Abstract:
A MEMS mirror is disclosed having thickness correlated with the intensity profile of an impinging optical beam, so as to reduce moment of inertia of the MEMS mirror while preserving optical quality of the reflected beam. It is the mirror edges that contribute the most to the moment of inertia, while it is generally the mirror center that contributes the most to a reduction of the quality of an optical beam reflected from the mirror. Accordingly, by providing a mirror having laterally varying thickness matched to the local variation of the intensity of the optical beam, the quality of the latter may be preserved while the moment of inertia of the mirror may be significantly reduced. The thickness of MEMS mirrors may be varied continuously or stepwise; in one direction or in two mutually orthogonal directions.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present invention claims priority from U.S. Provisional Patent Application No. 61/289,473, filed Dec. 23, 2009, which is incorporated herein by reference. 
     
    
     TECHNICAL HELD 
       [0002]    The present invention relates to micro-electro-mechanical (MEMS) devices, and in particular to tiltable MEMS mirrors for redirecting beams of light. 
       BACKGROUND OF THE INVENTION 
       [0003]    Micro-electro-mechanical systems (MEMS) arc increasingly used in optical switching and scanning applications. Visual displays based on switchable MEMS micromirrors capable to withstand billions of switching cycles are now common. Using MEMS devices in fiberoptic switches attracts a particular interest. Light emitted by optical fibers can be tightly focused, which facilitates utilization of MEMS micromirrors to reliably switch optical signals between different optical fibers or waveguides. 
         [0004]    In recent years, multiport wavelength-selective optical switches have been used to provide wavelength-specific switching of optical signals between different optical ports. To increase the number of optical ports in a wavelength-selective optical switch, there has been a tendency to focus optical beams reflected by MEMS micromirrors tighter and tighter, down to a value limited by diffraction. It is a well known principle of optics that a tighter focusing requires a larger beam size before focusing, to reduce the diffraction limit value. This calls for larger MEMS micromirrors to be able to redirect larger optical beams. To ensure good quality of a reflected optical beam, the mirrors have to be very flat. To keep the mirror flatness at a larger mirror size, the MEMS micromirrors have also to be made thicker. 
         [0005]    Increased thickness of MEMS micromirrors, however, causes another problem to occur. The problem is related to dynamic performance of MEMS micromirrors. It takes longer to tilt larger, bulkier MEMS micromirrors because of increased moment of inertia (also called mass moment of inertia or rotational inertia) of the MEMS micromirrors. Furthermore, increased mass and moment of inertia increases sensitivity of MEMS mirrors to shock and vibration. These highly detrimental effects could be overcome by increasing stiffness of torsional hinges used to suspend MEMD micromirrors. However, increasing the stiffness of hinges requires increasing electrostatic torque created by MEMS actuators to offset the increased spring force of stiffer hinges. Unfortunately, there is a limit to a magnitude of the torque that can be generated, due to geometrical and electronic driver limitations. 
         [0006]    A general approach used in the prior art to solving the problem of reducing mirror mass is to make the mirrors hollow and/or to provide “rigidity ribs” or truss structures to reinforce the larger MEMS mirrors. By way of example, Dewa in U.S. Pat. No. 6,704,132 incorporated herein by reference, discloses a micromirror having a plurality of truss members disposed under a gimbal portion of the micromirror, allowing the gimbal and mirror portions to be made of a thinner material, thereby reducing the mass and increasing the resonant frequency of the micromirror device. Sniegowski et al. in U.S. Pat. No. 6,791,730, incorporated herein by reference, discloses a reinforced mirror microstructure, in which adjacent structural layers are interconnected by a plurality of vertically disposed columns, or a plurality of laterally extending rails or ribs. 
         [0007]    Moidu in U.S. Patent Application Publication 20080018975, incorporated herein by reference, discloses a large “micromirror”, for example 3 mm by 4 mm, having sufficient rigidity to ensure a low mirror curvature, for example a radius of curvature greater than 5 m, and a high resonance frequency of greater than 1 kHz. The micromirror of Moidu has a honeycomb structure sandwiched between two solid and smooth silicon layers. 
         [0008]    One drawback of the ribs and honeycomb-reinforced MEMS micromirror structures of the prior art is the difficulty of manufacturing complex three-dimensional structures. For example, the honeycomb structure of Moidu, although providing a very good stiffness to rotational inertia ratio, requires multiple wafer stacked together to form the honeycomb core and skins, thus increasing manufacturing complexity and cost. 
         [0009]    The prior art is lacking a large, for example more than 1 mm in size, MEMS mirror having a high quality of its reflective surface and low moment of inertia, that would also be relatively easy to manufacture. Accordingly, it is a goal of the invention to provide such a MEMS mirror, as well as a method of lessening the moment of inertia of a MEMS mirror, while preserving a high quality of its reflective surface, for example low curvature of the surface. A high quality of a MEMS reflective surface results in a high quality of an optical beam reflected from that surface, and ultimately in an improved performance of an optical device the MEMS mirror is used in. 
       SUMMARY OF THE INVENTION 
       [0010]    In the present invention, it is recognized that it is the mirror edges that contribute the most to the moment of inertia (rotational inertia), while it is generally the mirror center that contributes the most to a reduction of the quality of an optical beam reflected from the mirror. This is because the local intensity of an optical beam is typically the highest at the beam center, and the beam center is usually aligned to the mirror center. Accordingly, by providing a mirror having laterally varying thickness matched to the local variation of the intensity of the optical beam, the quality of the latter may be preserved while the moment of inertia of the mirror may be significantly reduced. 
         [0011]    In accordance with the invention there is provided a MEMS mirror device including a substrate, a MEMS mirror having a top reflective surface and a profiled bottom surface, and a hinge extending from the MEMS mirror enabling the MEMS mirror to pivot about a tilt axis above the substrate. The MEMS mirror is absent any voids or ribs. It has a longitudinal central axis perpendicular to the tilt axis and crossing the tilt axis at a first point, with first and second ends being disposed on the longitudinal axis at the outer free ends of the MEMS mirror. The profiled bottom surface is such that the MEMS mirror thickness, between the top and bottom surfaces, decreases in going from the first point towards the first and the second ends of the MEMS mirror, for reducing a moment of inertia of the MEMS mirror about the tilt axis. 
         [0012]    In accordance with another aspect of the invention there is provided a MEMS optical switch for switching an optical beam having a laterally varying intensity, comprising the tiltable MEMS mirror device for steering the optical beam, the MEMS mirror having a variation of the thickness correlated with the beam intensity variation, whereby the moment of inertia of the MEMS mirror is lessened while keeping a pre-defined quality of the steered optical beam, so as to ensure a pre-defined extinction ratio and insertion loss of the MEMS optical switch. 
         [0013]    The mirror thickness can decrease smoothly and monotonically, or it can decrease in stepwise fashion for rnanufacturability considerations. The thickness is correlated with the beam intensity variation, so that the moment of inertia of the MEMS mirror is lessened while keeping a pre-defined quality of the optical beam. For example, the thickness can vary laterally as t(x,y), the beam intensity varies laterally as I(x,y), wherein t(x,y)=c*I n (x,y), wherein preferably n&gt;=0.5 and c is a constant. For stepped mirrors, the step position can be correlated with a local beam intensity decreasing to a pre-determined percentage of a peak beam intensity. 
         [0014]    In accordance with another aspect of the invention there is further provided a method of manufacturing a MEMS mirror having a tilt axis and a longitudinal central axis perpendicular to the tilt axis and crossing the tilt axis at a first point, and having first and second ends disposed on the longitudinal axis at the outer free ends thereof, the method comprising:
       (a) providing a mirror wafer having a top surface for supporting a mirror layer, and a bottom surface, the mirror wafer being absent any voids or ribs therein; and   (b) profiling the bottom surface of the mirror wafer, so as to cause the MEMS mirror to have thickness decreasing in going from the first point towards the first and the second ends for reducing a moment of inertia of the MEMS mirror about the tilt axis.       
 
         [0017]    The thickness of the MEMS mirror is correlated with the beam intensity variation, whereby the moment of inertia of the manufactured MEMS mirror is lessened while keeping a pre-defined quality of the optical beam. 
         [0018]    In accordance with another aspect of the invention, there is further provided a method of manufacturing a MEMS optical switch for switching an optical beam having a laterally varying intensity, comprising manufacturing a MEMS mirror having the thickness correlated with the beam intensity variation, whereby the moment of inertia of the manufactured MEMS mirror is lessened while keeping a pre-defined quality of the switched optical beam, so as to ensure a pre-defined extinction ratio and insertion loss of the MEMS optical switch. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]    Exemplary embodiments will now be described in conjunction with the drawings, in which: 
           [0020]      FIG. 1  is a side cross-sectional view of a conventional flat uniform mirror having an optical beam intensity distribution superimposed thereupon; 
           [0021]      FIG. 2  is a side cross-sectional view of a flat mirror with a spatially varying thickness, having an optical beam intensity distribution superimposed thereupon; 
           [0022]      FIG. 3  is a side cross-sectional view of a flat mirror having a linearly varying thickness; 
           [0023]      FIGS. 4 and 5  are side cross-sectional views of a flat mirror having a stepwise varying thickness; 
           [0024]      FIG. 6  is a side cross-sectional view of a MEMS mirror having a hinge structure in the middle; 
           [0025]      FIG. 7  is a side cross-sectional view of a MEMS mirror having a “hidden-hinge” structure; 
           [0026]      FIGS. 8A and 8B  are top and side views, respectively, of a flat mirror having a stepwise varying thickness along the mirror and across the mirror; 
           [0027]      FIGS. 9A and 9B  are three-dimensional views of pyramid- and cone-shaped MEMS mirrors; and 
           [0028]      FIGS. 10A and 10B  are three-dimensional views of stepped pyramid- and cone-shaped MEMS mirrors. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0029]    While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. 
         [0030]    Referring now to  FIG. 1 , an optical beam  12  having a spatial intensity distribution  11  impinges on a conventional flat MEMS mirror  10  having a substrate  18  supporting a reflective coating  13 . The optical beam  12  reflects from the reflective coating  13 , as shown at  14 . The MEMS mirror  10  has a torsional hinge  15  for tilting the MEMS mirror  10  as shown by arrows  16 , thus steering the reflected optical beam  14 . The MEMS mirror  10  has a uniform thickness. 
         [0031]    The reflective coating  13  of the MEMS mirror  10  typically has a non-zero curvature due to residual stresses, or thermally induced stresses in the reflective coating  13  due to thermal mismatch with the substrate  18 . When the MEMS mirror  10  is used in an optical switch, the curvature of the reflective coating  13  of the MEMS mirror  10  has an adverse effect on the optical insertion loss and the extinction ratio of the optical switch. The magnitude of these adverse effects is approximately proportional to the fourth power of the mirror size or optical beam size. High port count wavelength selective switch (WSS) devices require relatively large optical beams. Thus, the flatness of the MEMS mirror  10  is of a considerable concern, especially for high port count WSS devices. 
         [0032]    As noted above, one traditional solution to ensuring flatness of the MEMS mirror  10  is to increase the thickness of the substrate  18 . However, increased thickness of the substrate  18  worsens dynamic performance of the MEMS mirror  10 . Due to a requirement for the MEMS mirror  10  to withstand shock and vibration, the MEMS mirror  10  should have a resonance frequency of rotational oscillations above a certain threshold. The resonance frequency is proportional to a ratio of the spring constant of the torsional hinge  15  to the moment of inertia of the MEMS mirror  10 , which depends on the thickness of the substrate  18 . The spring constant of the torsional hinge  15  is limited by a maximum torque created by an actuator, not shown, which depends on a maximum voltage applied to the actuator. Therefore, the moment of inertia and the maximum thickness of the substrate  18  are limited in case of the MEMS mirror  10  by the maximum driving voltage available, and by the resonance frequency requirement. 
         [0033]    The present invention overcomes this limitation by providing a MEMS mirror having a laterally varying thickness, which preferably matches laterally varying optical beam intensity. Referring now to  FIG. 2 , a MEMS mirror  20  has a top reflective surface  23  and a bottom surface  29 . The bottom surface  29  is profiled (non-flat), so that the MEMS mirror  20  has a laterally varying thickness. To simplify the mirror structure, no voids or ribs are present in the MEMS mirror  20 . The MEMS mirror  20  has a hinge  25  defining a tilt axis  25 ′ of the MEMS mirror  20  for tilting as shown with arrows  26 . A longitudinal axis  21  is perpendicular to the tilt axis  25 ′ and is crossing the tilt axis  25 ′ at a point  1 . The thickness of the MEMS mirror  20  decreases in going from the point  1  towards ends  2  and  3  of the MEMS mirror  20 . The ends  2  and  3  are disposed on the longitudinal axis  21 . As noted above, thinning down the MEMS mirror  20  at its ends  2  and  3 , where the optical beam intensity is reduced, facilitates reducing the moment of inertia without a significant reduction of the quality of the reflected optical beam  14 . Preferably, the lateral profile of the thickness variation of the MEMS mirror  20  correlates with the optical intensity profile  11  of the incoming optical beam  12 . In this way, the moment of inertia of the MEMS mirror  20  can be lessened while keeping a pre-defined quality of the reflected optical beam  14 . Note that the moment of inertia is proportional to square of a distance to the pivot axis; therefore the moment of inertia can be reduced dramatically by having less mass farther from the pivot, as is the case in the present invention. 
         [0034]    The MEMS mirror  20  is the thickest at the point  1 , where the intensity profile  11  of the impinging optical beam  12  is at maximum. At or near the point  1 , the undesired curvature of the reflective layer  23  of the MEMS mirror  20  is at minimum, which lessens the optical losses upon subsequent fiber coupling, and also improves switching ratio (extinction ratio) of a MEMS optical switch the MEMS mirror  20  is used in. 
         [0035]    Preferably, the thickness profile t(x,y) of the MEMS mirror  20  varies as 
         [0000]        t ( x,y )= c*I   n ( x,y )  (1)
 
         [0036]    wherein I(x,y) is the intensity profile  11  of the impinging optical beam  12 , the plane (x,y) is a plane of the reflective layer  23 , n&gt;=0.5, and c is a constant. It follows from Eq. (1) that when the function I(x,y) is exponential, as is commonly the case, the function t(x,y) is also exponential. 
         [0037]    The thickness of the MEMS mirror  20  decreases smoothly and monotonically in going from the point  1  toward the ends  2  and  3 . However, it may be difficult to realize such a smoothly varying thickness profile using existing MEMS fabrication methods. Other, simpler forms of the thickness profile can be more practical. Referring now to  FIG. 3 , a bottom surface  39  of a MEMS mirror  30  is profiled so that the MEMS mirror  30  has a linearly varying thickness profile. This thickness profile is an approximation of a “desired” Gaussian thickness profile, corresponding to the bottom surface  29  shown in  FIG. 3  in a dashed line for comparison purposes. The linearly varying thickness profile due to the bottom surface  39  can be obtained using a linearly graded etching mask. 
         [0038]    Another practical form of a thickness profile is a stepped profile. Turning to  FIG. 4 , a MEMS mirror  40  has a bottom surface  49  having a stepped profile. The total number of steps is four, two for each end of the MEMS mirror  40 . This “stepped” profile is also an approximation of the “desired” Gaussian thickness profile  29  shown in  FIG. 4  in a dashed line. More steps can be used if desired, for a better approximation of the Gaussian profile  29 . The step location is preferably correlated with a location where a local beam intensity decreases to a pre-determined percentage of a peak beam intensity. 
         [0039]    Referring now to  FIG. 5 , a MEMS mirror  50  has a bottom surface  59  having only one step. One advantage of the MEMS mirror  50  is manufacturability. Only two masks are required to manufacture a step in the MEMS mirror  50 . By way of example, the silicon MEMS mirror  50  having a length of 1300 um, thickness of 30 um in the middle and 15 um at the ends, a step location half-way to the mirror center, that is 750 um from each edge, has an optical performance comparable to that of the mirror  10  of  FIG. 1  of the same length and uniform thickness of 30 um, while having only 33% of the moment of inertia of the MEMS mirror  10  of  FIG. 1 . 
         [0040]    When a “polarization diversity” arrangement is used in an optical switch to achieve a polarization independent functionality, two beams of light, corresponding to two orthogonal polarization components of the original optical beam, co-propagate in an optical switch. To ensure low polarization sensitivity, a MEMS mirror must be able to steer the two beams in a nearly identical fashion. Turning to  FIG. 6 , a MEMS mirror  60  is shown having two rigidly connected halves  68 A and  68 B and a torsional hinge structure  65  for tilting the MEMS mirror  60  about a tilt axis  65 ′. The two halves  68 A and  68 B are coated with a reflective coating  63 . In operation, two optical beams  62 A and  62 B, having intensity profiles  61 A and  61 B, impinge on the reflective coating of the two halves  68 A and  68 B, forming reflected optical beams  64 A and  64 B, respectively. Although in this case the mirror thickness of the mirror halves  68 A and  68 B does not correspond directly to the local intensity of the impinging optical beams  64  and  65 , nonetheless, spatially varying the thickness of the MEMS mirror  60  also helps reduce the mirror&#39;s moment of inertia. Furthermore, it is possible to customize the mirror  60  for the two-beam application (that is, for steering the two beams  62 A and  62 B) by thinning down sections  67 A and  67 B of the two halves  68 A and  68 B, respectively, because the sections  67 A and  67 B correspond to low power density of the optical beams  62 A and  62 B. 
         [0041]    Turning now to  FIG. 7 , a MEMS mirror  70  having a “hidden-hinge” configuration is shown. In the MEMS mirror  70 , the hinge structure  65  is “hidden” beneath a mirror layer  77  disposed over the mirror halves  68 A and  68 B. In this case, the thickness of the MEMS mirror  70  can also be correlated to an intensity profile  71  of an impinging optical beam  72 , so that optical quality of a reflected optical beam  74  can be preserved. 
         [0042]    Referring to  FIGS. 8A and 8B , a MEMS mirror  80  has a tilt axis  85 ′, a longitudinal, e.g. central, axis  81  perpendicular to the tilt axis  85 ′ and crossing the tilt axis  85 ′ at the point  1 . The MEMS mirror  80  has the two ends  2  and  3  disposed on the longitudinal axis  81 , and two more ends  4  and  5  disposed on the tilt axis  85 ′. The thickness of the MEMS mirror  80  decreases in going from the point  1  towards the points  2  and  3 ; and towards the points  4  and  5 . In the MEMS mirror  80 , the thickness decreases in stepwise fashion. The location and the magnitude of steps are correlated with the intensity distribution of an impinging optical beam, not shown in  FIGS. 8A and 8B . The steps are formed by three rectangular layers  87 ,  88 , and  89 , and a pair of torsional hinges  85  for tilting the MEMS mirror  80  about the tilt axis  85 ′. A reflective layer  83  is disposed on the top rectangular layer  87 . 
         [0043]    Preferably, the torsional hinges  85  are associated with the thinnest top layer  87 . The stepped MEMS mirror  80  can be formed using etching through a succession of generally rectangular etch masks; the mask for the layer  87  can include hinge structures. During etching the layer  87 , the torsional hinges  85  can also be formed. 
         [0044]    Instead of stepped shape as shown in  FIGS. 8A and 8B , the MEMS mirror  80  can have a shape of a cone or a pyramid, or a stepped cone or a pyramid. Referring to  FIGS. 9A and 9B , the pyramid-shaped and cone-shaped MEMS mirrors  90 A and  90 B are shown, respectively. In  FIGS. 10A and 10B , truncated (frusto-conical) pyramid-shaped and cone-shaped MEMS mirrors  90 A and  90 B are presented, respectively. In the MEMS mirrors  90 A and  90 B, the thickness decreases in going from a centrally located generally flat section  102 A and  102 B, respectively, to the ends of the MEMS mirror. In  FIGS. 9A ,  9 B,  10 A, and  10 B, the vertical scale is exaggerated for clarity of presentation. 
         [0045]    The MEMS mirrors  20 ,  30 ,  40 ,  50 ,  60 ,  70 ,  80 ,  90 A,  90 B,  100 A, and  100 B can be manufactured using micromachining methods known to one of skill in the art. Generally, at a first step, a continuous mirror wafer, having no voids or ribs therein, is provided. At a second step, the bottom surface is profiled, so as to have its thickness decrease in going from the middle of the mirror towards its edges. The bottom surface profiling is preferably achieved by etching. A graded etch mask can be used to manufacture the MEMS mirrors  20 ,  30 ,  90 A,  90 B,  100 A, and  100 B; or a plurality of uniform etch masks can be used to manufacture the MEMS mirrors  40 ,  50 ,  60 ,  70 , and  80 . The thickness of the MEMS mirrors  20 ,  30 ,  40 ,  50 ,  60 ,  70 ,  80 ,  90 A,  90 B,  100 A, and  100 B is preferably correlated with the beam intensity variation, so that the moment of inertia of the manufactured MEMS mirrors can be lessened while keeping a pre-defined quality of the optical beam, which is important in ensuring a good extinction ratio and insertion loss of the MEMS optical switch the MEMS mirrors  20 ,  30 ,  40 ,  50 ,  60 ,  70 ,  80 ,  90 A,  90 B,  100 A, or  100 B are used in. For the stepped MEMS mirrors  40 ,  50 ,  60 ,  70 , and  80 , height and position of the steps are correlated with the beam intensity variation to achieve the effect of reducing moment of inertia of the MEMS mirrors  40 ,  50 ,  60 ,  70 , and  80 , while keeping a pre-defined optical quality of the reflected optical beam. The reduced moment of inertia helps increase a frequency of a mechanical resonance of the MEMS mirrors  20 ,  30 ,  40 ,  50 ,  60 ,  70 ,  80 ,  90 A,  90 B,  100 A, and  100 B. 
         [0046]    The foregoing description of one or more embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.