec
`crosstalk, induced by scattering fro• surface roughness,
`* ca.brillge University Engineering Dept., 'I'nlllpington Street, ca.bridge CB2 lPZ, England.
`I Departaent of Electronic and Electrical Engineering, King's College, The Strand, Inndon WC2R 2LS.
`
`211
`
`FNC 1004
`
`

`
`wavelength-routing nodes [ 5], two tajor problets have
`been discovered to afflict wavelength-routing networks.
`The problets are bandwidth narrowing and botodyne beat
`noise, and they interact at the design stage. Wavelength
`routing necessarily involves a wavelength selection
`process (in the detux stage and perhaps the lUX stage) :
`every wavelength selection process bas a finite filter
`bandwidth, and each subsequent filtering operation leads
`to a narrowing of the net bandwidth perceived by a routed
`channel. For a large wavelength-routed network the net
`end-to-end bandwidth can becole very narrow, leading to
`the detand for
`tight control on
`the trannitter
`wavelengths: good wavelength stability can be achieved
`with fibre gratings [6]. In a large network we would
`then have tany transtitter lasers at alJOSt (within the
`wavelength referencing tolerance) the sue wavelength.
`As a signal traverses the network, crosstalk in the
`routing optics will lead to the acCIIIIIlation of in-band
`crosstalk, originating frot other transtitters at the
`sate ( notinal) systet wavelength. Because the receiver
`is a square-law device, the crosstalk will beat with the
`signal. If the frequency difference between the signal
`and crosstalk is within the receiver bandwidth, the
`crosstalk will corrupt the data.
`lismrLl.: Transparent Optical Cross-Connect
`
`) ! END
`!
`x )
`Rx X
`l.£~€H~9~~<2~_dii~!!:l!..~fio/llj
`Even without tight wavelength referencing, botodyne beat
`noise will still arise due to crosstalk originating fro•
`the sate transtitter as the signal itself: this occurs
`due
`to non-perfect wavelength delultiplexing and
`retultiplexing [7], and depends on the routing con(cid:173)
`figuration.
`
`The net crosstalk atplitude can be reduced by taking the
`tultiplexer wavelength dependent [8], but this requires
`an extra filtering operation per routing node, and so
`will exacerbate the bandwidth narrowing problet. Reducing
`the device crosstalk will very often lead to a reduction
`in the allowed filter bandwidth, again taking the
`bandwidth narrowing worse. A narrower end-to-end
`bandwidth requires
`tighter wavelength referencing,
`leading to worse hotodyne beat noise.
`
`The conclusion fro• this cycle, is that for the wavelength
`filtering devices we should seek to witise the bandwidth
`we can achieve for a given crosstalk, and for the
`space-switches we should seek to tiniaise the crosstalk.
`
`ile have used a statistical approach to si1ulate the
`aceutulation of beat-noise terts for an optical transport
`network with as ruy nodes as the current OK inner-core
`network, and have found that (for a wiiUI receiver
`penalty of 2 dB at error rates of 1 in 109
`), the crosstalk
`requiretents vary between -43 dB and -50 dB, depending
`on the network architecture.
`
`3 Space Sllitcb design for low crosstalk.
`
`For wavelength-routing the space-switches need reason(cid:173)
`able fan-out, e.g. 4 or s, rather than fast switching
`speed: for exatple the reconfiguration tite for an
`electronic (SDH) crossconnect is 20 IS [9]. The routing
`configuration is controlled by electronic signals sent
`by the local eletent ruagewt centre: all-optical
`switching is not necessary. Therefore very fast nonlinear
`'all-optical' switches are outside the scope of this
`study, although they uy have other roles to play in iiDM
`networks for use as wavelength converters, for exatple.
`
`The design of a space-switching co1p0nent breaks down
`into 3 stages: the first is the choice of a process or
`aethod for pertoraing a space-switching function; the
`second is the choice of a particular architecture or
`arrangeaent of the sub-switch coaponents; the third stage
`is the choice of a particular itpletentation: that is
`the device technology and the details of the device
`design. Decisions tade at all 3 stages of the design
`process have iaplications for the final crosstalk levels.
`
`3.1 SWitch aethod.
`
`lil Guided-wave §!litche5: Guided-wave switches fall into
`two classes: those based on interferoaeters, and those
`perforaing a tore digital,
`'gating' function. The
`interteroteter-based switches are operated by adjusting
`the effective indices of parallel waveguides. This
`process will inevitably be prone to high crosstalk,
`because slall changes in the effective index of one guide
`can lead to large changes in the power coupled across.
`Possibly the best crosstalk results that have been
`obtained with an interteroteter aethod are - 24 dB
`crosstalk in a 4 by 4 utrix switch using electro-optic
`effects in a directional coupler [ 10 ].
`
`'gating' class of guided-wave switches is less
`The
`crosstalk-prone: one tethod involves splittinq the input
`power so as to take several 'copies' of the input signal.
`The passage of one copy of the signal in a particular
`direction is controlled by turning gain blocks on and
`off: in the 'on' state the gain coapensates for the
`splitting loss, and in the 'off' state the signal is
`blocked by the attenuation of the gain block. Both
`seaiconductor laser a.plifiers and rare-earth doped fibre
`aaplifiers have been used as gain blocks to perfon
`
`2/2
`
`

`
`a switching function. Another 'gating' switch is based
`on the 'digital optical' Y switch. The crosstalk for
`this class of switch depends on the extinction ratio of
`each individual switch ele1ent. For 'gating' switches
`i1ple1ented
`into
`integrated se.iconductor devices,
`reported extinction ratios for the SLA are 40 dB [ 11],
`and for the Y-switch are 40 dB [12].
`
`!iil Free-space switches: 'Shadow-routing' switches are
`the free-space equivalent of the se1iconductor laser
`uplifier guided-wave switch, except that the sha(cid:173)
`dow-routing uses attenuation instead of gain to control
`the routing. For the shadow-routing, a fixed hologru
`acts as a splitter to take .any copies of the input
`signal. All but the chosen copy are blocked with an
`luplitude) spatial light .odulator: at present typical
`•odulator contrast ratios are in the range 150 to 200,
`but experbental studies indicate that an order of
`1agni tude increase in the contrast ratio is possible
`with refined substrate properties. The shadow routing
`switches can have very high fan-out: for exuple a 64
`by 64 crossbar switch has been delonstrated as part of
`the OCPM project [ 13]. However, to achieve such high
`fan-out requires the use of 1ul tiiOde fibre in the output
`plane, and this would preclude the use of such switches
`in a transparent optical network.
`
`The second free-space switching ethod for perfoning a
`switching function is to 'bea•-steer' the input signal
`to the required output waveguide. This 1ethod is perhaps
`the
`least prone
`to crosstalk out of all four
`( guided-wave+free-space) 1ethods discussed
`in this
`paper: assuling we have steered the beu to the correct
`output, the resulting crosstalk will coe fro• the
`evanescent tails of beus steered to an adjacent output
`port. For Gaussian output beus of spot size 'x', latched
`into output waveguides spaced distance 's' apart, the
`theoretical crosstalk is- 4.34 (sfx)" (using [14]). For
`'standard' type telecons fibres spaced 250 Ul apart,
`and planar silica waveguides spaced 50 Ul apart, this
`theoretical crosstalk is only -10,400 dB and - 940 dB,
`respectively ( ! ) . This is far too s1all to be 1easured
`and would not contribute to ho1odyne beat noise probleiS
`in even the largest of networks. Exuples of heal-steering
`switches include 'Start' fibres, acousto-optic beu
`deflectors and liquid-crystal holograiS.
`
`3.2 SWitch architecture.
`
`It is well-known that dilated switch architectures will
`reduce the net crosstalk for a space-switch. For exuple,
`a logical H by H (crossbar) switch can be foned fro• a
`l:H switch at every input port, fibre 'wired' to H:l
`switches at every outport port. For this architecture,
`2 'crosstalk events' 1ust occur for crosstalk to appear
`at the output. Bence the net crosstalk is second-order:
`
`a net crosstalk of -60 dB for a space-switching stage
`can be achieved with l:H and H:l switches with crosstalk
`between ports of -30 dB.
`
`A secondary advantage of a dilated architecture is that
`it is easily upgraded: a dilated H by H switch can be
`progressively upgraded to a MH by MH switch by placing
`l:M switches at each of the ofp's of the l:H switch.
`
`3.3 SWitch i1pleentation.
`
`The choice of device technology can also influence the
`crosstalk.
`
`( i I Guided wave switcbe5: The lowest crosstalk guided(cid:173)
`wave switches are those using se1iconductor 'gating'
`eleents. These are
`integrated
`into a planar
`seliconductor device, with connection between
`the
`gain/loss blocks in waveguide foil. The se.iconductor
`device fabrication process can introduce i1perfections
`in the waveguide walls. The typical feature size for
`these i1perfections is close to the carrier wavelength
`for optical signals. lie were interested to see whether
`scattering fro• these surfaces would lead to a significant
`'background' level to the crosstalk, that would occur
`even for switch elmnts with infinite extinction ratio.
`
`In this technology, significant attenuation in the
`waveguides occurs as a result of 1ode coupling fro• the
`funduental waveguide IOde(s) to radiation and substrate
`lOdes, where the lOde coupling is excited by the surface
`roughness of the waveguide walls. Typical loss coeffi(cid:173)
`cients for this scattering lechanis1 are between 3 Cl-~
`and 5 Cl-~. The coupling can be interpreted as being
`equivalent to a given probability (per unit length) of
`a photon being coupled out of the waveguide. on reaching
`an adjacent waveguide, the photon will have the sa1e
`probability of being coupled into ~ waveguide. Bence
`the lode coupling will lead to a 'background 1 level of
`crosstalk, even
`for switch blocks with
`infinite
`extinction ratios. Earlier theory developed to calculate
`the attenuation due to this surface roughness [ 15], bas
`been adapted to calculate the crosstalk. It was found
`that the ratio of the (absolute) crosstalk, C, to the
`square of the loss coefficient due to this scattering
`1echanis1 is given by:
`C!a 2 cxL 2 1D
`
`(l)
`
`where L is the length of parallel waveguides, D their
`separation, and the constant of proportionality depends
`strongly on the correlation length of the surface
`roughness, but is insensitive to all other para1eters.
`The 1axi1ut crosstalk occurs at short correlation lengths
`of the order of 0.05 ut: with a loss coefficient of 5
`Cl-~, and a 1 u length of parallel waveguides separated
`by 250 Ul, we esti1ate the crosstalk to be - 50 dB.
`
`2/3
`
`

`
`( iil Free-space switches: Reflections in a free-space
`optical syste1 can lead to two distinct crosstalk
`techanists: reflection into the wrong ojp port (not the
`intended o Jp) , leading to a crosstalk of say, -c dB per
`switch, can be reduced to a net crosstalk level of - 2C
`dB, given a dilated switch architecture. However,
`coherent (unwanted) reflections into the intended o/p
`port, cannot be retoved with a dilated architecture. '1'he
`coherent scattering should therefore be less than - 50
`dB, while the adjacent channel crosstalk can be -25 dB
`with a dilated architecture. Unwanted diffraction orders
`in a holographic systel can also lead to crosstalk.
`
`In a free-space holographic optical systet, unwanted
`reflections will occur fro• the input and output lenses,
`the hologr• surfaces, the cleaved fibre ends, and the
`fibre 10unts. High-quality couercialAR coatings on the
`lens surfaces will bring these reflectances doim to less
`than 0.12 \ (equivalent to - 29 dB) over a 40 u window
`[ 16]. For Fresnel reflection off the fibre end we assUie
`an effective fibre
`index of 1.445, giving a net
`reflectance of 3. 3 l or -14.8 dB. One side of the hologrilll
`will be rough, due to the devices/pixels used to foil
`the hologrilll: it would be difficult to 1R coat this
`surface so we assuu a reflectance of around 4 \ (- 14
`dB). The other side of the holograt could be 1R coated
`with a reflectance of - 29 dB (as for the lens surfaces).
`Figure 2:
`Hologram used in transmission.
`
`input lens hologram output lens
`f
`f
`f
`f
`For a holographic syste1 used in transtission (figure
`2) , two reflections tust occur for coherent scattering
`or crosstalk to be coupled into the ojp fibres, so that
`the net effect is a second-order function of the
`reflection fro• a single surface. In order to taxiaise
`transaitted power and ainiaise spherical aberrations we
`assuu the use of precision-toulded plano-aspheric lenses
`for the i/p lenses, with the planar surfaces closest to
`the fibre ends. We have estiaated the size of the
`reflections fro• each possible pair of surfaces.
`Single-aode fibres will only accept light fro• ijp bealS
`that are well-focused, at near-nortal incidence, and
`with a beat centre close to the fibre core: we have also
`estiaated how auch of the reflected power is coupled
`into the input and output fibres, using the standard
`fortulae [ 14] for the coupling efficiency of Gaussian
`beaas into standard telecoiiS fibres.
`
`BealS reflecting fro• a lens surface will diffract and
`be defocused on the fibre ends: the resulting phase-front
`
`curvature leads to very weak coupling into the fibre,
`therefore 1ost reflection pairs including a reflection
`fro• a lens surface will cause negligible coherent
`scattering. The strongest event in this set occurs for
`light that is initially reflected fro• the cleaved end
`of the output fibre, then again reflected fro• the near
`surface of the output lens. After reflection fro• a
`plane lens surface and coupling back into the ojp fibre,
`the net crosstalk level is estiuted to be - 80 dB, for
`a lens surface 5 u fro• the fibre end.
`
`Beats reflecting fr01 the rough hologrp surface: norul
`reflections fro• the holograt surfaces will be refocused
`by the lenses and can therefore be strongly coupled into
`the i/p and ofp fibres. lie assuu that the rougb surface
`of
`the hologrilll is facing towards
`the i/p fibre.
`Reflection fro• this bologrilll surface, followed by
`transaission througb the i/p lens, will lead to a
`significant back-reflection into the i/p fibre. In a
`dilated switch architecture, two such scattering events
`will lead to coherent scattering levels of - 28 dB or
`tore, depending on the roughness of the bolograt surface,
`leading to significant beat-noise. l!eflection froa the
`rough bolograt surface, followed by reflection froa the
`cleaved end of the input fibre would also lead to - 28
`dB coherent scattering in the output fibre. However, we
`can avoid these crosstalk aechanisas by placing the i/p
`fibre slightly off-axis (figure 3). For an i/p fibre
`offset by 'o' Ul, the reflected beat would be offset by
`2'o' Ul, and the fraction of backscattered power coupled
`into the ijp fibre would be -4.343(2o/X) 2 dB [14] : an
`offset of 11 Ul
`is sufficient
`to suppress
`the
`backscattered power by 80 dB.
`Figure 3:
`Reflected beam paths with angle-polished fibre ends
`and i/p beam in off-normal incidence to the hologram.
`
`output fibres
`'-,
`
`=
`------c:
`
`input lens hologram output lens
`f
`f
`f
`f
`
`BealS reflecting fiOI the cleaVed end of both fibres:
`the estiuted crosstalk for this aechanisa would be -
`50 dB. This effect can be suppressed by polishing the
`face of the input fibre: an angle of 8 degrees is known
`to give the best coaprotise between (out )coupling loss
`and suppression of backscatter.
`
`Reflection otf the cleaved end of the o/p fibre, followed
`by reflection froa the stooth (and AR coated) surface
`of the holograa (figure 3) aay lead to crosstalk into
`other ofp fibres, depending on their position. With
`worst-case positioning, the crosstalk would be -43 dB.
`
`2/4
`
`

`
`With careful choice of the position of the ojp fibres,
`this crosstalk could be reduced considerably. A 15 UJ
`separation between the centre of the crosstalk bea1, and
`the nearest o/p fibre, would reduce the crosstalk to
`below - 80 dB. Alternatively we could polish the end of
`the output fibres to suppress the reflection.
`erosstalk fiOI UDVa!!ted diffraction or!lers.
`The crosstalk and coherent scattering due to reflections
`will occur in any i1ple~entation of a beu-steering
`hologru. The crosstalk fro• unwanted diffraction orders
`depends on the specific details of the hologru technology
`and design.
`
`Holographic beu-steering can be i1ple1ented with phase
`I:Odulation of a spatial light 1odulator (SUI)
`[17].
`Polarisation-independent operation (18] can be achieved
`with a binary phase hologru, foiled fro• a 2-D pixellated
`array of ferroelectric liquid-crystal, eJbedded in, and
`controlled by, a VLSI silicon backplane consisting of 2
`UJ CMOS. Binary-phase holograJS are so-called because
`they can induce two different values of path difference
`in light passing through the pixels. The relative phases
`are usually 0 and pi, and are controlled by rotating the
`liquid-crystal 1olecules, so as to adjust the refractive
`index experienced by light passing through the liquid
`crystal. The fraction of incident power diffracted by
`the hologru varies as sin2 (2t), where t is half the
`angle through which the Jolecule is rotated. Half-angles
`of 36 degrees have recently been achieved [19], with a
`switching tiJe of 80 us: such devices will allow
`diffraction of 90 % of the power incident on the pixels.
`These devices are an attractive co1ponent for future
`telecous networks because they are potentially very
`cheap, they require only standard 10V digital supply
`voltages, and the 2-D operation allows a large fan-out
`per switch. other exuples of heal-steering switches are
`acousto-optic beu deflectors, which require RF supply,
`and 'Start' switches, which are li1ited to 2:2 (crossbar)
`operation, although bigger switches can be Jade by
`cascading 1any 2 by 2 crossbars.
`
`An SUI is used as a beaJ-steerer by changing ( elec(cid:173)
`tronically) the phase of chosen pixels in order to
`construct a phase diffraction grating with a tuneable
`period and pattern. For pure beu-steering we require a
`perfect sawtooth phase diffraction grating: for this
`case we would get diffraction into a single grating
`order, and the output angle of the switched light would
`then be given by:
`
`sinS=A./Q
`
`(2)
`
`where Q is the grating (sawtooth) period. By changing
`the sawtooth period we change the output angle, and
`swi tcb the output between different waveguides (fig 4).
`
`Figure 4: Principle of nolographic bean> steering
`
`c::
`c::
`c::
`
`input
`beam
`
`s
`output
`L
`fibres
`M
`SLM acts as diffraction grating with
`a digitally tuneable grating period.
`
`For binary-phase operation we are li1i ted to 2 discrete
`phase levels, so we cannot foil a sawtooth phase
`variation. The closest binary-phase approxiJation to a
`sawtooth is a 'square wave', as shown in figure 5, with
`equal width stripes inducing alternate phase shifts of
`0 and pi. For this case (and with 1-D fanout) 80% of the
`input power is diffracted into two (equal) Jain orders,
`positioned syuetricall y about the optical axis. The
`rest of the power goes into higher-order grating lOdes:
`the relative upli tude of each lode is shown in figure
`6, where the output angle of the 1 1th grating order is
`given by:
`
`sine= mA./Q
`
`(3)
`
`Figure 5:
`
`a square wave grating.
`
`For a square-wave SLM, we choose the grating period such
`that the light diffracted into one of the first-order
`grating lodes is coupled into the selected output fibre.
`tlnfortunately, the higher-order grating lodes will then
`lead to severe crosstalk whenever the light diffracted
`into these orders is coupled into another (HOT selected)
`output waveguide. one Jethod to suppress this crosstalk
`is to change the grating pattern: fro• a square wave to
`a lore co1plex ( co1puter-opti1ised) structure, designed
`to suppress the higher-orders. Crosstalk levels of -35
`dB have been achieved by this Jethod, but the penalty
`is that a large nUJber of pixels are required in each
`period, leading to a stall output angle for a fixed pixel
`pitch, and consequently long devices.
`
`Acousto-optic bea1 deflectors can also be used to
`ilple1ent a free-space optical switch. We have not
`calculated the crosstalk levels in these devices but
`note that the acoustic wave is usually at around 100
`MHz. Hence at room te1perature we would expect 50,000
`
`2/5
`
`

`
`z is a tultiple of this case, so we exclude Z=l. The
`lowest possible value of Z is then 2.
`Figure 7:
`SLM divided into
`input lenses
`
`We now investigate specific designs for 'prite nUJber'
`holographic switches. By taking use of both horizontal
`and vertical directions, we tay design the switches such
`that a single transtissive SLM can perfortl:ll switching
`for every liDII channel on a specific i/p fibre into the
`routing node. To service an 8-channel liDII syste1, we
`divide the SLM into 9 equal area hologratS (figure 7).
`We arrange the wavelength allocation of each bolograt,
`such that crosstalk frot an adjacent holograt will be
`two or tore wavelength channels away. Bence we tay render
`insignificant this crosstalk by using wavelength-de(cid:173)
`pendent tultiplexing at the routing node output fibres
`[8].
`
`lie 1ay define periodic gratings in both the horizontal
`and vertical directions. For any pair of (horizontal and
`vertical) integer tultiples of twice the pixel pitch,
`Zb and Zv, and with binary phase operation, 64 % of the
`diffracted power will be directed to 4 equal ofp's, at
`ofp positions, (relative to the input fibre), given by:
`/'A
`/'A )
`(x,y)out= ±2Zhp,±2ZuP
`(
`
`( 6 )
`
`Figure 6: binary pbaac o/p amplitudes for 1-D fanout
`from a 'sqWU"e-wave' grating.
`
`11.6
`0
`., 0.5
`
`.e 0.-4 a 0.]
`8 0.2
`:
`0.1
`'8 0.0 h~~..L.y..L.y-'-'---y--&--y--&--y--&--y--&""T""""""i
`::e -41.1
`-41.2
`-41.3~-~~~~S~~~O~~~O~~S~I~O~IS~Z~O
`Orating mode order (m)
`
`tberlally-excited acoustic phonons per acoustic lode.
`The lOdes would be in an allost continuous spectrul,
`leading to a continuous angular distribution of crosstalk
`diffracted fro• the therlally excited acoustic waves,
`which cannot be avoided by appropriate positioning of
`the ofp fibres. By contrast, the unwanted diffraction
`orders fro• a holograt fort a discrete spectrul, such
`that the crosstalk can be avoided by appropriate fibre
`positioning.
`
`In the following section we investigate a new itple(cid:173)
`tentation of beat-steering liquid-crystal hologratS: we
`present a very sitple technique for suppressing the
`crosstalk frot higher grating orders, and show that the
`potential for 2-D fan-out can lead to cotpact and low
`loss devices.
`
`4 Beat-steerinq switches with very low crosstalk.
`
`To see how to avoid the crosstalk frot higher diffraction
`orders we return to the sitple square-wave SUI. The
`tinitUJ period of such a binary phase grating is twice
`the pixel pitch, and in general the grating period tust
`be an integer tultiple of twice the pixel pitch (to
`tinitise the power lost to the zeroth grating order),
`such that the possible output angles are given by:
`sine z = m 'A I ( 2 Z p)
`( 4)
`
`where Z is the integer 1ul tiple, and p is the pixel
`pitch. For any pair of integers, hand l.2 1 a higher-order
`grating output will be coupled perfect! y into the wrong
`fibre, whenever the following condition holds, for sote
`integer 1:
`m'A/(2Z 1 p) = 'AI(2Z 2 P)
`
`(5)
`
`Rearranging this expression we find that h=t.Z2, in
`other words we tay avoid perfect coupling of the crosstalk
`if we ensure that we never select a grating period that
`is an integer tultiple of another grating period that
`we are intending to use: a sitple way to achieve this
`is to use only prite values of Z. We also wish to use
`the lowest possible values of Z so as to taxitise the
`output angle fro• the SLM. If we use Z=l, then any other
`
`•
`
`•
`
`Figure 8: Output positions for the 1 :4 switch
`(X.Y) positions
`g1ven by
`
`Y
`
`• •
`
`(f>' ' ~)., \
`LZh p 2L,, r)
`uses Z = 2 and 3
`• = possible o/p
`I ~ :
`~ :
`[!] = collected o/p
`We tay fort a 1:4 switch using the first two prite nUJbers
`for Zb and Zv. The resulting ofp positions are shown in
`figure 8. We tay collect the o/p light froa any of the
`4 positions for each (Zb, Zv) pair. Our choice of collected
`orders is that which tiniaises the required o fp lens
`focal
`length for a given separation between ofp
`waveguides. For the ojp choice shown in figure 8, and a
`separation, s, between ofp waveguides, the ojp focal
`length, fout, is given by:
`f out= 2.4s piA
`
`(7)
`
`2/6
`
`

`
`Figure 9; Output positions for the 1:8 switch
`(X,Y) positions
`given by
`\
`fA
`fA
`(
`24, p2Z., pi
`uses Z : 2, 3 and 5
`
`y
`
`[!)•[!)
`
`. . .
`. •[!]
`
`• [!] •
`
`• {!] •
`
`X
`• • [!}
`
`1!1• .
`
`•: possible o/p
`
`El ••
`[!): collected o/p
`For a 1:8 switch we use the first three priae nuabers
`(2,3 and 5) for Zb and Zv. All ofp positions are as shown
`in figure 9. For a ainiaua separation, S.1n, between ofp
`waveguides, fout is given by:
`fout=6.67sp/"'A.
`
`(8)
`
`The choice of ofp lens focal length, i/p lens focal
`lenqth and phel pitch depends on a tradeoff between 3
`loss aecbanisas.
`
`Dead space loss: the 'dead space' between the active
`pixel blocks bas a width of between 1 and 5 ua. The
`effect of the dead space is to aodify the uplitude of
`each grating order, but the bologru periodicity is not
`changed by the dead space, so the position of each grating
`order retains the sue. For a dead space of width d, the
`power diffracted into each switch output is reduced to
`a fraction T40 of the ofp power with no dead space,
`independent! y of the transaission properties of the dead
`space. Tbe saaller the pixel pitch, the greater the dead
`space loss. For a bolgru with a 'square-wave' pattern
`in both horizontal and vertical directions, T40 is given
`by:
`
`T ds = ( l -_:! { _::__ ~{ sin ( n n)}) 4
`Z
`p 2Z n•l
`For Z = 2, 3 and 5, the value of the {} tera is o. 785,
`0. 907 and 0. 967 respectively.
`
`( 9)
`
`Iuput loss: A typical SLM silicon backplane device is
`14 u square. When divided into 9 blocks, each boloqru
`is 4.67 u square. Any of the incident light that falls
`outside of this boloqraa area cannot be swi tcbed to the
`correct output. Dsinq a Gaussian beall approxiaation for
`the fibre aode, and approxiaating the boloqru to a disk
`of diaaeter w, the fraction of input power reaching the
`boloqrat is given by (for std telecous fibre of 1/e2
`angle 11 degrees ) :
`Tmput= l-exp{-(w/(O.l36f,n))t)IO)
`
`where f1n is focal length of the i/p lens.
`
`output loss: on reaching the output fibre, the beat
`spot-size is aagnified by a fraction fout/fino Assuaing
`the lodes of the i/p and O/p fibres to have the sue
`spot-size, the aisaatch at the ofp fibre leads to a
`transaission loss. The fraction of incident power coupled
`
`Tout=
`
`(
`
`2
`
`)
`
`( I l )
`
`into the ofp fibre is given by:
`2/out/fin
`2
`l + (f out f fin)
`The overall switch transaission is given by (for a 1.55
`ua optiaised SUI) :
`
`T switch= O.l6sin 2 (29){T in T ds T ou0l2)
`
`For rotation angles of 36 degrees, the ten outside the
`{} brackets is 0.148 ( -8.3 dB), and the tera inside the
`{} brackets bas been calculated as a function of the
`pixel pitch and device length, L=2(fout+fin), for 8
`parallel 1:8 and 1:4 switches froa a single SUI. The
`results are sbown in figures 10 and 11, assuaing a
`dead-space of 3 ua, and for ojp waveguides separated by
`at least 250 ua. For 1:4 switching the {} tera bas a
`aaxiaua value of o. n, at a fibre to fibre device length
`of 8 ca and pixel pitch of between 50 and 60 ua. For
`such a 1:4 switch the overall transaission loss should
`be -9.5 dB. For 1:8 switching the {} tera bas a aaxiaua
`value of 0.55 at a device length of 11 ca and pixel pitch
`of 25 ua. For such a 1:8 switch the overall translission
`loss would be - 11 dB. The guided-wave equivalent switch
`block would require 64 seaiconductor uplifiers to
`perfon the sue function. Bence the insertion loss is
`irrelevant, coapared to the cost savings by using a
`free-space swi