CA2079907A1 - Optical interconnection device - Google Patents

Abstract

2079907 9115790 PCTABS00007 An optical interconnection device suitable for an N x N' coupler as used, for example, in a local area network, comprises diffraction means in the form of a body (106) having a refractive index which varies spatially and periodically in one plane of the body.
The arrangement is such that light incident upon the body in the plane and at a predetermined angle will be refracted to emerge at a plurality of discrete angles determined by the spatially varying refractive index. The incident light is distributed substantially equally among the plurality of output refracted beams and substantially all of said incident light is coupled to the plurality of refracted beams. The diffraction means comprises a cylindrical body (106), and the device further comprises two arrays (108, 110) of optical emitters and/or receivers. The arrays are disposed at opposite faces (112, 114), respectively, of the body, each of the optical receivers having an optical axis aligned with one of the discrete angles. A perfect shuffle network may comprise a plurality of nodes (121-128) interconnected by such a coupler, each node comprising a transmitter (131-138) operable at several wavelengths, a receiver (141-148), and means for determining whether a received signal is to be relayed and, if so, the appropriate transmission wavelength.

Description

.~` 1 2~79~7 ITLE: Optlcal Interconnect1on Device DESCRIPTION
TECHNICA' FIEL5:
Tnls lnvention relales ~o optlcal aevlces. ana is _ esDecially. bu~ no~ excluslvel~. applicable t- N x N' lnterconnectors or couDlers such as are used in local area networks and backplanes of telecommunications and computer equipment. Embodiments of the invention may also be used tc lnterconnect components ln integrated clrcuits, tc 1C lnterconnec~ lntegrated cir_ults on a circui~ board. an~ lr analogous situatlons in the fleld of ODt 1 cal communlcations.
especially where single mode optical fibres are to be nterconnected.
The invention also relates to oPtlcal lnterconnects or 15 couplers having limited or selective coupling capability ln that each input port is coupled to preselected ones o,~ a plurality of output ports. The lnvention alsG encompasses lightwave co~munications systems incorporating such couDlers and, for example, the so-called "multihop" networks including 20 the afore-mentioned couplers having limited or selective coupling capability. '-In this specification, the term "optical" lS used to embrace both visible and invisible lightwaves. ~ ~

25 BACKGROUND ART: -An N x N' star coupler is one of the key elements in Local Area Network (LAN) applications cc optical fibre. The simplest single~mode 2 x 2 star coupler can be manufactured by bringing the cores of two single-moae fibres sufficiently 30 close together over an appropriate coupling length. Various such structures have been built by using etching, grinding and polishing, or fusion. A 2 x 2 star coupler can be used as a basic building block to construct larger N x N' couplers where ' N is equal to an arbitrary power of two. However, this 35 involves interconnecting a large number of 2 x 2 couplers, increasing the excess loss for larger values of N.
European patent application number 0340987, published November 8, 1989, [which is incorporated herein by reference]

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2~79907 , ~
dlscloses an N x N' star optical coupler comPrlslng 3 dielectric slab and two arrays of strlp waveguide formea or a glass substrate. Opposlte surfaces cr the dielectrlc sla~.
: to which tne s~rlD waveguides are attachec, are curved. Tne 5 radius of curvature anc the dlstance between the surfaces ar~
such tha~ the octical axis of each wavegulae at one surfact extends radially across tne slab to the centre of the other curved surface.
The configuration is said 'o provlde even distributlon 10 cf light from each waveguide to the waveguide at the oP~oslte side of the dielec~ric slab. The optimized efficlency of sucr, a coupler varies between 0.34 at the edge and 0.~ at the middle of the array, which is not entirely satisfaclory. Tnls gives better coupling efflc1ency compared with a sla~ navlnc 15 parallel sides, in which lighL ~rom a partlcular inpu~
waveguide will cover more than the entire area of the opposite face, so it is relatively inefficient since much of the ligh~
is diffused before it reaches the output side of the coupler.
US patent number 4,057,319 discloses a coupler connecting 20 one fibre in a bundle to the fibre in another bundle. A phase hologram plate is interposed between an input bundle of fibres and the output bundle of fibres. The phase hologram effectively focuses the light onto the output oPtical fibre and so improves coupling efficiency. A disadvantage of this 25 device is that it is suitable only for individual connections and hence not suitable for applications requiring N x N' coupling.
US patent number 4,838,630, issued June 13, 1989 [and incorporated herein by reference] discloses a planar optical 30 interconnector for 1 x N or N x 1 coupling in interconnecting integrated circuits. The interconnector comprises a Bragg planar volume hologram which distributes optlcal signals, DUt is not capable of N x N' coupling.
US patent number 4,705,344, issued November 10, 1987, 36 [which is incorporated herein by reference] disclosed an interconnection device for optically interconnecting a plurality of optical devices. The interconnection device comprises an optically transparent spacer with photosensitive ., . , ::
:-. .:, . ~ . - . - : .

~ ~ 2~7~9~7 material on its opposite siaes. Fringes are formed, fixedly positioned. on one of the surfaces. The fringes comDrise a plurality of "sub-holograms". The other surface has Posltlons for the optical devices. The fringe pattern is formed b~
5 directing a coherent light Deam through the sPacer anc photosensitive material to one position and ~lrectlng a seconc conerent light beam from a secona position to in~erfere w1th the first beam. Each source device emits a light beam wnlch traverses the transparent spacer, is reflected b~ the 1C holograph on the opposite face. and returns to a different position. The hologram is, in effect a plurality of dtscrete holograms each one dedicated to one Pair of positions. This klnd of interconnection device provides loglc functions for optical computing but is limitea to 1 x N coupling.
1~ Thus, none of these known aevices can proviae N by N
coupling with an efficlency anc simplicity which can De considered satisfactory.
There remains a need for an optical interconnector with improved coupling efficiency for use in coupling single mode 20 waveguides, for example optical fibres, in a number of applications such as local area networks, back planes of telephone switches and also in integrated circuits or circuit boards and similar situation where a large number of connections need to be made in a very limited space.
DISCLOSURE OF INVENTION:
According to one aspect of the invention, there is provided an optical device comprising a stratified volume Bragg diffraction means, for example a hologram, having its 30 refractive index varying spatially according to the expression:

n(x, z) - 1 + ~ sin (~,z"", ~ ) m m/
where x and z are ordinates of the block;
~,~ is the spatial frequency vector;

, ~ : .
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WO 91/1~790 PCI/CA91/00113 2~7~a~
m is an input position or mode, correspond7ng to one optical axis;
m' is an output position or mode, corresPon~lng to one optical axis:
m and m' taklng on integer values that determlne the number of lnput/output moaes;
A~ is the coefficient of coupl7ng between m and m';
and r ls the sPace vector.
In one, preferred, embodiment of the present lnventlon.
suitable for interconnecting optlcal communication channels.
the device comprises a body having cylindrical opDosed faces.
said stratified volume Bragg diffractlon means ~ei~g provide~
in said body such that its refractive index varles sPatlall~
1~ and periodically in one plane of the body, the arrangement Deing such that a planar light wave incident uDon one OT saic faces of the body in said plane, at a predetermined angle, with the electric field of such light wave extending in the same direction as the axes of said cylindrical opposed faces, 20 will be refracted to emerge at one or more discrete angles determined by the spatially varying refractive index, such incident light being distributed substantially equally among the plurality of output refracted beams.
Such a diffraction means may be arranged to couDle 25 substantially all of the input light to the predetermined refracted beams, i.e. with minimal loss.
According to another asPeCt of the invention, an N x N' optical interconnector comprises a planar body having cylindrical opposed faces and two arrays of optical emitters 30 and/or receivers, said arrays being disposed one at each of said faces, respectively, said body having a refractive index which varies spatially and periodically with the electric field of such light wave extending in the same direction as the axes of said cylindrical opposed faces, such that light 35 emanating from each of said emitters is distributed equally among the receivers at the opposite face.

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WO 91/15790 PCr/CA91/00113 ~ 2~799~7 In such embodiments, the refractive index n(x,z) of the stratified volume Bragg diffract70n means varles spatiall~ lr, accordance with the expression:-n(x, ~ 1 + ~ I~m~/sin (~
m--~ m--M
where x and ~ are ordinates of the block;
d is the radius of curvature of the curved faces;
~ ~ ls the spatial frequency vector;
m is an input positlon or mode, corresponding tc one optical axis; -m' is an output position or mode~ correspon~lng to one optlcal axis;
m and m' taking on integer values that determine the 5 number of input/output modes;
is the coefficient of couDling between m and m ;
r is the space vector; and N is the total number of modes and is equal to 2M + 1.
The optical emitters/receivers may comprise waveguides.
20 for example optical fibres, or electro-optic devices for directing or receiving light. Each optical emitter is positioned so as to direct light along an optical axis extending radially of one face to the middle of the opposite face. Conversely, each optical receiver is positioned to 25 receive light along an optical axis extending radially of the face with which the receiver is associated from the middle of the opposite face. Preferably the arrangement is such that substantially all of the light from each emitter is received by the optical receivers.
According to still another aspect of the invention, there is provided a method of making a diffraction means for an optical interconnector by irradiating a body of photorefractive material having cylindrical opposed faces using a two wave mixing process employing two light beams 35 comprising substantially planar waves, the method comprising the steps of:-(i) aligning the body with its cylindrical axes transverse to the plane of said substantially plane waves;

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WO 91/15790 PCI`/CA91/00113 2~79~7 ~
(ii) directing one of said llght ~eams across saia body in said plane;
(iii) cirecting the other of said light beams across said body, in said plane. in successior,. a~ a plurality OT
5 predetermined angles to the flrs~ llght beam;
(iv) directing saia one of said llght Deams across said body at a different angle and repeatlng steps (iiij and (iv), such that the refractive lndex of the irradiated body varies spatially and Periodically in the plane of said waves, 1C such that light incident upon sald body in said p7ane at on~
of said discrete angles will be refracted to emerge in sa1a plane at a plurality of different angles.
According to a further asPect of the lnventlon, a metho~
of making a diffractlon means for an optical 1nterconnector 15 comprises the stePs of :-(i) irradiating a planar body of photorefractive material by means of a first coherent light source along an axis at a predetermined axis to the body, the light comPrislng a substantially planar wave in the plane of the body;
(ii) irradiating the body by means of a second coherent light source along an axis at a predetermined axis to the light from the first source, and (iii) recording the resulting interference pattern in the slab;
(iv) maintaining the position of the first source, (v) rotating the second source stepwise, each step by a predetermined angle, and repeating steps (i), (ii) and (iii), for each step; rotating the first source stepwise by a plurality of predetermined angles and, for each step, 30 repeating step (v).
According to yet another aspect of the invention,apparatus for producing a diffraction means for an optical interconnection device comprises first and second sources of substantially planar light wave, means for supporting a body 35 of photorefractive material, said body having cylindrical opposed faces, so as to be irradiated by light from both said sources, the electric fields of the plansr light waves extending in the same direction as ~he cylindrical axes of WO 91/15790 PCr/CA91/00113 ,~`
~ 7 - 2~7~307 said opposed faces, means for rotat1ng one of said sources stepwlse relative to the other source and abou~ an axis extending through said bo~y~ means fo! rotating the other source stepwise about the same point as the rotation of ~he 5 flrst source, the resultina interference pattern be~nc recoraed in said boay SUCh that a ligh~ Deam inciaent upon one of said opposed faces will be refracted and distributea equally among a plurality o~ outDut beams emerging from the other of said opposed faces.
According to a further embodimen~ c the inventior~
apparatus for providing a dlffraction means for an oct7ca interconnector comprises:
a support for the body of photorefractive mater~al hav~nc cylindrical opposed faces;
a plurality of optical devices in two planar arrays, one each side of the supPOrt, the devices being positione~ witr their optical axes extending radially from a common polnt and mutually spaced by a predetermined angle, said devlces comprising plane wave light sources for providing planar light 20 waves with their electric fields extending in the same direction as the cylindrical axes of said cylindrical opposed faces;
means for selectively energizing pairs of said devices in succession to vary the refractive index of the body 25 spatially and periodically in the plane of said arrays such that a light beam incident upon one of said opposed faces will be refracted and distributed equally among a plurality of output beams emerging from the other of said opposed faces.
One embodiment of the present invention comprises an 30 optical interconnection device which has its spatially-varying refractive index configured so that each individual input light wave is coupled to selected ones of a plurality of outputs. Such a coupler finds application in so-called multihop lightwave communication networks.
The design of multigigabit local lightwave networks has received great attention. Some of the proposed optical fiber based networks adopt packet switching which was originally designed for data traffic. There is currently a trend to .
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WO 91/15790 PCl`/CA91/00113 2~79~7 combine various types of traffic on one network. Varlouc techniques have been proposed or deve~oped for this purpose.
These networks are intended for multi-user apP1ications, e.g., local and metropolitan area networks with potentially more _ than a terahert_ of banawidth, even thOUgh each user lS
constrained by the electronics IO access only a small portlor of the available bandwidth. For example, in a wavelength division multiplexing (WDM) passlve broadcast star networ,~.
although the rate at which any one user transmits informatlon 10 is limited by the electronics, multiple users can transml~ o~
wavelengths A~ where m = 1, 5, . . ., N and the llghtwaves are combined in the Passive star coupler. The superimposed 1 igh~
signals are made available to all the recelvers, wltn eacn recelver tuning to one wavelength. A disadvantage of thls 15 approach is that pretransmission coordination is requlred so that each receiver knows to which channel lt must tune for each time interval. Also, users need to rapidl~ an~
accurately tune the receivers (or transmitter) over the available band to allow any user to communicate with any other 20 user.
In order to overcome these disadvantages of standard multichannel systems, it has been proposed to use a so-called "multihop" approach. In a multihop system, to transmit a packet from one user to another, may require routing the 25 packet through intermediate users, each repeating the Packet on a new wavelength, until the packet is finally transmitted on a wavelength that the destination user receives. In other words, a packet may need to take multi hops to reach its destination. With the multihop approach, many packets are 30 concurrently circulating ~hrough the network; some fraction of these are new packets and the remainder are repeated packets. US patent number 4,914,648 by A. Acampora et al, issued April 3, 1990, discloses a multihop lightwave communication system implemerited using a perfect shuffle 35 topology.
Although such multihop networks offer advantages, a limitation can arise from the relaying of the signals. If a W O 91/1~790 PC~r/CA91/00113 9 2~79~07 ::
conventional passlve star coupler ls used, the data packets will be attenuated significantly each time they traverse it.
An object of the presen~ invention ls to mitigate this problem.
According to yet another aspect of the 7nvention~ there ls provided an optlcal aevice comprising a stratified volume Bragg diffraction means, for examPle a hologram, having its refractive index varying spatially according tc the expression:

n(X,Z)-1+~ m",r~sin(i~
m wherein sin(y~d) = 1 m ls an inleger value where Y~'- 2C~/

and where x and z are ordinates of the block;
~ ~ is the spatial frequency vector;
m is an input position or mo~e, corresponding to one optical axis;
m' is an output position or mode, corresponding to one 30 optical axis;
m and m' taking on integer values that determine the number of input/output modes;
, is the coefficient of.coupling between m and m'; and r is the space vector.
The physical configuration of such an optical interconnection device may be similar to that described above with reference to the first aspect of the invention. It may " ' ` ' , ' . , 1 "~ . ' , ` , ~
., . .

WO 91/15790 PCr/CA91/00113 2~79~7 ~o ~`
also be made using much the same method of maufacture as described above.
A limited-broadcast coupler comprising such a body car be designed for vlrtually any arbltrary shuffle network with 5 the following parameters:
p: Degree of graph I: Number of columns N = Ip : Total number of interface nodes.
According to another aspect of the invention, there 10 provided a communication networ~. comprising a plural j~! C_ nodes interconnected by such a limited or selective coupler.
The limited-broadcast couPler effects the necessar~
physical connections of two successive columns of the snuffle network. Having access to such a limited-broadcast couPler 15 as a central piece of the network will make many desire~
architectures feasible for future oPtical networks. A space-varying refractive index slab is introduced as a key deslgn element for such a coupler.
The network may comprise a plurality of said opticai 20 devices connected in tandem, each device having a passband overlapping the passband of the device to which it is coupled, whereby signals having wavelengths within the overlapping regions of the band will be relayed through said interconnecting devices. i The network may be arranged such that the wavelengths of light beams transmitted through the network are selected to correspond substantially with peaks of the period of the periodic refractive index.

30 BRIEF DESCRIPTION OF DRAWINGS:
Figure 1 is plan view, partially cut away, of an optical interconnector;
Figure 2 is a schematic representation of the optical interconnector.
Figure 3(a), 3(b) and 3(c) depict refraction of an input light beam into three specified modes;
Figure 4(a), 4(b) and 4(c) illustrate coupling modes individually and collectively;

: ,' ' ' ' , ~: ~ , -,: . , . ~ . , , t~ 1 2979~7 Figure 5 is a schematic diagram of aPParatUs for preparing a body having a spatially varying refractive index - for use in the optical in~erconnector of Figure 1;
Figure 6(a) and 6(b) illustrate amplitude and direction 5 of different spatial frequencies ~,~ that are necessary to couPle the input m = 0th mode to all output modes.
Figure 7 represents regions of different refractive index in the body;
Figures 8(a), 8(b) 9(a), 9(b) 10(a) and 10(b) illustrate 10 vectors ~,~ for star cou~lers having ~ and 4 out~u modes, respectively;
Figure 11 is a block schematic diagram of an alternatlve apParatus for making a diff!action means having a spatiall~
varying refractive index; and Figure 12 is a simplified schematic diagram of a "shuffle net" lightwave communication system incorporating a limlted-broadcast coupler and a plurality of user interfaces;
Figure 13 is a connectivity graph for the shuffle net of Figure 12; and Figure 14 is a block diagram of one of the user interfaces of Figure 12.

MODES FOR CARRYING OUT THE INVENTION
Figure 1 shows an optical interconnector comprising a 25 glass substrate formed by two plates 102 and 104, respectively. A diffraction means in the form of body 106, of dielectric material, such as lithium nioba~e (LiNbO ) formed as a 3ragg volume hologram, is sandwiched between the two plates 102 and 104. For other suitable materials the 30 reader is directed to a paper entitled "Two-Wave Mixing in Nonlinear Media", IEEE Journal of Quantum Electronics, Vol.
25, No. 3, March l9, 1989 which is incorporated herein by reference. Juxtaposed surfaces of the glass plates 102 and 104 are recessed to accommodate the block 106. Two arrays of 35 single mode optical fibres 108 and 110, respectively, abut opposite faces 112 and 114, respectively, of the block 106.
The opposite faces 112 and 114 are cylindrical sections and symmetrical. The distance between the faces 112 and 114, at ..

, .

WO9l/15790 PCT/CA9l/00113 2~79~ 12 ~
their midpoints, is equal to the radius of curvature, d, o,~
the surfaces 11~ and 11~.
The end portions 116 of the optical fibres 108~ 110.
where the~ abut the block 106, are enlarged to a~out 10C
5 microns diameter which is about ten tlmes the diameter of ~ne typical single mode optical fi~re. The transition De~wee~
each single mode fiDre and its enlarged end portion is graaua~
i.e. tapered.
The thickness of the dielectric body 106, is equal to the 10 width of each of the enlarged portions 116, i.e. abou~ 105 microns for a 9 x 9 coupler, so that substantially all o,~ tne light incident upon its end faces 112, 1~4 is channelled into the attached optical fibres. The op~ical fibres 108 an~ ~1 serve as emitters or receivers, the emitters being arrangen 15 to transmit "nearly plane wave-- light beams.
The optical interconnector is represented schematicall~
in Figure 2. The number of fibres in each array 108, 110 is ~ = 2M + l. Thus there are N = 2M ~ 1 nearly plane wave I inputs directed from arcuate surface 112 towards the centre 20 of arcuate surface 114, and vice versa. The transit distance i.e. the distance between the arcuate surfaces 112 and 114 at their mid-points is d and the arc length of each arcuate surface is D. Each enlarged end portion 116 on the input array has a width _ such that aN = D
The width a should be large enough compared to the spatial wavelength of n(x,z), i.e., a > ~2n m,m/
30 The width of the body 106, i.e. the distance d between the arcuate surfaces 112, 114 at their midpoints, is defined as:
M ~0 The width should be large enough to satisfy the thick grating 35 condition given later by Equation (3); while the geometry should also meet the condition defined later by Equation (28).
The same arguments apply to the output surface of the coupler.

: ~ ' ~ ' . : . .

. ~: - . . : :.

W09l/15790 PCT/CA9l/00113 ~` 13 2~7~7 A simple lnvestigation shows tha~ D increases as M- while d ncreases as M.
In use, a beam o~ ght emanating from any one of the array of opt~cal fibres 108 will be diffracted by the thln 5 film body 106 into a plurallty of modes, one for eacn o- the array of optlcal fibres 110 at the opposite siae of the Dody 106. Conversely, light emanatlng from any one of the arra~
of optical fibres 110 will be diffracted into a plurality of modes, one for each of the array of optical fibres 108.
As shown in Figure 2, the - ordinate extends 1n the direction of the axis joinlng the mlddles of the arcuate faces 112, 114, and the x ordinate is perpendicular to i~. The arcuate faces 112, 114 are actually cylindrical segment~. Th-refractive index of the block 106 is n(x,z). The numDer o,~
15 optical fibres in each array, N, is 2M+1 and the angle between the optical axes of adjacen~ oprical fibres is 0~ degrees.
The optical fibre whose optical axis coincides wlth the middle of the two arcuate surfaces 112 and 114, respectively, is deemed to be the 0th mode and the modes on either side of 20 that axis are numbered 1 to +M and 1 to -M.
Figure 3 illustrates refraction for a single perturbation term, the 0th mode in the array of optical fibres 108. In Figure 3(a), the angle of refraction is M80 degrees, resulting in the Mth mode being transmitted to the endmost optical fibre 25 in the array 110. Figure 3(b) shows that the 0th mode is refracted at an angle (M-1)00 degrees and Figure 3(c) shows that the 0th mode is refracted at an angle a~ degrees. The same refractive index grating pattern will couple the O to Mth modes of the array of oPtical fibres 110 to the 0th mode of 30 the array of optical fibres 108. The block 106 can thus be considered to be a plurality of sub-holograms, each providing a different output mode for a given input mode.
Each sub-hologram which, in effect, can be considered to be a 1 x (2M+1), or (2M+1) x 1 coupler, is formed by two-wave 35 mixing on a holographic film.
Figure 4(a) and Figure 4(b) illustrate how the coupler embodying the invention would couple the Mth mode and (M-2)th , :

WO 91/1~790 PCr/CA91/00113 2~79~7 14 . ~
mode, respectively, to all output modes. For the Mth mod~i.
the refractive lndex n(x,~) is given as:

n (x, z) - 1 + ~ sin (h~

For the (M-2)th mode, the refractive index n(x,z) is given as:

n (x, z) ~ A,~-2"~ sin (~-2 ~

Flgure 4(cj illustrates how all of the moaes are proviaea 15 to achieve N x N' coupling, the refractive index n(x,z~
varying in accordance with the expression:
~ ~h' n(x,z) - 1 + ~ l~m,m/ sin (~m,m/

Thus the block 106 comprises a holographic pattern characterized by a spatial variation of this refractive index n(x,z).
Such a pattern can be implemented using known techniques.
25 see for example a Ph.D. thesis by M. Tabiani entitled "Spatial Temporal Optical Signal Processing", M.I.T., August 1979, a paper entitled 'Bragg Gratings on InGaAsP/InP Waveguides as Polarization Independent Optical Filters", by C.Cremer et al, IEEE Journal of Lightwave Technology, Vol. 7, No. 11, November 30 1989, and also the disclosures of European patent application number 0,339,657, US Patent number 4,705,344 and US. patent number 4,838,630. All of these disclosures are incorporated herein by reference. The pattern may be provided on a single film of photorefractive material (thick grating or volume 35 holography on a single crystal or film).
Figure 5 illustrates manufacture of the body 106 with its spatially varying refractive index for an N x N' coupler. The implementation is based on two wave mixing employing a 2 ~ 7 ~ 9 ~ 7 rotating mechanism, to mix E. and E~ by varying m and m' ln successive steps.
In each step, with m and m' fixed, the interaction of the two beams E, and E, is written on the photorefractive media.
5 Then keeping m fixed, we vary m 'rom M + 1 to N -(M -1) an~
repeat the writing process for each ComDination of ', and E , respectfully. Next, we vary m from 1 to M and repeat the procedure.
Figure 5 is a block schematic diagram of the apparatus 10 for implementing such two-wave mixing, comprising two coherent light sources 502 and 504, respectively, mounted for rota~ior, by two motors 506 and 508, resDectively. The light sources 502 and 504 generate nearly plane waves ~. and E ,.
respectfully. The centre of rotation for both of the motors 15 506 and 508, is the middle of the arcuate surface 112 which is furthest away as indicated at 510. The relative positions of the drive motors 506 and 508 are controlled by drive control means 512 which rotates the motors about point 510.
The first motor, 506, rotates the first nearly plane wave 20 source 502 (Em) such that its propagation vector ~n makes an angle [m-~+l)] fl20 with the - z axis. Second motor 508 aligns the second nearly plane wave source 504 (E~ such that its propagation vector ~ makes an angle [~ - ~M~l)] 2 with the -z axis. For a fixed m, second motor 508 varies the ~J direction 25 incrementally such that m' varles between m + 1 to N - (m -1).
Then, by varying m, the first motor 506 will bring the first source 502 to the new position and the process continues. In each position, the beams E~ and E~, from the two sources, 502 and 504 are mixed to form (print) a desired term of Equation 30 (8) on the photorefractive material. After printing all the terms of Equation (8), the body will have a refractive index varying in accordance with the equation (8). When placed between the two circular arrays 108 and 110 of the coupler shown in Figure 1, the body 106 will form an N x N' optical 35 interconnection.

. .

WO 91/15790 PCI`/CA91/00113 2~ a~ 16 The coupling pattern can be modified by varying the intensitles of the beams E. and E~,at any particular step to provide other then N x N' coupl ing. The intensity i~
controlled by means of attenuation filters 514 and 516 in the 5 optical paths of light sources 502 and 504, respectively. The at~enuation filters 514 and 516 are controlled by means of ar intensity control means 518 which operates in conjunction with the drive means 512.
It is also possible to fabrlcate a star coupler which 1G couPles selectively rather than broadcast. There are appllcations in which it is desirable to couple, for example, one of a plurality of inputs to a limited number of a plurality of outputs. The photorefractive stratified 8rag~
volume hologram for such a coupler could be made in a similar 15 manner to the full broadcast Bragg volume hologram described hereinbefore with a refractive index varying accordlng to the general expression:

,~ ~
n(x, z~ - 1 + ~ ~ ~m~m~sin (~
D7-~ M

where sin(ymd) = 1 m = -M,...,O,...,M

25 and where r~- 2~C ~

30 with C being the speed of light, then the power coupling coefficient between any input mode m and any output mode m' will be proportional to ~,, an element of the routing matrix.

.
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- . -, . : : :. , WO 91/15790 PCI`/CA91/00113 '~ 17 .2~7~7 ,. .
.
. ., ~ _ ~ ~m,ml ~ ' ' foI m,rn~ - -M, . . ., O , . . ., +M
.
.
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One application for such a select~ve coupler 1S high 10 capacity local area networks. Figure 1~ illustrates a multihop perfect shuffle network comPrislng a passlve optical star coupler 120 and a set of eight user interfaces 121 - 128.
respectively. Eight input ports 1 - 8 are distributed along one curved face 129 of the coupler 120 and eight output ports 15 1' - 8' are distributed along opposed curved face 130. The interfaces 121 - 128 comprise laser transmitters 131 - 138 and phctodiode receivers 141 - 148, respectively. The input ports 1 - 8 are connected to respective outputs of laser transmitters 121 - 128 and output ports 1' - 8' are connected 20 to respective ones of the inputs of photodiode receivers 141 -148.
The star coupler 120 comprises a stratified volume holographic medium having a spatially-varying refractive index. As in the case of the coupler of Figure 1, the 25 refractive index varies according to the general expression n(x,z) - 1 + ~m,~sin(~ r) ~ M

The transmitters 121 - 128 are each capable of transmitting signals with either of two wavelengths, by selecting either of two lasers. Of course, a single laser which can be switched between two wavelengths might be substituted. The receivers 1il - 148 each have a photodiode 35 receiver stage for detecting two wavelengths. These are not the same as the transmitter wavelengths but correspond to wavelengths of two other user interfaces to which the receiver is connected. When a signal from an individual transmitter : . - . . . .

WO 91~15790 PCI/CA91/00113 ?.,~79~97 18 ~`
arrives at the corresponding input port, and is launched ~nto the coupler 120, it will be directed to one or the other o two output ports depending upon its wavelength. For examp7e.
a signal with wavelength A.transmitted from laser transmitter 5 121 to input port 1 will be coupled to output port 5', whereas a signal a~ wavelength A, ~ransmitted by way of the same lnpu~
port 1 will be directed ~o outpu~ port 6'.
In this particular case, the stratif7ed volume hologram has a refractive index varying according to the expression n(x,z) - 1 + ~ m~sin(i~

Hence, the coupler 120 functions to couPle ~ out of ~, i.e.
each lnput port 1 - 8 can couple to a predetermined two of the 15 output ports 1' - 8'.
The connectivity of the shuffle network of F7gure 1~ is illustrated in Figure 13. The network is a "perfect" shuffle network in that each user can communicate with every other user, even though each individual user interface has only two 20 direct linkages to other user interfaces. In order to achieve this connectivity, some signals will be relayed. For example, . if user 1 wishes to transmit a packet of data to user 6, user interface 121 will append user 6's address onto the packet, select wavelength l2, and launch the signal into input port 1.
25 The signal will go directly to output port 6' and thence to receiver interface 146 where it will be demodulated, the address detected, and the packet delivered to user 6.
If user 1 wishes to send a packet to user 8, user interface 121 will address the packet, select a wavelength A, 30 to direct the signal to receiver interface 146 of user 6. In receiver interface 146, the address information will be detected and indicate that the packet is to be relayed to receiver interface 144 of user 4 on 112. In receiver interface 144 the address will' be detected and again indicate 35 that the packet is to be relayed. Consequently, user interface 124 selects a wavelength of A8 and transmits the packet by way of input port 4 and output port 8' to receiver - '9 2~9~7 :
interface 148. In rece~ver interface 148, the signal will De detected and the packet delivered to user 8.
Figure 14 illustrates, as an example, recelver interface 141, which comprises a photodetector receiver stage 150 5 connected to output port 1'. The photodetector receiver stag-15G includes two photodiode detectors (not shownj for detecting signals having wavelengths A, and l.~. respectively.
Detecting circuitry 151 decodes the address information prefixed to the incoming signal. Ir the address is i~s own, 10 it directs the incoming signal to a hardware interface 152 for user 1. If, on the other hand, the address lndicates that the message is to be relayed, in which case lt wil7 also contain information as to which user interfaces are ln th- rela~
chain. Laser transmitter stage 131 includes a selector 153 15 and lasers 1~4 and 155 having operating wavelengths A. and A , respectively. Detecting means 151 will -ontrol selector 15~
to direct the outgoing signal to the apPropriate one of transmitters 154 and 155.
When user 1 wishes to initiate a transmission, user 20 hardware interface 152 will prefix the message with the appropriate routing address and detecting means 151 will select the appropriate one of lasers 154 and 155 for its transmission. The limited or selective star coupler 120 can be fabricated using similar techniques and apparatus as that 25 illustrated in Figures 5 and 11 and described with respect to the manufacture of the full broadcast star coupler.
By way of example, for a 9 x 9 limited-broadcast coupler, the input array width is chosen such that a - lO~Y ( where MAX stands for maximum; and M0~ - 0.4 ~5 Using M = 4 for a 9 x 9 switch and a = loOA, D = 900A, where A is the wavelength of the optical signal and is equal to 2.5D, for A ~ 1~m, the dimensions are aPproximately 1mm x .
~ ,, ; ' :

., . , ' ' ' .
, ` 2 ~ 7 ~ 20 PCTtCA91/00113 ~.5mm in the x x ~ directions. In the y direction 1~ lS
assumed o be larger.
It ls preferable to expand the diameter of each slngle-mode lnput/outDut fiber. This exPansion can De done by uslng a apProPrlate tapers. Beam expanslon ratios ~n the range cf a-10 are feasible with a correspondlng insertlon loss per taDer of less than 0.01 - 0.02a dB. By using these numerlcal values, the thick grating condition holds. The sPecifiec routing matrix ~ can be constructed by the wave-mlxlnG

10 method as discussed earlie~-.
Although a skilled artisan should be able to imDlemenr the invention on the basis of the foregoing aescriptior,. tn~
following mathematical exPlanation is provided to facilitate an understanding of the concepts upon which the invention is 15 predicated.
Intuitive AnalYsis of sPace-varyinq Refractlve Index BoaY
Referring again to Figure 2, we define the m-th mode as a plane wave travelling in the direction that makes an angle m0~ with the z axis; independent of y as:
E e~l~t-k~xsin(m0o)~zco~ o)]i + C C
( 1 ) where c.c. means complex conjugate of the first term, x,y and z are spatial coordinates, and ~ and k refer to optical ; frequency and wave vector, respectively.
This analysis is based upon an intuitive Bragg diffraction approach as disclosed by A. Yariv in the book "Optical Electronics", Holt, Rinehart and Winston, 1985, but modified to achieve appropriate mode interaction for N x N' couplers.
In order to couple the m-th input mode to the m'-th output mode as shown in Figure 2, we must establish the following pattern of refractive index:
n(x,z) - 1 + ~m"~ 3in (i~ I) (2) 35 where ~r~ is the coupling coefficient between input m-th and output m'-th modes and ~represents dimensions of the sPace, :, ' ' ' ' ' ~ ' ' WO 91/1~790 PCI/CA91/00113 ~ 2~7~9~7 where I ~ X ' lX +Y Iy + z lz ~nd i is tne unlty vector.

5 The following constraints on the d1rection and amDlituae of ~.
vector spatial freauency ~ ~ must hold in order to satisfy tne Bragg-diffractlon thick grating conditions according to A. Yariv and M. Tab1ani, repectively, 1 C I mm~ d~l ( 3 ) where d is the thickness of the body 106 and K refers to the optical wave vector, ~m,~ ~ 2ksin ~f~o - m ~o ~
(4) and ~m,or~ ~ ¦ ~m,m~ ¦ (IX Cog~3m~ o,Iz sin~m"~) where ~m,ml ~ 2 (m + ml) (6) COUD1 inq m = L-th InPut Mode to N = 2M + 1 OUtDut Modes Based on the previous discussion on coupling the m = Lth 30 input mode to N = 2M + 1 output modes (m' = -M,...,O,...,M), we must maintain the following refractive index variation relation:

.
:. . :
..
r :

WO 91/15790 PCr/CA91/00113 '~2 2~79~ n(x,z) - 1 + ~ ~L,m/ sin (~ ,lr r ) Wlth ~L~< 1 plus conditlons on ~L~ deflnea by ~quatlon- :_ 5 ~G ( 6~ witn m = L and wl tn m = -M ...., C ~ .... +~i .
As an examDle, consiae- vec~o- ~ ~ Tor some sDe_i,l-cases liKe M = 2 and M = ~ ana Dlot ~ ~ for L = G.
Flgure 6A shows a plot of ~ ~ to coucle L = 0-th lnDu mode to outDut modes m' = -2. -1. 0, 1 and ~. Figure 69 snows 10 a Dlot of h~ ~ to coUPle L = o-tn lnDu~ moce to OUtDU_ ~.oaec r .
rrl ' = ~ 4 . ~ 3, --2, ~ 1 . G, 1 ~ 4, It should be realizea that with tne spatial varylng refractive index glven by Equation (7) wlth the constrain~s lnlroduced in Equatlons (3) to (6j, only m = L-th inpu~ mo~e 1~ will interact with all other ~ = 2M + 1 output ~odes (m' = -M,...,O,...,+M). The degree of interactlon aepends on ~ ~
which is a vector of ~ , the routing matrix. However, by the condition on n(x,z) defined in Equation (7), no other lnput mode (m~L) can be strongly coupled to any of the N = 2M + 1 20 output modes. This is due to the fact that none of the existing spatial vector frequencies ~ ~ meet the conditions in Equations (4) to (6) for such an input. For more matnematical details, the reader is directed to the paper by M. Tabiani referred to hereinbefore.
COUD1 in~ N = 2M + 1 InDut SDatial Modes to N = 2M + 1 Output Modes (m~m' = -M.... O.... ,+M) In order to couple all the N = 2M + 1 input modes to all the N = 2M + 1 output modes, i.e. the case where N = N', the 30 following refractive index expression needs to be maintained:
I b' M
n(x,z) ~ 1 + ~ ~ Am m/ 8in (~
m~
( 8 ) ,, . . , ~, .,: . , . . . . :

WO ~ 790 PCI/CA91/001~3 J~
23 2~7~7 wlth ~m ~c 1 and ~ ~ satistylng the conditlons aeflnea b~
Equa~lons (3) to (6) for all m,m = -M,...,0, ....+M.
Mathematical analyses indicate that if (~, ana sin ( 2`rc ~ 101 10 whe!e 0 ls the speed o~ light, tnen the power couPling coefficlent among lnput/outDùt mo~es will De tne same and equal to l/N, namely:
T(m, m~) ~ N
( 1 1 ) .
Such a power division is 100% efficient. This situation, with ~2~ r constant, gives broadcast coupling, i.e. each input couples to every output.
If we take ~0~, from a specific preselected N x N' matrix ~ _ ~m ~ . . . wi th, m,nt - -M, . . ., O, . . . ,M . .

then, the power of any arbitrary m-th input element will be distributed to all N = 2M +1 output elements by a transmission coefficient proportional to ~2~ 2' for all m' = -M,...,O,...,M.
In this case, the implementation is still based on two-wave mixing with a rotating mechanism and with an intensity control apparatus comprising the intensity control means 518 and attenuation filters 514, 516 described earlier with reference to Figure 5.
Each time we mix E2 and E~. with a fixed m and m', but with a variable intensity, the interaction of the two beams is written on the photorefractive medium. Now, with a fixed m, we vary m' from m + 1 to N -(m-1) while source intensities vary according to ~2n~l. Next, we vary m from 1 to M and we 35 continue this procedure.
In the case of the selective or limited-broadcast coupler, ~r~' is an element of the ~ routing matrix and . . .
' : .. .
., . ;. . . . .
.:

~ :

WO 91/15790 PCI`/CA91/00113 24 .

; ~ must satisf~ tne conditions defined in equatlons 3 ~c for all m,m' = -M....,O,....+M.
Mathematical analyses lndicate that if sln(y,d) = l m = -M, . . . ,0, . . . ,M

where :-rm ~ 2C~
l~ (lla) witn C being the sPeed of light, then tne power coupllnacoefficient between any input mode m ana any outpu~ moae m will be proportional to ~, an element of the routlng 15 matrix. Hence, because the coupllng coefficient is no constant, the coupler will attenuate some signals anc not others, depending upon whether or not a particular propagation moae has been selected.

20 Mathematical AnalYsis of SPace-VarYinq Refractive Index Bodv. - -The followlng discussion is based on the mathematical analyses in the paper by M. Tabiani supra. In this discussion we will see how input m = L-th mode couples to output m' = (L
+ 1),..., (L + M) modes with the specific refractive index 25 variation in space. This analysis will specify the coupling coefficients among different input/outPut modes.

Mathematical Analvsis of SPace-Varvinq Refractive Index Slab.
Consider the medium shown in Figure 7 with the following 30 refractive index variation in region II: - -n(X,z)-l+~ ~L,~sin k,~x cos(~ 2 ~t~)-zsi~ L~o 2nt~O)]~

3~ (12) .~, : , W091/l5790 PCT/CA9t/001l3 ~ 25 . 2~7~07 with ~L ~l~ 1 and the conditlons glven by Equations (3) to (6) for m = L. Notice that, for al~ mathematical analysis n(x,~) has been chosen to have M components, whereas for coupllng applications n(x,z) ls assumed ~o have N = 2M + 1 components.
ssume tnat tne inDut wave is the sum of M ~ 1 moaes as:

M xsin(n~O)+zcos(n~ ) EI (X, Z, t) - Dinc~7exp i~ t~ C +C. c 10 (13) where Dl, . is the inciaental wave coefficien~ of the m-tn mode. Because of the form of the refrac~ive lndex ln Eauatlor.
(12), the field in region II will be as follows:
~ xsin(n~O)+zcos(~O) Ell(X,Z, t)-~ Dm(Z)eXp~7~Lt- C ~ I

I C . C . ( 1 4 ) 20 where D~(z) is the m-th coefficient of the wave in the second region.
Defining EII(x,z,t) by the summation term on the right in Equation (14), we can accommodate n(x,z) by using the wave equation:

v2E (X Z t) -- [n (x, z) ] 2 EII (X, Z, t) o ( 15) M. Tabiani had shown in the thesis refarred to earlier, that two equations (12) and (14) may be substituted into Equation (15) to obtain the fol.lowing coupled-mode equations:

35 dD~(Z) _ ~i~ L),L D~(Z) ( .

~,. . , ~, .

WO 91/15790 PCI'/CA91/00113 dz 2c /~ L),L D~z) L + ls m :: L +

- ~lse 5 dz Equatlon (16) ls tne coupled-moae eauatlon for the system shown in Figure 7 with n(x,z) given by Equation (12). We can see that input mode L couPles simultaneously to output modes 10 m =L ,,...,! + M, but input mode (L + m') and output moa_ (L + m ) with m ~ m and m',m ~ 0 not coupled with eacr, other, directly.
Thus Equation (16) shows that the reiractive index n(x.z;
glven by Equation (12) serves the purpose, as stated earller.
15 A detaited analysis of the system governed by Equation (16) can be Performed as we will discuss it in the following subsection.
Solution of the Mode-Equation We shall see the solution of Equatlon (16) for the case 20 of L = 0 by means of state-variable representation. Without loss of generality, we only need to consider modes 0 through M. Thus, if we let _(z) be an (M + 1) dimensional column vector with components D?( Z ), we obtain:

dz (17) where _ is an (M + 1) x (M + 1) matrix with elements ¦ i 2C~~0 ml-O,m~0 ¦ j 2C~~ m-o m/~O J
o otheIwis (18) Suppose the slab in region II (Figure 7) is illuminated by an input wave of the type presented by Equation (13), then the field in region III is ~: , '- . . - ~ , . .

27 2~799~ ~
M

~II (X~ Z~ t) --~, D", ( d) eXp{j~{t-- lx 8in (~o) + Z cos (D~o) ] } }

( 19) wnere D( d ) - _ ( d ) Dinc ( 20 ) . .
and ~(d) ls the transition matrix associate~ with the state 10 Equation (17).
The transitlon matrix ~(z) can be found by a Fourler Transform method such as is disclosed by R. W. Brackett i~
Chapter 11 of the book entitled "Finite Dimensional Llnea Systems , J. Wiley, New YorK, 1970. The result is as follows:

Cos (yOd) m -m~ - O
-j2~i~C O~sin(yOd) m- O, m' ~ O
~(d) - . ~, sin (ycd) ~~ 2C~ m lJt~- 0, m ~ O
/ ~ \2 [cos(yOd) -1]
~m,m/+~ 2C¦ Ao,~o,m~ y2 m, nt ~ O
(21 ) , .
25 where;

y ~ 2 ( 22 ) Considering Equation (21 ) in the specific case of the full broadcast NxN coupler, where ~ o ~ = A ( 23 ) and sin (yOd) = 1 (24) 35 we can reach the following conclusions. The O-th input mode is divided among M output modes m' - 1,...,M by the amplitude factor 1 or power factor 1 . The O-th inPut mode does not 2Q~ 99 a~ 28 get coupled as depicted in Flgure 7, since cos(y~d) ls zero.
However, referring to Figure 2, since the distance between an-~nput/output pair is not a constant. there will be some power at these output modes.
IT we take n(Y~,z) glven by Equation (12) with any arbitrary L instead of L = 0; tnen L-th input mode couples simultaneously to M output modes m = L + 1,...,L + M, but ~L
+ M') and (L + M") with m' ~ m" ana m', m" ~ 0 not couDled tc each other, directly. Therefore, n(x,z) in Equation (8) will 10 coucle all N = 2M + 1 input modes to all N = 2M + 1 out3u modes with a 100% efficiency.
We use the configuration in Figure 2 such that N inpu~
elements are equally spaced on the surface of the outer circle, while each input is aligned with the centre of tne 15 circle. Based on this conf~guration, the distance between the -m-th input mode and m'-th output mode, dm~ ls no longer a constant, it depends on m, m' and 3c parameters, such that for - small angles: -2~ d= ~ - d ~ 1 + nFt ( 2)¦ (25) Therefore, we must choose the parameters such that N2 ~2 d A ~ In teger (26) in order to keep Equation (24) valid for the configuration in Figure 2. Then by properly choosing n(x,z) as given by Equation (8), for ~m~ = ~ and satisfying Equations (24) and (26), each input wave will be equally divided among the output 30 array ports.
Considering Equation (21) in the alternative case of the selective or limited broadcast coupler of Figure 12, where ~0, is chosen as the zero-th column of the routing matrix ~ and . . . .
, . ~

'.: ' . . ~ - .

29 2~79907 sin (yGd) = 1 for m = 0 we can reach the fol1Ow1ng conclusions. The 0-th input mode is divided among the M output modes m' = 1,...,M Dy the amplitude factor ~m,~
M m--O
m ( 2 7 ) or the power factor y ''~ m-0 i-m As in the broadcast case, the 0-th mode does not go through since cos(~Od) tends to zero. If we take n(x,z) from 20 equation 12 with any arbitrary non-zero L; the L-th input mode couples simultaneously to M output ports and no other input mode couples to any output mode. However, n(x,z) in equation 8 will couple all the N = 2M + 1 input modes to all the 2M +
1 output modes with a coupling coefficient proportional to 25 ~,, the elements of the routing matrix ~ .

As before, the N input elements are equally spaced on the surface of the outer circle, while each input is aligned with the centre of the circle. Also, the distance between the m-th input mode and the m'-th output mode, dn~l, again depends on 30 m,m' and 0~ parameters, such that for small angles:

d~ d ¦ 1 + nK~ ( 20) 1 (27a) In this case, however, the parameters are chosen such that:
.

: : , : . ., . ., . ., .:.. . . .. . . .

WO 91/15790 PCl/CA91/00113 2~7~9~ 3~ . ~
t~
~2d~ ~ ~m,~
'r/A~ IntegeI m--M, . . ., O, . . . ,M
(27b) in order to Keep equation 2~ valld tor any m-th lnDut mo~e for ` the configuration. Proper choice of n(x,z) as given by equation 8, for ~ selected by the coupler routing matrix and satisfying equation 24 for any m anc satisfying equation 10 27a, will result in each input wave being divided among other ports witn a coupling coefflcien~ proportional to ~.................. ~ .
:
Pa t ~ern f or i~
~ ,J

To realize the refractive index glven by Equation (8), 15 let us consider ~ ~ , as a vector whose amplitude and direction satisfy the conditions given by Equations (4) to (6j for m,m' = -M,...,0,1 ,2,3, . . . ,M.
For small angles as : ¦M~OI~, (28) 20 by carefully examining the ~ ~ vectors, we discover an interesting pattern which can easily be reali2ed by wave mlxing.
For simplicity, let us consider h~m m/ Pattern in the following two simple cases:
a) M = 2 for a 5 x 5 star coup1er b) M = 4 for a 9 x 9 star coupler Figure 8A is a plot of ~m~ for M = 2, for a 5 x 5 star coupler (m,m' = -2, -1, 0, 1, 2). Figure 8B is a plot of ~,~ for M = 4, 9 x 9 star coupler (m,m' = -4, -3, -2, -1, 30 0, 1, 2, 3, 4). If we examine these vectors carefully as depicted in Figures 9A and 9B, tips of the ~. ~ vectors are located on different circles all with the same radius.

- ~ - . . - - : . . . : . .
. .

. . .

~ v 31 2~79~7 A more careful examlnation of these vectors as snown in Figures lOA and 10B, indicates the radius R ~ 9) where K represents the oPtical wave vector.
For an arbitrary M, there are M circles on eacn side, each with a radius R - 1~ j . If we numDer these circles as shown in Figures 9A and 9B, on the first circle there are 2M
10 vector tlps. On the second clrcle, there are 2(M - 1) vector lips and so on. That is, on the i-th circle there are ~(M -i + 1) vector tips.

Wave Mixinq Realization Interaction of two laser beams inside a photorefractive medium, when the two beams have the same frequency, forms a stationary interference pattern. Its intensity makes a spatial variation inside the medium and proportionally creates refractive index variations in space as described by Pochiz 20 Yeh in his paper entitled 'Two-Wave Mixing in Non-Linear Media", IEEE Journal of Quantum electronics, Vol 25, No. 3, ; March 19, 1939, which is incorporated herein by reference.
The electric field of these waves can be exPressed as 25 Ei - Aej(~t fl + C.C. i - 1, . . . ,2M + 1 (30) where ( 3 1 ) 30 with the direction of ~ being a variable.

According to Pochiz Yeh, the refractive index perturbation will be a periodic function in space with a spatial frequency ~ - ~ when Er and E'n are mixed.
Consider two previously described examples on 35 construction of *. ~ in creating the necessary refractive WO 91/1:)790 PCI/CA91/00113 9Q~a~ 32 index given by Equation (8) for a 5 x 5 and a 9 x 9 couple! :
(see Figure 10).

a) M = 2, for a 5 x 5 star couPler: ~
In this case, we need to have N = 5 waves E., E^, c , E
ana E; as shown in Fi gure lOA to create all corresponding ~ ~ . In order to configure four vectors located on the first circle, we must mix E. with E,. E , E, and E. To construct two vectors h~m ~ on the second circle ~and 10 the last for M = 2 case) accordlng to the specific geometry shown in Figure 10A, we need to mix E- with E,, E~.

b; M = 4, for a 9 x 9 star couDler:
As shown in Figure 10g we need to have N = 9 waves 15 (E....... E~) to create all corresponding ~3~ . In oraer ~o configure eight vectors ~m~ located on the first circle, we must mix E~ with E2 to Eo~ To construct six vectors R~m~ located on the second circle, we must mix E~ with E~ to E8. For four vectors ~ ~ located on the third circle, 20 we must mix E3 with E4 to E.. Finally, in order to create two vectors ~, ~ located on the fourth circle (the last for this example) we must mix E4 with E5 and E6.
.Based on these examples, with no loss in generality, to create all vectors ~ ~ in Figures 10A and 10B for an N x N' 25 coupler with N = 2M + l, we have to mix El with E2 to EH
E2 with E3 to EN-I

-~0 E~ with E~t~ and E~2.
Notice that, all of these waves have the same frequency but different directions. El has an angle _ h2~o with -z direction and Ej has an angle 00 with Ejl, and so on.

:. - : . - . . . ; .
': ' ' . . :, :' ;, ` ' .'' ~.' '' '' ~
.. .. . . . ...
. ~
- . .. ..

'`'~ 33 2 ~ 7~
Therefore, we have to have only two waves at the same frequency. We mix the first one in the proposed E. direction.
Then by rotation, we bring the second one in the direction of E~, E"... and E~, respectively. In each position, we mix the 5 field with the first one. In the next round, we brlng the first one in the proposed E~ direction and rotate the secona field to bring it into the airection of E,... and Eh.. In each position we mix the fleld with the firs' one. The procedure is continued. In the last step, the first field is 10 placed in the E~ direction and the second wave on the Ey,~ and the Eu,, direction while mixing the pairs in each position.
Therefore, with this method, by two wave mlxing we can create all vectors ~ ~ corresPonding tO n(x,z) given by Equation (8).
DESIGN REQUIREMENT AND AN EXAMPLE
The proposec N x N star optical coupler is shown in Figure (2). There are N = 2M + 1 nearly plane wave inputs directed towards the center of the circular input surface with 20 a diameter D. Each element on the input array has a width _ such that aN = D (32) The width a should be large enough compared to the spatial wavelength of n(x,z), i.e., a ~ 2 (33) 30 The width of the slab is _ and is defined as:

d - M~ (34 o 35 The slab width should be large enough to satisfy the thick grating condition given by Equation (3); while the geometry should also meet the condition defined by Equation (28). The same arguments apply to the output surface of the coupler.

.. . , . . ~ . ., . . -, .

WO 91/15790 PCr/CA91/001 13 ~9~ 34 A simple investigation shows that D increases as M- while d ncreases as M. The medium with sPace-varying refractlve lndex n(x,z) given by Equation (8) may be created by the twc wave mixing methods mentioned herein for a given N.
In order to obtain 100% efficiency, the parameters are selected in a way that conditions given by Equatlons (4), (6j, (10) and (27b) are sa~isfied.
For the selective or limited-broadcast coupler, ~ s determined by the routing matrix To achieve wavelength division multiplexing, le~ us assume that l can vary between A - ~ to A + ~. The coupler will still operate if we keep the perturbation on term ~ of Equation (10) to be much smaller than ~. This 15 can be done by limiting ~ such that:

~ A (34A) A 2d~
which means that the optical signal bandwidth is limited by the geometry of the coupler.
EXAMPLE
For a 9 x 9 coupler _ is chosen such that Equation (33) is 25 satisfied as a _ 10~ 2 (1~,~) (35) where MAX stands for maximum. Also, the condition given by 30 Equation (26) is satisfied by choosing MOo = 0 4 (36) Using M = 4 for a 9 x 9 star coupler given by Equation (4) we will have:
a = 100A (37) 35 and : . - ~. .
,.. . : ,. - . :, ., . . - - . .

WO 91/15790 PCr/CA91/00113 ~ 2~7~7 D = gooA (38), where A is the wavelength of the oPtical signal and d is equal to 2.5D. That is, for 1~1um the dimensions are approxlmately 1mm x 2.5mm in the x by z direct,on. In the y direction it 5 is assumed to be larger.
Equation (37? points to expanaing the diameter for each sinale-mode input/output fibre. This expansion can be done by using appropriate tapers. Beam expansion ratios in the range of 5-10 are feasible with a corresponding insertion loss 10 per taPer of less than 0.01 - .025dB. By using these numerical values, the thick gratlng condition governed by Equation (3) holds. The refractive index n(x,z) in Equation (8) for a given M will be created as described hereinbefore with two wave mixing and rotation operation. Parameter ~
15 should be chosen such that the conditions in Equation (9), (10) and (26) are satisfied.
It should be appreciated that, since N was defined as 2M
+ l, the number of ports is an odd number. In the practical embodiments, where an even number of ports is preferred, the 20 ninth port is simply not used. In essence, a row of zeros will appear in the connectivity matrix.

Bandwidth Considerations.
To achieve wavelength division multiplexing, we need to 26 know the bandwidth of the limited-broadcast coupler. Let us assume that the optical signals with wavelengths A, varying between A - ~ and l + o can go through the coupler without any major attenuation. We would like to calculate the 3 - dB
bandwidth for the coupler. The couPle- will respond to 30 signals, if we keep the wavelength perturbation on 2C ~

of e~uation 11a to be much smaller than ~. To calculate the 3~ 3 - dB bandwidth, instead of equation 11a, we must have:

.- ... . . : , - . . -WO 91/15790 PCr/CA91/00113 Q, r ~

~ 2 C
(391 Since C ~ 2A~ ,the 3 - dB bandwidth wi11 De a Tunctlon - of d, M ana the routing matrix elements. However, the coefficients must satisfy the condition expressed by equatlon 27b, as well. To calculate the bandwidth in general, we will 10 also use the condition expressed by equations 32, 34 and 36.
Then we will present some numerical data for the sDeclal case of the 9 x 9 coupler.
Applying conditions expressed by equations 32, 34, and 36 in equation 27b, we will arrive at the following equation:

0 4Na~ _ Io for m/ - -~, . . ., O, . . ., +M
( 40 ) ., .
20 where Io is an integer. With M - 2 approximately, we will have:
: ' NIoA
~ (41) Using the above result in equation 39 will result in the following constraint on the available bandwidth in wavelength domain:

Bandwidth_ 0-16A

(42) where in equation 42, A is the light wavelength, N is the number of input.output ports, and Io is an integer.

, ~ , . .
- ::
, .:: . .

WO 91~1~790 PCI/CA91/00113 ~, 37 2~799~7 To maximize the available bandwidth, we choose I, ~
~ ~ .
20 - Max, Bandwidth _ 0-16A

~43j -Tne Dandwl~tn presente~ ln equatlon 43 is the availaDle ~and arouna the nomlnal central wavelength l.
As apDarent from the periodic nature of equation 11a, such a bandwidth as expressed ~y equation 43 is also available 10 around all other wavelengths sPaced by an integer multiDle of ~l form Awhere:
~' A _ . 6 4 A

(44j That is, any other wavelength that produces a phase shift proportional to an integer multiple of 2~ inside the argument of the sine function in equation 1la has available around it an equivalent amount of 3 - d8 bandwidth.
For the special case of a 9 x 9 coupler, where N = g and ? for N = 16, the available maximum bandwidth is about 3nm and 1nm, respectively. In general, by using the number of input/output ports N, we can use equation 43 to find the maximum available band.
Such a coupler can be designed around the central 25 wavelength lo for dense wavelength division multiplexing applications. All wavelengths used around lo that fall within the 3 - dB band of the coupler will get through the coupler.
Going back to Figure 12, we can choose 16 wavelengths around A~, such that they fall within the 3 - dB band of the coupler.
30 By forming the proper holographic patterns on the photosensitive slab, the perfect shuffle connectivity can be established.
To increase the coupling capacity, one way is to cascade several couplers with mutually overlapping passbands and use 35 wavelengths within the overlapped regions of the band as a means of connecting couplers. Hence, we can build economy-of-scale into the coupler design. Another alternative is to select the wavelengths used in a WDM network such that their : ' ' ' ~ ., , , ~ , : 2~7~ values match those at the Deaks of the sine function ~r, equatlon 11a. Us~na the latter methoc, the coupl~n eff~iency rema~ns at ~ts Dea~:
F~gure 11 illustrate_ an alternat~ve aopara~us for preparing a diffractlon means w~tn 2 SDat~al lv Varyln9 refract~ve ~ndex as aescrlDec nereinDefore. The bloc~ o`
pnotorefractlve materlal 106' ls positioned in a recess 110~-in a jig 1104 Tne jig 1104 has a plurality of oDtlcal fiDrec ln two arrays 1108 and 111G, respectively. These arrays cf 1~ opllcal fibres corresPond to the arrays of optical ,ibres 10_ and 11C, respectively, in tne optlcal interconnector snown ~n Figure 1. Each of the oPtlcal fibres in array 10~ l~
connected to a respective one cf a plurality of llgn- sources - 1112. The light sources may De any commercial single mode 15 source Likewise, each of the oPtical fibres in array 110 is connected to a respective one of an array of light sources 1114 Light sources 1112 are connected to drive means 1116 and light sources 1114 are connected to drive means 1118. The drive means are controlled by control means 1120 whlch 20 selectively and sequentially energizes the light sources in pairs to irradiate the block 106' in order to write the spatially varying refractive index described with respect to Figure 1.
As mentioned previously, with reference to the embodiment 25 of Figure 5, selective coupling, i.e. ~ is not the same as N', may be achieved simply by varying the intensity of the light sources so as to omit to write the photorefractive material at any position where no coupling is required. The embodiment of Figure 11, can be modified to achieved this quite easily 30 by controlling the individual light sources by way of their respective drive means 1116 and 1118. Thus intensity control means 1122 operates in conjunction with drive lndexing means to vary the intensity at the appropriate positions.
The embodiments of the invention described herein are by 35 way of example. Various modifications and alternatives may be apparent to one skilled in the art without departing from the scope of the invention which is defined by the claims appended hereto.

- .
.
, ..... , - , :

' ... -:. ~

WO91/1~790 PCTtCA91/00113 '~ 39 2~7~7 The coupler described as a specifled emboaiment nas an oda num~e! of lnPuts and outputs if could be modifiea au~te readily to Drovlde an even number of inDuts and output_, for example by omltt-ng the 0-th mode Moreover, although ~n the described embod~ment the number of ~nputs ~s the same as tne number of oU~Puts~ t~ey coula be differenL i,~ so ces~rec 5 This could be achleved qulte readily by omltting to write the specific part of the diffraction pattern as descriDea with reference to Figures 5 and 11.

Claims (27)

1. An optical device characterized by a stratified volume Bragg diffraction means (106) having its refractive index varying spatially according to the expression:

where x and z are ordinates of the diffraction means;
??,m' is the spatial frequency vector;
m is an input position or mode, corresponding to one optical axis;
m' is an output position or mode, corresponding to one optical axis;
m and m' taking on integer values that determine the number of input/output modes;
.DELTA.m,m' is the coefficient of coupling between m and m';
and r is the space vector.

2. An optical device characterized by diffraction means in the form of a body (106) having cylindrical opposed faces (112,114) and a refractive index which varies spatially and periodically in one plane of the body, such that a planar light beam incident upon one of said faces of the body in said plane at a predetermined angle and with the electric field of such light beam extending in the same direction as the cylindrical axes of said cylindrical opposed faces, will be refracted to emerge at a plurality of discrete angles determined by the spatially varying refractive index, such incident light being distributed substantially equally among the plurality of output refracted beams.

3. An optical device as claimed in claim 1, characterized by a body (106) having cylindrical opposed faces (112,114), said stratified volume Bragg diffraction means being provided in said body such that its refractive index varies spatially and periodically in one plane of the body, such that a planar light beam incident upon one of said faces of the body in said plane at a predetermined angle and with the electric field of such light beam extending in the same direction as the cylindrical axes of said cylindrical opposed faces, will be refracted to emerge at one or more of a plurality of discrete angles determined by the spatially varying refractive index, such incident light being distributed substantially equally among the output refracted beams.

4. An optical device as claimed in claim 2, or 3, characterized in that the diffraction means is arranged to couple substantially all of said incident light to the said output refracted beams.

5. An optical device as claimed in claim 1, further characterized by two arrays of optical emitters and/or receivers (108,110), said arrays being disposed at opposed faces, respectively, of said diffraction means, each of said optical emitters and/or receivers having an optical axis corresponding to one of said modes.

6. An optical device as claimed in claim 2 or 3, further characterized by two arrays (108,110) of optical emitters and/or receivers, said arrays being disposed at said opposed cylindrical faces (112,114), each of said optical receivers having an optical axis aligned with one of said discrete angles, wherein each said optical axis extends radially of the one of said faces, the respective optical axes of each array converging at a position on the other of said faces.

7. An optical device as claimed in claim 6, characterized in that said position is at the middle of said other of said faces (112,114).

8. An optical device as claimed in claim 3, characterized in that each of said optical emitters (108) is positioned to direct light along an optical axis extending radially of the face (112) with which the emitter is associated, such axis extending from a position on the other (114) of said faces.

9. An optical device as claimed in claim 8, characterized in that said position is at the middle of said other of said faces.

10. An optical device as claimed in claim 2 or 3, characterized in that the thickness of said body in the direction of the cylindrical axes of said opposed faces is at least equal to the width of the incident light beam.
(108,110).

11. An optical device as claimed in claim 2 or 3, characterized in that the refractive index varies such that the plurality of discrete angles for light emanating from one face (112) of the body (106) is different in number from the plurality of discrete angles for light emanating from the other face (114) of the body.

12. An optical device as claimed in claim 1 or 2.
characterized in that said refractive index of the body varies spatially in accordance with the expression:- where x and z are ordinates of the diffraction means;
d is the radius of curvature of the curved faces;
??,m' is the spatial frequency vector;
m is an input position or mode, corresponding to one optical axis;
r is the space vector; and N is the total number of elements or modes.

13. An optical device as claimed in claim 6, characterized in that said optical emitters and/or receivers comprise optical waveguides.

14. A method of making a diffraction means for an optical device by irradiating a body (106) of photorefractive material having cylindrical opposed faces (112,114), using a two wave mixing process employing two light beams comprising substantially planar waves. the method comprising the steps of:-(i) aligning the body with the cylindrical axes of said faces extending in the direction of the electric fields of the two light beams;
(ii) directing one of said light beams across said body;
(iii) directing the other of said light beams across said body, in succession, at a plurality of predetermined angles to the first light beam;
(iv) directing said one of said light beams across said body at a different angle;
and repeating steps (iii) and (iv), such that the refractive index of the irradiated body varies spatially and periodically such that light incident upon said body at one of said discrete angles will be refracted to emerge at a plurality of different angles.

15. A method as claimed in claim 14, characterized in that steps (iii) and (iv) are repeated for each of a plurality of discrete angles.

16. A method as claimed in claim 15, characterized in that said light beams are provided by respective light sources (506, 508) and the varying angles at which they irradiate said body (106) are achieved by rotating said light emitters relative to said body.

17. A method as defined in claim 14, characterized in that said light beams are provided by means of a plurality of emitters (108) disposed in an array in the plane of said body (106), said emitters being operative in pairs to irradiate said body by two wave mixing, variation of the angles of said light beams being achieved by selecting different ones of said emitters.

18. A method as claimed in claim 16 or 17, characterized in that the intensity of the light beams is varied at predetermined positions so as to vary said refractive index to couple an incident light beam to selected ones of said plurality of discrete output angles.

15. A method of making a diffraction means for an optical device characterized by the steps of :-(i) irradiating a planar body (106) of photorefractive material having cylindrical opposed faces (112,114) by means of a first coherent light source along an axis at a predetermined axis to the body, the light comprising a substantially planar wave, the plane of said wave extending in the same direction as the cylindrical axes of said cylindrical opposed surfaces;
(ii) irradiating the body by means of a second coherent light source along an axis at a predetermined axis to the light from the first source;
(iv) recording the resulting interference pattern in the slab;
(v) maintaining the position of the first source;
and (vi) rotating the second source stepwise, each step by a predetermined angle, and repeating steps (i), (ii) and (iii), for each step;
(vii) rotating the first source stepwise by a plurality of predetermined angles and, for each step, repeating step (vi).

20. Apparatus for producing a diffraction means for an optical device characterized by first and second sources (502,504) of substantially planar light, means (510) for supporting a body (106) of photorefractive material in a common plane of said sources so as to be irradiated by light beams from both said sources, said body having cylindrical opposed faces (112,114), means (512,506) for rotating one of said sources stepwise relative to the other source and about an axis extending through said body, the electric fields of the planar light beams extending in the same direction as the cylindrical axes of the opposed faces, means (512,508) for rotating the other source 2 about the same point as the rotation of the first source, and means for recording the resulting interference pattern.

21. Apparatus for providing a diffraction means for an optical device characterized by a support (1104) for a body (106') of photorefractive material having cylindrical opposed faces;
a plurality of optical emitters (1112,1114) in two planar arrays, one array each side of the support, the emitters in each array being positioned so as to emit a substantially plane wave light beam, the optical axes of said light beams extending radially from a common point and mutually spaced by a predetermined angle;
means (1116,1118,1120) for selectively enabling emission by pairs of said emitters in succession, the arrangement being such that the refractive index of the body after irradiation will vary spatially and periodically in the plane of said arrays.

22. Apparatus as claimed in claim 20 or 21, characterized by control means (1120) for controlling variation of said angles such that the refractive index of said body, after irradiation, varies in accordance with the expression:

where x and z are ordinates of the diffraction means;
??,m' is the spatial frequency vector;
m is an input position or mode, corresponding to one optical axis;

m' is an output position or mode, corresponding to one optical axis;
m and m taking on integer values that determine the number of input/output modes;
.DELTA.m,m' is the coefficient of coupling between m and m';
and r is the space vector.

23. Apparatus as claimed in claim 18, further characterized by intensity control means (1122) for varying the intensity of said light at predetermined positions to vary said refractive index so as to couple an incident light beam to selected ones of said plurality of discrete angles.

24. A communications network charaterized by a plurality of nodes (121 - 124) interconnected by an optical interconnection device comprising a stratified volume Bragg diffraction means (120) having its refractive index varying spatially according to the expression:

where x and z are ordinates of the diffraction means;
??,m' is the spatial frequency vector;
m is an input position or mode, corresponding to one optical axis;
m' is an output position or mode, corresponding to one optical axis; and r is the space vector.

25. A network as claimed in claim 24, characterized in that each said node comprises a transmitter (131 - 138) and a receiver (141 - 148), each transmitter being operable to transmit, selectively, signals of different wavelength, each including an address of another of said nodes, each receiver having means (151) for detecting said address and means responsive to the address detection means for routing the signal to its associated transmitter for transmission at one of said different wavelengths if the address detected is not its own, and for output to an associated user if the address detected is its own.

26. A network as claimed in claim 24, characterized by a plurality of said optical interconnection devices (121 - 128) connected in tandem, each device having a passband overlapping the passband of the device to which it is coupled, whereby signals having wavelengths within the overlapping regions of the band will be relayed through said interconnecting devices.

27. A network as claimed in claim 24, characterized in that the wavelengths of light beams transmitted through the network are selected to correspond substantially with peaks of the period of the periodic refractive index.