Abstract:
An optical device for receiving input light and for acting on the input light to produce output light includes a first reflector and a second reflector supported in a spaced-apart, confronting relationship with the first reflector such that the input light received by the optical device, at least potentially, undergoes multiple reflections between the first and second reflectors. At least a selected one of the first and second reflectors is configured to subject each one of a plurality of different portions of the input light to one of a plurality of different reflectance values to produce an emitted light passing through at least the selected reflector in a way which is combinable to generate the output light.

Description:
RELATED APPLICATION  
       [0001]    The present application claims priority from U.S. Provisional Application No. 60/299,540, entitled DISPERSION COMPENSATION USING GRADED FILMS, filed Jun. 19, 2001 under 35 U.S.C. §119( e ). 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    The present invention relates to optical devices and, more specifically, to optical devices that enable control of dispersion in optical communication systems.  
           [0003]    The demand for greater bandwidth in optical communications is driving the fiber-optic telecommunications industry to explore technologies to achieve faster transmission speeds and increased capacity. The increase in bandwidth, however, is limited by a number of fundamental factors such as attenuation, noise and dispersion.  1,2  In particular, dispersion is problematic because it distorts and/or broadens the optical pulses used to carry information through the optical communication system, thereby leading to data transmission error, especially in long haul and/or high speed systems.  
           [0004]    Various attempts have been made to control or counteract dispersion in optical communication networks. For example, dispersion compensating fibers (DCFs) are available from companies such as Lucent Technologies/OFS and Corning to provide a negative dispersion across a specific operating band. 1,2  However, since DCFs provide essentially constant negative dispersion, DCFs are generally useful only for dispersion correction at one wavelength at a time. That is, a series of DCFs are needed to control dispersion over the full range of wavelengths used in the optical communication system. Therefore, dispersion compensation solutions based on DCFs tend to be complicated and expensive.  
           [0005]    Another approach to dispersion control is the use of fiber Bragg gratings.  1,2  A fiber Bragg grating includes a chirped Bragg grating or a number of Bragg gratings designed to reflect different wavelengths all formed in a length of fiber so as to provide dispersion compensation on input light. Like DCFs, however, fiber Bragg gratings are limited in the range of wavelengths over which they are effective. Therefore, several gratings are needed to provide dispersion compensation over the optical communication wavelength range. Fiber Bragg gratings can also induce dispersion ripple, which leads to undesirable distortion of the optical signals.  
           [0006]    Still other dispersion compensation schemes involve the use of all-pass filters. 3-6  All-pass filters are optical filters designed to provide phase compensation without affecting the amplitude of input light. 3  For example, in U.S. Pat. No. 6,289,151 B1, Kazarinov et al. (hereinafter, Kazarinov) describes an all-pass filter based on a number of ring resonators in a plurality of feedback loops. The all-pass filter of Kazarinov compensates for optical signal dispersion by applying a frequency-dependent time delay to portions of the optical signal in the feedback loops. The frequency-dependent time delay is provided by cascaded or series ring resonators, each of the ring resonators having a different phase. One problem arises with respect to the all-pass filter of Kazarinov, however, is submitted since a plurality of ring resonators and couplers are needed to provide dispersion compensation over the optical communication bandwidth. Also high manufacturing tolerances are required to ensure balanced performance of the device in compensating the dispersion of optical signal at a range of frequencies.  
           [0007]    As another example of an all-pass filter, J. Ip in U.S. Pat. No. 5,557,468 (hereinafter, Ip) discloses a dispersion compensation device based on a reflective Fabry-Perot etalon. 7  The all-pass filter of Ip includes a Fabry-Perot etalon including two reflectors. Each reflector includes a single uniform reflectance value that is different from the reflectance value of the other reflector so as to provide an input port and a separate output port for monitoring, for example, the frequency of the signal output of the all-pass filter. Again, the range of frequencies over which the all-pass filter of Ip is effective remains limited. Ip suggests the use of two or more Fabry-Perot etalons with dissimilar reflectivity characteristics and offset center frequency response, but it is submitted that the manufacturing tolerances for such a multi-stage cascaded device make the device impractical.  
           [0008]    A Fabry-Perot etalon including a 100% reflectance mirror as one of its reflectors (also known as a Gires-Tournois interferometer) is also used as an all-pass filter. However, since the Fabry-Perot etalon generally provides an output in the form of a series of Gaussian peaks, it is difficult to manufacture a single stage Gires-Toumois ferometer exhibiting the desired phase response over a desired range of wavelengths.  
           [0009]    Still another example of an all-pass filter for dispersion compensation is a thin film-based coupled cavity all-pass (CCAP) filter as discussed, for example, by Jablonski et al. 8  The CCAP filter of Jablonski et al. is essentially a series of interference filters cascaded together. The CCAP filter of Jablonski et al. is similar to the aforedescribed Kazarinov approach in that the CCAP filter consists of two or more cavities disposed between reflectors and cascaded together to form a single filter. The thin film-based CCAP filter includes a plurality of alternating low index and high index thin films designed to form a stack of reflector sections separated by low index “cavity” sections. The thin film configuration allows the device to be compact compared to the use of a series of adjacent Fabry-Perot filters. However, the design of the thin film-based CCAP filter including more than two cavities is submitted to be mathematically problematic and, further, since the number of materials available for use as the low index and high index materials is limited, the filter is difficult to implement as a practical device.  
           [0010]    The present invention provides an optical device for dispersion compensation which serves to reduce or eliminate the foregoing problems in a highly advantageous and heretofore unseen way and which provides still further advantages.  
         REFERENCES  
         [0011]    1. K. Slocum et al., “Dispersion Compensators,” Wit SoundView Corp. Report, May 29, 2001.  
           [0012]    2. J. Jungjohann et al., “Will Dispersion Kill Next Generation 40 Gigabit Networks?” CIBC World Markets Equity Research, Jun. 19, 2001.  
           [0013]    3. R. Kazarinov et al., “All-Pass Optical Filters,” U.S. Pat. No. 6,289,151 B1, issued Sep. 11,2001.  
           [0014]    4. G. Lenz et al., “Optical Communication System including Broadband All-Pass Filter for Dispersion Compensation,” U.S. Pat. No. 6,259, 847 B1, issued Jul. 10, 2001.  
           [0015]    5. C. K. Madsen et al., “Integrated Optical Allpass Filters for Dispersion Compensation,” OSA TOPS vol. 29,  WDM Components , pp. 142-149.  
           [0016]    6. G. Lenz et al., “Optical Filter Dispersion in WDM Systems: A Review,” OSA TOPS vol. 29,  WDM Components , pp. 246-253.  
           [0017]    7. J. Ip, “Chromatic Dispersion Compensation Device,” U.S. Pat. No. 5,557,468, issued Sep. 17, 1996.  
           [0018]    8. M. Jablonski et al., “The Realization of All-Pass Filters for Third-Order Dispersion Compensation in Ultrafast Optical Fiber Transmission Systems,”  Journal of Lightwave Technology , vol. 19, no. 8, pp. 1194-1205, Aug. 2001.  
         SUMMARY OF THE INVENTION  
         [0019]    As will be disclosed in more detail hereinafter, there is disclosed herein an optical device for receiving input light and for acting on the input light to produce output light. The optical device includes a first reflector and a second reflector supported in a spaced-apart, confronting relationship with the first reflector such that the input light received by the optical device, at least potentially, undergoes multiple reflections between the first and second reflectors. At least a selected one of the first and second reflectors is configured to subject each one of a plurality of different portions of the input light to one of a plurality of different reflectance values to produce an emitted light passing through at least the selected reflector in a way which is combinable to generate the output light.  
           [0020]    In another aspect of the invention, there is disclosed a dispersion compensation module including the aforedescribed optical device.  
           [0021]    In still another aspect of the invention, a method for use in an optical device for receiving input light and for acting on the input light to produce output light is disclosed. The method includes the steps of supporting a first reflector and a second reflector in a spaced-apart, confronting relationship and configuring the first and second reflectors such that the input light received by the optical device, at least potentially, undergoes multiple reflections between the first and second reflectors. The method also includes the step of configuring at least a selected one of the reflectors to include a plurity of different reflectance values. The method further includes the step of subjecting a plurality of different portions of the input light, during the multiple reflections, to a plurality of different reflectance values at a selected one of the reflectors to produce an emitted light passing through the selected reflector in a way which is combinable to generate the output light. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0022]    The present invention may be understood by reference to the following detailed description taken in conjunction with the drawings briefly described below.  
         [0023]    [0023]FIG. 1A is a computer generated graph of a transmittance peak of a single cavity Fabry-Perot filter having opposing reflectors, each of which includes a uniform reflectance value.  
         [0024]    [0024]FIG. 1B is a computer generated graph of a reflectance trough of the single cavity Fabry-Perot filter shown in FIG. 1A.  
         [0025]    [0025]FIG. 1C is a computer generated graph of a group delay peak corresponding to the transmittance peak of the single cavity Fabry-Perot filter shown in FIG. 1A.  
         [0026]    [0026]FIG. 1D is a computer generated graph of a group delay peak corresponding to the reflectance trough of the single cavity Fabry-Perot filter shown in FIG. 1B.  
         [0027]    [0027]FIG. 2A is a computer generated graph of the composite transmittance profile of a single cavity Fabry-Perot device including a gradient reflector of the present invention, shown here to illustrate the composite transmittance of a including three reflectance regions.  
         [0028]    [0028]FIG. 2B is a computer generated graph of a group delay profile corresponding to the transmittance profile of the single cavity Fabry-Perot device including the gradient reflector shown in FIGS. 2A .  
         [0029]    [0029]FIG. 3A is a composite of the computer generated graphs of the transmittance profile of each of six reflectance regions of a single cavity Fabry-Perot device including a gradient reflector with six reflectance regions, shown here to illustrate the composition of a sawtooth function with a positive slope transmittance profile.  
         [0030]    [0030]FIG. 3B is a composite of the computer generated graphs of the transmittance profile of each of six reflectance regions of another single cavity Fabry-Perot device including a gradient reflector with six reflectance regions, shown here to illustrate the composition of a sawtooth function with a negative slope transmittance profile.  
         [0031]    [0031]FIG. 3C is a composite of the computer generated graphs of the transmittance profile of each of six etalon thickness regions of a single cavity Fabry-Perot device including an etalon with six thickness regions, shown here to illustrate the absence of slope variation in the transmittance profile.  
         [0032]    [0032]FIG. 4A is a schematic diagram of a gradient reflector with a step function reflectance profile.  
         [0033]    [0033]FIG. 4B is a schematic diagram of a gradient reflector with a continuous wedge reflectance profile.  
         [0034]    [0034]FIG. 4C is a schematic diagram of a gradient reflector with a non-uniform step reflectance profile.  
         [0035]    [0035]FIG. 4D is a schematic diagram of a gradient reflector with a reflectance profile which varies along two dimensions of the reflector.  
         [0036]    [0036]FIG. 4E is a schematic diagram of a circular gradient reflector with a radially-varying reflectance profile.  
         [0037]    [0037]FIG. 4F is a schematic diagram of a circular gradient reflector with a reflectance profile which varies around the circumference of the reflector.  
         [0038]    [0038]FIG. 4G is a schematic diagram of a single cavity Fabry-Perot device with a gradient reflector of the present invention, shown here to illustrate a possible device configuration including the gradient reflector with the step function reflectance profile of FIG. 4A.  
         [0039]    [0039]FIG. 5A is a schematic diagram of an optical configuration including the single cavity Fabry-Perot device with a gradient reflector of the present invention, the Fabry-Perot device being used as an dispersion compensator.  
         [0040]    [0040]FIG. 5B is a schematic diagram of an optical configuration including a balanced single cavity Fabry-Perot device with the gradient reflector of the present invention and a circulator.  
         [0041]    [0041]FIG. 6A is a schematic diagram of an optical configuration including an unbalanced single cavity Fabry-Perot device with the gradient reflector of the present invention and a circulator.  
         [0042]    [0042]FIG. 6B is schematic diagram of an optical configuration including an unbalanced single cavity Fabry-Perot device with the gradient reflector of the present invention, a high reflector and a circulator to provide a signal output as well as an additional monitoring output.  
         [0043]    [0043]FIG. 7 is a schematic diagram of an optical configuration including a single cavity Fabry-Perot device with the gradient reflector of the present invention but without the need for the use of a circulator to provide the output.  
         [0044]    [0044]FIG. 8 is a schematic diagram of an alternative optical configuration including a single cavity Fabry-Perot device with the gradient reflector of the present invention using a GRIN lens rather than a circulator to provide the output.  
         [0045]    [0045]FIG. 9 is a schematic diagram of an optical configuration in which the single cavity Fabry-Perot device with the gradient reflector of the present invention may be used as a dispersion compensation module, the optical configuration including an interleaver to increase the useful flat region group delay response.  
         [0046]    [0046]FIG. 10 is a schematic diagram of another optical configuration in which the single cavity Fabry-Perot device with the gradient reflector of the present invention is used as a dispersion compensation module, the optical configuration including multiple dispersion compensation modules in tandem to modify the total chromatic dispersion experienced by the input light.  
         [0047]    [0047]FIG. 11A is a schematic diagram of an optical configuration including a tunable single cavity Fabry-Perot device with the gradient reflector of the present invention.  
         [0048]    [0048]FIG. 11B is a schematic diagram of another optical configuration including a tunable single cavity Fabry-Perot device with the gradient reflector of the present invention.  
         [0049]    [0049]FIG. 11C is a schematic diagram of an alternative optical configuration including a tunable single cavity Fabry-Perot device with the gradient reflector of the present invention.  
         [0050]    [0050]FIG. 11D is a schematic diagram of still another configuration including a tunable single cavity Fabry-Perot device with the gradient reflector of the present invention.  
         [0051]    [0051]FIG. 12 is a schematic diagram of an optical configuration including a single cavity Fabry-Perot device with the gradient reflector of the present invention, in which the gradient reflector is configured on a curved surface. 
     
    
     DETAILED DESCRIPTION  
       [0052]    The following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and its requirements. Various modifications to the described embodiments will be readily apparent to those skilled in the art and the generic principles herein may be applied to other embodiments. Thus, the present invention is not intended to be limited to the embodiment shown but is to be accorded the widest scope consistent with the principles and features described herein.  
         [0053]    As mentioned in the above Background section, the single stage Fabry-Perot (FP) filter is not able to provide a smooth phase response profile over a range of wavelengths because the FP filter provides an output in the form of a series of Gaussian peaks. Although several FP filters (or equivalents thereof, such as the CCAP filters) may be cascaded together, the fabrication and alignment tolerances required in forming such a cascaded device is submitted to makes the device impractical. In contrast, the present invention achieves remarkable advantages by providing an effect equivalent to the cascaded interference filter device using only a single cavity.  
         [0054]    The optical device of the present invention is based on the single cavity FP configuration. Turning now to the drawings, wherein like components are indicated by like reference numbers throughout the various figures where possible, attention is immediately directed to FIGS.  1 A- 1 B, serving as a foundation and framework in understanding the teachings of the present invention and its associated advantages. In FIG. 1A, a transmittance peak  10  of a single cavity FP filter is shown. As mentioned above, the transmittance peak is Gaussian in shape. A corresponding reflectance trough  20  is shown in FIG. 1B (In a Gires-Toumois configuration, the transmittance and reflectance curves would be added together to provide an ideal total output of 100%). Transmittance peak  10  of FIG. 1A and reflectance trough  20  of FIG. 1B are mirror images of one another, assuming the absence of absorption in the FP filter.  
         [0055]    The corresponding phase response (i.e., group delay vs. wavelength) in transmission and reflection are shown in FIGS. 1C and 1D, respectively. Like the transmittance peak shown in FIG. 1A, phase response peak  30  shown in FIG. 1C is essentially Gaussian in shape. Although phase response peak  40  shown in FIG. 1D appears to have a negative value surrounding the center of the peak, the discontinuity in the peak shape is merely a computational artifact, and the actual phase response peak is a positive peak. Comparing the phase response in transmission and reflection, it can be noted that the transmitted phase and the reflected phase are not mirror images of each other. In fact, the phase response is a positive phase delay for both transmitted and reflected light. It is further noted that the general shape of the phase response peak in both the transmitted and reflected light “follows” the shape of the transmittance peak.  
         [0056]    It is recognized in the context of the present invention that this correspondence between the transmittance peak shape and the phase response is significant because this correspondence implies that, by manipulating the shape of the transmittance peak of the single cavity FP device, the shape of the phase response of the device can also be customized. In other words, when the FP configuration is used as a transmission device or as an all-pass Gires-Tournois filter, it is recognized herein that the phase response of the device corresponds in shape to the transmittance profile of the device. Therefore, the phase response of the device may be tailored by altering the transmittance profile.  
         [0057]    Chromatic dispersion can be defined as the first order derivative of the phase response as a function of wavelength. Therefore, it is further recognized that the chromatic dispersion characteristics of the device may consequently be manipulated by changing the transmission characteristics, and thereby the phase response, of the device. For example, to achieve a ripple-free chromatic dispersion profile, the group delay as a function of wavelength should be a straight line. If the slope of the phase response is linear and positive, the device would exhibit a constant positive chromatic dispersion. Similarly, if the slope of the phase response is negative, the device would yield a constant negative chromatic dispersion.  
         [0058]    It is important to appreciate that the transmittance profile of an FP device may be manipulated in a number of ways. For example, the reflectivity of the reflectors which define the cavity may be increased or decreased to change the shape and periodicity of the transmittance peaks. Also, the cavity length (or the distance between the reflectors) may be altered. By mathematical calculations, it can be shown that, for a given reflectivity, increased cavity length leads to reduced spacing between the transmittance peaks and increased group delay experienced by transmitted and reflected light. Also, for a given cavity length, increased mirror reflectivity leads to sharper transmittance peaks and increased group delay experienced by transmitted and reflected light. Any suitable method of altering the transmittance profile of a Fabry-Perot device in order to manipulate the phase response of the device, some of which methods are described herein, is considered to fall within the scope of the present invention.  
         [0059]    Any linear function, such as a desired linear group delay function, is represented by a straight line. In general, this straight line can be broken down into a staircase function such that integration of the staircase function, at least to an approximation, yields the straight line. A sawtooth function, for example, can be considered a series of staircase functions. As described above, a single cavity FP filter exhibits a transmittance profile consisting of a series of discrete peaks. Clearly, these peaks, one of which is seen in FIG. 1A, are not representative of a staircase or sawtooth function. Applicants have recognized, however, that manipulation and adding of such discrete functions yet to be described may be used to attain, for example, a sawtooth function. Remarkably, a substantially linear transmittance profile, and thereby a linear phase response, can be achieved using an FP device by adding the transmittance peaks in such a way that the total, overall transmittance function is in the form of a staircase or sawtooth function.  
         [0060]    It is further recognized herein that it is possible achieve this substantially linear transmittance profile by designing at least one of the reflectors forming the cavity to include a gradient reflectance profile. In other words, one of the reflectors is configured to have two or more reflectance regions with different reflectance values. When light is incident on such a single cavity FP device including a gradient reflector, different portions of the incident light encounter different reflectance regions. Consequently, the incident light encounters different interference conditions within the FP device, depending on which of the different reflectance regions on which the light is incident, and, consequently, light emanating from the different reflectance regions interfere to result in an output light. If, for example, each reflectance region is designed such that the resulting peaks in the transmittance profile of that reflectance region are offset with respect to the peaks in the transmittance profiles of other reflectance regions, then it the aforedescribed staircase or sawtooth function is achieved using only a single cavity FP device with such a gradient reflector. The single cavity FP device with the gradient reflector of the present invention is referred to as an gradient FP device hereinafter.  
         [0061]    To illustrate the above concept of tailoring the phase response of the single cavity FP device by manipulating the transmittance profile of the device, attention is directed to FIGS. 2A and 2B. FIG. 2A shows a composite transmittance profile  50  of an gradient FP device with three reflectance regions. The reflectance regions yield transmittance profiles  52 ,  54  and  56 , respectively, such that composite transmittance profile  50  is essentially a sawtooth function with a positive slope. In other words, by combining the transmittance profiles of the three reflectance regions of this FP gradient device, a composite transmittance profile in the form of a sawtooth function is achieved. FIG. 2B shows a phase response (group delay vs. wavelength) profile  60  corresponding to composite transmittance profile  50  of FIG. 2A. Like composite transmittance profile  50  of FIG. 2A, phase response profile  60  resembles a sawtooth function with substantially similar periodicity. That is, as asserted earlier, FIG. 2B demonstrates that the phase response of the gradient FP device “follows” the transmittance profile of that device such that, by altering the transmittance profile, the phase response of the device may be tailored as desired.  
         [0062]    As a further example, a gradient FP device with six reflectance regions in one of the reflectors is described. The transmittance peaks from each of the six reflectance regions are overlaid in a composite graph shown in FIG. 3A. The transmittance profiles in FIG. 3A have been calculated assuming that the reflectance regions are formed of quarterwave stacks, wherein one of the layers in one of the reflecting stacks is reduced in optical thickness from one quarterwave to 0.8, 0.6, 0.4, 0.2 and 0 quarterwave at a design wavelength of 1550 nm (shown as curves  70 ,  72 ,  74 ,  76 ,  78  and  80 , respectively). That is, the reflecting stack exhibits different reflectance values depending on the thickness of the altered layer, thereby producing different transmittance profiles at the reflectance regions. As indicated in FIG. 3A, the transmission peaks decrease in transmitted amplitude and increase in peak full width half maximum (FWHM) values while the center wavelength of the peaks move progressively to shorter wavelengths as the altered layer thickness is reduced. When the transmittance profiles from the six reflectance regions are added together, they cooperate to yield a sawtooth function in the total transmittance. Accordingly, the total group delay profile will be a corresponding sawtooth function, resulting in a positive value of chromatic dispersion.  
         [0063]    An alternative example is shown in FIG. 3B, illustrating the overlaid transmittance peaks from six reflectance regions of an gradient FP device in which one of the layers in one of the reflecting stacks is increased in optical thickness from one quarterwave to 1.2, 1.4, 1.6, 1.8 and 2.0 quarterwave at the design wavelength of 1550 nm (shown as curves  90 ,  92 ,  94 ,  96 ,  98  and  100 , respectively). Again, the reflecting stack exhibits different reflectance values depending on the thickness of the altered layer such that, in this case shown in FIG. 3B, the center wavelength of the transmission peaks move progressively to longer wavelengths as the altered layer thickness is increased. The transmittance peaks also decrease in transmitted amplitude and increase in peak FWHM values as the layer thickness is increased. Consequently, when the transmittance peaks from the six reflectance regions are combined, the total transmittance profile is a sawtooth function, and the corresponding total group delay profile will also be a sawtooth function, this time resulting in a negative chromatic dispersion.  
         [0064]    It is notable that the tailoring of the transmittance profile, and thereby the group delay profile, in the aforedescribed manner involves the manipulation of the amplitude as well as the position of the center wavelength of the transmittance peaks. For instance, the center wavelength positions of the transmittance peaks may be altered, for example, by changing the thickness of the etalon portion of a Fabry-Perot device (e.g., by using a wedge shaped etalon) without changing the reflectance of the reflectors. The computer generated transmittance profiles of a single cavity Fabry-Perot device with six etalon thickness regions are shown in FIG. 3C. Curves  110 ,  112 ,  114 ,  116 ,  118  and  120  are calculated transmittance profiles of this device as the etalon thickness is reduced by increments of 0.2 quarterwaves at the design wavelength of 1550 nm, respectively, while the reflectance values of the reflectors in the device are kept constant. As can be seen in FIG. 3C, although the peak position moves toward shorter wavelengths as the etalon thickness is reduced, the peak amplitudes and the FWHM values do not change. Therefore, the total transmittance profile will not be a sawtooth function, and the resulting device would not affect chromatic dispersion.  
         [0065]    FIGS.  4 A- 4 G illustrate several possible gradient reflector configurations and a possible Fabry-Perot configuration. As shown in FIG. 4A by a reflector  130 , the gradient reflector may include a number of discrete reflectance regions  132 A- 132 F in which, for example, the reflectance values increase or decrease in a stepwise fashion. Alternatively, as shown by a reflector  135  in FIG. 4B, the gradient reflector may be formed with a continuous wedge profile by using a sloped surface  136  such that the reflectance values vary smoothly or continuously across the gradient reflector. Although reflector  135  is shown having a linear wedge profile, the gradient reflector of the present invention can also have a continuous, non-linear wedge profile to provide the desired transmittance profile. The gradient reflector can also be in the form of a step profile with non-uniform steps, as shown by a reflector  138  in FIG. 4C, including a number of surfaces indicated as  139 A- 139 K, designed to yield a desired transmittance profile, and thereby a desired group delay profile and chromatic dispersion response. Furthermore, the reflectance values may be varied along two dimensions of the reflector. For example, as illustrated by a reflector  140 in FIG. 4D, the reflectance values may be graded along two orthogonal directions of the reflector such that reflector  140  includes two sloped surfaces  142 A and  142 B. Similarly, as shown in FIGS. 4E and 4F, the reflectance value can vary radially, as in a circular reflector  145  of FIG. 4E, or around the circumference, as in a circular reflector  150  of FIG. 4F. The various reflectance regions may be formed, for instance, by lithography during the coating process in the manufacture of the reflector as a quarterwave stack. The gradient reflector, for example, may be formed of one or more layers of a metallic, dielectric or semiconductor material. For instance, the gradient reflector may include a plurality of layers divided into regions having a plurality of different reflectance values.  
         [0066]    Referring now to FIG. 4G in conjunction with FIG. 4A, an example of a single cavity FP device including a gradient reflector is illustrated in FIG. 4G. An gradient FP device  160 , as shown in FIG. 4G, includes first and second substrates  161  and  162 , respectively, separated by an etalon layer  164 . Second substrate  162  includes a reflective surface  163  having a predetermined, fixed reflectance value. A front face  164  of first substrate  161  effectively acts as an aperture, which determines the maximum diameter (and thereby amount) of an incident light beam accepted by gradient FP device  160 . An additional aperture or iris (not shown) may be positioned in front of front face  164  for further controlling the amount of an incident light beam that strikes the gradient FP device. Reflector  130  of FIG. 4A is mounted on first substrate  161  to form a gradient reflector arrangement  165 . Due to the different values of reflectivity displayed by discrete reflectance regions  132 A-F, gradient reflector arrangement  165  is essentially divided into zones  167 A-F, each zone having a different value of reflectivity. When a collimated input beam  170  is incident on gradient FP device  160 , different portions of input beam  170  strike different zones  167 A-F such that the different portions of the input beam experience different values of reflectivity. As a result, different portions of an output beam  172  emanating from gradient FP device  160  exhibit different transmittance profiles, and, when output beam  172  is focused using, for example, a lens (not shown), the transmittance profiles of the different portions of output beam  172  are combined into a total transmittance profile. In this way, by controlling the sizes and reflectivity values of zones  167 A-F, the total transmittance profile, and thereby the phase response, of gradient FP device  160  can be tailored as desired. In general, the gradient FP device should be oriented such that the input beam strikes the gradient FP device at a normal angle in order to avoid introducing effects of off-normal incident angles in the total transmittance profile. However, the gradient FP device may be oriented at an off-normal angle with respect to the input beam if necessary to achieve the desired total transmittance profile and thereby phase response.  
         [0067]    Referring now to FIGS.  5 A- 10 , possible optical configurations including the gradient FP device are described in detail immediately hereinafter. FIG. 5A illustrates an arrangement  200  in which a balanced gradient FP device  210  is used as a dispersion compensator in a fiber optic system. Balanced gradient FP device  210  includes a gradient reflector  212  and a second reflector  214  separated by an etalon layer  216 . Gradient reflector  212  may take the form of, for example, any of the gradient reflector configurations shown in FIGS.  4 A- 4 F. Second reflector  214  may be, for example, a fixed or variable reflector, and the reflectivity value the second reflector and an average reflectivity value of the gradient reflector are generally similar. Arrangement  200  includes a fiber optic input  220 , through which an input light  222  is inserted into arrangement  200  and a first collimator  224  for collimating input light  222  into a collimated input beam  226  to be incident on balanced gradient FP device  210 . Collimated input beam  226  should be spread out and substantially collimated such that the collimated input beam encounters two or more different reflectance values of gradient reflector  212 . A collimated output beam  228  from balanced gradient FP device  210  is refocused by a second collimator  230  into an output light  232 , which is directed into a fiber optic output  234 . Balanced gradient FP device  210  is used to introduce a predetermined phase response to input light  222  and provide output light  232  with the desired group delay (and thereby chromatic dispersion). While the light entering balanced gradient FP device  210  is shown to be collimated in FIG. 5A, the incident light does not necessarily need to be collimated. Balanced gradient FP device  210  will still provide a phase response, although the resulting output light will have a more complicated phase profile than in the case of the collimated input beam due to the blue shift experienced by light entering an interference filter at non-normal angles of incidence.  
         [0068]    [0068]FIG. 5B illustrates an arrangement  250 , which is essentially identical to arrangement  200  of FIG. 5A except that arrangement  250  includes a non-reciprocal circulator  252  with a second fiber optic output  254  for extracting a second output light  256 . In this case, both the transmitted light (output light  232 ) and reflected light (second output light  256 ) from balanced gradient FP device  210  are collected, for example, by circulator  252  such that the transmitted and reflected light may be added together. In this way, balanced gradient FP device  210  may be made to act as an all-pass filter providing an amplitude response of unity, minus insertion and absorption losses. The phase response provided by balanced gradient FP device  210  of FIG. 5B is a sum of wavelength-dependent group delays experienced by the transmitted and reflected light.  
         [0069]    [0069]FIGS. 6A and 6B illustrate arrangements  300  and  320 , respectively, which include an unbalanced gradient FP device  310 . Unbalanced gradient FP device  310  includes a gradient reflector  312  and a second reflector  314  separated by an etalon layer  316 . The reflectance value of second reflector  314  in this case is significantly higher than the reflectance values inherent in gradient reflector  312 . As a result, second reflector  314  reflects substantially all of the light incident on unbalanced gradient FP device  310 , after at least a roundtrip (or potentially multiple reflections) through etalon layer  316  such that unbalanced gradient FP device  310  acts essentially as an all-pass filter with a predetermined phase response, which is dependent on the reflectance profile of gradient reflector  312 . In arrangement  320  of FIG. 6B, most of collimated input beam  326  is reflected back toward fiber optic input  220  by second reflector  314 , but a small portion  328  of the transmitted light is extracted through second reflector  314  from unbalanced gradient FP device  310 . Extracted portion  328  of the transmitted light is then focused by second collimator  230  into an output light  332 , which is directed into fiber optic output  234 . This extracted portion  328  may be used, for example, to perform in-situ optical measurements and/or monitoring for feedback or adjustment purposes.  
         [0070]    [0070]FIG. 7 illustrates an alternative arrangement  400  including an gradient FP device (balanced or unbalanced)  410  with a gradient reflector  412  and a second reflector  414  separated by an etalon layer  416 . Fiber optic input  420  guides an input light  422  into a first collimator  424 , which produces a collimated input beam  426 . Collimated input beam  426  is directed at a non-normal angle onto gradient FP device  410  such that a collimated output beam  428  produced at gradient FP device  410  emanates at another non-normal angle from the device and into a second collimator  430 . In this way, the A light entering gradient FP device  410  is not collinear with the light exiting the device. Therefore, the need for a non-reciprocating circulator to extract the output from the device is eliminated, thus reducing the possibility of insertion loss from the arrangement. Collimated output beam  428  is then focused by a second collimator  430  to produce an output light  432 , which is directed into a fiber optic output  434 .  
         [0071]    In another scheme to obviate the need for a circulator, a GRIN lens is used to separate the light entering and exiting the FP gradient device. An arrangement  450 , shown in FIG. 8, includes gradient FP device (balanced or unbalanced)  410 . Fiber optic input  420  directs input light  422  onto a first location  451  of a GRIN lens  452 , which spreads out the input light to direct a substantially collimated input beam  456  onto gradient FP device  410 . The device then reflects the collimated input beam incident thereon to produce a substantially collimated output beam  458 , including a phase response determined by the reflectance profile of gradient reflector  412 . Collimated output beam  458  travels through GRIN lens  452  to emanate at a second location  459  of GRIN lens  452  so as to be directed into fiber optic output  434  as output light  432 . Again, since the input light and the output light are physically separated, the use of a non-reciprocating circulator in the arrangement is not required.  
         [0072]    [0072]FIG. 9 illustrates an optical scheme in which an interleaver is used to increase the flat region group delay response, and thereby the chromatic dispersion profile, of the gradient FP device used as a dispersion compensation module (DCM). Arrangement  500  includes a fiber optic input  520 , which directs an input light  522  onto an interleaver  524 . Input light  522  includes a plurality of channels at, for instance, different wavelengths. Interleaver  524  splits input light  522  into first and second split inputs  526  and  528 , respectively, such that, for example, first split input  526  contains the odd channels and second split input contains the even channels. First and second split inputs  526  and  528  are directed into first and second DCMs  530  and  532 , respectively, such that the odd and even channels are subjected to different phase responses at the DCMs. DCMs  530  and  532  then produce first and second split outputs  534  and  536 , respectively, which are directed into a second interleaver  540 . Second interleaver  540  combines first and second split outputs  534  and  536  to produce a dispersion compensated output light  542 , which is directed away from arrangement  500  through a fiber optic output  544 . In other words, in applications where it might not be feasible to manufacture an gradient FP device which provides continuous phase response across the wavelength region of interest, the incoming signal may be split into two or more split signals using an interleaver and the chromatic dispersion in the split signals may be corrected at any number of different DCMs. Then, the resulting outputs from the DCMs may be combined to form a dispersion compensated output signal containing all of the original channels.  
         [0073]    Furthermore, DCMs may be cascaded in order to increase the total chromatic dispersion correction or to modify the chromatic dispersion slope of an input signal. For example, as shown in FIG. 10, an arrangement  550  includes first and second DCMs  552  and  554 , respectively, which are cascaded together. An input light  560  is first processed through DCM  552 , which produces an intermediate output  562 . Intermediate output  562  includes the phase response provided by DCM  552  and is directed into DCM  554  for further dispersion compensation. DCM  554  then provides additional phase response to produce an output signal  564 . Additional DCMs may be cascaded together to provide other dispersion compensation effects. DCMs may be identical or different depending on the desired total phase response.  
         [0074]    As another variation, FIGS.  11 A- 11 D illustrate a number of possible ways in which the FP gradient devices of the present invention may form tunable dispersion compensation modules. For example, as shown in FIG. 11A, an arrangement  600  includes an gradient FP device  610  with adjustable spacing between the reflectors forming the Fabry-Perot cavity. Gradient FP device  610  includes a gradient reflector  612 , which is mounted on a first substrate  613 , and a second reflector  614 , which is mounted on a second substrate  615 . Gradient reflector  612  and second reflector  614  are disposed in a spaced apart, confronting relationship. The space between the gradient reflector and the second reflector is filled with an etalon material  616 , such as air. Gradient reflector  612  and second reflector  614  are secured on piezoelectric spacers  619  such that the spacing between the two reflectors is variable so as to alter the transmittance profile of gradient FP device  610 . The change in the transmittance profile thereby results in a change in the group delay profile, and therefore the phase response, of gradient FP device  610 . Second reflector  614  can have a reflectivity value of 100% or less, depending on whether an additional output through the second reflector is desired, for example, for monitoring purposes.  
         [0075]    [0075]FIG. 11B illustrates an arrangement  630  including an gradient FP device  632 , in which gradient reflector  612  and second reflector  615  are separated by a micro-electromechanical system (MEMS) element  634 . MEMS element  634  acts as an electrostatic actuation mechanism to vary the spacing between the two mirrors such that the transmittance profile, and thereby the group delay profile, of gradient FP device  632  may be tuned.  
         [0076]    Alternatively, as shown in FIG. 11C, an arrangement  650  may include an gradient FP device  652 , which is configured to include a wedge-shaped MEMS element  654 . In gradient FP device  652 , then, an air gap  656  is formed such that air gap  656  is adjustable by modulating MEMS element  654  by, for example, an applied voltage signal (not shown). As a result, the reflectivity exhibited by the combination of MEMS element  654  and air gap  656  may be changed. Also, the thickness of etalon material  616  may also be made adjustable by using, for instance, a tunable electro-optic material so as to change the distance between the reflective elements in gradient FP device  652 .  
         [0077]    An arrangement  670  shown in FIG. 11D is substantially the same as the arrangement shown in FIG. 6A but the gradient FP device is mounted on a movable stage  672 . Gradient reflector  312  may be configured to have variable reflectivity values along two dimensions (such as, for example, shown in FIGS.  4 D- 4 F) such that, by moving the movable stage in a direction indicated by double-headed arrows  674  or in an orthogonal direction, for instance, collimated input beam  326  is incident on different portions of gradient FP device  310  such that the resulting transmittance profile, and thereby the group delay profile, is variable. Additionally, gradient FP device  310  can also be designed to have a plurality of sections which provide different chromatic dispersion effects (such as, for instance, positive dispersion, negative dispersion, constant dispersion, etc.) such that physically moving the gradient FP device yields different modes and levels of dispersion compensation on the incident light.  
         [0078]    Another possible modification to the gradient FP device of the present invention is to mount or form the gradient reflector on a curved surface. For instance, FIG. 12 illustrates an arrangement  680  including a curved gradient FP device  682 . The curvature of curved gradient FP device  682  may be designed, for example, to match the numerical aperture of the fiber optic input such that light  684  exiting the end of the optical fiber will spread but still be incident on each point of the curved surface at normal incidence. Therefore, the use of a collimator is not required in arrangement  680 .  
         [0079]    The reflectance values across the gradient reflector may be arranged in any number of ways so as to achieve the desired transmittance profile, and thereby the desired phase response, from the gradient FP device of the present invention. Either positive or negative chromatic dispersion profiles may be created, and the resulting chromatic dispersion profile may be designed to be periodic, non-periodic, continuous or discrete in wavelength, depending on the specific application. Moreover, with proper selection of the materials used in the substrate, coatings, etc., the gradient FP device may be designed to be effective in essentially any wavelength range from the ultraviolet to far-infrared. Some materials suitable for use in the device include, but are not limited to, dielectrics, metals, semi-conductors, electro-optic materials, piezo-electric materials and birefringent materials. The variation in the reflectance values across the reflector may be formed by any suitable methods currently available or yet to be developed such as, for instance, mechanical grinding and polishing, use of specialized mask and vacuum deposition technologies, and use of a grayscale mask and photolithography. Substrate and/or etalon may be any suitable material including, but not limited to, a dielectric, metallic or semiconducting material such as, for example, vacuum, air, glass or quartz, as long as the material is transparent in the spectral region of interest. Furthermore, the substrate and etalon thickness can range from a few hundred nanometers to few tens of millimeters, depending on specific applications, desired values of group delay and chromatic dispersion, wavelength range, etc. Since subtle variations in reflectivity of the gradient reflector may be readily controlled by judicious material selection and fabrication procedure, it is possible to tailor the transmittance profile, and thereby the group delay and chromatic dispersion profiles, of the gradient FP device over a range of wavelengths. Furthermore, to alleviate polarization mode dispersion (PMD) and/or polarization-dependent loss (PDL), birefringent elements may be added into the aforedescribed arrangements to control the polarization of the input light prior to striking the FP gradient device.  
         [0080]    Therefore, the present examples are to be considered as illustrative and not restrictive, and the invention is not to be limited to the details given herein, but may be modified within the scope of the appended claims.