Integrated optical switch array

An optical switch array in which at least three input waveguides are coupled to at least three output waveguides. Each of the output waveguides is coupled in the same order to each of the input waveguides by a switching element such as a 1.times.2 switch, via an intermediate waveguide and a combining mechanism that includes a coupling element such as a y-junction combiner. For compactness, the switching elements that couple to the same output waveguide are mutually displaced along the input waveguides. Optionally, each of the input waveguides is coupled to an auxiliary waveguide, which in turn is coupled to further output waveguides.

FIELD AND BACKGROUND OF THE INVENTION
 The present invention relates to optical switch arrays and, more
 particularly, to an optical switch array, of particularly compact
 geometry, in which arbitrary combinations of the inputs and outputs are
 explicitly addressable.
 Integrated optical switches are well-known. For an early review of the art,
 see Lars Thylen, "Integrated optics in LiNbO.sub.3 : recent developments
 in devices for telecommunications", Journal of Lightwave Technology vol. 6
 no. 6 (June 1988), pp. 847-861. Waveguides are created in a lithium
 niobate substrate by processing the substrate locally to increase the
 index of refraction. For example, the index of refraction of lithium
 niobate may be increased locally by diffusing titanium into the substrate.
 To divert light from one waveguide to another, the waveguides are coupled
 by local optoelectrical manipulation of their indices of refraction.
 Well-known examples of optoelectrical switches include directional
 couplers, BOA couplers, digital-optical-switches and x-switches. Depending
 on the voltage applied to such a switch, light is thus partly or
 completely diverted from an input waveguide to an output waveguide.
 By appropriately combining waveguides and switches, a switch array is
 formed to switch light from a plurality of input waveguides among a
 plurality of output waveguides. A variety of switch array geometries are
 known. FIG. 1A is a conceptual illustration of a switch array of one such
 geometry: crossbar geometry. A set of input waveguides 10 crosses a set of
 output waveguides 12. At the crossing points, the waveguides are coupled
 by 2.times.2switches 14. For simplicity, only four input waveguides 10 and
 four output waveguides 12 are shown in FIG. 1A. Typically the numbers of
 input waveguides 10 and output waveguides 12 are equal powers of 2, up to
 a practical maximum of 32.
 FIG. 1B shows, schematically, the actual layout of the switch array of FIG.
 1A. Switches 14 are shown as directional couplers, in which parallel
 segments of the waveguides are flanked by electrodes (not shown) to which
 the coupling voltages are applied. Note that input waveguide 10a leads
 directly into output waveguide 12a, that input waveguide 10b leads
 directly into output waveguide 12b, that input waveguide 10c leads
 directly into output waveguide 12c, and that input waveguide 10d leads
 directly into output waveguide 12d. To allow arbitrary coupling of inputs
 to outputs, three auxiliary waveguides 11a, 11b and 11c are provided.
 Waveguides 10a-12a and 10b-12b are coupled in switch 14a. Waveguides
 10b-12b and 10c-12c are coupled in switches 14b and 14c. Waveguides
 10c-12c and 10d-12d are coupled in switches 14d, 14e and 14f. Waveguides
 10d-12d and 11a are coupled in switches 14g, 14h, 14i and 14j. Waveguides
 11a and 11b are coupled in switches 14k, 14l and 14m. Waveguides 11b and
 11c are coupled in switches 14n and 14o. Note that switches 14g, 14k and
 14n actually are 1.times.2 switches, that switches 14j, 14m and 14o
 actually are 2.times.1 switches, and that there is no switch corresponding
 to the lowermost 2.times.2 switch 14 of FIG. 1A. (A 1.times.2 switch is a
 2.times.2 switch with one input deactivated; a 2.times.1 switch is a
 2.times.2 switch with one output deactivated.)
 Switch arrays based on geometries such as the crossbar geometry of FIGS. 1A
 and 1B can be used to divert input signals to output channels arbitrarily.
 Signals from any input channels can be directed to any output channel, and
 even to multiple output channels, in broadcast and multicast transmission
 modes.
 Despite the conceptual simplicity of the crossbar geometry of FIGS. 1A and
 1B, this geometry has been found inferior, in practice, to two other
 geometries, the tree geometry, illustrated in FIG. 2, and the double
 crossbar geometry, illustrated in FIG. 3. FIG. 2 shows the tree geometry,
 for four input waveguides 20 and four output waveguides 22. Waveguides 20
 lead into a binary tree of 1.times.2 switches 24. Waveguides 22 emerge
 from a complementary binary tree of 2.times.1 switches 26. The highest
 order branches of the binary trees are connected by intermediate
 waveguides 28. FIG. 3 shows the double crossbar geometry, for four input
 waveguides 30 and four output waveguides 32. Each input waveguide 30
 traverses four 1.times.2 switches 34a, 34b, 34c and 34d. Each output
 waveguide 32 traverses four 2.times.1 switches 36a, 36b, 36c and 36d. The
 remaining outputs of switches 34 are connected to respective inputs of
 switches 36 by intermediate waveguides 38. Note that, in principle,
 switches 34d and 36a are not needed, because input waveguides 30 could
 lead directly to switches 36d and output waveguides 32 could emerge
 directly from switches 36a; but, in practice, the illustrated
 configuration has been found to reduce cross-talk.
 The tree and double crossbar geometries require larger numbers of switches
 than the equivalent crossbar geometry. Nevertheless, the tree and double
 crossbar geometries have certain advantages over the crossbar geometry:
 1. The tree and double crossbar geometries have lower worst-case crosstalk
 than the crossbar geometry.
 2. In general, the path from a particular input waveguide to a particular
 output waveguide through a crossbar switch array is not unique. Therefore,
 computational resources must be devoted to reconfiguring a crossbar switch
 array in real time. In a tree switch array or in a double crossbar switch
 array, the path from any particular input waveguide to any particular
 output waveguide is unique, so it is trivial to compute how to reconfigure
 such a switch array in real time.
 3. To prevent loss of optical power by radiation, the intermediate
 waveguides of an optical switch array must have gentle curvature. In the
 case of the crossbar geometry, this requires that the switches be arranged
 in a diamond pattern, as illustrated in FIGS. 1A and 1B. This is a less
 efficient packing of the switches than, for example, the rectangular
 matrix pattern of the double crossbar switch as illustrated in FIG. 3.
 SUMMARY OF THE INVENTION
 According to the present invention there is provided an optical switch
 array including: (a) at least three input waveguides; (b) a first group of
 at least three output waveguides; (c) for each of the output waveguides of
 the first group: for each of the input waveguides, a switching element
 coupling the each input waveguide only to the each output waveguide; and
 (d) for each of the output waveguides of the first group, a combining
 mechanism for coupling all of the input waveguides to the each output
 waveguide; the input waveguides, the output waveguides, the switching
 elements and the combining mechanism all being arranged substantially in a
 common plane; all of the input waveguides traversing successively
 respective the switching elements in a common order relative to the output
 waveguides of the first group.
 According to the present invention there is provided a method for switching
 signals from at least one of at least three input channels to at least one
 of at least three output channels, each output channel receiving signals
 from only one input channel, including the steps of: (a) providing an
 optical switch array including: (i) at least three input waveguides, each
 of the input waveguides corresponding uniquely to one of the input
 channels, (ii) at least three output waveguides, each of the output
 waveguides corresponding uniquely to one of the output channels, (iii) for
 each of the output waveguides: for each of the input waveguides, a
 switching element coupling the each input waveguide only to the each
 output waveguide, and (iv) for each of the output waveguides, a combining
 mechanism for coupling all of the input waveguides to the each output
 waveguide, the input waveguides, the output waveguides, the switching
 elements and the combining mechanism all being arranged substantially in a
 common plane, all of the input waveguides traversing successively
 respective the switching elements in a common order relative to the output
 waveguides; and (b) for each of the output waveguides: setting the
 switching element, that couples the each output waveguide to the input
 waveguide that corresponds to the input channel wherefrom a signal is to
 be switched to the output channel corresponding to the each output
 waveguide, to divert at least a portion of the signal to the each output
 waveguide.
 According to the present invention there is provided a method for
 multicasting from at least one of at least three input channel to at least
 two of at least three output channels, each output channel receiving input
 from only one input channel, including the steps of: (a) providing an
 optical switch array including: (i) at least three input waveguides, each
 of the input waveguides corresponding uniquely to one of the input
 channels, (ii) at least three output waveguides, each of the output
 waveguides corresponding uniquely to one of the output channels, (iii) for
 each of the output waveguides: for each of the input waveguides, a
 switching element coupling the each input waveguide only to the each
 output waveguide, thereby coupling the input channel corresponding to the
 each input waveguide to the output channel corresponding to the output
 waveguide, and (iv) for each of the output waveguides, a combining
 mechanism for coupling all of the input waveguides to the each output
 waveguide, the input waveguides, the output waveguides, the switching
 elements and the combining mechanisms all being arranged substantially in
 a common plane, all of the input waveguides traversing successively
 respective the switching elements in a common order relative to the output
 waveguides; and (b) for each output channel: setting the switching
 element, that couples the each output channel to the input channel
 wherefrom a signal is to be switched to the each output channel, to divert
 at least a portion of the signal to the each output channel, at least one
 of the switching elements being set to divert only a portion of the
 signal.
 We have discovered that, by rearranging the connections of the double
 crossbar geometry of FIG. 3, a new geometry is obtained that allows a
 spatially more compact configuration of switches and interconnecting
 waveguides. Compactness is an important consideration, because it allows a
 larger switch array (more inputs and outputs) to be fabricated on a
 substrate of a given size. One substrate suffices for a switch array of
 the present invention that is functionally equivalent to a prior art
 switch array that may require two (double crossbar geometry) or three
 (tree geometry) substrates.
 FIG. 4 shows the geometry of a switch array of the present invention, in
 the case of four input waveguides 40 and four output waveguides 42. As in
 the double crossbar geometry of FIG. 3, each input waveguide 40 traverses
 four 1.times.2 switches 44, each output waveguide 42 traverses four
 2.times.1 switches 46, and the remaining outputs of switches 44 are
 connected to respective inputs of switches 46 by intermediate waveguides
 48. Unlike the double crossbar geometry of FIG. 3, switches 46a all are
 traversed by the same output waveguide 42a, switches 46b all are traversed
 by the same output waveguide 42b, switches 46c all are traversed by the
 same output waveguide 42c, and switches 46d all are traversed by the same
 output waveguide 42d, so that all input waveguides 40 are coupled to
 output waveguides 42 in the same order: first to output waveguide 42a,
 then to output waveguide 42b, then to output waveguide 42c, and finally to
 output waveguide 42d. This allows intermediate waveguides 48 that lead to
 a particular output waveguide 42 to be geometrically adjacent, with a
 corresponding increase in the compactness of a switch array of the present
 invention as compared to an equivalent double crossbar switch array.
 As in the double crossbar geometry of FIG. 3, strictly speaking, 1.times.2
 switches 44d and the first 2.times.1 switches 46 traversed by output
 waveguides 42 are not necessary, and are present only to reduce
 cross-talk. Co-pending U.S. patent application Ser. No. 09/085,369 teaches
 a similar switch array geometry, in which these switches are in fact not
 present.
 In the days before integrated optics, Fulenwider, in U.S. Pat. No.
 3,871,743, described an optical switch array having a topology similar to
 that of the present invention. Unlike the present invention, the
 particular embodiment described by Fulenwider is not well-suited to
 fabrication as an integrated optical device. By contrast, a switch array
 of the present invention is easily fabricated, essentially in a single
 plane, as an integrated optical device, for example on a Z-cut lithium
 niobate substrate.
 1.times.2 switches 44 and 2.times.1 switches 46 are indicated on FIG. 4 for
 illustrative purposes only. More generally, the scope of the present
 invention includes any suitable switching element in the role of 1.times.2
 switch 44 and any suitable coupling element in the role of 2.times.1
 switch 46. In particular, passive y-junction combiners may be substituted
 for 2.times.1 switches 46.
 To switch signals from an input channel, associated uniquely with a
 corresponding input waveguide, to one or more output channels, each output
 channel associated uniquely with a corresponding output waveguide, the
 output waveguides are considered in turn. For each output waveguide, the
 switching element that couples the input waveguide associated with the
 desired input channel is set to divert the appropriate portion of the
 input signals of that channel to the target output waveguide. If signals
 from other input channels are to be switched to other output waveguides,
 then the corresponding other switching elements associated with the target
 output waveguide are set to pass those signals without diversion.

DESCRIPTION OF THE PREFERRED EMBODIMENTS
 The present invention is of an integrated optical switch array whose
 geometry allows it to be fabricated more compactly than similar known
 optical switch arrays.
 The principles and operation of an optical switch array according to the
 present invention may be better understood with reference to the drawings
 and the accompanying description.
 Referring now to the drawings, FIG. 5 is a schematic illustration of an
 optical switch array of the present invention, for coupling input
 waveguides 140a, 140b, 140c and 140d to output waveguides 142a, 142b, 142c
 and 142d. Input waveguide 140a is coupled to output waveguide 142a by a
 1.times.2 switch 144aa via an intermediate waveguide 148aa and a passive
 y-junction combiner 146aa, to output waveguide 142b by a 1.times.2 switch
 144ab via an intermediate waveguide 148ab and a passive y-junction
 combiner 146ab, to output waveguide 142c by a 1.times.2 switch 144ac via
 an intermediate waveguide 148ac and a passive y-junction combiner 146ac,
 and to output waveguide 142d by a 1.times.2 switch 144ad via an
 intermediate waveguide 148ad and a passive y-junction combiner 146ad.
 Input waveguide 140b is coupled to output waveguide 142a by a 1.times.2
 switch 144ba via an intermediate waveguide 148ba and a passive y-junction
 combiner 146ba, to output waveguide 142b by a 1.times.2 switch 144bb via
 an intermediate waveguide 148bb and a passive y-junction combiner 146bb,
 to output waveguide 142e by a 1.times.2 switch 144bc via an intermediate
 waveguide 148bc and a passive y-junction combiner 146bc, and to output
 waveguide 142d by a 1.times.2 switch 144bd via an intermediate waveguide
 148bd and a passive y-junction combiner 146bd. Input waveguide 140c is
 coupled to output waveguide 142a by a 1.times.2 switch 144ca via an
 intermediate waveguide 148ca and a passive y-junction combiner 146ca, to
 output waveguide 142b by a 1.times.2 switch 144cb via an intermediate
 waveguide 148cb and a passive y-junction combiner 146cb, to output
 waveguide 142c by a 1.times.2 switch 144cc via an intermediate waveguide
 148cc and a passive y-junction combiner 146cc, and to output waveguide
 142d by a 1.times.2 switch 144ed via an intermediate waveguide 148cd and a
 passive y-junction combiner 146ed. Input waveguide 140d is coupled to
 output waveguide 142a by a 1.times.2 switch 144d a via an intermediate
 waveguide 148da and a passive y-junction combiner 146da, to output
 waveguide 142b by a 1.times.2 switch 144db via an intermediate waveguide
 148db and a passive y-junction combiner 146db, to output waveguide 142c by
 a 1.times.2 switch 144dc via an intermediate waveguide 148dc and a passive
 y-junction combiner 146de, and to output waveguide 142d by a 1.times.2
 switch 144dd via an intermediate waveguide 148dd and a passive y-junction
 combiner 146dd.
 Waveguides 140 and 142, as well as 1.times.2 switches 144 and y-junction
 combiners 146, are fabricated by standard techniques, for example on the
 surface of a Z-cut lithium niobate crystal, essentially in a single plane.
 As a result, some of the intermediate waveguides intersect all but one of
 the input waveguides. Specifically, intermediate waveguide 148ba
 intersects input waveguide 140a at intersection 150ba; intermediate
 waveguide 148ca intersects input waveguide 140a at intersection 150ca and
 input waveguide 140b at intersection 150ca'; intermediate waveguide 148da
 intersects input waveguide 140a at intersection 150da, input waveguide
 140b at intersection 150da' and input waveguide 140c at intersection
 150da"; intermediate waveguide 148bb intersects input waveguide 140a at
 intersection 150bb; intermediate waveguide 148cb intersects input
 waveguide 140a at intersection 150cb and input waveguide 140b at
 intersection 150cb'; intermediate waveguide 148db intersects input
 waveguide 140a at intersection 150db, input waveguide 140b at intersection
 150db' and input waveguide 140c at intersection 150db"; intermediate
 waveguide 148bc intersects input waveguide 140a at intersection 150bc;
 intermediate waveguide 148cc intersects input waveguide 140a at
 intersection 150cc and input waveguide 140b at intersection 150cc'; and
 intermediate waveguide 148dc intersects input waveguide 140a at
 intersection IS5de, input waveguide 140b at intersection 150dc' and input
 waveguide 140c at intersection 150dc".
 1.times.2 switches 144 are illustrative of switching elements for coupling
 input waveguides 140 to output waveguides 142. The scope of the present
 invention includes all such switching elements. The particular 1.times.2
 switches 144 illustrated in FIG. 2 are directional couplers. For
 simplicity, the electrodes of directional couplers 144 are not shown. As
 in the case of the prior art switch arrays, any suitable 1.times.2
 switches, including BOA couplers, digital-optical-switches and x-switches,
 may be used as 1.times.2 switches 144.
 Passive y-junction combiners 146 are illustrative of coupling elements for
 coupling input waveguides 140 to output waveguides 142. The difference
 between a "switching element" and a "coupling element", as these terms are
 used herein, is that a coupling element may be either passive or active,
 whereas a switching element is necessarily active. In FIG. 4, coupling
 elements 46 that couple input waveguides 40 to output waveguides 42 are
 active coupling elements, specifically 2.times.1 switches. As in the case
 of 1.times.2 switches 44 and 144, these 2.times.1 switches may be any
 suitable 2.times.1 switches, including directional couplers, BOA couplers,
 digital-optical-switches and x-switches.
 The advantage of passive couplers 146 over active couplers 46 is that in an
 optical switch using passive couplers 146, fewer active elements need to
 be addressed than in an optical switch using active couplers 46. The
 advantages of active couplers 46 over passive couplers 146 are that a
 passive coupler 146 requires an elaborate design geometry to prevent loss
 of part of the incoming radiation to a second order mode; and that an
 active coupler 46 in its off state reduces crosstalk by actively blocking
 incoming signals from the associated intermediate waveguide 48.
 In the general case of N input waveguides 40 or 140 and M output waveguides
 42 or 142, an optical switch array of the present invention includes NM
 switching elements 44 or 144, NM coupling elements 46 or 146, and
 N(N-1)M/2 intersections 28.
 To switch optical signals from input waveguides 40 or 140 to output
 waveguides 42 or 142 efficiently, with minimal losses, implementations of
 the optical switches of FIGS. 4 and 5 must obey certain geometric
 constraints. These constraints depend on the wavelength of the light used.
 For the commonly used wavelength of 1550 nm, the following constraints
 apply: Except where coupled in switching elements 44 or 144 or coupling
 elements 46 or 146, waveguides 40, 42, 140 and 142 should be at least
 about 0.5 mm apart. 1.times.2 switches 44 and 144 and 2.times.1 switches
 46 typically are between 5 mm and 7 mm long. Parallel columns of 1.times.2
 switches, for example the column including switches 44a and the column
 including switches 44b, should be at least about 1 mm apart. The
 intersection angle at intersections 150 should be such that input
 waveguides 140 and intermediate waveguides 148 are not coupled at
 intersections 150. The radii of curvature of the curved portions of
 intermediate waveguides 48 and 148, and the radii of curvature of the
 curved portions, if any, of input and output waveguides 40, 42, 140 and
 142, should be at least 25 mm, and more preferably at least 30 mm. Within
 these geometric constraints, it is possible to fit as many as 32 input
 waveguides 40 or 140 and as many as 32 output waveguides 42 or 142 on the
 face of a Z-cut 4" diameter lithium niobate crystal.
 Depending on the voltages applied to their electrodes, 1.times.2 switches
 44 or 144 and 2.times.1 switches 46 may be placed in a straight-through
 state, in which the two channels of the switch are uncoupled, a crossover
 state, in which the two channels exchange signals, and any state
 in-between, for partial exchange of signals. In general, it is
 straightforward to select switch configurations to achieve any desired
 switching pattern of signals from input waveguides 40 or 140 to output
 waveguides 42 or 142. Switch configurations are selected by successive
 consideration of the desired output waveguides 42 or 142, taking advantage
 of the fact that each output channel receives input from only one input
 channel. For each output waveguide 42 or 142, switch 44 or 144 that
 couples the desired input waveguide 40 or 140 to the target output
 waveguide 42 or 142 is set to the state that diverts the desired portion
 of the input signal to the target output waveguide 142, and, if necessary,
 some or all of the rest of switches 44 or 144 that couple to the target
 output waveguide 42 or 142 are set to the straight-through state. This
 applies both to ordinary switching, in which signals from each input
 channel is switched to only one output channel, and to multicasting, in
 which signals from one of the input channels are split among two or more
 output channels. An important special case of multicasting is
 broadcasting, in which signals from only one input channel are distributed
 among all the output channels.
 For example, using the embodiment of FIG. 5, and associating channel a with
 waveguides 140a and 142a, channel b with waveguides 140b and 142b, and
 channel c with waveguides 140c and 142c, suppose that it is desired to
 direct input signals from channel a to output on channel b, input signals
 from channel b to output on channel c, and input signals from channel c to
 output on channel a. In the leftmost column of switches 144, that couples
 to output waveguide 142a, switch 144ca is set to the crossover state,
 while switches 144aa and 144ba are set to the straight-through state. In
 the next column of switches 144, that couples to output waveguide 142b,
 switch 144ab is set to the crossover state, while switch 144bb is set to
 the straight-through state. The state of switch 144cb is arbitrary,
 because the entire incoming signal on channel c was diverted to channel a
 by switch 144ca. Finally, in the next column of switches 144, that couples
 to output waveguide 142c, switch 144bc is set to the crossover state. The
 states of the remaining switches 144 is arbitrary.
 Similarly, to broadcast equally from channel a to all three output
 channels, switch 144aa is set to divert 1/3 of the incoming signal, switch
 144ab is set to divert 1/2 of the incoming signal, and switch 144ac is set
 to the full crossover state. The states of the remaining switches 144 is
 arbitrary.
 In this context, it should be noted that the switches used by Fulenwider,
 which consist of input gratings and acoustic beam steerers, can assume
 only the straight-through state and the crossover state. Partial diversion
 of a signal from one channel to another, as is necessary for multicasting,
 requires the use of more modern switches, such as the integrated optic
 switches used in the present invention.
 Active couplers 46a collectively constitute a combining mechanism for
 coupling input waveguides 40 into output waveguide 42a. Likewise, active
 couplers 146aa, 146ba, 146ca and 146da collectively constitute a combining
 mechanism for coupling input waveguides 140 into output waveguide 142a.
 Similarly, active couplers 46b collectively constitute a combining
 mechanism for coupling input waveguides 40 into output waveguide 42b;
 active couplers 46c collectively constitute a combining mechanism for
 coupling input waveguides 40 into output waveguide 42c; and active
 couplers 46d collectively constitute a combining mechanism for coupling
 input waveguides 40 into output waveguide 42d. Likewise, active couplers
 146ab, 146bb, 146cb and 146db collectively constitute a combining
 mechanism for coupling input waveguides 140 into output waveguide 142b;
 active couplers 146ac , 146bc, 146cc and 146dc collectively constitute a
 combining mechanism for coupling input waveguides 140 into output
 waveguide 142c; and active couplers 146ad , 146bd, 146cd and 146dd
 collectively constitute a combining mechanism for coupling input
 waveguides 140 into output waveguide 142d. FIGS. 6A and 6B show
 alternative combining mechanisms.
 FIG. 6A shows four intermediate waveguides 148 merging into a passive
 funnel structure 152 at an input end 143 of an output waveguide 142.
 Funnel structures 152 must be designed geometrically to minimize losses
 due to generation of high order modes at the funnel necks.
 FIG. 6B shows four intermediate waveguides 148 coupled into input end 143
 of output waveguide 144 by a planar lens 154. Planar lens 154 may be
 fabricated in a lithium niobate substrate by proton exchange, to locally
 increase the index of refraction of the lithium niobate. Planar lens 154
 is shown as a refractive lens. Alternatively, planar lens 154 may be a
 Fresnel lens.
 FIG. 5 illustrates another feature of the present invention that increases
 the compactness of an optical switch of the present invention,
 particularly when many more than the only four input waveguides 140 shown
 in FIG. 5 are coupled to many more than the only four output waveguides
 142 shown in FIG. 5. Specifically, switching elements 144 that couple
 input waveguides 140 into a particular output waveguide 142 are displaced
 relative to each other along input waveguides 140. As drawn in FIG. 5,
 switching element 144aa is displaced rightward of switching element 144ab,
 switching element 144ab is displaced rightward of switching element 144ac,
 and switching element 144ac is displaced rightward of switching element
 144ad. Switching elements 144ab, 144bb, 144cb and 144db that couple input
 waveguides 140 into output waveguide 142b, switching elements 144ac,
 144bc, 144cc and 144de that couple input waveguides 140 into output
 waveguide 142c, and switching elements 144ad, 144bd, 144cd and 144dd that
 couple input waveguides 140 into output waveguide 142d are mutually
 displaced along their respective input waveguides 140 in a similar manner.
 In the case of a large number of input waveguides 140 and output
 waveguides 142, this mutual displacement allows an intermediate waveguide
 148, that couples a last (bottommost in FIG. 5) input waveguide 140 to one
 of output waveguides 142 (for example, output waveguide 140a), to avoid
 intersecting intermediate waveguides 148 that couple first (topmost in
 FIG. 5) input waveguides (for example, input waveguides 140a and 140b) to
 the next output waveguide (for example, output waveguide 142b). It will be
 appreciated that limiting the number of waveguide intersections, to the
 N(N-1)M/2 minimum number of intersections required by the geometry of the
 present invention, minimizes the cross-talk between input and output
 channels. Of course, the mutual displacement shown for switching elements
 144ad, 144bd, 144cd and 144dd is not strictly necessary, because there is
 not "next output waveguide" following last output waveguide 142d.
 Inspection of FIG. 5 also shows that the mutual displacement of switching
 elements 144 that couple into the same output waveguide 142 also allows
 intermediate waveguides 148 that lead to that waveguide 142 to be
 positioned closer to each other than would otherwise be possible. The
 upper bound on the mutual displacement of those switching elements 144 is
 set by the constraint that, just as parallel waveguides 140 or 142 must be
 separated by a minimum distance in order to prevent crosstalk, so parallel
 waveguides 148, that lead to the same output waveguide 142, must be
 separated by a minimum distance in order to prevent crosstalk.
 FIG. 7 is a schematic illustration of a second embodiment of the optical
 switch array of the present invention, for coupling three input waveguides
 240 to six output waveguides 242. Each input waveguide 240 is coupled to a
 corresponding, parallel auxiliary waveguide 241 by a splitting switch 243.
 Input waveguides 240 are coupled to output waveguide 242a by switching
 elements 244a via intermediate waveguides 248a and coupling elements 246a;
 to output waveguide 242b by switching elements 244b via intermediate
 waveguides 248b and coupling elements 246b; and to output waveguide 242c
 by switching elements 244c via intermediate waveguides 248c and coupling
 elements 246c. Auxiliary waveguides 241 are coupled to output waveguide
 242d by switching elements 244d via intermediate waveguides 248d and
 coupling elements 246d; to output waveguide 242e by switching elements
 244e via intermediate waveguides 248e and coupling elements 246e; and to
 output waveguide 242f by switching elements 244f via intermediate
 waveguides 248f and coupling elements 246f. As in the embodiment of FIG.
 5, switching elements 244a are mutually displaced along input waveguides
 240, as are switching elements 244b and switching elements 244c.
 Similarly, switching elements 244d are mutually displaced along auxiliary
 waveguides 241, as are switching elements 244e and switching elements
 244f. The configuration of FIG. 7 allows increased compactness because the
 two groups of intermediate waveguides 248 and output waveguides 242 branch
 away from input waveguides 240 on opposite sides of input waveguides 240.
 Because some intermediate waveguides 248d, 248e and 248f intersect some
 intermediate waveguides 248a, 248b and 248c, there are more intersections
 in the embodiment of FIG. 7 than in an equivalent embodiment configured
 according to FIG. 5; but this does not add appreciably to the
 cross-coupling because the angles of mutual intersection of intermediate
 waveguides 248 is about twice the angles of intersection of intermediate
 waveguides 248 with input waveguides 240 and auxiliary waveguides 241.
 FIG. 8 is a partial schematic illustration of a third embodiment of the
 optical switch array of the present invention, for coupling three input
 waveguides 340 to six output waveguides (not shown). Each input waveguide
 340 is coupled to a corresponding, parallel auxiliary waveguide 341 by a
 50% coupler 343 and a 100% reflector 350. In effect, each auxiliary
 waveguide 341 is an extension of the corresponding input waveguide 340 in
 the opposite direction, because half the light entering an input waveguide
 340 and reaching the corresponding 50% coupler 343 is coupled into the
 corresponding auxiliary waveguide 341, and the remaining half of the light
 is coupled into the corresponding auxiliary waveguide 341 by the
 corresponding 50% coupler 343 after reflecting off of reflector 350. Input
 waveguides 340 are coupled to a first output waveguide by switching
 elements 344a via intermediate waveguides 348a, to a second output
 waveguide by switching elements 344b via intermediate waveguides 348b, and
 to a third output waveguide by switching elements 344c via intermediate
 waveguides 348c. Auxiliary waveguides 341 are coupled to a fourth output
 waveguide by switching elements 344d via intermediate waveguides 348d, to
 a fifth output waveguide by switching elements 344e via intermediate
 waveguides 348e, and to a sixth output waveguide by switching elements
 344f via intermediate waveguides 348f. As in the embodiments of FIGS. 5
 and 7, switching elements 344a are mutually displaced along input
 waveguides 340, as are switching elements 344b and switching elements
 344c. As in the embodiment of FIG. 7, switching elements 344d are mutually
 displaced along auxiliary waveguides 341, as are switching elements 344e
 and switching elements 344f. For illustrational simplicity, the output
 waveguides and the coupling elements that couple intermediate waveguides
 348 thereto are not shown. The configuration of FIG. 8 allows increased
 compactness because the two groups of intermediate waveguides 348 and
 corresponding output waveguides branch away from input waveguides 340 in
 opposite directions.
 If the embodiment of FIG. 8 is fabricated on the surface of a z-cut lithium
 niobate crystal, then reflector 350 is formed by depositing a metal
 coating on a flattened and polished surface perpendicular to waveguides
 340 and 341, or by depositing a series of dielectric layers, appropriate
 to the wavelength of the light being switched, on that flattened and
 polished surface, or by mechanically attaching a mirror to that flattened
 and polished surface.
 FIG. 9 shows the preferred layout of a switch array of the embodiment of
 FIG. 5, on a surface 202 of a z-cut lithium niobate crystal 200, for
 coupling twelve input waveguides 140 to twelve output waveguides 142.
 Light enters input waveguides 140 via a surface 204 that is etched
 perpendicular to input waveguides 140. Light exits output waveguides 142
 via a surface 206 that is etched perpendicular to output waveguides 142.
 Waveguides 140 and 142 are curved, with a radius of curvature of about 35
 mm. If waveguides 140 and 142 are straight, as drawn in FIG. 5, then input
 waveguides must be separated by about 0.7 mm to make sure that
 intermediate waveguides 148 cross input waveguides 140 at intersections
 150 at at least a minimum angle .theta. of 11.5.degree. to minimize
 cross-talk. Curving waveguides 140 and 142 as in FIG. 9 allows input
 waveguides 140 to be separated by only about 0.35 mm while still
 intersecting intermediate waveguides 148 at an angle .theta. of at least
 11.5.degree..
 The illustrative geometric parameters given above are for an optical switch
 array of the present invention that is fabricated in a lithium niobate
 substrate. It will be clear to those skilled in the art how to apply the
 present invention to other substrates, for example, polymer substrates and
 silica/Si substrates. In particular, the geometric constraints relevant to
 these other substrates will be clear to those skilled in the art
 While the invention has been described with respect to a limited number of
 embodiments, it will be appreciated that many variations, modifications
 and other applications of the invention may be made.