Abstract:
An optical flattening filter is cascaded with an optical filter between an input and an output of an optical arrangement to provide a substantially widened flat passband at an output of the optical arrangement. The optical filter is responsive to an input signal for generating a periodic or a periodic output response waveform having a cosine squared or Gaussian passband or any rounded passband shape. The optical flattening filter is designed to generate a response waveform having a spectral profile which is complementary to the periodic or aperiodic output response waveform of the optical filter. The interaction of the response waveforms of the optical filter and the optical flattening filter provide a resultant response waveform at the output of the optical arrangement wherein each peak therein is substantially flattened to provide a passband which is wider than the response waveform provided by the optical filter.

Description:
FIELD OF THE INVENTION 
     The present invention relates to method and apparatus for flattening the passband of optical Dense Wavelength Division Multiplexer (DWDM) or Demultiplexer devices having rounded passband shapes. 
     BACKGROUND OF THE INVENTION 
     The implementation of a low cost, low insertion loss optical Dense Wavelength Division Multiplexer (DWDM) or Demultiplexer is of great advantage in high capacity optical transmission system. Unfortunately, most high capacity DWDM devices have a high insertion loss or a high cost of manufacture associated with them. A design capable of accomplishing dense wavelength division multiplexing with low insertion loss is obtained by using an unbalanced Mach-Zehnder (UMZ) interferometer. However, UMZ filters suffer from a characteristic problem of a narrow pass bandwidth near the transmission peak. This narrow pass bandwidth near the peak is undesirable because it provides unwanted shaping of the signal. This problem is further exacerbated when a plurality of UMZs are cascaded in order to perform multiple channel demultiplexing or multiplexing. 
     U.S. Pat. No. 5,809,190 (Chen), issued on Sep. 15, 1998, discloses an unbalanced Mach-Zehnder (UMZ) interferometer capable of accomplishing dense wavelength division (DWD) multiplexing with low insertion loss. More particularly, Chen discloses apparatus and method of making a fused dense wavelength division multiplexer (DWDM) using a fused-biconical taper technique. The DWDM comprises multiple Multi-window Wavelength Division Multiplexers (MWDMs) which are cascaded in several stages where the MWDMs in each stage have an identical window spacing. For an N-channel DWDM, there are a predetermined plurality of DWDMs in each stage, and the stages are cascaded to form the MWDM. Unfortunately, the UMZ is by nature sensitive to temperature fluctuations of the environment, and typical temperature fluctuations expected in the terminal environment can render the DWDM device unusable. Therefore, the disclosed UMZ device is unstable because of the occurrence of variations in phase due to temperature fluctuations. A similar device is also discussed in an article titled “Fused-Coupler Technology for DWDM Applications” by F. Gonthier in the magazine  Fiber Optic Product News , September 1998, at pages 54 and 56. 
     It is desirable to provide an optical filtering arrangement that is especially designed to flatten the passband of a unbalanced Mach-Zehnder filter. It is further desirable to provide an optical filtering arrangement that can be applied to enhance the passband flatness of any optical filter or DWDM arrangement with a rounded type of passband shape. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to method and apparatus for flattening the passband of optical Dense Wavelength Division Multiplexer (DWDM) or Demultiplexer devices having rounded passband shapes. 
     Viewed from an apparatus aspect, the present invention is directed to an optical arrangement which comprises an optical filter and an optical flattening filter. The optical filter is responsive to an input signal for generating at an output thereof one of a group consisting of a periodic and a periodic output response waveform having a rounded passband shape. The optical flattening filter is coupled in cascade with the optical filter between an input and the output of the optical arrangement for generating a response waveform having a spectral profile which is complementary to the periodic or aperiodic output response waveform of the optical filter and interacts with the response waveform of the optical filter such that each peak in a resultant response waveform at the output of the optical arrangement is substantially flattened to provide a passband which is wider than the response waveform provided by the optical filter. 
     Viewed from a process aspect, the present invention is directed to a method of generating a substantially widened flat passband at an output of an optical arrangement. The method comprises a first step of generating, in response to an input signal to an optical filter, one of a group consisting of a periodic output response waveform and a aperiodic output response waveform having a rounded passband shape. The method further comprises a second step of generating a response waveform having a spectral profile which is complementary to the periodic or aperiodic output response waveform of the optical filter in an optical flattening filter coupled in cascade with the optical filter between an input and the output of the optical arrangement. The method further comprises a third step of generating a passband which is wider than the response waveform provided by the optical filter at the output of the optical arrangement by the interaction of the response waveforms of the optical filter obtained in the first step and the optical flattening filter obtained in the second step such that each peak in a resultant response waveform at the output of the optical arrangement is substantially flattened. 
     The invention will be better understood from the following more detailed description taken with the accompanying drawings and claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 shows a block diagram of a prior art unbalanced Mach-Zehnder interferometer; 
     FIG. 2 graphically shows exemplary output waveforms that are obtainable from the prior art single stage Mach-Zehnder filter shown in FIG. 1; 
     FIG. 3 shows a block diagram of a Dense Wavelength Division Multiplexer/Demultiplexer found in the prior art including cascaded Mach-Zehnders interferometers for separating eight signals received in a wavelength division multiplexed signal; 
     FIG. 4 graphically shows exemplary output waveforms having wavelengths between 1548 and 1551 nanometers that are obtainable from the prior art cascaded Mach-Zehnder interferometers shown in FIG. 3; 
     FIG. 5 graphically shows an exemplary output waveforms that are obtainable for one channel from the prior art cascaded Mach-Zehnder interferometers shown in FIG. 3; 
     FIG. 6 shows an arrangement of a periodic or aperiodic filter in cascade with a flattening filter and one or more optional flattening filters in accordance with the present invention; 
     FIG. 7 shows an arrangement of a flattening low Finesse Fabry-Perot filter for use as a flattening filter in the arrangement of FIG. 6 in accordance with a first embodiment of the present invention; 
     FIG. 8 graphically shows exemplary output response waveforms that are obtainable for a Mach-Zehnder filter to be flattened, a flattening filter, and a flattened Mach-Zehnder filter; and 
     FIG. 9 shows an arrangement of flattening Mach-Zehnder filter for use as a flattening filter in the arrangement of FIG. 6 in accordance with a second embodiment of the present invention. 
    
    
     The drawings are not necessarily to scale. 
     DETAILED DESCRIPTION 
     Referring now to FIG. 1, there is shown a prior art unbalanced Mach-Zehnder multi-wavelength interferometer or filter  10  (shown within a dashed line rectangle) comprising first and second fused taper 3 dB couplers (CPLR.)  12  and  14 . Each of the two fused taper couplers  12  and  14  is formed by, for example, heating two optical fibers (e.g., optical fibers  16  and  17 ) and fusing a section thereof together while tapering the fused section to a central point before dividing again. Alternatively, the fused tapered couplers  12  and  14  can be formed from planar waveguides to obtain a similar structure. The first fused taper coupler  12  is coupled to receive first and second optical input signals (INPUT  1  and  2 ) via optical fibers  16  and  17 , respectively. After passing through the first fused taper coupler  12 , the resultant combined first and second output signals are transmitted via first and second optical fibers  18  and  19 , respectively, for providing respective first and second input signals at separate inputs of the second fused taper coupler  14 . The optical path lengths of the optical fibers  18  and  19  have a predetermined difference and their lengths are hereinafter referred to as L 18  and L 19 , respectively. After passing through the second fused taper coupler  14 , the resultant combined signals are transmitted as first and second output signals (OUT  1  and  2 ) from the Mach-Zehnder interferometer  10  via first and second output optical fibers  20  and  21 , respectively. 
     Based on the principles of interferometry, the transmission profiles “T” of the filter  10  in the first and second output optical fibers  20  and  21  are given by the equations: 
     
       
         T 20 =cos 2 (φ), and T 21 =sin 2 (φ),  (Eq. 1) 
       
     
     
       
         φ=2πnδL/w,  (Eq. 2) 
       
     
     where n is the refractive index of the interferometer medium, δL is the relative path length difference (δL=L 19 -L 8 ), and w is the wavelength of light. 
     Referring now to FIG. 2, there is graphically shown exemplary output waveforms obtained in the optical fibers  20  and  21  from the Mach-Zehnder multi-wavelength filter (interferometer)  10  of FIG.  1 . The horizontal axis represents wavelength in nanometers (nm), and the vertical axis represents normalized transmission. The solid waveform represents the exemplary waveform obtained in the output optical fiber  20 , and the dashed line waveform represents the exemplary waveform obtained in the output optical fiber  21 . The waveforms for the optical fibers  20  and  21  are complementary to each other as is shown in Equation (1), and the peaks are separated by δw, where w is the wavelength of light and δw is given by the equation 
     
       
         δw=w 2 /(2nδL).  (Eq. 3) 
       
     
     The filtering property of a Mach-Zehnder interferometer  10  can be exploited to separate densely packed signals at different wavelengths by cascading Mach-Zehnder interferometers with different δw&#39;s. 
     Referring now to FIG. 3, there is shown an exemplary Dense Wavelength Division Multiplexer (DWDM) or Demultiplexer  30  (shown within a dashed line rectangle) found in the prior art comprising a cascading of unbalanced Mach-Zehnder interferometers  10   a - 10   g . A first stage of the cascaded arrangement comprises the Mach-Zehnder interferometer  10   a  which is capable of receiving first and second input signals and generate first and second output signals via optical waveguides  31  and  32 , respectively. A second stage of the cascaded arrangement comprises the Mach-Zehnder interferometers  10   b  and  10   c . The interferometer  10   b  is coupled to receive the first output from the interferometer  10   a  via the optical waveguide  31  at one of its two inputs with the other input being pigtailed (unused). The interferometer  10   c  is coupled to receive the second output from the interferometer  10   a  via the optical waveguide  32  at one of its two inputs with the other input being pigtailed (unused). A first output of the interferometer  10   b  is coupled to one of two inputs of the interferometer  10   d  via an optical waveguide  34  while a second output therefrom is coupled to one of two inputs of the interferometer  10   e  via an optical waveguide  35 . The other input of the interferometers  10   d  and  10   e  are pigtailed (unused). Similarly, a first output of the interferometer  10   c  is coupled to one of two inputs of the interferometer  10   f  via an optical waveguide  34  while a second output therefrom is coupled to one of two inputs of the interferometer log via an optical waveguide  35 . The other input of the interferometers  10   f  and  10   g  are pigtailed (unused). First and second outputs from each of the interferometers  10   d ,  10   e ,  10   f , and  10   g  provide separate output channel signals from the DWD Demultiplexer arrangement  30 . For multiplexing eight channel signals, the DWDM arrangement  30  would be used in a reverse direction with the eight channels signal being inputted at the right side (at OUT  1  to OUT  8 ) of FIG. 3 and a single wavelength division multiplexed signal being generated at one of the two outputs (at INPUT  1  or  2 ). 
     In the cascading arrangement of the unbalanced Mach-Zehnder interferometers  10   a - 10   g , the δw (delta wavelength) of each Mach-Zehnder interferometer in a stage is adjusted to be twice that of the Mach-Zehnder interferometer(s) in a previous stage. 
     Referring now to FIG. 4, there is graphically shown enlarged exemplary output waveforms for one section of a frequency spectrum used with the prior art cascaded unbalanced Mach-Zehnder interferometers  10   a - 10   g  shown in FIG.  3 . It is to be understood that the waveforms shown in FIG. 4 are essentially for one channel area and are repetitious in a corresponding manner below 1548 nm and above 1551 nm for the other channel areas. The horizontal axis represents wavelength in nanometers (nm) between 1548 and 1551 nanometers, and the vertical axis represents normalized transmission between 0.001 and 1. From the graphical display in FIG. 4, it can be seen that cascading three levels of unbalanced Mach-Zehnder interferometers  10   a - 10   g  (as is shown in FIG. 3) can allow for the separation of eight channels when demultiplexing an input DWD multiplexed signal. The dotted line waveform  42  is representative of an output on either leg  31  or  32  of the Mach-Zehnder interferometer  10   a  in the first stage of the DWD demultiplexer  30 , where, for example, wavelengths  1 , 3 , 5 , 7  are found propagating in output leg  31  and wavelengths  2 , 4 , 6 , 8  are found propagating in output leg  32 . The dashed line waveform  44  is representative of an output on any one of the output legs  34  or  35  from the Mach-Zehnder interferometers  10   b  and  10   c  in the second stage of the cascaded Mach-Zehnder interferometers  10   a - 10   g . More particularly, the wavelengths  1  and  5  are found propagating in output leg  34  of interferometer  10   b , wavelengths  3  and  7  are found propagating in output leg  35  of interferometer  10   b , the wavelengths  2  and  6  are found propagating in output leg  34  of interferometer  10   c , wavelengths  4  and  8  are found propagating in output leg  35  of interferometer  10   c . The solid line waveform  46  is generally representative of an output on any one of the output legs  37  or  38  from the Mach-Zehnder interferometers  10   d ,  10   e ,  10   f , or  10   g  in the third stage of the cascaded Mach-Zehnder interferometers  10   a - 10   g . The bold solid line waveform  48  is representative in greater detail, of an output on either leg  37  or  38  from the Mach-Zehnder interferometers  10   d ,  10   e ,  10   f , or  10   g  in the third stage of the cascaded Mach-Zehnder interferometers  10   a - 10   g . As was stated hereinabove, the waveforms shown in FIG. 4 are repetitious in a corresponding manner below 1548 nm and above 1551 nm so that the peak of the bold line waveform  48  corresponds to only one of the outputs from one of the Mach-Zehnder interferometers  10   d ,  10   e ,  10   f , or  10   g . Each of the remaining outputs from the Mach-Zehnder interferometers  10   d ,  10   e ,  10   f , or log has a peak at a different wavelength such that a separate demultiplexed channel of a received eight-channel multiplexed signal is obtained at each output (OUT  1 -OUT  8 ) from the cascaded unbalanced Mach-Zehnders  10   a - 10   g in the DWDM  30 . If, for example, it is assumed that wavelengths of channels  1 ,  3 ,  5 , and  7  are found propagating in output leg  31  of interferometer  10   a , and wavelengths of channels  2 ,  4 ,  6 , and  8  are found propagating in output leg  32  of interferometer  10   a , then the first and second outputs via optical waveguides  37  and  38  from interferometer  10   d  are the demultiplexed channel  1  and  3  signals, respectively. Similarly, the first and second outputs via optical waveguides  37  and  38  from interferometer  10   e  are the demultiplexed channel  5  and  7  signals, respectively, the first and second outputs via optical waveguides  37  and  38  from interferometer  10   f  are the demultiplexed channel  2  and  4  signals, respectively, and the first and second outputs via optical waveguides  37  and  38  from interferometer  10   g  are the demultiplexed channel  6  and  8  signals, respectively. The cascade unbalanced Mach-Zehnder arrangement as is shown in FIG. 3 is suggested in U.S. Pat. No. 5,809,190 (Chen), issued on Sep. 15, 1998. 
     Referring now to FIG. 5, there is shown the results of a numerical modeling of unbalanced Mach-Zehnders  10   a - 10   g cascaded as is shown in FIG. 3 to illustrate an extraction of a single channel shown by the solid line waveform from an output leg of an eight channel device (seven cascaded unbalanced Mach-Zehnders  10   a - 10   g ). The horizontal axis represents wavelength in nanometers (nm) between 1548 and 1551 nanometers, and the vertical axis represents normalized transmission between 0.001 and 1. 
     From the waveforms shown in FIGS. 2,  4  and  5 , it can be seen that the prior art arrangements  10  and  30  of FIGS. 1 and 3, respectively, have a characteristic problem of a narrow transmission bandwidth near the rounded transmission peak. Such narrow pass bandwidth near the rounded peak is undesirable because it provides unwanted shaping to the optical signal. 
     Referring now to FIG. 6, there is shown an arrangement of a periodic or aperiodic filter  70  in cascade with a flattening filter  72   a , and optionally with additional one or more flattening filters  72   b  and  72   n  (shown in dashed lined rectangles) in accordance with the present invention. A periodic filter  70  is defined as having an output response that includes equally spaced periodic peaks as shown, for example, in FIG. 2, whereas an aperiodic filter  70  has an output response (not shown) that includes only one or two spaced-apart peaks. The filter  70  to be flattened can comprise a 1×N Multiplexer or Demultiplexer as is shown, for example, in FIGS. 1 and 3 or any other suitable device. In accordance with the present invention, the filter  70  preferably has a cosine squared or Gaussian passband having rounded peaks, and the flattening filter  72   a  is arranged to have a response that is substantially complementary to the response curve of the filter  70  while maintaining a minimal insertion loss. The flattening filter  72   a  can be optionally located in an optical path either prior to the filter  70  as is shown in FIG. 6, or after the filter  70  as is shown by the flattening filter  72   b . Still further, in accordance with the present invention, a plurality of flattening filters with different periodicities can be cascaded in the optical path of the filter  70  as shown by the flattening filters  72   a  and  72   n , where flattening filter  72   n  can comprise one or more cascaded flattening filters with different periodicities. For example, the flattening filter  72   a  can have the periodicity that is the same as the periodicity of the filter  70 , the first flattening filter  72   n  can have a periodicity that is two times that of filter  70 , and a second flattening filter (not shown but like filter  72   n  and cascaded after the first filter  72   n ) can have a periodicity that is four times that of filter  70 . Such cascading of two or more flattening filters ( 72   a  and  72   n ) is equivalent to building a Fourier series with different flattening filters  72 . It is preferred, but not mandatory, that when a plurality of flattening filters  72   a  and  72   n  are used to build a Fourier series, that the flattening filters  72   a  and  72   n  be located on the same side of the filter  70  to be flattened. 
     Referring now to FIG. 7, there is shown an arrangement of a flattening low Finesse Fabry-Perot interferometer or filter  80  (shown within a dashed line rectangle) for use as a flattening filter  72   a ,  72   b , or  72   n  in the arrangement of FIG. 6 in accordance with a first embodiment of the present invention. The filter  80  comprises a first and second optical fiber  87  and  88  that are terminated with a first and second GRIN lens  82  and  84 , respectively. The first and second GRIN lenses  82  and  84  have a finite predetermined cavity spacing (Lg)  86  therebetween that has optical path differences designed to yield a free spectral range equal to, or a multiple of, the filter  70  of FIG. 6 to have its response flattened. For example, to flatten a Mach-Zehnder filter  70  (of the type shown in FIG. 1) with a 100 GHz free spectral range, a cavity spacing  86  of approximately 1.5 millimeters would be needed. Still further, end faces  83  and  85  of the GRIN lenses  82  and  85 , respectively, are not coated with an anti-reflection (AR) coating, but are coated with a film that provides a certain coefficient of reflectivity (r). The transmission of the filter  80  is described by the following equation:              T   =     1     1   +     F              [         sin                2          (     2        π   ·   Ng   ·     Lg   /   w         )       ]                 (Eq.  4)                                
     where F=4r 2 /(1−r 2 ) 2 , r is the reflection coefficient, Ng is the index of refraction of the medium in the cavity  86  between the GRIN lenses  82  and  84 , Lg is the length of the cavity  86  between the GRIN lenses, and w is the optical wavelength of the signal. The low finesse Fabry-Perot filter  80  has the advantage that, in transmission, the response peaks have zero loss while the minima have non-zero transmission. 
     Referring now to FIG. 8, there is graphically shown exemplary output response waveforms  110 ,  112 , and  114  that are obtainable for a Mach-Zehnder (MZ) filter  70  of FIG. 6 to be flattened, a flattening filter  80  of FIG. 7, and a flattened Mach-Zehnder filter  70  produced by the cascading of the filters  70  and  80 , respectively. The horizontal axis represents wavelength in nanometers (nm) and the vertical axis represents normalized transmission between 0.1 and 1. More particularly, the exemplary dashed line response waveform  110  is for the MZ filter  70  to be flattened, the exemplary dotted line response waveform  112  is for the flattening filter  80 , and the exemplary bold line waveform  114  is for the resultant flattened response of the MZ filter  70 . As can be observed from FIG. 8, for an exemplary 100 GHz Fabry-Perot filter  80 , the total bandwidth at a normalized transmission value of  0 . 5 dB below the peak between waveforms  110  and  114  is almost doubled from 0.17 nm to 0.3 nm. Such enhancement has a significant impact on optical transmission systems because high capacity signals can now be transmitted without any signal deterioration or biasing. In principle, a classical MZ filter  70  has a peak response at a normalized transmission value of 1, and the response drops down from the peak very sharply. Depending on the how deep the drop goes (where the curve dies out), the ratio of the maximum to the minimum is called an Extinction ratio. The flattening filter  80  (or  72   a ) has a response that is substantially complementary to that of the filter  70  to be flattened, but the flattening filter is designed to not have an extinction ratio that is equal to that of the filter  70  to be flattened. In FIG. 8 the response curve  112  of the flattening filter  80  is at a maximum value at 1 and at a minimum value at 0.5 for an extinction ratio which is different from the response curve  110  of the filter  70  where the maximum value is at 1 and the minimum value is less than 0.1. Therefore, in accordance with the present invention, the flattening filter  80  has a reduced extinction ratio and a complementary response to that of the filter  70  to be flattened. The extinction ratio can be reduced by experimentation or design to a point where a desired flat passband results with a minimal predetermined amount of insertion loss. 
     Where a plurality of, for example, two flattening filters  72   a  and  72   n  of FIG. 6 are used, the flattening filter  72   a  would have a response shown for waveform  112 , and the flattening filter  72   n  might have a response (not shown) with a corresponding extinction ratio similar to that of filter  72   a  but with a frequency which is, for example, twice that of the flattening filter  72   a . Under such flattening filter arrangement, the flattening filter  72   a  will produce a flattened response as shown for waveform  114  and the flattening filter would affect the flattened waveform  114  to further increase the bandwidth at the peak and add some slight ripple in the increased flattened pass bandwidth. The addition of second and third flattening filters  72   n  (not shown) in cascade with the first flattening filter  72   n  but with different periodicities would further widen the passband of response curve  114  and tend to reduce the amount of ripple caused by the first flattening filter  72   n . Effectively, the flattening filters  72   a  and first to third flattening filters  72   n  with different periodicities builds a Fourier series to flatten the response of the filter  70 . 
     Referring now to FIG. 9, there is shown an arrangement of flattening Mach-Zehnder (MZ) filter  90  for use as a flattening filter  72   a  in the arrangement of FIG. 6 in accordance with a second embodiment of the present invention. The flattening MZ filter  90  comprises first and second fused tapered couplers  92  and  94  which are interconnected by parallel optical paths  97  and  98  of predetermined different path lengths. The flattening MZ filter  90  has a similar structure and operation to that of the prior art unbalanced MZ filter  10  of FIG. 1 discussed hereinbefore, but with certain differences. The MZ filter  90  is constructed with a low contrast ratio using two design rules of (1) selecting splitting ratios of the first and second couplers  92  and  94 , at optimized values for the contrast ratio, to result in an appropriate flattening of the response of the filter  70 , and (2) choosing a path length imbalance between the optical paths  97  and  98  to match the periodicity of the filter  70  that needs to be flattened. More particularly, for a typical Mach-Zehnder filter  70 , the splitting ratios of the two fused tapered couplers  12  and  14  (shown in FIG. 1) are 50:50 whereby full contrast is obtained in which the fringes of the response curve go all the way to down to a 0 normalized transmission. This is the equivalent of the response curve of FIG. 2 going in a negative direction all the way down to 0 normalized transmission. By changing the splitting ratio so that each of the couplers  92  and  94  have a splitting ratio of, for example, 05:95, the resultant response waveform will have a lower extinction ratio as shown for example by waveform  112  in FIG.  8 . The transmission of such flattening MZ filter  90  is described by the following equation: 
     
       
         T=2·(α−α 2 )·[1+cos(Lf·Nf·2π/w], 0&lt;α&lt;1  (Eq. 5) 
       
     
     where α is the splitting ratio of the two couplers  92  and  94  (assumed to be equal), Nf is the index of refraction of the optical fiber  97  and  98 , Lf is the path length difference between the two paths  97  and  98 , and w is the optical wavelength of the signal. 
     While both a Fabry-Perot filter  80  and a Mach-Zehnder (MZ) filter  90  are appropriate for flattening applications, in many cases the MZ filter  90  is preferred because of the lower insertion loss and higher stability (using passive and active techniques). 
     The flattening filters  72   a ,  72   b , and  72   n  are suitable for use with optical Dense Wavelength Division Multiplexer (DWDM) or Demultiplexer devices having rounded passband shapes where a wide passband is required either due to a large information bandwidth or large laser drift due to aging, etc. Still further, the invention described hereinbefore is simple and independent of the device to be flattened, and is capable of flattening the response of units already installed in the field simply by introducing the flattening filter  72  in the optical path before or after the unit to be flattened. Additionally, the flattening filter  72   a ,  72   b , or  72   n  can be used to flatten the response of an Arrayed Waveguide (AWG) device such as disclosed in the article “An N×N Optical Multiplexer Using a Planar Arrangement of Two Star Couplers” by C. Dragone,  IEEE Photonics Technology Letters , Vol. 7, No. 9, September 1991, at pages 812-815. An AWG is basically a silicon or silica chip having a planar waveguide with multiple paths wherein an incoming signal is split up and the split signals go through all of the paths. When properly designed, each output leg of an AWG has an output wavelength that is different from each of the other output legs. 
     It is to be appreciated and understood that the specific embodiments of the present invention described hereinbefore are merely illustrative of the general principles of the invention. Various modifications may be made by those skilled in the art which are consistent with the principles set forth.