Note: Descriptions are shown in the official language in which they were submitted.
WO 91/15790 PCI/CA91/00113
.~` 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]
.... ... . ~ ..................... . .
.
.
WO 91/15790 PCI/CA91/00113
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
., . , ::
:-. .:, . ~ . - . - : .
WO 91/15790 PCI/CA91/00113
~ ~ 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;
, ~ : .
''
, , . . .
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.
. . . . . , .: :. .. , - . - : ~ , . - :~ :
WO 91/15790 PCr/CA91/00113
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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 the5 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;
. . - - . ~ . . -,: . : : ,. :.
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:
1G
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;
: ,' ' ' ' , ~: ~ , -
,: . , . ~ . , ,
WO 91/15790 PCI/CA91/00113
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:
0
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
WO 91/15790 PCT/CA91/00113
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.
.
- -
-' -, ,-
. . ~ , ., i , .. ,, ", .
- . -, . : : :. ,
WO 91/15790 PCI`/CA91/00113
'~ 17 .2~7~7
,. .
.
. .,
~ _ ~ ~m,ml ~ ' ' foI m,rn~ - -M, . . ., O , . . ., +M
.
.
, .
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
2 8
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
WO 91/15790 PCI/CA91/00113
- '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
~: , '- . . - ~ ,
. .
WO 91/15790 PCI/CA91/00113
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
WO 91/15790 PCI/CA91/00113
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
. . . .
, . ~
'.: ' . . ~ - .
WO 91/15790 PCI/CA91/00113
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.
- ~ - . . - - : . . . : . .
. .
. . .
WO 91/15790 PCI/CA91/00113
~ 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.
:. - : . - . . . ; .
': ' ' . . :, :' ;, ` ' .'' ~.' '' '' ~
.. .. . . . ...
. ~
- . .. ..
WO91/15790 PCT/CA91/00113
'`'~ 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
1 0
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
36
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
N2I
(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
N2
~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
N2
(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
: ' ' ' ~ ., , , ~ ,
WO 91/15790 PCI/CA91/00113
: 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.
