Abstract:
The present invention relates to an articulated micro-electro-mechanical (MEMS) device, which is constructed in such a way as to enable several of the devices to be closely packed together, i.e. high fill factor, for redirecting specific wavelengths of light from a dispersed optical signal to different output ports. The articulated MEMS device includes multiple pivotally connected sections that are pivotable about two perpendicular axes for limiting the amount of dynamic cross-talk as the device is rotated between different positions.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     The present invention claims priority from U.S. Patent Application No. 60/653,086 filed Feb. 16, 2005, which is incorporated herein by reference. 
     
    
     TECHNICAL FIELD  
       [0002]     The present invention relates to an articulated micro-electro-mechanical (MEMS), and in particular to an articulated MEMS structure for tilting a reflective surface about two perpendicular axes.  
       BACKGROUND OF THE INVENTION  
       [0003]     Conventional MEMs mirrors for use in optical switches, such as the one disclosed in U.S. Pat. No. 6,535,319 issued Mar. 18, 2003 to Buzzetta et al, redirect beams of light to one of a plurality of output ports, and include an electrostatically controlled mirror pivotable about a single axis. Tilting MEMs mirrors, such as the ones disclosed in U.S. Pat. Nos. 6,491,404 issued Dec. 10, 2002 in the name of Edward Hill, and 6,677,695 issued Jan. 13, 2004 in the name of Dhuler et al, which are incorporated herein by reference, comprise a mirror pivotable about a central longitudinal axis. The MEMs mirror device  101 , disclosed in the aforementioned Hill patent, is illustrated in  FIG. 1 , and includes a rectangular planar surface  102  pivotally mounted by torsional hinges  104  and  105  to anchor posts  107  and  108 , respectively, above a substrate  109 . The torsional hinges may take the form of serpentine hinges, which are disclosed in U.S. Pat. No. 6,327,855 issued Dec. 11, 2001 in the name of Hill et al, and in United States Patent Publication No. 2002/0126455 published Sep. 12, 2002 in the name of Robert Wood, which are incorporated herein by reference. In order to position conventional MEMs mirror devices in close proximity, i.e. with a high fill factor (fill factor=width/pitch), they must be positioned with their axes of rotation parallel to each other. Unfortunately, this mirror construction restraint greatly restricts other design choices that have to be made in building the overall switch.  
         [0004]     When using a conventional MEMs arrangement, the mirror  101  positioned on the planar surface  102  can be rotated through positive and negative angles, e.g. ±2°, by attracting one side  110   a  or the other side  110   b  of the planar surface  102  towards the substrate  109 . Unfortunately, when the device is switched between ports at the extremes of the devices rotational path, the intermediate ports receive light for fractions of a millisecond as the mirror  1  sweeps the optical beam past these ports, thereby causing undesirable optical transient or dynamic cross-talk.  
         [0005]     Articulated MEMs devices, such as those disclosed in U.S. Pat. Nos. 6,495,893 issued Dec. 17, 2002 to Lin et al; 6,760,144 issued Jul. 6, 2004 to Hill et al; and 6,822,370 issued Nov. 23, 2004 to Clark et al, can provide high fill factors, and magnified angular ranges, but do not solve the problem of dynamic cross-talk because of laterally extending fixed hinges, which prevent rotation about two axes. Another advantage of articulated MEMs devices is the separation of actuating electrodes from the mirrored platforms.  
         [0006]     One solution to the problem of dynamic cross-talk is to initially or simultaneously rotate the mirror about a second axis, thereby avoiding the intermediate ports. An example of a MEMs mirror device pivotable about two axes is illustrated in  FIG. 2 , and includes a mirror platform  111  pivotally mounted by a first pair of torsion springs  112  and  113  to an external gimbal ring  114 , which is in turn pivotally mounted to a substrate  116  by a second pair of torsion springs  117  and  118 . Examples of external gimbal devices are disclosed in U.S. Pat. Nos. 6,529,652 issued Mar. 4, 2003 to Brenner, and 6,454,421 issued Sep. 24, 2002 to Yu et al. Unfortunately, an external gimbal ring greatly limits the number of mirrors that can be arranged in a given area and the relative proximity thereof, i.e. the fill factor. Moreover, the external gimbal ring may cause unwanted reflections from light reflecting off the support frame  113 ,  114 .  
         [0007]     Another proposed solution to the problem uses high fill factor mirrors, such as the ones disclosed in U.S. Pat. No. 6,533,947 issued Mar. 18, 2003 to Nasiri et al, which include hinges hidden beneath the mirror platform. Unfortunately, these types of mirror devices require costly multi-step fabrication processes, which increase costs and result in low yields.  
         [0008]     Yet another solution to overcome the shortcomings of the prior art is disclosed in U.S. Pat. No. 6,934,439 issued Aug. 23, 2005 to Mala et al (incorporated herein by reference), which provides a high fill factor MEMs mirror device that pivots about the same axis as an adjacent mirror and includes an internal gimbal ring for rotating about perpendicular axes.  
         [0009]     An object of the present invention is to overcome the shortcomings of the prior art by providing a MEMs device providing an articulated MEMs device with a high fill factor and extended tilt range, which is tiltable about perpendicular axes.  
       SUMMARY OF THE INVENTION  
       [0010]     Accordingly, the present invention relates to an articulated micro-electro-mechanical device suspended above a substrate comprising:  
         [0011]     a main platform having a longitudinal axis pivotable about first and second perpendicular axes;  
         [0012]     a first moveable actuator, one end of which is pivotally connected to the main platform, for pivoting the main platform about the first axis;  
         [0013]     a first actuating means for moving the first moveable actuator, thereby pivoting the main platform about the first axis; and  
         [0014]     a second actuating means for pivoting the main platform about the second axis. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]     The invention will be described in greater detail with reference to the accompanying drawings which represent preferred embodiments thereof, wherein:  
         [0016]      FIG. 1  is an isometric view of a conventional tilting MEMs mirror device;  
         [0017]      FIG. 2  is a plan view of a pair of conventional external gimbal ring MEMs mirror devices;  
         [0018]      FIG. 3  is an isometric view of an articulated MEMs device according to the present invention in a rest position;  
         [0019]      FIG. 4  is an isometric view of serpentine torsional hinges on the device of  FIG. 3 ;  
         [0020]      FIG. 5  is an isometric view of a double serpentine torsional hinge on the device of  FIG. 3 ;  
         [0021]      FIG. 6   a  is a top view of a serpentine torsional hinge having folds extending in perpendicular directions;  
         [0022]      FIG. 6   b  is a top view of a serpentine torsional hinge having folds extending in perpendicular directions;  
         [0023]      FIG. 7   a  is a side view of the device of  FIG. 3  in the rest position;  
         [0024]      FIG. 7   b  is a side view of the device of  FIG. 3  in the deflected position;  
         [0025]      FIG. 8  is an isometric view of the device of  FIG. 3  in a deflected position about the Z-axis;  
         [0026]      FIG. 9  is an isometric view of the device of  FIG. 3  rotated about the X-axis;  
         [0027]      FIG. 10  is an isometric view of an articulated MEMs device according to an alternative embodiment of the present invention;  
         [0028]      FIG. 11  is an isometric view of a single serpentine torsional hinge on one end of the device of  FIG. 10 ;  
         [0029]      FIG. 12  is an isometric view of the device of  FIG. 10  rotated about the X-axis;  
         [0030]      FIG. 13  is an isometric view of the hinge of  FIG. 10  with a motion restrictor;  
         [0031]      FIG. 14  is an isometric view of an articulated MEMs device according to another embodiment of the present invention;  
         [0032]      FIG. 15  is an isometric view of an end of the device of  FIG. 14  with a single actuator;  
         [0033]      FIG. 16  is an isometric view of the other end of the device of  FIG. 14 ;  
         [0034]      FIG. 17  is an isometric view of an alternative embodiment of the present invention;  
         [0035]      FIG. 18  is a plan view of an alternative hinge for the embodiment of  FIG. 17 ;  
         [0036]      FIG. 19  is an isometric view of an alternative hinge for the embodiment of  FIG. 17 ;  
         [0037]      FIG. 20   a  is an isometric view of an articulated MEMs device according to another embodiment of the present invention;  
         [0038]      FIG. 20   b  is an isometric view of the device of  FIG. 20   a  with the platform pivoted about the X-axis;  
         [0039]      FIG. 20   c  is an isometric view of the device of  FIG. 20   a  with the platform pivoted about the Z-axis; and  
         [0040]      FIG. 21  is an isometric view of an articulated MEMs device according to another embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION  
       [0041]     With reference to FIGS.  3  to  9 , a first embodiment of an articulated MEMs device according to the present invention comprises a main pivoting body, in the form of a rectangular platform  1 , (although other shapes are possible) pivotable about a first (primary, Z or tilt) axis and a second (secondary, X or roll) axis, perpendicular to the first, above a substrate  2 . Typically, the platform  1  is coated with a highly reflective material, e.g. gold, forming a mirror for reflecting incident beams of light at various output angles. Ligatures enabling the platform  1  to rotate about axes in two dimensions are provided in the form of first and second torsional hinges  3  and  4  extending from opposite ends of the platform  1  into contact with first and second pivoting actuators  6  and  7 , respectively. In a first embodiment, each of the first and second torsional hinges comprises a pair of serpentine (or articulated) resilient torsional beams  3   a ,  3   b ,  4   a  and  4   b , one on each side of the longitudinal axis (X-axis) of the main platform  1 . The ends of the beams  3   a  and  3   b  are fixed to the platform  1  and the first actuator  6  along lines parallel to the longitudinal axis of the platform  1 . Similarly, the ends of the beams  4   a  and  4   b  are fixed to the platform  1  and the second actuator  7  along lines parallel to the longitudinal axis of the platform  1 , so that the platform  1  is free to rotate (or roll) about its longitudinal axis (X-axis) and tilt about its central transverse axis (Z-axis). In the illustrated embodiment the beams  3   a ,  3   b ,  4   a  and  4   b  are folded such that the folds, i.e. the long bar portions, run perpendicular to the longitudinal axis of the platform  1  (Z-dimension), and perpendicular to a line joining the ends thereof, however, providing the hinges  3   a ,  3   b ,  4   a  and  4   b  with folds running in the perpendicular direction, i.e. perpendicular to the longitudinal axis of the platform  1  (X-dimension), or with folds running in both directions (two dimensions X and Z), as in  FIGS. 6   a  and  6   b , is possible depending upon the relative spring constant requirements of the hinges, as will be discussed below. In the illustrated embodiment, the ends of the beam  3   a  are collinear with the ends of the beam  4   a , and the ends of the beam  3   b  are collinear with the ends of the beam  4   b . The serpentine hinge with a plurality of folds is effectively longer than a normal torsional hinge, which spans the same distance, thereby providing greater deflection and strength, without requiring the space that would be needed to extend a normal full-length torsional hinge. Each beam making up the serpentine (or articulated) hinge has a height (or thickness), e.g. 10 to 20 μm, much larger than width, e.g. 1.0 to 2.0 μm, defining a large aspect ratio, e.g. 5 to 20, (thickness/width), which provides the necessary flexibility.  
         [0042]     The first actuator  6  is in the form of a rectangular rotating platform, although other shapes are possible, and is pivotally mounted to an anchor support  9  extending from the substrate  2  by another ligature in the form of a third torsional hinge  11 . In the illustrated embodiment, the third torsional hinge  11 , like the first and second torsional hinges  3  and  4 , is comprised of a pair of serpentine compliant beams  11   a  and  11   b , one on each side of the longitudinal axis of the first actuator  6 . The second actuator  7  is in the form of a rotating platform, e.g. rectangular, and is pivotally mounted to an anchor support  12  extending from the substrate  2  by a fourth torsional hinge  13 . In the illustrated embodiment, the fourth torsional hinge  13 , like the first and second torsional hinges  3  and  4 , is comprised of a pair of serpentine compliant beams  13   a  and  13   b , one on each side of the longitudinal axis of the second actuator  7 . The beams  11   a ,  11   b ,  13   a  and  13   b  are folded such that the folds run perpendicular to the longitudinal axis of the platform  1 , and perpendicular to a line joining the ends thereof (one dimension); however, providing the hinges  11   a ,  11   b ,  13   a  and  13   b  with folds running in the perpendicular direction, i.e. perpendicular to the longitudinal axis of the platform  1 , or with folds running in both directions (two dimensions), as in  FIG. 6 , is possible depending upon the relative spring constant requirements of the hinges, as will be discussed below. In this embodiment, the ends of the beams  11   a  and  11   b  are collinear with the ends of the beam  3   a  and  3   b , respectively, and the ends of the beams  13   a  and  13   b  are collinear with the ends of the beams  4   a  and  4   b , respectively.  
         [0043]     A compound hinge  3   c  illustrated in  FIG. 6   a , previously disclosed in U.S. Pat. No. 6,760,144, can be adapted to extend between the main platform  1  and the first actuator  6 , and includes a first serpentine torsional hinge  22  fixed along the longitudinal X axis with folds running in one direction parallel to the longitudinal X axis, and a second serpentine torsional hinge  24  fixed perpendicular to the longitudinal X axis with folds running in a second direction, perpendicular to the longitudinal X axis providing better control over the spring constants in both the X and Z dimensions. The thinner folds  22  facilitate the pivoting of the main platform  1  about the rolling axis (X axis), while the thicker folds  24  facilitate the pivoting of the main platform  1  about the tilting axis (Z axis). The second torsional hinge  4  can have folds running in either direction or both directions.  
         [0044]     Similarly, with reference to  FIG. 6   b , a multi-dimensional hinge  3   d  includes three single dimensional torsional serpentine (or articulated) hinges. A first hinge  22 ′ has one end extending from a point on either the actuator  6  or the main platform  1 . Second and third hinges  24   a ′ and  24   b ′ have outer ends fixed to points on supports extending from the substrate  2 , and extend from opposite sides of the first hinge  22 ′ into contact with each other and the end of the first hinge  22 ′. As above, the first hinge  22 ′ facilitates roll about the longitudinal X axis, while the second and third hinges facilitate tilting about the Z axes.  
         [0045]      FIG. 7   a  illustrates the MEMS device in a rest position, in which the main platform  1 , and the first and second actuators are all coplanar. To rotate, i.e. tilt, the main platform  1  in a counterclockwise direction about fulcrum point  10 , the first actuator  6  is rotated in the opposite direction, i.e. clockwise, about the third torsional hinge  11 , by actuation of an electrostatic electrode  15  or some other form of attracting/repulsing means disposed above or beneath the free end of the first actuator  6  proximate the first torsional hinge  3 , which attracts or repulses the free end of the first actuator  6  towards or away therefrom. Typically, the fulcrum point  10  is a post extending from the substrate  2  pivotally contacted to the main platform  1  proximate the intersection of the longitudinal and lateral axes providing a pivoting point for the main platform  1  when pivoting about both axes. To enable the main platform  1  to rotate about the fulcrum point  10 , the second actuator  7  is rotated in the opposite direction, i.e. clockwise. The second actuator  7  can be a slave actuator for stabilizing the end of the main platform  1  or a second electrode can be placed above or below the second actuator  7  for rotation thereof. Accordingly, the acute angle of rotation, e.g. from 0° to 6°, of the main platform  1  about the central transverse (Z or tilt) axis is adjusted by controlling the amount of voltage applied to the electrode(s) beneath the first and/or the second actuators  6  and  7 .  
         [0046]     Alternatively, the first and second actuators  6  and  7  can be provided with fixed pivot points  10   a  and  10   b , e.g. fulcrums, shown in outline in  FIG. 7   a , and the main platform  1  can be unattached, thereby pivoting about a phantom hinge point. With this arrangement, the tilt angle of the main platform  1  can be controlled by both the first and second actuators  6  and  7 , e.g. by electrodes therebeneath, thereby increasing, e.g. up to doubling, the range over which the main platform  1  can be rotated. The maximum tilt angle will be dictated by the maximum displacement, i.e. the gap, between the main platform  1  and the substrate  2 , and the relative lengths of the main platform  1  and the first and second actuators  6  and  7 . In alternative embodiments the first and second actuators  6  and  7  have longer lengths than the main platform  1 , whereby a small tilt angle on the first actuator  6  results in a larger tilt angle on the main platform for the same displacement.  
         [0047]     With reference to  FIG. 9 , one way to rotate (or roll) the main platform  1  about an X-axis, e.g. about its longitudinal axis, is to actuate an electrostatic electrode  16  or some other form of attracting/repulsing means above or beneath one side of the main platform  1 , i.e. beneath the section of the main platform  1  on one side of the longitudinal axis thereof, to attract or repulse the one side of the main platform  1  thereto or therefrom. Typically only 2° to 6° of roll are required, although higher angles are possible, depending on the gap between the platform and the substrate. As illustrated in  FIG. 9 , the spring constants of the first and second torsional hinges  3  and  4  are less than those of the third and fourth torsional hinges  11  and  13 , whereby the main platform  1  will rotate (or roll) about its longitudinal axis, while the first and second actuators  6  and  7  will not roll or will roll less than the main platform  1 . As illustrated in  FIG. 9 , the main platform  1  includes several longitudinally extending lines corresponding to a relatively large roll angle, while the first and second actuators  6  and  7  only have one longitudinally extending line corresponding to a relatively small roll angle. The longitudinal lines are contours representing vertical deflection of the platform surfaces, the closer the spacing of the contours, the steeper the angle. The direction of the contours indicates the tilt axis, i.e. the contours are parallel to the tilt axis. Reducing the spring constants of the first and second torsional hinges  3  and  4  can be done by replacing the pairs of serpentine beams  3   a ,  3   b  and  4   a ,  4   b  with a single serpentine beam, and/or by adjusting the shape of the serpentine beams, e.g. by reducing the thickness of the beam, by increasing the length of the beam, by increasing the number of folds in each beam, by reducing the height of each beam, by choosing a more flexible material for each beam. Alternatively or in addition thereto, electrodes  17  can be actuated beneath one side of each of the first and second actuators  6  and  7 , i.e. beneath the section of the first and second actuators on one side of the longitudinal axis thereof to rotate the main platform  1  and both actuators  6  and  7  together, as will be discussed with reference to FIGS.  10  to  12 . A restoring force can be provided by additional electrodes beneath the opposite side of the main platform  1  and/or the first and second actuators  6  and  7  to better control the motion of the main platform  1 . Alternatively, the spring force provided by the torsional hinges can restore the main platform  1  back to the rest position.  
         [0048]     In an alternative embodiment, illustrated in FIGS.  10  to  12 , the third torsional hinge  11  and the fourth torsional hinge  13  are each formed by a single serpentine compliant beam  21  and  23 , respectively, with the ends thereof collinear with the longitudinal axes of the first and second actuators  6  and  7  and the main platform  1 . The beams  21  and  23  are folded such that the folds run parallel to the longitudinal axis of the platform  1 , and parallel to a line joining the ends thereof, thereby making the beams  21  and  23  more compliant, i.e. reduced spring constant, to roll about the longitudinal X axis relative to the Z axis.  
         [0049]     As above, the main platform  1  can be rotated about its longitudinal axis by either actuating an electrode  16  beneath one side of the main platform  1  and/or by actuating electrodes beneath the first and second actuators  6  and  7 . The single serpentine compliant beam  21  and  23  with spring constants in the roll direction lower than the first and second torsional hinges  3  and  4 , enable the main platform  1  and the first and second actuators  6  and  7  to rotate simultaneously much easier than the double beam hinges  11  and  13 . As illustrated in  FIG. 12 , the first and second actuators  6  and  7  include as many longitudinally extending lines as the main platform  1 . Preferably a single electrode  16  is used to roll the main platform  1 , and a single electrode  15  beneath one or both of the first and second actuators  6  and  7  is used to pivot the main platform  1 , whereby the two electrodes  15  and  16  can be easily isolated from each other, thereby eliminating any interference therebetween. Moreover, separating the two electrodes  15  and  16  decouples their relationship during the design and manufacturing processes.  
         [0050]     In order to restrict the motion in the lateral and longitudinal directions, i.e. X and Z directions, of the main platform  1  during normal use, and particular during shock, a motion restrictor can be provided. Ideally the motion restrictor is in the form of one or more posts  25 , e.g. cylindrical, which extends upwardly from the substrate  2  into an opening or notch  26  formed in the main platform  1 , thereby preventing the main platform  1  from moving beyond the normal range of motion from side to side or in the direction of the longitudinal axis (see  FIG. 13 ).  
         [0051]     Another embodiment of the present invention having a simpler construction, but providing a more limited amount of angular rotation to a main platform  31 , is illustrated in FIGS.  14  to  16 . The main platform  31  is pivotally mounted above a substrate  32  by a first torsional hinge  33  extending from one end thereof and a second torsional hinge  34  extending from an opposite end thereof. One end of a single pivoting actuator or cantilever  36  is pivotally connected to an end of the first torsional hinge  33 , while the opposite end of the pivoting actuator  36  is pivotally connected to a first anchor  39  by a third torsional hinge  41 . The second torsional hinge  34  is connected to a second anchor  42 . In the illustrated embodiment, the first torsional hinge  33  comprises a pair of parallel serpentine compliant beams  33   a  and  33   b , one on each side of the longitudinal axis of the main platform  31  to partially resist rolling about the longitudinal X axis, while facilitating tilting of the main platform  31  about a lateral Z axis. The folds in the pair of compliant beams  33   a  and  33   b  run perpendicular to the longitudinal X axis providing a relatively large spring constant against rotation about the X axis, i.e. roll. Accordingly, the first torsional hinge  33  is substantially a one dimensional hinge enabling the main platform  1  to pivot about a lateral Z axis, while resisting roll about the longitudinal X axis due to a relatively high spring constant against roll.  
         [0052]     Each of the second and third torsional hinges  34  and  41  comprise a single serpentine compliant beam having ends fixed along the longitudinal axes of the main platform  31  and the actuator  36 , respectively. The second and third torsional hinges  34  and  41  include folds extending parallel to the longitudinal X axis providing a relatively small spring constant against rotation about the X axis, while facilitating tilting of the main platform  41  and the single actuator  36  about lateral Z axes. Accordingly, when either the main platform  31  or the single actuator  36  is rotated about the longitudinal X axis by an attraction/repulsion means, e.g. electrodes  16  or  17 , they will both roll together. As in the above embodiments, the second and third torsional hinges  34  and  41  can be substituted for by a pair of parallel beams or by one or more beams with folds extending perpendicular to the longitudinal X axis or with folds running both parallel and perpendicular to the longitudinal X axis, as in  FIGS. 6   a  and  6   b , as long as the overall spring constant against roll is less than that of the first torsional hinge  33 . Accordingly, the second and third torsional hinges  34  and  41  are substantially two dimensional hinges enabling both the main platform  31  and the single actuator  36  to roll together about the longitudinal X axis, and enabling the main platform  31  and the single actuator  36  to pivot about separate, but parallel lateral X axes.  
         [0053]     Alternatively, the third torsional hinge  41  can have a higher spring constant against roll than the first and second torsional hinges  33  and  34 , i.e. substantially providing one dimensional rotation about only the tilt or lateral Z axis, whereby the main platform  31  will roll about the longitudinal X axis, when actuated by the attraction/repulsion means, e.g. electrode  16 , while the single actuator  36  will remain level or only slightly roll, as described above with reference to  FIG. 9 . As above, the spring constant of the third torsional hinge can be increased by: providing a plurality, e.g. a pair, of parallel serpentine beams, increasing the thickness of the beam relative to the other, by reducing the length of the beam relative to the other, by reducing the number of folds in each beam relative to the other, by increasing the height of each beam relative to the other, by choosing a less flexible material or materials for each beam relative to the other. Therefore, the first and second torsional hinges  33  and  34  facilitate rotation in two dimensions about both the roll and tilt axes.  
         [0054]     Pivoting the actuator  36  about a lateral, e.g. Z, axis at the third torsional hinge  41  either in a clockwise or counterclockwise direction causes the main platform  31  to rotate in the opposite direction about the second torsional hinge  34 . An electrostatic electrode or some other form of attracting/repulsing means is placed below the outer free end of the actuator  36 , proximate the hinge  33 , to attract or repulse the end of the actuator  36 , thereby rotating the actuator  36  about the third torsional hinge  41 . In the illustrated embodiment of FIGS.  14  to  16 , a fulcrum point can be eliminated depending on the overall length of the main platform  31  and actuator  36 . Alternatively, the fulcrum point can be provided either beneath the main platform  31 ; however, it is preferable that the fulcrum point is disposed below the single actuator  36  to ensure that the fulcrum does not interfere with the mirrored surface, i.e. extend through the upper surface of the main platform  31 , thereby dividing the upper surface in half. Accordingly, the single actuator  36  would have a rigid extensions on both sides of the fulcrum. As above, rotation about the longitudinal (X) axis can be initiated by an electrostatic electrode or some other form of attracting/repulsing means disposed below one side of the longitudinal axis of the main platform  31  and/or by providing an electrostatic electrode or some other form of attracting/repulsing means disposed below one side of the longitudinal axis of the actuator  36 .  
         [0055]     In some applications the input beam of light is divided into two sub-beams, and one or both of the polarizations of the sub-beams is rotated, whereby both sub-beams have the same polarization while traveling through the device. Accordingly, in an alternate embodiment illustrated in  FIG. 17 , the main platform  31  is replaced by a two-part platform including first and second planar sections  43   a  and  43   b , e.g. 200 to 300 μm long, connected by a connecting rod  44 , e.g. 100 to 200 μm long, extending therebetween. The second torsional hinge  34  is replaced by an first and second intermediate serpentine torsional hinges  45   a  and  45 , with laterally extending folds, extending from proximate the middle of the connecting rod  44  into contact with anchor posts on each side thereof. The intermediate torsional hinges  45   a  and  45   b  have a combined lateral dimension less than the width of the first and second planar sections  43   a  and  43   b , e.g. 80 to 150 μm, to enable the planar sections of adjacent devices to be closely packed, i.e. a high fill factor. The single actuator  36  is pivotally connected to the anchor  39  via the third torsional hinge  41  and to the first planar section  43   a  via the first torsional hinge  33  in the form of a single serpentine beam. As in the aforementioned embodiments, the first torsional hinge  33  can either have a low spring constant against roll relative to the intermediate and third torsional hinges  45   a ,  45   b  and  41 , which enables the two-part platform to roll substantially independently of the actuator  36  or have a high spring constant against roll, thereby enabling the two-part platform to roll along with the actuator  36  about the longitudinal X axis. In the latter case the first torsional hinge becomes a simple one dimensional hinge, which only enables the two-part platform and the actuator  36  to tilt about Z axes. Actuation of an electrode or some other attraction/repulsion means below an end of the actuator  36  tilts the actuator about a lateral Z axis, which causes the two-part platform to tilt about the lateral Z axis defined by the first and second intermediate torsional hinges  45   a  and  45   b.    
         [0056]     In an alternate embodiment illustrated in  FIG. 18 , inner ends of the first and second intermediate torsional hinges  45   a  and  45   b  are connected at a point to a longitudinally extending torsional bar hinge  46 , which extends between anchor posts  47   a  and  47   b  extending upwardly from the substrate  32 . The outer ends of the first and second intermediate torsional hinges  45   a  and  45   b  are connected to supports  48   a  and  48   b , respectively, extending between the first and second planar sections  43   a  and  43   b . As above, the distance between the supports  48   a  and  48   b  is less than or equal to the width of the first and second planar sections  43   a  and  43   b  to enable adjacent devices to be closely packed.  
         [0057]      FIG. 19  illustrates yet another embodiment in which the first and second intermediate serpentine (or articulated) torsional hinges  45   a  and  45   b  have their inner ends fixed at respective points along the main Z axis to a post  49  extending upwardly from the substrate  32  at the intersection of the main longitudinal and lateral axes. The outer ends of the first and second intermediate hinges  45   a  and  45   b  are fixed to a gimbal ring  50 , which at least partially surrounds them. The gimbal ring  50  connects the outer ends of the first and second intermediate hinges  45   a  and  45   b  together. The longitudinally extending bar hinge  46  takes the form of two serpentine (or articulated) torsional hinges  46   a  and  46   b , each having one end connected to the gimbal ring  50  and one end connected to the first and second planar sections  43   a  and  43   b , respectively, along the main longitudinal axis. The gimbal ring  50  connects the outer ends of the first and second intermediate hinges  45   a  and  45   b  to the ends of the two torsional hinges  46   a  and  46   b . As above, the folds of the first and second intermediate hinges  45   a  and  45   b  extend laterally facilitating tilting about the Z axis, and the folds of the torsional hinges  46   a  and  46   b  extend longitudinally facilitating rolling about the X axis, thereby defining a two dimensional hinge.  
         [0058]     In a more complex embodiment, illustrated in  FIGS. 20   a  to  20   c , a main platform  51 , e.g. circular or rectangular, is pivotable about two perpendicular axes above a substrate  52  utilizing first and second actuators  53  and  54 . The main platform  51  is pivotally connected to the first and second actuators  53  and  54  by first and second torsional hinges  56  and  57 , respectively, extending from opposite sides of the main platform  51 . In the illustrated embodiment the first and second torsional hinges  56  and  57  comprise straight compliant beams, but serpentine beams or other forms of hinges are possible. In the illustrated embodiment, each of the first and second actuators  53  and  54  is comprised of a piston in the form of a rectangular or square platform  58  (although other shapes are possible) suspended above the substrate  52  by a longitudinally extending torsional hinge  61  and a pair of laterally extending torsional hinges  62   a  and  62   b . Each of the longitudinally extending torsional hinges  61  and the laterally extending torsional hinges  62   a  and  62   b  comprise serpentine compliant beams fixed to anchors extending from the substrate  52 . The beams  61 ,  62   a  and  62   b  are folded such that the folds run perpendicular to a line joining the ends thereof.  
         [0059]     To tilt the main platform  51  about its longitudinal axis, i.e. X-axis, as illustrated in  FIG. 20   b , an electrostatic electrode or some other attracting/repulsing means disposed beneath one side of the main platform  51 , i.e. on one side of the longitudinal axis, is actuated to attract or repulse the side of the main platform  51  causing the entire platform  51  to rotate about the first and second torsional hinges  56  and  57 .  
         [0060]     To rotate the main platform  51  about a lateral axis, i.e. about an axis defined by the pair of laterally extending torsional hinges  62   a  and  62   b , an electrostatic electrode or some other attracting/repulsing means disposed above or beneath one of the square platforms  58  is actuated to attract or repulse the square platform  58  towards or away from the substrate  52 , which tilts the main platform  51  (see  FIG. 20   c ). All three of the torsional hinges  61 ,  62   a  and  62   b  stretch downwardly as the square platform  58  is attracted towards the substrate  52 . The inherent spring force in the torsional hinges  61 ,  62   a  and  62   b  restores the square platform  58  and therefore the main platform  51  to the horizontal rest position, when the electrode is deactivated. The square platform  58  does not stay horizontal during the reciprocal motion, but, due to the unequal spring forces applied thereto, rotates slightly to enhance the tilting of the main platform  51 .  
         [0061]     With reference to  FIG. 21 , the second actuator  54  can be eliminated, and the second torsional hinge  57  can be attached directly to an anchor. The main platform  51  is rotated in the same manner as above, except that the lateral axis about which the main platform  51  rotates upon reciprocal, i.e. piston-like, movement of the actuator  53  is defined by the second torsional hinge  57  instead of the lateral torsional hinges  62   a  and  62   b . In other words, an attracting/repulsing means, e.g. an electrostatic electrode, disposed beneath one side of the main platform  51 , rotates the main platform  51  about its longitudinal X axis, while an attracting/repulsing means disposed beneath the square platform  58  rotates the main platform  51  about the lateral Z axis.  
         [0062]     Since all of the aforementioned embodiments provide the actuators, the main platforms and the hinges in the same plane, each embodiment can be constructed unitarily using a single lithographic step followed by a DRIE etch from one or more of the materials selected from the group consisting of silicon, polysilicon, silicon nitride, silicon dioxide, etc.