Abstract:
A strict-sense nonblocking N×N spatial optical cross connect that employs planar lightwave beam steerers. The beam steerers allow for a modular design without requiring two-dimensional chip-to-chip waveguide interconnections. The modular design and the fact that the number of electrical control leads scales as NlogN in turn allows the possibility of constructing large, robust, solid-state cross connects. A cascaded beam-steerer design that substantially relaxes phase shifter strength requirements is also described.

Description:
FIELD OF THE INVENTION 
     The present invention relates to optical cross connects and beam steerers. 
     BACKGROUND OF THE INVENTION 
     Network nodes often require strict or wide-sense nonblocking N×N cross connects. A nonblocking cross connect can connect any of N ports on one side of the cross connect to any of N ports on the other side of the cross connect in any of the N! possible connection setups. A strict or wide-sense nonblocking cross connect can change a pair of connections without interrupting any of the other connections. (See R. Ramaswami et al., “Optical Networks: A Practical Perspective,” Morgan Kaufmann Publishers, San Francisco, 1998.) Furthermore, performing the switching optically allows for very large connection bandwidths. 
     One approach to making an optical cross connect is to use bulk optics with moving parts. Strict-sense nonblocking micro and macro-mechanical space switches with N as large as 8 and 72, respectively, have been reported. (See, e.g., L. Y. Lin et al., “High-Density Connection-Symmetric Free-Space Micromachined Polygon Optical Crossconnects With Low Loss for WDM Networks,” Optical Fiber Comm. Conf., paper PD24-1, 1998; and the Astarte company web site at http://www.starswitch.com/7250spec.htm.) 
     Another approach is to use planar lightwave circuits, which can be completely solid-state. Strict-sense nonblocking space switches in AlGaAs, InGaAsP, LiNbO 3 , and silica with N as large as 8, 4, 8 (16 using multiple chips), and 16 (actually only wide-sense nonblocking), respectively, have been demonstrated. (See, e.g., T. Goh et al., “Low-loss and high-extinction-ratio silica-based strictly nonblocking 16×16 thermooptic matrix switch,” IEEE Photon. Technol. Lett., vol. 10, pp. 810-812, 1998.) 
     The planar approaches have used either arrangements of 1×2 or 2×2 switches or a broadcast-and-select architecture. (See M. Gustavsson et al., “Monolithically integrated 4×4 InGaAsP/InP laser amplifier gate switch arrays,” Electron. Lett., vol. 28, pp. 2223-2225, 1992.) Although such arrangements can have very low crosstalk, they have several drawbacks in terms of scaleability. First, in such arrangements, the number of switches and/or gates is ≧N 2 , consuming nearly an entire wafer for N=16. (See, e.g., Goh et al.) Second, the electrical-lead-number and settings number is ≧N 2 . Third, there are often many waveguide crossings. 
     SUMMARY OF THE INVENTION 
     The present invention provides a planar lightwave circuit strict-sense nonblocking cross connect that has an electrical-lead-number proportional to NlogN and settings number proportional to N (1+1/logN) logN; has no waveguide crossings, which permits a compact size; and is modular. It is thus suitable for very large-N, maintainable cross connects. Additionally, the present invention does not rely on gain or loss elements and so can be made with virtually any lightwave circuit material. 
     In a further exemplary embodiment of a cross connect in accordance with the present invention, a tilted glass block is used to provide a large free-space length for switching large numbers of ports. 
     The present invention also provides a novel beam steerer comprising two or more cascaded stages. The multi-stage beam steerer of the present invention can cover a large steering angle with a limited available controllable phase shift. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 shows an exemplary embodiment of an optical cross connect in accordance with the present invention. 
     FIG. 2 shows an exemplary embodiment of a 3×3 optical cross connect comprising two-stage, cascaded beam steerers in accordance with the present invention. 
     FIGS. 3A and 3B show an exemplary waveguide layout for a cross connect with two-stage beam steerers in accordance with the present invention. 
     FIGS. 4A and 4B are plots of the transmissivities through a 9×9 cross connect with single-stage beam steerers. 
     FIGS. 5A and 5B are plots of the transmissivities through a 9×9 cross connect with two-stage beam steerers. 
     FIG. 6 shows transmissivities measured for an exemplary cross connect constructed in accordance with the present invention. 
     FIGS. 7A through 7E show transmissivities measured for various steering configurations between ports of an exemplary cross connect constructed in accordance with the present invention. 
     FIG. 8 shows an exemplary embodiment of a modular optical cross connect in accordance with the present invention. 
     FIG. 9 shows a further exemplary embodiment of a modular optical cross connect in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION 
     An exemplary embodiment of a planar optical cross connect in accordance with the present invention is shown in FIG.  1 . The exemplary cross connect of FIG. 1 comprises two facing arrays of planar beam steerers  10  and a central star coupler  12 . Each beam steerer  10  includes a star coupler  14  which is coupled to the central star coupler  12  by an array of waveguides  16  of substantially equal length. The waveguides  16  of the beam steerers  10  are arranged as in a conventional star coupler. (See, C. Dragone, “Efficient N×N star couplers using Fourier optics,” J. Lightwave Technol., vol. 7, pp. 479-489, 1989.) 
     The planar cross connect of the present invention is implemented on a planar substrate, such as InP (indium phosphide). The various optical features such as the waveguides and star-couplers are formed as areas of a higher index of refraction than the surrounding material. Such features can be formed by selectively doping the substrate, in the desired pattern, with materials such as indium or galium-arsenide. Various known fabrication techniques and materials can be used. 
     Each beam steerer  10  includes dynamic phase shifters  18   a,    18   b  arranged on the waveguides  16 . The phase shifters, under the control of externally applied signals, alter the index of refraction of the waveguides  16 , thereby changing the phase of an optical beam therethrough. By changing the phase linearly across the waveguides  16  via the dynamic phase shifters  18   a,    18   b,  the beam emanating from a beam steerer  10  can be steered. A connection is made by aiming beam steerers  10  on the left and right sides of the cross connect at each other. Since the beam steerers operate independently, this switch is strict-sense nonblocking. 
     The phase shifters can be fabricated in a known way, such as described in C. R. Doerr et al., “Wavelength-division multiplexing cross connect in InP,” IEEE Photon. Technol. Lett., vol. 10, pp. 117-119, 1998. Possible implementations include forward- or reverse-biased p-n junctions in InP and heated regions in silica. 
     In the exemplary embodiment of FIG. 1, two triangular phase shifters  18   a  and  18   b  are used in each beam steerer  10  to achieve the linear phase change across the waveguides  16 . One of the triangular phase shifters is used for steering the beam in one direction and the other for steering the beam in the other direction. It should also be noted that each beam steerer  10  can be implemented with only one phase shifter. In that case, however, the one phase shifter would have to be capable of generating a larger phase difference between adjacent waveguides than would one of a pair of phase shifters. Moreover, with one phase shifter, the default steering direction would be set at one extreme of the desired steering range, assuming the phase shifter deflected the beam in only one direction. 
     In the exemplary embodiment of FIG. 1, each of the phase shifters  18   a  and  18   b  is formed in the shape of a triangle which spans an array of waveguides  16  for each beam steerer. Because each phase shifter pair controls multiple waveguides, as opposed to only one waveguide, the number of electrical leads that are required to couple the phase shifters to the control circuitry (not shown) is significantly reduced. 
     While phase shifters such as those of FIG. 1 which span the entire array of waveguides  16  of each beam steerer  10  reduce the number of electrical traces required, in order to steer the full range, the phase shifters should be capable of controlling the phase difference between adjacent waveguides to change from −π to π. For M waveguides in the beam steerer, the phase shift in the outermost waveguides should thus be controllable from 0 to approximately (M−1)π. For large M (often required for large N) this may not be feasible. 
     One solution to reduce the required phase-shifting strength is to divide the waveguide arrays into smaller arrays, each with an associated independently controllable triangular phase shifter (or, in the limit, control each waveguide independently). Unfortunately, the gaps between controls required for isolation will increase the center-to-center spacing between adjacent beam steerers. This will greatly increase the device size, since a linear increase in beam-steerer spacing results in a quadratic increase in the radius of the central star-coupler. Also, it can be difficult to have isolated controls within the waveguide array without creating phase distortions. 
     FIG. 2 shows an exemplary embodiment of a cross connect with beam steerers  100  which overcome the aforementioned limitations. Each beam steerer  100  of FIG. 2 comprises a first stage  110  and a second stage  120  which are cascaded. The first and second stages perform coarse and fine steering, respectively. The two-stage beam steerers  100  of FIG. 2 can be used in place of the single-stage beam steerers of FIG. 1, however, the beam steerers  100  can cover a larger steering angle with a limited available controllable phase shift. 
     As in the case of the single-stage beam steerer, the required phase shift across the array of M 1  waveguides of the first stage  110  is approximately (M 1 −1)π. For the second stage  120 , however, which performs fine steering about the coarser, N 1  beam steering angles steered by the first stage, the required phase shift across the array of M 2  waveguides is approximately only [(M 2 −1)/N 1 ]π. In general, for a stage i in a multi-stage beam steerer, the required phase shift to steer across all ports is more specifically:            (       M   i     -   1     )          (       N   i     -   1     )        Π         ∏     j   =   1     i                     N   j                              
     The exemplary, two-stage cascaded beam steerer  100  of FIG. 2 comprises a first star-coupler  111 , a first pair of phase shifters  112   a,    112   b,  a second star-coupler  113 , a third star-coupler  114  and a second pair of phase shifters,  115   a,    115   b.  As in the single stage beam steerer of FIG. 1, each stage  110  and  120  comprises an array of waveguides  116  and  126 , respectively. The two stages  110  and  120  are coupled by an array of connecting waveguides  130  between the star-couplers  113  and  114 . 
     The first stage  110 , which can be thought of as performing coarse steering, can steer the input lightwave into a choice of relatively coarsely spaced connecting waveguides  130 , which by virtue of their coarse angular spacing give coarse steering in the central star coupler  12 . The second stage  120  then performs fine steering about the coarsely-steered angles; i.e., the fine steerer  120  can steer the beams by small angles about the coarse-steered angles. Thus, if the first beam steerer stage  110  can steer the input to one of N 1  connecting waveguides  130  and the second beam steerer stage  120  can steer a range of N 2  receiving (or transmitting) beam steerers, the cascaded combination can steer over a range of up to N 1 N 2  receiving (or transmitting) beam steerers. 
     Although the exemplary cascaded beam steerer  100  shown in FIG. 2 comprises two stages, larger numbers of stages can be cascaded as needed. If each stage has the same steering range Ns, then for a N×N cross connect, each beam steerer would comprise log Ns N stages. This logarithmic dependence on N allows for large practical cross connects. 
     The cascaded beam steerers of the present invention can also be used in applications other than cross connects, such as laser printers, optical disk readers, etc. 
     To minimize the sensitivity of the cross connect to wavelength, all of the waveguides in the beam steerer should have the same effective length. In an exemplary embodiment of the present invention, this is achieved by constructing each waveguide path with five straight segments and four bends of equal bend radius. FIG. 3A shows a partial schematic representation of an exemplary cascaded beam steerer  100  in an exemplary cross connect. In FIG. 3A, only one waveguide is shown for each stage  110  and  120  for clarity. 
     In the exemplary embodiment of FIG. 3A, each stage  110 ,  120 , steers among three settings (i.e., Ns=3). Such a cascaded beam steerer  100  would thus be used, for example, as one of nine beam steerers on one side of a 9×9 cross connect. The first stage  110  comprises an array of five equal-length waveguides  116  connected to the star couplers  111  and  113  whereas the second stage  120  comprises an array of  12  equal-length waveguides  126  connected to the star coupler  114  and the central star coupler  12  of the cross connect. The two stages are connected to each other by three waveguides  130 . The coarse steering stage  110  steers the input to one of the three waveguides  130 , and the fine steering stage  120  steers the beam in the central star coupler  12  a small amount about the angle determined by each of the input waveguides  130 . As in the embodiments of FIGS. 1 and 2, the phase shifters  112   a,    112   b  and  115   a,    115   b,  which perform the beam steering, comprise triangular regions of p-n junctions over the waveguides. 
     As shown in FIG. 3A, each waveguide  116 ,  126  in each stage  110 ,  120  comprises five straight sections and four curved sections, all of the same bend radius. The five straight sections in each stage are labeled 1-5 (encircled). The total lengths of the straight sections are the same for all waveguides in each stage. Likewise, the total lengths of the curved sections are the same for all waveguides in each stage. As a result, phase errors in the beam steerers due to overall waveguide length variations are avoided. 
     If the angles (with respect to some fixed reference line such as the axis of the central star coupler) of the five straight sections of waveguide m (where m=1 through M) are α 1 (m) through α 5 (m), in order of connection, then the above-discussed goal is achieved by making 
      α 2 ( m )=[α 1 ( m )+α 3(   m )]/2+ c   1   
     and 
     
       
         α 4 ( m )=[α 3 ( m )+α 5 ( m )]/2+ c   2 , 
       
     
     where c 1  and c 2  are chosen constants. A description of the foregoing can be found in U.S. patent application Ser. No. 09/232,109, filed on even date herewith, entitled OPTICAL DEVICE HAVING EQUAL LENGTH WAVEGUIDE PATHS, and incorporated herein by reference in its entirety. 
     FIG. 3B shows the actual waveguide layout of an exemplary 9×9 cross connect implemented in InP using two-stage beam splitters with two cascaded stages of Ns=3 laid out in the above-discussed manner. The size of the exemplary device shown in FIG. 3B is approximately 2.2 mm×34.4 mm, with approximately half of the length being occupied by a 14.5 mm long central free-space region for the central star coupler  12 . 
     For clarity, the phase shifters are not shown in FIG. 3B, but would be arranged as shown in FIG.  3 A. In the exemplary embodiment shown, triangular phase shifters can be used, with the triangle bases and heights for the first (coarse) and second (fine) beam steering stages being 1.2×0.054 mm and 1.2×0.081 mm, respectively. 
     In an exemplary embodiment of a cross connect constructed in accordance with the present invention, the forward and reverse break voltages of the phase-shifter triangles are +0.9V and −30V, respectively. With no electrical signal applied, each steerer is centered, and thus each port is pointed at the center port (e.g., port 5 in a 9×9 cross connect) of the other side in the quiescent state. The beam steerers steer approximately 1 port per 125 mA applied with forward injection into a triangle, and approximately 1 port/50V with reverse voltage into a triangle; i.e., the coarse stage steers by one waveguide or the fine stage steers by one port. Using reverse bias to steer is preferred because it entails virtually zero power dissipation and is fast. However, because reverse bias steering requires voltages greater than the break-down voltage, forward injection current is used. To achieve good steering, the injected current should preferably be uniform over the phase shifters. In the exemplary embodiment, which uses triangles, the injected current is uniform over the phase shifter triangles. The etching of the sacrificial layer before metal deposition aids in achieving such uniformity. 
     The waveguide structure of the exemplary device can be implemented as a buried rib-loaded slab, and its cross section is essentially the same as that described in C. R. Doerr et al., “Wavelength-division multiplexing cross connect in InP,” IEEE Photon. Technol. Lett., vol. 10, pp. 117-119, 1998. An exemplary method for fabricating such a device requires only two mask plates and begins with the step of growing the base wafer containing the graded-index slab and rib. The waveguides are then patterned and wet-etched through the rib. Approximately 0.6 μm of non-intentionally doped InP is then regrown over the entire wafer. Then, SiO 2  is deposited over the wafer and triangular openings over the beam steerer waveguide arrays are etched through the SiO 2 . p-doped InP is then grown on the wafer, finishing with a quaternary cap and a 15-nm InP layer. Using the same mask plate as for the SiO 2  patterning, photoresist is patterned and gold-zinc is deposited on top. However, before the metal deposition but after the photoresist patterning, the top thin InP layer is etched off, providing a pristine surface for the metals. Finally, the wafer backside is coated with gold. 
     An analysis of a cross connect with non-cascaded beam steerers, as shown in FIG. 1, will now be described. The transmissivity through a N L ×N R  cross connect from the outer port of beam steerer n L  on the left side, which is pointed at beam steerer P L  on the right side, and from the outer port of beam steerer n R  on the right side, which is pointed at beam steerer P R  on the left side, is                    t       n   L     ,     n   R              (       p   L     ,     p   R       )       =       ∑       m   L     ,       m   R     =   1           M   L     ,     M   R                           a   L          [     0   ,       (       m   L     -         M   L     +   1     2       )            Δα   L       M   L           ]                             a   c          {         [       m   L     -         M   L     +   1     2     +       M   L          (       n   L     -         N   L     +   1     2       )         ]                       2      π         M   L          N   L          ks   R           ,       [                  m   R     -                    M   R     +   1     2     +       M   R          (       n   R     -         N   R     +   1     2       )         ]        2        π       M   L          N   L          ks   L             }                           a   R          [         (       m   R     -                    M   R     +   1     2       )            Δα   R       M   R         ,   0     ]                       exp        [       j        (       p   L     -         N   R     +   1     2       )              2      π       N   R            m   L       ]                       exp        [     j                   (       p   R     -         N   L     +   1     2       )            2      π       N   L            m   R       ]                 (   1   )                                
     where a is the amplitude transmissivity through a star coupler, and is given by                  a   i          (       α   1     ,     α   2       )       ≈       exp        (       -   j                     kR   i          α   1          α   2       )                     ∫     -   ∞     ∞              u     i   ,   2            (   x   )            exp        (     j                 kx                   α   1       )               x            ∫     -   ∞     ∞              u     i   ,   1            (   x   )            exp        (     j                 kx                   α   2       )               x                          2        πR   i       k            ∫     -   ∞     ∞                     u     i   ,   1            (   x   )            2             x            ∫     -   ∞     ∞                     u     i   ,   2            (   x   )            2             x                             (   2   )                                
     R i  are the radii, R L  and R R , of the star couplers  14  on the left and right sides, respectively, of the cross connect. R L  is given by: 
     
       
           R   L   =r   L   M   L /Δα L . 
       
     
     The expression for R R  is analogous. The radius of the central star coupler  12  is given by: 
     
       
           R   C   =kM   L   N   L   s   L   s   R /(2π). 
       
     
     r and s are the center-to-center spacing of the waveguide arrays at the outer star couplers  14  and central star coupler  12 , respectively, and Δα is the chosen capture angle of the waveguides from the input and output ports. k is the propagation constant in the star couplers, and u(x) is the orthogonalized mode amplitude across the waveguide at the star-coupler/waveguide junction. Moreover, in general: 
     
       
           M   L   N   L   =M   R   N   R . 
       
     
     The symmetric case, i.e., in which all left- and right-side parameters are equal, will be calculated for an exemplary, non-cascaded beam steerer embodiment of a cross connect with N=9, M=13, and Δα such that the power in the outermost waveguides is approximately −7 dB of the power in the center waveguides in each beam steerer. InP is selected as the material with waveguide Δn/n=0.0086. s=8.0 μm with gaps of 0.8 μm between the waveguides. 
     There are 9 18 ≈1.5×10 17  combinations of beam steerers steering at each other. 9!=362,880 of these combinations are generally useful, consisting of left-right pairs of beam steerers pointing at each other. Plots of |t 5,nR (P L ,5)| 2  vs. p L  and |t 5,nR (5,p R ) 2  vs. p R  are shown in FIGS. 4A and 4B, respectively. 
     FIG. 4A shows the transmissivity from the center left beam steerer to each of the nine beam steerers on the right when the right beam steerers are all pointed at the center left beam steerer as it steers through its range. FIG. 4B shows the transmissivity with the left center beam steerer pointed at the right center beam steerer, while the right beam steerers steer through their ranges. FIG. 4B shows the transmissivity for varying n R . The values of n R  are labeled in FIG.  4 B. 
     From FIG. 4B, one can see the contributions to crosstalk. The worst-case crosstalk contribution to a connection, approximately −24 dB, occurs when a nearest neighbor beam steerer on one side is pointing to a nearest neighbor beam steerer on the other side. The crosstalk is substantially smaller for all other possibilities. The crosstalk can be reduced by increasing the ratio M/N. 
     Such an exemplary embodiment of a cross connect can be difficult to build because it requires phase shifters that can deliver approximately 11π of phase shift. Cascaded beam steerers in accordance with the present invention can advantageously be used for such a configuration. 
     An exemplary embodiment of a cross connect with two-stage cascaded beam steerers, similar to those shown in FIG. 2, will now be analyzed, with the first stage having N 1 =3, M 1 =5, and the second stage having N 2 =3, M 2 =13. In such an embodiment, the required phase shift across the waveguide array is only 8π/3 in the first stage and 8π/3 in the second stage. Such a beam steerer is shown in FIGS. 3A and 3B. 
     The transmissivity of such a cross connect can be designated: 
     
       
           t   n     L     ,n     R     (2) ( p   L1   ,p   L2   ,p   R1   ,p   R2 ), 
       
     
     where the p run from 1 to 3. P 1  denotes the connecting waveguide  130  to which the first beam steerer points and P 2  denotes one of the three positions to which the second stage can deflect. Based on a modified Eq. 1, FIG. 5A shows a plot of |t 5,n     R     (2) (p L1 , p L2 ,2,2| 2  vs. 3p L1 +p L2 −3 and FIG. 5B shows a plot of |t 5,n     R     (2) (2,2,p R1 ,p R2 )| 2  vs. 3p R1 +p R2 −3, with varying n R . The values of n R  are labeled in FIG.  5 B. The plots of FIGS. 5A and 5B are analogous to those of FIGS.  4 A and  4 B, respectively. 
     For the plots of FIGS. 5A and 5B, the phase difference between the three connecting waveguides between the two stages is zero. Using finite phase differences changes the fine structure of the ripples in the plots, but leaves the overall crosstalk levels effectively unchanged. Although the loss is higher for the two-staged steerer case, the crosstalk is substantially the same as the single-stage case. For larger N, the insertion loss should remain the same except that the addition of each cascaded stage adds approximately 2.5 dB to the loss. 
     FIG. 6 shows the measured switching performance and wavelength sensitivity of an exemplary 9×9 cross connect constructed in accordance with the present invention. In obtaining the results shown, spontaneous emission from an Er-doped fiber amplifier was sent through port  4  on the left side and measured from port  6  on the other side, via lensed fibers. The bottom trace shows the transmissivity measured when no currents are applied, in which case all ports are aimed at port  5 . The top trace shows the transmissivity when approximately 125 mA is applied to the downward-steering triangle of the fine steerer of the left-hand port  4  and approximately 125 mA is applied to the upward-steering triangle of the fine steerer of the right-hand port  6 ; i.e., ports  4  and  6  are steered at each other. As can be seen, the switching extinction ratio is 15-25 dB, with the highest extinction occurring at approximately 1551 nm. This is near the wavelength (1555 nm) for which the star couplers are designed. Note that this is the worst-case extinction ratio, which occurs when one port is steered towards a neighboring port (port  5  here) of the other port. 
     FIGS. 7A-7E show the measured switching performance for several different steering configurations of the exemplary 9×9 cross connect. Light from a laser at 1555 nm was launched into a port on the left-hand side, starting from port  1  and proceeding to port  5 , and the amount exiting each of the nine ports on the right-hand side was measured, using a bandpass filter to filter out any 1.3-μm spontaneous emission generated by the phase shifters. For each port combination, the beam steerers were steered to make a connection. After making a connection, the optical powers appearing at the other eight ports on the right-hand side, to which no currents were applied, were measured. An exception is when the left-hand launch port was number  5 , in which case the other ports were steered to a neighboring port (by applying current to one of the fine-steerer triangles of the measured right-hand port). 
     In the performing the measurements shown in FIG. 7A, light was launched into left-hand port  1  and measured at right-hand port  1 . The coarse and fine steerers of ports  1  on both sides were adjusted to maximize the transmitted optical power. In this condition, the optical power exiting right-hand ports  2  through  9  was also measured, without applying any steering signals to these right-hand ports. The results thus measured are represented in FIG. 7A by circles. 
     A similar procedure was then performed for left-hand port  1  and right-hand port  2 . The procedure is the same for FIGS. 7A-7D, but in FIG. 7E, when measuring the non-steered-to ports, their fine steerer stages were driven in order to steer them away from left-hand port  5 . Note that the extinction ratio degrades for the worst case of beam steerers pointing at one of the other&#39;s nearest neighbors, the case in FIGS. 7D and 7E. The crosstalk values shown range from approximately −5 to −25 dB. 
     The loss for TM-polarized light was approximately 4.4 dB more than for TE-polarized light, and the steering angle was also slightly polarization-dependent. Insertion loss can be reduced by reducing the spacing between the waveguide connections to the central star coupler. 
     As can be seen in FIG. 3B, most of the length of a cross connect device with cascaded beam steerers in accordance with the present invention is taken up by the central star coupler  12 , whose length increases quadratically with N. With much larger values of N, the device becomes too long to fit on a conventional wafer. For instance, a 64×64 cross connect implemented in silica would have a free-space length of several meters (but a width of only a few centimeters). Such a free-space length, however, can be achieved in bulk optics using a configuration such as shown in FIG.  8 . 
     FIG. 8 shows an exemplary embodiment of a modular optical cross connect using planar lightwave circuit beam steerers  210 ,  290  in accordance with the present invention. The beams from the beam steerers  210  on the left side of the cross connect are collimated in the vertical direction by a cylindrical lens  230 , enter a “tilted” glass block  250 , undergo multiple reflections in a zig-zag fashion, and are focused into planar beam steerers  290  on the right side. Like the left-side beam steerers  210 , the beam steerers  290  on the right side are coupled to the block  250  by a cylindrical lens  270 . The left and right end surfaces of the glass block  250  are high-reflection (HR) coated except for narrow windows where the beams enter and exit the block. 
     In the exemplary embodiment of FIG. 8, the glass block is tilted; i.e., it has a rhomboid cross-section as seen from the side, with the lenses  230  and  270  coupled to the acutely angled edges of the block. The degree to which the block is tilted determines how many times a light beam will zig-zag though the block and thus the effective length of the optical free space provided by the block. 
     In an exemplary embodiment of a 64×64 cross connect implemented in silica with four bounces inside the glass block  250 , the size of the block is approximately 15 cm wide×50 cm long×1 cm high. Furthermore, due to the large optical free-space length provided by the block  250 , the end faces of the block  250  can be flat as opposed to being arched. Nonetheless, the end faces can be arched, thereby allowing a reduction of the required free-space length and thus of the size of the block  250 . 
     FIG. 9 shows a side view of another exemplary embodiment of a modular beam steering cross connect. In this embodiment, the beam steerers  210 ,  290  are arranged along an edge of a glass block  350  which has one flat reflective surface  355  and an arched reflective surface  365 , as shown. The arched surface  365  acts as a cylindrical reflector with a focal length f which is half the radius of curvature of the arched surface. A beam emitted from a beam steerer  210  is reflected by the arched surface  365  to the flat surface  355 . The flat surface  355  reflects the beam back to the arched surface  365  which reflects it to a receiving beam steerer  290 . Naturally, the direction of the beam is reversed for signals directed from the beam steerer  290  to the beam steerer  210 .