Abstract:
A chromatic dispersion compensator in a single-pass and a double-pass version is disclosed. In a single-pass version, the compensator has a diffractive grating for spatially separating an input optical signal into spatially spaced frequency components and a MEMS array of separate phase shifters, each for imparting an independent phase shift to a channel containing a range of the spatially spaced frequency components. In a double-pass version, a retroreflector is disposed to effect a double pass of the light beam through the grating and the phase shifters. The arrangement is effecting in reducing chromatic dispersion of the optical signal.

Description:
This application claims priority benefit of U.S. provisional applications No. 60/296,444 filed Jun. 8, 2001 and No. 60/350,432 filed Jan. 22, 2002. 

   FIELD OF THE INVENTION 
   This invention relates to chromatic dispersion, and more specifically to compensating for chromatic dispersion in optical waveguides. 
   BACKGROUND OF THE INVENTION 
   Fiber optic systems have become widely used for high capacity telecommunications networks. In fiber optic systems, data is typically transmitted as a stream of light pulses, within an optical spectrum covering some range of optical frequencies around a central frequency. Such a stream of pulses is known as a “channel”. The capacity of fiber optic communications systems has been increased both by increasing the data rate for each channel, and by multiplexing channels at different wavelengths onto a single optical fiber (known in the art as Wavelength Division Multiplexing, or WDM). Future fiber optic networks are also envisioned to be “agile”, with the capability of adding and dropping optical channels at intermediate nodes in a network, and dynamically reconfiguring the optical paths through the network taken by each channel. These advanced networks require careful management of the distortions to optical pulses caused by propagation through optical fibers. 
   An optical pulse propagates through an optical system at a velocity known as the group velocity. The time delay for a pulse to propagate through an optical system is known as the group delay. For optical fibers, the group velocity varies with wavelength, such that the longer wavelength components of an optical pulse propagate slightly faster or slower (depending on the sign of the chromatic dispersion) than the shorter wavelength components. This typically leads to a broadening in time of an optical pulse propagating through an optical fiber. This broadening is known as chromatic dispersion. As the pulses broaden, they eventually overlap in time, and can no longer be distinguished at an optical receiver. Thus, chromatic dispersion represents one of the fundamental limitations to the maximum data rates and transmission distances which can be achieved in a fiber optic communications system. 
   In the art, chromatic dispersion D is conventionally defined as the derivative of group delay τ g  with respect to wavelength λ: D=dτ g /dλ. Group delay is in turn defined as the negative of the derivative of optical phase φ with respect to frequency ω: τ g =−dφ/dω. Chromatic dispersion is conventionally expressed in units of ps/nm, and group delay in units of ps. 
   In order to increase the data rates and transmission distances in a fiber optic network, one or more chromatic dispersion compensator devices are typically included in the network. The chromatic dispersion compensator is designed to create a chromatic dispersion opposite in sign and at least approximately equal in magnitude to the chromatic dispersion of a segment of the network. The function of the chromatic dispersion compensator is to undo the pulse distortion caused by propagation through the fiber optic network 
   Chromatic dispersion compensator devices can be broadly classified as either single or multi-channel, and either fixed or tunable. Single channel devices compensate chromatic dispersion for a single optical channel, while multi-channel devices operate simultaneously on a plurality of channels. For fixed chromatic dispersion compensators, the amount of chromatic dispersion is fixed at the time of manufacture or installation, while for tunable dispersion compensators, the amount of dispersion may be dynamically adjusted during operation of the network. 
   For WDM fiber optic systems, it is desirable to have multi-channel dispersion compensators, in order to avoid the cost and complexity of demultiplexing the WDM channels and routing each channel through a separate single channel dispersion compensator. 
   In general, the required amount of chromatic dispersion compensation may vary from one WDM channel to another, due for example to the variation of chromatic dispersion with wavelength for optical fibers, or due to a different routing through the fiber optic network for different optical channels. The required amount of chromatic dispersion compensation may also vary with time, due for example to changes in the chromatic dispersion of the fiber links with ambient temperature, or due to dynamic re-routing of optical channels through the network. Thus, it is desirable to have a chromatic dispersion compensator that can impart separately and dynamically adjustable amounts of compensation to each channel. 
   U.S. Pat. No. 5,166,818 issued to Chase et al. discloses a dispersion compensating device based on the principle of spatially separating the frequency components of a single optical channel, applying a phase correction to the frequency components, then recombining the frequency components. The application of this device is limited, since it operates only on a single optical channel, and because the optical passband narrows as the amount of chromatic dispersion increases. 
   U.S. Pat. No. 6,392,807 issued to Barbarossa et al. discloses a tunable chromatic dispersion compensator based on the Virtually Imaged Phased Array (VIPA). This device is capable of simultaneously compensating chromatic dispersion for a plurality of channels, but it is limited in application by the fact that it cannot adjust the chromatic dispersion of each channel separately. Instead, the tuning mechanism adjusts the chromatic dispersion of all channels together. 
   It is an object of the present invention to provide a chromatic dispersion compensator that would perform simultaneous chromatic dispersion compensation for multiple channels, with separately adjustable compensation for each channel. A method for widening and flattening the optical passband of such a device is also envisaged. 
   SUMMARY OF THE INVENTION 
   In accordance with one aspect of the invention, herein denoted as a “single pass” version, there is provided a chromatic dispersion compensator comprising: a dispersive means for spatially separating an input optical signal into spatially spaced frequency components, and a plurality of separate phase shifters, each disposed for imparting a phase shift to a channel containing a range of the spatially spaced frequency components. The compensator may further have means for recombining the spatially spaced frequency components into a single output signal. 
   The plurality of phase shifters may be embodied by a MEMS mirror array or by lenses. 
   The mirrors in the array may be deformable mirrors. Control means may be provided for adjusting the shape and position of the deformable mirrors. Alternatively, the mirror array may comprise fixed mirrors. 
   In one embodiment, the dispersive means is a diffraction grating, either transmissive or reflective. The reflective grating may have a concave shape to facilitate the focusing of the diffracted light beams. 
   Collimating means, e.g. a lens or a mirror may be provided for directing the input signal to the diffraction grating (dispersive means). 
   The compensator may further comprise a focusing means for focusing the separated frequency components onto the separate phase shifters. 
   In another aspect of the invention, denoted as a “dual-pass” compensator, a chromatic dispersion compensator comprises:
         an input port for inputting an input optical signal,   a first dispersive means optically coupled for spatially separating the input optical signal into spatially spaced frequency components,   at least one phase shifter optically coupled for imparting a phase shift to a range of the spatially spaced frequency components,   a second dispersive means optically coupled for recombining the spatially spaced frequency components into a first output signal,   a retroreflecting means coupled to redirect the first output signal back to the second dispersive means to undergo a second pass to the at least one phase shifter and a second pass to the first dispersive means to produce a second output signal, and   an output port for outputting the second output signal,   wherein the arrangement is such that an input signal is directed to the first dispersive means, the spaced frequency components are directed to the at least one phase shifter, the phase-shifted components are directed to the second dispersive means to produce a first output signal which is redirected by the retroreflecting means for a second pass to the second dispersive means, the phase shifter, the first dispersive means and to the output port.
 
The first and second dispersive means may be a single dispersive means as shown in  FIG. 7   a  or may be separate dispersive means  16   a  and  16   b  as shown in  FIG. 7   b.  
 
The at least one phase shifter may be a plurality of separate phase shifters. Each separate phase shifter may be adapted for imparting a phase shift to a channel containing a range of the spatially spaced frequency components, independently of the other phase shifters.
 
The retroreflecting means may be a mirror (flat or spherical) or a prism.
       

   According to the invention, two configurations of multi-channel chromatic dispersion compensator devices are provided. The two configurations are referred to as “single pass” and “dual pass” devices. 
   The “single pass” device consists generally of a means of collimating an input optical beam received from an optical fiber (e.g. with a spherical mirror), spatially separating the optical frequency components of the beam (e.g. with a diffraction grating), focusing these sub beams of different frequency components (e.g. with a spherical mirror) onto an array of phase filters (herein also termed “phase shifters”), arranged such that there is one phase filter element for each channel or group of adjacent channels, recollimating the sub-beams (e.g. with a spherical mirror) after the phase filters, recombining the frequency components into a single beam (e.g. with a diffraction grating), and focusing the beam into an optical fiber (e.g. with a spherical mirror). Each phase filter in the array is designed to generate a frequency dependent phase shift across one optical channel or group of adjacent optical channels, such that the phase shift substantially cancels a phase distortion in the input optical signal. This phase shift arises from a variation of the optical path length of the phase filter element with position along the dispersion direction. Each phase filter may be separately and dynamically adjustable using various control means. 
   The dual pass configuration is similar to the single pass configuration, except that after the frequency components are recombined (e.g. by a grating), they are retro-reflected (e.g. by a plane mirror perpendicular to the beam). The light beams then retrace their path through the device, with a second separation into frequency components, a second focusing onto the phase filter (phase shifter) array, a second recombination of the frequency components into a single beam, and finally focusing back into an optical fiber. Compared to the single pass device, the dual pass configuration doubles the phase shift, and cancels an angular error that causes an excess coupling loss into the output optical fiber. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be described in more detail by way of the following description in conjunction with the drawings, in which like reference numerals denote like elements throughout the figures, and in which: 
       FIG. 1  is a schematic diagram of a preferred embodiment of a chromatic dispersion compensator device in which light is reflected once from an array of phase shifters, showing representative light paths from an input optical fiber to the array of phase shifters, 
       FIG. 2  is a more detailed cross-sectional view of a preferred embodiment of the phase shifter array, in which the phase shifters are deformable membrane mirrors, 
       FIG. 3  is a schematic illustration of optical ray paths at the reflective phase shifters, 
       FIG. 4  is a schematic diagram of the preferred embodiment of  FIG. 1 , showing representative light paths for light returning from the array of phase shifters to the optical fiber, 
       FIG. 5  is a schematic diagram of a preferred embodiment of a chromatic dispersion compensator device in which light is reflected twice from an array of phase shifters, showing representative light paths from an input optical fiber to the array of phase shifters, and then back to a retro-reflector, 
       FIG. 6  is a schematic side-view diagram of the embodiment of  FIG. 5 , showing light paths for the first reflection from the phase shifter array, 
       FIG. 7   a  is a schematic side-view diagram of the embodiment of  FIG. 5 , showing light paths at the retro-reflector, 
       FIG. 7   b  is a schematic side-view diagram similar to  FIG. 7   a , wherein two separate dispersive means are utilized, 
       FIG. 8  is a plot of measured optical transmission and group delay for an experimental version of the preferred embodiment of a chromatic dispersion compensator device in which light is reflected once from a phase shifter array, 
       FIG. 9  is a plot of measured optical transmission and group delay for an experimental version of the preferred embodiment of a chromatic dispersion compensator device in which light is reflected twice from a phase shifter array, 
       FIG. 10  is a schematic diagram of an alternative embodiment of the chromatic dispersion compensator, wherein the spherical mirror, reflective grating, and reflective phase shifters of  FIG. 1  are replaced with transmissive elements, 
       FIG. 11  is a schematic diagram of an alternative embodiment of the chromatic dispersion compensator, wherein the spherical mirror and grating of  FIG. 1  are replaced with a concave reflective grating, and 
       FIG. 12  is a schematic diagram of an alternative embodiment of the chromatic dispersion compensator wherein the flat mirror is replaced with a prism. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment. 
   Single-pass Dispersion Compensator 
   In an embodiment of the single pass chromatic dispersion compensator, illustrated in  FIG. 1 , optical signals enter the device from an optical fiber  10 . The beam waist size of the light beam  40  from the input fiber is expanded with a micro-lens  12  or a plurality of lenses. The optical beam  42  from the micro-lens  12  is substantially collimated with a spherical mirror  14 , and directed toward a diffraction grating  16 . The collimated beam  44  incident on the diffraction grating  16  is spread into a plurality of reflected collimated sub-beams  46  of the different optical frequency components of the incident beam, with an angular separation between sub-beams of different frequency components. This angular spreading of optical frequency components is referred to as an “angular dispersion”. The spherical mirror  14  transforms the plurality of collimated sub beams  46  to a plurality of focused sub-beams  48  that converge to a plurality of focused spots  49 . The focused spots  49  are located substantially along a line, so the spreading of focused spots of different frequency components is referred to as a “linear dispersion”, and the direction of the line is referred to as the “linear dispersion direction”  80 . A reflective MEMS membrane array  30 , hereinafter referred to as the “MEMS array”, is disposed at or near the line of focused spots  49 . The distance from the grating  16  to the spherical mirror  14  is at least approximately equal to the focal length of the spherical mirror  14 , so that there is little or no angular spread between the focused sub-beams  48  incident on the MEMS array  30 . 
   Referring now to  FIG. 2 , the MEMS array  30  consists of a plurality of flexible reflective membranes  32 , each attached to anchor points  34  along the two sides transverse to the linear dispersion direction. The cross-sectional profile of each membrane  32  is substantially constant along a direction transverse to the linear dispersion direction. The MEMS array  30  is positioned such that the focused spots corresponding to the channel center frequencies are located at least approximately at the centers of the membranes, and the anchor points  34  are between the channel centers. Electrodes  36  are located under each membrane  32 , and the membranes  32  are separately and controllably deformed by varying the voltage on the electrodes  36  to adjust the electrostatic attraction between membrane  32  and electrode  36 . A control means  38  is electrically coupled to the electrodes  36  and membranes  32  to effect the controllable deformation. The anchor points  34  and electrodes  36  are supported by a substrate  37 . 
   The function of the MEMS array  30  is to impart a frequency dependent phase shift across each channel. The amount of phase shift can be derived from the cross sectional profile of the MEMS membrane  32 , as illustrated in  FIG. 3 . Let x be a linear coordinate along the linear dispersion direction, and let z be a linear coordinate along the direction of incidence of the focused sub-beams  48 . Consider a reference plane  70  located just above the MEMS membrane  32 , and perpendicular to z. Let the function h(x) be the distance in the z direction from the reference plane  70  to the MEMS membrane  32 . An optical ray  72  of wavelength λ 1  incident on the reference plane  70  at position x=x 1  will travel a distance h(x 1 ) from the reference plane  70  to the MEMS membrane  32 . At the MEMS membrane  32 , the incident ray  72  will be reflected through an angle 2θ(x 1 ), where θ(x)=dh(x)/dx is the local slope of the MEMS membrane  32  at x=x 1 . The reflected ray  74  will then travel a distance h(x 1 )/cos(2θ(x 1 )) from the MEMS membrane  32  back to the reference plane  70 . The optical phase of the reflected ray  74  at the reference plane  70  relative to the optical phase of the incident ray  72  at the reference plane  70  is then (2πnh(x 1 )λ 1 )*(1+1/cos(2θ(x 1 ))), where n is the refractive index of the medium between the reference plane  70  and the MEMS membrane  32 . The angle 2θ is typically small, so the quantity 1/cos(2θ) is approximately equal to 1, and the optical phase shift can be approximately written as 4πnh(x 1 )/λ 1 . 
   Thus, for a frequency component incident at position x, the phase shift is proportional to h(x), the group delay is proportional to the first derivative dh(x)/dx, and the chromatic dispersion is proportional to the second derivative d 2 h(x)/dx 2 . For compensation of chromatic dispersion across one channel, the preferred membrane  32  profile has a constant second derivative, i.e. a parabolic profile. However, an arbitrary phase shift as a function of frequency can be generated with an appropriate MEMS membrane  32  profile h(x). 
   The path of a sub-beam from the input fiber to the MEMS array will be referred to as the “nominal path”. In  FIG. 1 , the nominal path for a sub-beam consists of the sequence of beam paths of  40 ,  42 ,  44 ,  46 , and  48 . The angle 2θ(x) between the incident and reflected sub-beams at the MEMS array will be referred to as the “angular deviation”. A sub-beam traveling from the optical fiber to the MEMS array will be described as traveling in the “forward” direction, and a sub-beam traveling from the MEMS array to the optical fiber will be described as traveling in the “backward” direction. 
   Referring now to  FIG. 4 , the plurality of linearly dispersed sub-beams  58  reflected from the MEMS array  30  are re-collimated by the spherical mirror  14 , and the re-collimated sub-beams  56  are directed towards the grating  16 . The spherical mirror  14  converts the linear dispersion of focused sub-beams  58  back to an angular dispersion of collimated sub-beams  56 . However, the angular deviation of each backward traveling sub-beam  58  relative to its nominal path results in a linear displacement of the collimated sub-beam  56  relative to its nominal path. Thus, between the spherical mirror  14  and the grating  16 , each backward traveling sub-beam  56  is parallel to but possibly displaced from its nominal path. 
   The plurality of angularly dispersed collimated sub-beams  56  incident on the grating  16  is transformed to a plurality of parallel but linearly displaced collimated sub-beams  54  upon reflection from the grating  16 . The plurality of sub-beams  52  reflected from the spherical mirror  14  is focused into the optical fiber  10  by the combination of the spherical mirror  14  and micro-lens  12 . The angle of incidence of each focused sub-beam  50  into the optical fiber  10  is proportional to the angle of deviation of the reflected sub-beam  58  at the MEMS array  30 . 
   An optical circulator  20  is disposed to separate the backward traveling output light from the forward traveling input light in the optical fiber  10 . The output light is directed by the circulator  20  into an output optical fiber  22 . 
   There is an excess coupling loss for sub-beams  50  that are focused into the optical fiber  10  at a non-zero angle relative to the nominal path, and the coupling loss increases as a function of the angle of incidence into the fiber  10 . For a parabolic MEMS membrane  32  profile h(x), this excess coupling loss results in a rounded optical transmission versus wavelength characteristic. The optical transmission versus wavelength across one channel will be hereinafter referred to as the “channel shape”. Furthermore, the bandwidth of the optical transmission decreases as the magnitude of the curvature of the MEMS membrane  32  is increased, i.e. as the magnitude of the chromatic dispersion increases. 
   This foregoing specification has described an embodiment of the invention using reflective optical elements to perform the functions of collimating, dispersing, focusing, and phase shifting the light. Any or all of these functions may instead be performed with transmissive optical elements.  FIG. 10  illustrates an embodiment of the invention wherein the collimating and focusing means are lenses  90  instead of spherical mirrors  14 , the dispersive means is a transmissive diffraction grating  92  instead of a reflective diffraction grating  16 , and the plurality of phase shifters is an array of lenses  94  instead of an array of mirrors  30 . A flat mirror  96  is further disposed after the array of lenses  94  to reflect the light back through the lens array  94 , the lens  90 , diffraction grating  92 , lens  90 , and micro-lens  12  to the optical fiber  10 . The phase shift due to the lens array  94  arises from a variation along the dispersion direction  80  of the optical thickness of the lens array  94 . The optical thickness of the lens array  94  is equal to the physical thickness of the lens array  94  times the refractive index of the optical material in the lens array  94 . 
   In another embodiment, the spherical mirror  14  and reflective diffraction grating  16  may be replaced with a reflective concave diffraction grating  98 , as illustrated in  FIG. 11 . The concave grating  98  both disperses and focuses the incident light beam  42  to a plurality of focused spots  49  corresponding to the optical frequency components of the incident beam  42 . 
   An experimental single pass dispersion compensator device was built with a 120 mm focal length spherical mirror, 1200 lines/mm reflective diffraction grating, and an array of 20 deformable MEMS membrane reflectors. Optical transmission and group delay of this device were measured with a commercial test set. Measured optical transmission and group delay for one of the 20 channels at two different MEMS electrode voltages are shown in  FIG. 8 , where the values corresponding to the two different electrode voltage settings are illustrated as solid and dotted lines. A variation of the chromatic dispersion (slope of the group delay vs. wavelength) with applied voltage is evident in  FIG. 8 . Also, a rounded channel shape and narrowing of the optical transmission bandwidth with increasing chromatic dispersion are evident in  FIG. 8 . 
   Dual Pass Dispersion Compensator 
   The narrow bandwidth at larger chromatic dispersion settings limits the usable chromatic dispersion tuning range of the single pass device. Therefore, we disclose an improved multi-channel chromatic dispersion compensator with widened and flattened channel shape, and increased chromatic dispersion tuning range relative to the single pass chromatic dispersion compensator. The improved chromatic dispersion compensator is referred to as a “dual pass” device, since the optical signal is reflected twice from the MEMS array. 
   In an embodiment of the dual pass chromatic dispersion compensator, illustrated in  FIG. 5 , the optical path from the input optical fiber  10  to the MEMS array  30  is similar to the corresponding optical path in the single pass device illustrated in  FIG. 1 . For clarity, the optical path of only one representative sub-beam is shown in  FIG. 5 . Where required, the illustrated optical path should be understood to represent a plurality of different paths corresponding to sub-beams of different frequency components. 
   For the dual pass device illustrated in  FIG. 5 , the MEMS array  30  is tilted slightly in a direction transverse to the linear dispersion direction  80 , such that the plurality of focused sub-beams  68  reflected from the MEMS array  30  is redirected with an angular displacement relative to the plurality of incident sub-beams  48 , with the direction of said angular displacement transverse to the linear dispersion direction  80 . This is illustrated in the side view of  FIG. 6 . 
   Referring again to  FIG. 5 , the plurality of sub-beams  68  reflected from the MEMS array  30  is re-collimated by spherical mirror  14 , and the plurality of collimated sub-beams  66  is directed back toward the grating  16 . The spherical mirror  14  converts the linear dispersion of focused spots  49  back to an angular dispersion of collimated sub-beams  66 . Reflection from the grating  16  removes the angular dispersion, resulting in a plurality of parallel and collimated sub-beams  64 . As shown in  FIG. 7 , the plurality of parallel and collimated sub-beams  64  lie in a plane that is spatially separated from the forward traveling input beam  44 . In the illustration of  FIG. 7 , this separation is in the vertical direction. The spatial separation is due to the aforementioned tilt of the MEMS array  30 . 
   A retro-reflecting element  18  is disposed between the grating  16  and spherical mirror  14  such that the plurality of parallel backward traveling sub-beams  64  is redirected by the retro-reflector, without blocking or otherwise redirecting the forward traveling input beam  44 . The plurality of sub-beams  64  is redirected by the retro-reflector  18  back through the grating  16  and spherical mirror  14  to the MEMS array  30 , such that following a second reflection from the MEMS array  30 , each backward traveling sub-beam is substantially parallel to its nominal path. 
   In a preferred embodiment, the retro-reflecting element  18  is a plane mirror disposed perpendicular to the plurality of backward traveling parallel sub-beams  64  between the grating  16  and the spherical mirror  14 . In this embodiment, each retro-reflected sub-beam retraces its path along  64 ,  66 , and  68  from the retro-reflector  18  back to the MEMS array  30 . Each retro-reflected sub-beam is then reflected from the MEMS array  30  for a second time. For this second reflection from the MEMS array  30 , the angular deviation imparted to each sub-beam is equal in magnitude and opposite in sign to the angular deviation imparted by the first reflection from the MEMS array  30 , such that the two angular deviations mutually cancel and the sub-beam is directed back along its nominal input path after the second reflection from the MEMS array  30 . The phase shift imparted to the sub-beams by the second reflection from the MEMS array  30  is equal in sign and equal in magnitude to the phase shift imparted by the first reflection from the MEMS array  30 . Thus, the phase shift, group delay, and chromatic dispersion of the dual pass device are substantially doubled compared to a single pass. 
   Following the second reflection from the MEMS array  30 , each sub-beam retraces its nominal path back to the optical fiber  10 , following in sequence the optical paths  48 ,  46 ,  44 ,  42 , and  40 . 
   Since the second reflection from the MEMS array  30  substantially cancels the angular deviation imparted by the first reflection from the MEMS array  30 , there is substantially no angular error for the output beam incident along optical path  40  at the optical fiber  10 . As a result, the channel shape is substantially flat-topped for the dual pass device, and the transmission bandwidth is wider for the dual pass chromatic dispersion compensator compared to the single pass chromatic dispersion compensator. The amount of chromatic dispersion obtained with a given MEMS membrane  32  profile h(x) is also doubled for the dual pass device compared to the single pass device. 
   An alternative embodiment of the retro-reflector is shown in  FIG. 12 , wherein the retro-reflector is a prism  19  instead of a flat mirror  18 . 
   An experimental dual pass dispersion compensator device was built with a 120 mm focal length spherical mirror, 1200 lines/mm diffraction grating, and an array of 20 deformable MEMS membrane reflectors. Optical transmission and group delay of this device were measured with a commercial test set. Measured optical transmission and group delay for one of the 20 channels at two different MEMS electrode voltages are shown in  FIG. 9 , where the values corresponding to the two different electrode voltage settings are illustrated as solid and dotted lines. A variation of the chromatic dispersion (slope of the group delay vs. wavelength) with applied voltage is evident in  FIG. 9 . A substantially flat topped channel shape for the dual pass device is evident in  FIG. 9 , and the transmission bandwidth is wider than for the single pass device shown in  FIG. 8 . 
   In the foregoing specification, the invention has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes can be made thereto without departing from the broader spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.