Abstract:
A 2D diffraction grating light valve modulates an incident beam of light. A plurality of elements each have a reflective surface with their respective reflective surfaces substantially coplanar. Alternatively, the reflective surfaces of the plurality of elements lie within one or more parallel planes. The elements are supported in relation to one another. Preferably, a planar member includes a plurality of holes arranged in a symmetrical two-dimensional array and configured such that the holes substantially optically extend the elements. Alternatively, one or more elements substantially optically extends the plurality of holes. The planar member includes a light reflective planar surface that is parallel to the plane of the elements within a functional area of the device. The planar member is supported in relation to the elements. By applying an appropriate biasing voltage to the planar member, the planar member can be moved in a direction normal to the plane of the elements. When the planar member and the plurality of elements are in a first configuration, the 2D diffraction grating reflects the incident beam of light as a plane mirror. When the planar member and the plurality of elements are in a second configuration, the 2D diffraction grating diffract the incident beam of light. Preferably, the planar member is a membrane circumferentially coupled to a support structure.

Description:
FIELD OF THE INVENTION 
     The present invention relates to a method of and an apparatus for modulation of a beam of light. More particularly, this invention is for a substantially flat reflective surface having selectively deformable portions for providing a diffraction grating. 
     BACKGROUND OF THE INVENTION 
     Designers and inventors have sought to develop a light modulator which can operate alone or together with other modulators. Such modulators should provide high resolution, high operating speeds (kHz frame rates), multiple gray scale levels, e.g., 100 levels or be compatible with the generation of color, a high contrast ratio or modulation depth, have optical flatness, be compatible with VLSI processing techniques, be easy to handle and be relatively low in cost. One such related system is found in U.S. Pat. No. 5,311,360. 
     According to the teachings of the &#39;360 patent, a diffraction grating is formed of a multiple mirrored-ribbon structure such as shown in FIG. 1. A pattern of a plurality of deformable ribbon structures  100  are formed in a spaced relationship over a substrate  102 . The substrate  102  preferably includes a conductor  101 . Both the ribbons and the substrate between the ribbons are coated with a light reflective material  104 , such as an aluminum film. The height difference that is designed between the surface of the reflective material  104  on the ribbons  100  and those on the substrate  102  is λ/2 when the ribbons are in a relaxed, up state. If light at a wavelength λ impinges on this structure perpendicularly to the surface of the substrate  102 , the reflected light from the surface of the ribbons  100  will be in phase with the reflected light from the substrate  102 . This is because the light which strikes the substrate travels λ/2 further than the light striking the ribbons and then returns λ/2, for a total of one complete wavelength λ. Thus, the structure appears as a flat mirror when a beam of light having a wavelength of λ impinges thereon. 
     By applying appropriate voltages to the ribbons  100  and the conductor  101 , the ribbons  100  can be made to bend toward and contact the substrate  102  as shown in FIG.  2 . The thickness of the ribbons is designed to be λ/4. If light at a wavelength λ impinges on this structure perpendicularly to the surface of the substrate  102 , the reflected light from the surface of the ribbons  100  will be completely out of phase with the reflected light from the substrate  102 . This will cause interference between the light from the ribbons and light from the substrate and thus, the structure will diffract the light. Because of the diffraction, the reflected light will come from the surface of the structure at an angle Θ from perpendicular. 
     If a wavelength of other than λ impinges thereon, there will only be partial reflectivity when the ribbons are in the “up” 0  state, since Θ is dependent on the wavelength λ. Similarly, the light will only be partially diffracted to the angle Θ when the ribbons arc in the “down” 0  state. Thus, a dark pixel will display some light and a bright pixel will not display all the light if the wavelength of the light is not exactly at λ. It is very expensive to utilize a light source that has only a single wavelength. Commercially viable light sources typically provide light over a range of wavelengths. 
     For the above described device to function within desired parameters requires that the heights and thickness of the ribbons and reflecting layers to provide structures are precisely λ/2 when up and λ/4 when down. Because of variances in manufacturing processing, the likelihood is small that the relative heights will be precisely λ/2 when up and λ/4 when down. Therefore, the expected parameters will be much poorer than theoretically possible. 
     Another difficulty with the above described structure results from an artifact of the physical construction. In particular, once in the down position, the ribbons tend to adhere to the substrate. Texturing the surface of the substrate aids in overcoming this adhesion. Unfortunately, the textured surface substantially degrades the reflective properties of the surface. This degrades the performance of the device. 
     The &#39;360 patent teaches an alternate structure as shown in FIG.  3 . According to this conventional structure, a plurality of elongated elements are disposed over a substrate  200 . A first plurality of the elongated elements  202  are suspended by their respective ends (not shown) over an air gap  204 , as in the embodiment of FIGS. 1 and 2. A second plurality of the elongated elements  206  are mounted to the substrate  200  via a rigid support member  208 . The height of the support members  208  is designed to be λ/4. A reflective material  210  is formed over the surface of all the elongated elements  202  and  206 . 
     In theory, the elongated elements  202  and  206  are designed to be at the same height when at rest. Thus, when all the elongated elements are up and at the same height there will be no diffraction. (In fact there may be some modest amount of diffraction due to the periodic discontinuities of the gaps between elongated elements. However, this period is half the period of the grating so that it diffracts at twice the angle of the desired diffracted light. Because the optics are configured to pick up diffracted light from only the desired angle, this unwanted diffraction is not captured and does not degrade the contrast ratio.) 
     In order to build a structure such as shown in FIG. 3, a layer must be formed of a first material having a predetermined susceptibility to a known etchant. Portions of that layer are removed through known techniques such as photolithography and etching. A second material is then formed in the voids of the removed material such as by deposition. This second material has a known susceptibility to the etchant which is different than the first material. The layer is formed of the elongated element material. This structure is etched to form ribbons of the elongated elements. Finally, the second material is removed by etching to form the suspended elongated elements  202 . A popular use for light modulators of the type described in the &#39;360 patent is for use as a variable optical attenuator, VOA, for signals in a fiber-optic network. 
     FIGS. 4A and 4B show how an articulated one-dimensional grating can be used to control the amount of light reflected into an optical fiber. FIG. 4A illustrates a reflective grating  320  in an undeformed state in which an incident light  310  from an optical fiber  305  impinges upon the reflective grating  320 . A numerical aperture (NA) of the optical fiber  305  determines an acceptance cone  315  in which the optical fiber  305  accepts light. In its undeformed state, the reflective grating  320  behaves much like a mirror; the incident light  310  is simply reflected back into the optical fiber  305  with no attenuation . FIG. 4B illustrates the reflective grating  320  in a deformed state in which the incident light  310  is diffracted at predominantly predetermined diffraction angles  325 . The diffraction angles  325  can be adjusted to be larger than the acceptance cone  315  of the optical fiber  305  thereby allowing attenuation of the incident light  310 . By controlling the deformation of the grating, the amount of light reflected back into the fiber can be controlled. 
     Unfortunately, when arbitrarily polarized light impinges on a linear one-dimensional (1D) grating, each polarization state interacts with the grating differently. Such a scenario is illustrated in FIG. 5 in which an incident light beam  350  impinges upon a 1D grating  360  comprising a series of reflective ribbons placed in parallel. The incident light  350  includes a polarization state P and a polarization state S. Light polarized parallel to the ribbons (polarization state P) interacts with the 1D grating  360  differently than light polarized perpendicular to the ribbons (polarization state S). Polarization states S and P each “see” 0  different environments at the 1D grating  360 . This can lead to Polarization Dependent Losses (PDL) in which one polarization state is attenuated more than the other. These problems become especially acute as the gap between each adjacent ribbon approaches the wavelength of the incident light. 
     What is needed is a grating system that treats each polarization state equally. Further, a system is desired that substantially eliminates Polarization Dependent Losses. What is also needed is a variable optical attenuator in fiber optic networks that does not suffer from Polarization Dependent Losses. 
     SUMMARY OF THE INVENTION 
     According to embodiments of the present invention, a light modulator performs variable optical attenuation in fiber optic networks without incurring Polarization Dependent Losses. Preferably, the light modulator is a two-dimensional (2D) MEMS (MicroElectroMechanical System) diffraction grating. The 2D diffraction grating modulates an incident beam of light. A plurality of elements each have a reflective surface with their respective reflective surfaces substantially coplanar. Alternatively, the reflective surfaces of the plurality of elements lie within one or more parallel planes. The elements are supported in relation to one another. Preferably, a planar member includes a plurality of holes arranged in a symmetrical two-dimensional array and configured such that the holes substantially optically extend the elements. In an alternative embodiment, one or more elements substantially optically extends the plurality of holes. The planar member includes a light reflective planar surface that is parallel to the plane of the elements within a functional area of the device. The planar member is supported in relation to the elements. By applying an appropriate biasing voltage to the planar member, the planar member can be moved in a direction normal to the plane of the elements. When the planar member and the plurality of elements are in a first configuration, the 2D diffraction grating reflects the incident beam of light as a plane mirror. When the planar member and the plurality of elements are in a second configuration, the 2D diffraction grating diffracts the incident beam of light. Preferably, the planar member is a membrane circumferentially coupled to a support structure. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 illustrates a cross section view of a conventional 1D diffraction grating light valve wherein ribbon elements are in an up position. 
     FIG. 2 illustrates a cross section view of the conventional 1D diffraction grating light valve of FIG. 1 wherein the ribbon elements are in a down position. 
     FIG. 3 illustrates a cross section view of an alternate embodiment of a conventional 1D diffraction grating light valve having a plurality of planarly arrayed elongated elements, a portion of which are supported by support members. 
     FIG. 4A illustrates a reflective 1D grating in an undeformed state in which an incident light from an optical fiber impinges upon the reflective 1D grating. 
     FIG. 4B illustrates the reflective 1D grating in a deformed state in which the incident light is diffracted at predetermined angles. 
     FIG. 5 illustrates an incident light impinging upon a 1D grating comprising a series of reflective ribbons placed in parallel. 
     FIG. 6 illustrates an arbitrarily polarized light impinging a conceptualized 2D grating according to the present invention. 
     FIG. 7 illustrates a plan view for a 2D grating according to the preferred embodiment of the present invention. 
     FIG. 8 illustrates a representative section of a functional area of the 2D grating in FIG.  7 . 
     FIG. 9 illustrates a cross-sectional view of a portion of the 2D grating according to the preferred embodiment of the present invention. 
     FIG. 10A illustrates a cross section view of a functional portion of the 2D grating in the non-diffracting/up mode according to the preferred embodiment. 
     FIG. 10B illustrates a cross section view of a functional portion of the 2D grating in the diffracting/down mode according to the preferred embodiment. 
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Embodiments of the present invention substantially eliminate PDL by using a light modulator to treat the S and P polarizations symmetrically. Preferably, the light modulator is a 2D MEMS diffraction grating. A preferred embodiment uses conventional grating light valve process technology comprising standard CMOS materials and processes, and XeF 2  etchant technology for releasing ribbons of the MEMS structure. A conventional 1D linear-array grating light valve can be used as an optical attenuator. However, because of a low order of symmetry, the 1D linear-array grating light valve suffers from substantial PDL. Embodiments of the present invention incorporate higher degrees of rotational symmetry to substantially eliminate PDL. Embodiments of the present invention can be used as a means for performing variable optical attenuation in fiber optic carriers without incurring PDL. It should be clear to those skilled in the art that the present invention can also be used in other applications in which low PDL is desirable. The specifications on fiber-optic systems are stringent regarding PDL. In a fiber containing multiple wavelengths, where each wavelength represents a different channel, each wavelength can exit the fiber having a different polarization state. It is undesirable to have varying attenuation between the channels because the polarization of each channel is different. In this case, it is desirable to attenuate across the entire spectrum with a flat attenuation profile. Embodiments of the present invention are preferably suited to communications applications using wavelength division multiplexing (WDM) or Dense WDM (DWDM) with multiple wavelengths on a standard grid. 
     FIG. 6 illustrates a two-dimensional grating that substantially eliminates PDL according to embodiments of the present invention. An arbitrarily polarized incident light 370 impinges upon a 2D grating  380 . The 2D grating  380  comprises a reflective membrane including a plurality of holes and a plurality of reflective elements (not shown in FIG.  6 ). Each reflective element resides within one of the plurality of holes of the membrane. The incident light  370  includes a polarization state P and a polarization state S. The polarization states S and P each “see” 0  identical environments at the 2D grating  380 . Because of its higher order symmetry, the 2D grating  380  treats the polarization states S and P equally, thereby mitigating PDL. 
     FIG. 7 illustrates a plan view for a 2D grating  400  according to the preferred embodiment of the present invention. Although the 2D grating  400  is preferably configured as a hexagonal array of holes and reflective elements, the 2D grating  400  can be designed as any 2D rotationally symmetric array including, but not limited to, a square and an octagon. The materials, film sequence and processing steps are identical to those for fabricating a linear array grating light valve. A sacrificial layer (sacrificial layer  530  in FIG. 9) lies underneath the 2D grating  400  shown in FIG.  7 . Preferably, the sacrificial layer is a poly-silicon. The sacrificial layer is defined by an etched annulus  415 . A circular array of etched support posts  410  are located directly inside the annulus  415  to provide a rigid support for a taut silicon-nitride membrane  405 . A light reflective material forms the top layer of the membrane  405 . A plurality of optical posts  420  are arrayed in the interior of the membrane  405  to form the 2D grating  400 . Each of the optical posts  420  are separated from the membrane  405  by a nitride cut  430 . To achieve optimum contrast ratio, the diameter and spacing of the optical posts  420  is adjusted such that there is equal area inside and outside the circular nitride cuts  430 . This relationship between the area inside and outside the nitride cuts  430  is discussed in detail below in relation to FIG.  8 . The optical posts  420  are anchored to the substrate similarly as the etched support posts  410  around the perimeter of the device. In a release step, XeF 2  flows into the nitride cuts  430  and removes the sacrificial layer, thereby forming an air gap underneath the membrane  405 . This allows the membrane  405  to be deflected with respect to the static optical posts  420 , thereby forming the 2D diffraction grating  400 . In the preferred embodiment, each of the plurality of holes in the membrane  405  and each of the optical posts  420  are circular to provide symmetrical stress displacement. The circular shapes of the holes and reflective elements in addition to the array symmetry results in identical treatment of both polarization states S and P. It should be clear to those skilled in the art that the holes and reflective elements can be configured as symmetrical shapes other than circles, for example a square, hexagon, or octagon. 
     FIG. 8 illustrates a representative section of a functional area of the 2D grating  400 . It is a design consideration that the incident light impinges the 2D grating  400  within the functional area. It is also a design consideration to determine a ratio between the surface area of the membrane and the surface area of the reflective elements within the functional area. The surface area of the membrane can be represented by A in FIG. 8, and the surface area of the reflective elements can be represented by B+B+B, or  3 B. Neither of the surfaces areas A or B include the surface area of the nitride cuts  430 . Also, each optical post  420  includes a center  435  in which incident light is lost. Therefore, section B does not include a portion of the center  435 . In the preferred embodiment, the surface area of the membrane is equal to the surface area of the reflective elements such that  3 B=A. In this case where the surface areas are equal, the best possible cancellation is achieved, thereby causing the incident light to be diffracted as desired It should be clear to those skilled in the art, that a ratio different than  3 B=A can be used to achieve other desired results. 
     FIG. 9 illustrates a cross-sectional view of a portion of the 2D grating  400  according to the preferred embodiment of the present invention. A preferred manufacturing process is described in relation to the structure illustrated in FIG.  9 . FIG. 9 is not to scale. A layer of SiO 2  is thermally oxidized onto a silicon wafer to form a SiO 2  substrate  510 . A bottom electrode  515  is formed on top of the substrate  510 . The bottom electrode  515  is preferably comprised of a poly-silicon (doped poly) with low resistivity, but can also be another low resistance material. A SiO 2  etch stop  520  is then added. The etch stop  520  is resistant to XeF 2 . A sacrificial layer  530  is formed over the etch stop  520 . The sacrificial layer  530  is preferably comprised of titanium nitride. Alternatively, the sacrificial layer  530  is comprised of poly-silicon. Holes are then etched into the sacrificial layer  530  for the etched support posts  410  and the optical posts  420 . The support posts  410  are preferably smaller in diameter than the optical posts  420 . Preferably, each securing post  410  is separated from its neighbor by the diameter of the securing post. In the case where the diameter of the securing post  410  is 2 microns, for example, then spacing between each securing post is 2 microns. In other words, the spacing between the center of each adjacent securing post is 4 microns in this case. As discussed above in relation to FIG. 8, the spacing between each optical post  420  is determined by the designed ratio of the surface area of the membrane to the surface area of the reflective elements within the functional area. In the preferred embodiment, this ratio is one. A silicon nitride, Si 3 N 4 , layer  525  is then added. The Si 3 N 4  layer  525  is etched to form the nitride cuts  430 . An aluminum layer  535  is then added and etched to match the nitride cuts  430  in the Si 3 N 4  layer  525 . XeF 2  is then applied through the nitride cuts  430  to remove the sacrificial layer  530 . The annulus  415  is formed at the point where the Si 3 N 4  layer  525  meets the etch stop  520  along the outer rim of the membrane  405 . When the XeF 2  is released into the nitride cuts  430 , the XeF 2  progresses to the annulus  415  and stops there. Where the sacrificial layer  530  previously existed, now exists an air gap. The resulting 2D grating  400  includes the etched support posts  410 , the membrane  4005  and the optical posts  420 . The aluminum layer  535  on the membrane  405  is coupled to a voltage source, and the bottom electrode  515  is coupled to ground or some other voltage source. 
     It should be clear that the thicknesses illustrated in FIG. 9 related to the SiO 2  substrate  510 , the bottom electrode  515 , the etch stop  520 , the sacrificial layer  530 , the Si 3 N 4  layer  525 , and the aluminum layer  535  are for illustrative purposes only and are not to scale. Although there is a strong argument that the 2D grating of the present invention yields no PDL, defects in the membrane and the optical posts make those portions polarization sensitive. Therefore, due to imperfections in the device structure, trace amounts of PDL do exist, although they are minimal. Each step in the manufacturing process is a conventional step. Therefore, the process as well as the device according to embodiments of the present invention is CMOS compatible and can integrate CMOS devices onto this device. 
     In addition to substantially eliminating PDL, the 2D grating according to embodiments of the present invention provides structural advantages over conventional grating light valves utilizing reflective ribbons. The 2D grating remains substantially flat due to biaxial tension. Also, due to the biaxial tension present in the membrane, the present invention can resonate at a higher frequency than a 1D grating light valve. As a result, the 2D grating of the present invention provides a faster VOA as compared to conventional thermally controlled VOAs, or other ribbon grating light valve devices. 
     In operation, a voltage is applied to the aluminum layer  535  of the membrane  405  while the bottom electrode  515  remains grounded. Preferably, a voltage source (not shown in the figures) is coupled to the membrane  405  and to ground to apply the voltage difference. While in this “on” 0  position, the electrical potential between the aluminum layer  535  on the membrane  405  and the bottom electrode  515  produces electrostatic force that causes the membrane  405  to bend towards the etch stop  520 . The etched support posts  410  prevent the outer rim of the membrane  405  from collapsing, thereby maintaining tension in the membrane  405 . If the etched securing posts  410  were not present, then the outer rim would fold over, or collapse, under the tension of the membrane  405 . The etched securing posts  410  do not collapse because there is tension applied from inward tension of the membrane  405  and outward tension of the outer rim. The Si 3 N 4  layer  5 secures very well to the SiO 2  etch stop  5 thereby providing the outward tension of the outer rim. In the “on” 0  position, the membrane  405  is substantially flat in the middle, thereby forming the functional area. The functional area is located within the rotationally symmetric array of holes and reflective elements. The incident light must fall within this functional area. The preferred diameter of the incident light is about 25 microns. 
     Preferably, a controller is coupled to the voltage source. The controller provides appropriate control signals to the voltage source to control when and by how much the membrane  405  is deflected. 
     FIG. 10A illustrates a cross section view of a portion of the functional area of the 2D grating  400  in a non-diffracting/up mode according to the preferred embodiment. In the non-diffracting/up mode, no voltage is applied to the membrane  405 . As can be seen from FIG. 10A, the optical posts  4 are arranged to be coplanar with the membrane  405  and present a flat upper surface which is coated with the aluminum layer  535 . In this manner, the 2D grating acts as a plane mirror and it reflects incident light while in the non-diffracting/up mode. 
     FIG. 10B illustrates a cross section of the portion of the functional area of the 2D grating  400  in a diffracting/down mode according to the preferred embodiment. In the diffracting/down mode, a voltage is applied to the membrane  405 . The amount of voltage is determined by the restoring force associated with the membrane  405  and the distance λ/4 that the membrane is to be moved down, where λ is the wavelength of the incident light impinging the 2D grating  400 . The voltage must be sufficient to overcome the restoring force of the membrane  405  and pull the planar surface of the membrane  405  to a distance λ/4 below the planar surface of the optical post  420 . In this manner, the reflected light from the surface of the membrane  405  will be completely out of phase with the reflected light from the surface of the optical posts  420 . This will cause the 2D grating  400  to diffract the light. When the applied voltage is removed from the membrane  405 , restoring forces resulting from the biaxial tension of the membrane  405  return the membrane  405  to the non-diffracting/up mode as illustrated in FIG.  10 A. Accordingly, within the functional area of the 2D grating  400 , when the planar surface of the optical posts  420  and the planar surface of the membrane  405  are separated by a distance equal to about m/4 times a particular wavelength of the incident light, the 2D grating  400  acts as a plane mirror when m=an even whole number or zero and as a diffracting 2D grating when m=an odd whole number. 
     In the preferred embodiment where the holes in the membrane  405  and the optical posts  420  are circular, while in the diffracting mode, the light is diffracted as six light beams. Preferably, these six diffracted light beams are equally spaced along a perimeter of a cone. Each diffracted light beam can be collected. In this manner, embodiments of the 2D grating of the present invention can be used as a switch where each collected diffracted light beam is an output port of the switch. Similarly, the 2D grating can be used to uniformly adjust the intensity of the diffracted light beams. By moving the membrane  405  a distance between 0 and λ/4, the incident light is variably reflected such that a portion of the incident light is reflected and a remaining portion of the incident light is diffracted. In this manner, diffracted light can be attenuated by reflecting a portion of the light back into an input fiber of the incident light. A circulator or isolator can be used to block this reflected portion, while the attenuated diffracted light is collected as output. 
     It is understood that although the preferred embodiment includes the plurality of holes and corresponding plurality of reflective elements to be configured in a symmetric array, the plurality of holes and corresponding reflective elements can be configured as a randomized array. 
     In another alternative embodiment, an array of 2D gratings can be used as a dynamic band equalizer. As discussed above, fiber-optics typically carry a multiplicity of channels where each channel constitutes a different wavelength of the light transmitted within the fiber. In this alternate embodiment, an optical train isolates each channel and directs each channel as normal incident light to one of the array of 2D gratings. Each channel is tightly banded within a narrow band. Each 2D grating is tuned to equalize a specific channel. The 2D grating is tuned by adjusting the applied voltage to deform the membrane the necessary distance λ/4, where λ is the wavelength of the specific channel to be equalized. 
     In a further alternative embodiment, PDL can be minimized in a conventional 1D grating light valve by including a symmetrical array of holes into each ribbon and placing optical posts within each of the holes. 
     To this point, the 2D grating of the present invention has been described in terms of an incident light impinging normal to the 2D grating. Polarization sensitivity also results from incident light impinging a surface at some angle other than normal incidence. As such, a 2D grating according to the present invention can be designed that builds in polarization dependence to compensate for the angle of light incidence. To illustrate, in the preferred embodiment, the 2D grating provides for polarization independence when incident light normally impinges the circular optical posts and the membrane with circular holes. If the angle of incident light is not normal, a 2D grating can be constructed to offset this non-normal angle of incidence by making the holes and optical posts elliptical instead of circular. Therefore, the 2D grating can be designed to substantially eliminate PDL for any angle of light incidence. 
     It will be readily apparent to one skilled in the art that other various modifications may be made to the preferred embodiment without departing from the spirit and scope of the invention as defined by the appended claims. For example, the membrane is described as moving in relation to fixed optical posts; however, the same diffracting effect can be obtained by replacing the optical posts with a reflective layer resting directly on the etch stop and below the planar surface of the membrane. In general, the optical posts can lie in any plane that is m(λ/2) above or below the planar surface of the membrane, where m is an integer. This reflective layer can be a single reflective element or a plurality of reflective elements. In the case of a plurality of reflective elements, the size of each reflective element can either be greater than, equal to or less than the size of each of the plurality of holes in the membrane, depending on the particular design considerations. 
     Also, the functional area of the membrane can be increased by depositing a thick film on the center such that the membrane bends more towards the outer rim and less so in the center. 
     Further, instead of a membrane and a support structure that circumferentially couples the membrane to the substrate, a planar member replaces the membrane in an alternative embodiment. In this case, the planar member is coupled to the substrate at either or both ends of the planar member. Alternatively, the planar member is circumferentially coupled to the substrate. In a specific alternative embodiment, the planar member is an elongated ribbon including a plurality of holes, where the elongated ribbon is coupled to the substrate at either or both ends of the ribbon.