Abstract:
A reconfigurable optical add/drop multiplexer (ROADM) includes a first optical dynamic gain equalization filter (DGEF) having a first input for receiving an initial wavelength division multiplexed (WDM) signal, a first output for sending a phase shifted WDM signal, and a second output connected to a demultiplexer for demultiplexing a WDM drop signal thereby producing a plurality of drop channels. A second DGEF having a first input for receiving the phase shifted WDM signal, a second input connected to a multiplexer, for multiplexing a plurality of add channels to produce thereby a wavelength division multiplexed (WDM) add signal, and an output for sending a second adjusted WDM signal. The ROADM allows for the channels from the initial WDM signal to be dropped, added and equalized.

Description:
FIELD OF THE INVENTION 
   The invention relates generally to optical communications and, more particularly, to an arrangement suitable for adding and dropping channels in a wavelength division multiplexed (WDM) optical system. 
   BACKGROUND OF THE INVENTION 
   A dynamic gain equalization filter (DGEF) is a device or arrangement that is useful for controlling optical WDM channel powers, especially at the dispersion compensating module (DCM) port of an in-line amplifier (ILA) to provide the desired spectral flatness of the output channels. An example of a DGEF is described in U.S. Pat. No. 6,212,315 by C. R. Doerr et al. titled “Channel Power Equalization for a Wavelength Divisioned Multiplexed system,” filed on Jul. 7, 1998, which is hereby incorporated by reference in its entirety. 
     FIG. 1  depicts a block diagram of a DGEF  100  for controlling channel powers in wavelength-division multiplexed (WDM) systems. In the DGEF  100  of  FIG. 1 , a decrease in attenuation range can be traded for a decrease in insertion loss. The WDM signal channels enter a coupler  102  from a left port  101 . The coupler  102  splits the WDM signal into its signal components which are sent via upper and lower arms,  103  and  104  respectively. The output of the upper  103  and lower  104  arms are recombined in the second coupler  105  having the same splitting ratio as the first coupler  102 . The upper arm  103  is a simple waveguide; while the lower arm  104  includes a wavelength selective phase shifter apparatus  104   a  comprising a demultiplexer  106  coupled to a multiplexer  107  via an array of programmable phase shifters  108 . The number of phase shifters equals the number of channels in the WDM signal. In this illustrative example, the array of programmable phase shifters  108  includes four phase shifters; each programmable phase shifter is a device whose effective path length can be controlled externally via a control lead  111 . Therefore, the phase of certain frequencies can be selectively varied to produce the desired output signals. 
   In an add/drop mode, port  121  is the add port and port  122  is the drop port. To throughput one or more wavelengths (or channels) from port  101  to port  109 , the phase shift of phase shifter  104   a  must be 180 degrees for the throughput wavelength(s). Thus, if more than one wavelength (or channel) is to be throughput the phase shift of phase shifter  104   a  must be 180 degrees for each of those wavelengths. In contrast, to drop or cross-connect one or more wavelengths from port  101  to port  122 , the phase shift of phase shifter  104   a  must be 0 degrees for that wavelength. This means that wavelength does not appear at port  109 . 
   If more than one wavelength (or channel) is to be dropped the phase shift of phase shifter  104   a  must be 0 degrees for each of those wavelengths to be dropped. This cross-connect mode also enables a new wavelength (or channel) to be added at port  121  and appear at port  109  along with the throughput wavelengths from port  101 . If more than one wavelength (or channel) is to be added, they are added at port  121  and appear at port  109 . The phase shift of phase shifter  104   a  must be 0 degrees for the more than one added wavelength. Due to its symmetric nature, one can make a reflective arrangement by cutting the device in half with a mirror placed along the axis of symmetry. 
   The transfer function of the DGEF  100  is reflected by the following equations:
 
 E   OUT   /E   IN   =R −(1 −R ) e   jφ   √{square root over (T)}             
 
 P   OUT   /P   IN   =[R− (1 −R )cos(φ) √{square root over (T)} ] 2 +[(1 −R )sin(φ) √{square root over (T)} ] 2 =
 
 R   2 +(1 −R ) 2   T− 2 R (1 −R )cos(φ) √{square root over (T)}   (1)

   where E OUT , P OUT  and E IN , P IN  represent the electrical field and power of the complex envelope of an optical signal at the DGEF output and input ( 109 ,  101 ) respectively; 
   R reflects the coupler ratio (Rε[0,1]); 
   T is the power transmission of the phase shift section  104   a , where (Tε[0,1]); and 
   φ is the per channel relative phase change induced in the lower arm  104 . 
   When T is known, selection of an appropriate value for R offers a trade-off between the dynamic range and the maximum transmission of the DGEF  100 . 
   Unfortunately, it is a challenge to find a cost-effective solution for an in-service upgradeable in-line amplifier (ISUGILA) towards a reconfigurable optical add/drop multiplexer (ROADM). 
   SUMMARY 
   Various deficiencies of the prior art are addressed by the present invention of system method and apparatus for equalizing and add/dropping optical channels within an optical communications network using, illustratively, two cascading gain equalizing filters. The first gain equalizing filter, for processing a wavelength division multiplexed (WDM) input signal to provide thereby a first component WDM drop signal and a second component WDM drop signal. The second gain equalizing filter, for processing the first component WDM drop signal and a WDM add signal to provide thereby a WDM output signal. 
   Another embodiment for an optical add/drop multiplexer (OADM) includes a first and second coupler and a gain equalizing filter. The first coupler splits a wavelength division multiplexed (WDM) add signal into a first component WDM add signal and a second component WDM add signal. The gain equalizing filter processes a WDM input signal and the first component WDM add signal to provide thereby a first component WDM output signal and second component WDM output signal. The second coupler combines the second component WDM output signal and the second component WDM add signal to produce a WDM drop signal. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The teachings of the present invention can be readily understood by considering the following detailed description in conjunction with the accompanying drawings, in which: 
       FIG. 1  depicts a block diagram of a prior art dynamic gain equalization filter (DGEF); 
       FIG. 2  depicts a block diagram of a reconfigurable optical add/drop multiplexer (ROADM); 
       FIG. 3  depicts a block diagram of an alternative ROADM; 
       FIG. 4  depicts a block diagram of an alternative ROADM; 
       FIG. 5   a  depicts a block diagram of a dual-stage design of a combined DGEF/ROADM; 
       FIG. 5   b  depicts a block diagram of an alternative dual-stage design of a combined DGEF/ROADM; 
       FIG. 5   c  depicts a block diagram of an alternative dual-stage design of a combined DGEF/ROADM; 
       FIG. 6  depicts a block diagram of a combined DGEF/ROADM; and 
       FIG. 7  depicts a block diagram illustrating a general approach for realization of polarization insensitive DGEF/ROADM designs. 
   

   To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. 
   DETAILED DESCRIPTION OF THE INVENTION 
   The invention will be primarily described within the context of an in-line optical amplifier; however, those skilled in the art and informed by the teachings herein will realize that the invention is also applicable to any optical transmission system that employs gain equalization and add/drop functions. 
     FIG. 2  depicts a block diagram of a reconfigurable optical add/drop multiplexer (ROADM). Specifically, the ROADM of  FIG. 2  comprise an optical multiplexer  210 , the DGEF  100 , and a demultiplexer  220 . The DGEF of  100  of  FIG. 2  may be implemented in substantially the same manner as the DGEF  100  discussed with respect to  FIG. 1 . 
   The DGEF  100  in  FIG. 1  has two unused ports  121  and  122 . The ROADM of  FIG. 2  connects the optical multiplexer  210  to the unused input port  121  of the DGEF  100 . The unused output port  122  of the DGEF  100  is connected to the demultiplexer  220 . A plurality of optical channels is multiplexed at multiplexer  210  and inputted to the DGEF  100 . Depending on the mode of operation of the DGEF, a multiplexed optical signal could be outputted from output  122 , and the plurality of optical channels is demultiplexed at demultiplexer  220  where the channels are dropped. 
   The optical multiplexer  210  and demultiplexer  220  can be implemented using two waveguide grating routers connected to optical ports  121  and  122 . The channels can also be multiplexed and demultiplexed on a waveband level using waveband filters. Cascades of thin film filters can be used to separate all or just a few channels from the add/drop bundles. In this configuration, no expensive optical switching elements are required to have the in-line amplifier also perform the functions of an add/drop multiplexer. 
   The transfer function (disregarding the insertion loss of the Add multiplexer  210  and Drop demultiplexer  220 ) between add and drop ports ( 121 ,  122 ) are governed by the following equations:
 
 E   DROP   /E   ADD   =Re   jφ   √{square root over (T)} −(1− R )           
 
 P   DROP   P   ADD   =[R  cos(φ) √{square root over (T)}− (1 −R )] 2   +[R  sin(φ) √{square root over (T)}]   2 =
 
(1 −R ) 2   +R   2   T− 2 R (1 −R )cos(φ) √{square root over (T)}   (2)

   where E DROP , P DROP  and E ADD , P ADD  represent the electrical field and power of the complex envelope of an optical signal at the DGEF drop and add ports  122 , 121  respectively. The power ratios in Equations (1) and (2) reach a minimum for φ=0 and a maximum for φ=π. For ROADM operation, both ratios should reach 0 when a channel is switched to add/drop mode, i.e. φ=0. Using Equations (1) and (2) we arrive at 
                 R   =           T       1   +     T         ⁢           ⁢   or   ⁢           ⁢     T       =     R     1   -   R                 (   3   )               
(3)
 
   to satisfy the condition P OUT /P IN | φ=0 =0, and 
   
     
       
         
           
             
               
                 R 
                 = 
                 
                   
                     
                       
                         T 
                       
                       
                         1 
                         + 
                         
                           T 
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     or 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       T 
                     
                   
                   = 
                   
                     
                       1 
                       - 
                       R 
                     
                     R 
                   
                 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   to satisfy the condition P DROP /P ADD | φ=0 =0. Both conditions can only be met simultaneously when T=1, which is of little practical value; more realistic values for T are 0.5 and below. Satisfying only a single condition results either in residual power of drop channels appearing at the output or in add channel power appearing at the drop port. Nevertheless, the device can be used for only add or only drop mode of operation. 
     FIG. 3  depicts a block diagram of an alternative ROADM. This embodiment allows for full operation as ROADM while counteracting the undesired crosstalk effect. As shown in  FIG. 3 , an attenuator  310  is added to the upper arm  103  of the DGEF  100  of  FIG. 2 . Selecting R=0.5 and adding the attenuator  310  in the upper arm with α=T provides the desired power blocking between input  101  and output  109 , and between add port  121  and drop port  122 . However, the embodiment of  FIG. 3  has additional overall loss compared to the embodiment of  FIG. 2 . 
   Without attaching the multiplexer  210  and demultiplexer  220 , the embodiment of  FIG. 3  can also be used as a reconfigurable 2×2 optical cross connect. However, no equalization can be performed simultaneously as add/drop is being performed. 
     FIG. 4  depicts a block diagram of an alternative ROADM. This embodiment allows for full operation while counteracting the undesired crosstalk effect. This embodiment includes an optical multiplexer  410 , a third optical coupler  402 , an lower arm  403 , an upper arm  404  with DGEF  100 , a fourth optical coupler  405  and an optical demultiplexer  420 . 
   The optical multiplexer  410  is connected to the lower left port  421  of the third optical coupler  402 . The upper right port of the third coupler  402  is connected to the lower left port, also known as the add port  121 , of the DGEF  100 . The lower right port of the third optical coupler  402  is connected to the lower left port of the fourth coupler  405  through optical arm  403 . The upper left port of the fourth coupler  405  is connected to the drop port  122  of the DGEF  100  through optical arm  404 . The upper right port  409  of the fourth coupler  405  functions as the drop port and is connected to the demultiplexer  420 . Ports  401  and  422  are dummy ports which are not connected. 
   Couplers  402 ,  405  can be of many types, including Y-branch couplers, directional couplers, star couplers, and multimode interference couplers. Other types of couplers can also be used as long as no additional phase difference between the branches is introduced by coupler  402  and  405 . 
   The multiplexer  410  adds a plurality of optical input channels and outputs a signal with WDM signal channels. The WDM signal channels enter the third coupler  402  from the lower left port  421  of the third coupler  402 . The third coupler  402  splits the WDM signal into its signal components which are sent to the upper and lower arms,  404  and  403 , respectively. The lower arm  403  is a simple waveguide. The upper arm  404  includes the DGEF  100  which contains two couplers  102  and  105 , a demultiplexer  106  and multiplexer  107  connected by an array of programmable phase shifters  108 . The DGEF  100  of  FIG. 4  functions substantially the same as the DGEF  100  described above in  FIG. 1 . Therefore, it is able to perform equalization or add/drop of the signal entering from input port  101  as well as from the add port  121 . The signals to be dropped will pass through upper arm  404  to the upper left port of the fourth coupler  405  which will be combined with the component on the lower arm  403  which is connected to the lower left port of the fourth coupler  405 . That combined signal will be outputted to the demultiplexer  420  connected to the upper right port  409 . The demultiplexer demultiplexes that WDM signal and drops the plurality of channels. In one embodiment, the third and fourth couplers are Y-branch couplers because then the device can be cut in half with a mirror places along the axis of symmetry. 
   In this embodiment, the operation of the DGEF/ROADM regarding power transmission is now characterized by the following equations:
 
 E   OUT   /E   IN   =R   1 −(1− R   1 ) e   jφ   √{square root over (T)}             
 
 P   OUT   /P   IN   =[R   1 −(1 −R   1 )cos(φ) √{square root over (T)} ] 2 +[(1− R   1 )sin(φ) √{square root over (T)} ] 2 =
 
 R   1   2 +(1 −R   1 ) 2   T − 2 R   1 (1 −R   1 )cos(φ) √{square root over (T)}   (5)
 
 E   DROP   /E   IN =j[√{square root over (R 1 (1− R   1 ))}+ e   jφ √{square root over (R 1 (1 −R   1 ) T )}]√{square root over (1− R   2 )}         
 
 P   DROP   /P   IN   =R   1 (1 −R   1 )(1 −R   2 ){[1+cos(φ)√ {square root over (T)}]   2 +[sin(φ) √{square root over (T)}]   2 }=
 
 R   1 (1 −R   1 )(1 −R   2 )[1 +T+ 2 cos(φ) √{square root over (T)}]   (6)
 
 E   OUT   /E   ADD =−[√{square root over ( R   1 (1 −R   1 ))}+ e   jφ √{square root over (R 1 (1 −R   1 ) T )}]√{square root over (1−R 2 )}         
 
 P   OUT   /P   ADD   =R   1 (1 −R )(1− R   2 ){[1+cos(φ) √{square root over (T)}]   2 +[sin(φ) √{square root over (T)}]   2 }=
 
 R   1 (1 −R   1 )(1 −R   2 )[1 +T+ 2 cos(φ) √{square root over (T)}]   (7)
 
 E   DROP   /E   ADD   =jR   2   +j[R   1   e   jφ   √{square root over (T)}− (1 −R   1 )](1 −R   2 )         
 
 P   DROP   /P   ADD   =[R   2 +(1 −R   2 ){ R   1  cos(φ) √{square root over (T)}− (1 −R   1 )}] 2 +[(1 −R   2 ) R   1  sin(φ) √{square root over (T)}]   2 =
 
[(1 −R   1 )(1 −R   2 )− R   2 ] 2   +R   1   2 (1 −R   2 ) 2   T− 2 R   1 (1 −R   2 )[(1 −R   1 )(1 −R   2 )− R   2 ]cos(φ) √{square root over (T)}   (8)

   Applying the conditions P OUT /P IN | φ=0 =0 and P DROP /P ADD | φ=0 =0 to Equations (5) and (8) now yields 
   
     
       
         
           
             
               
                 
                   R 
                   1 
                 
                 = 
                 
                   
                     
                       
                         T 
                       
                       
                         1 
                         + 
                         
                           T 
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     or 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       T 
                     
                   
                   = 
                   
                     
                       R 
                       1 
                     
                     
                       1 
                       - 
                       
                         R 
                         1 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 9 
                 ) 
               
             
           
           
             
               
                 
                   R 
                   2 
                 
                 = 
                 
                   
                     
                       
                         
                           1 
                           - 
                           
                             T 
                           
                         
                         
                           2 
                           - 
                           
                             T 
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       or 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     - 
                     
                       T 
                     
                   
                   = 
                   
                     
                       R 
                       2 
                     
                     
                       1 
                       - 
                       
                         R 
                         2 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 10 
                 ) 
               
             
           
         
       
     
   
   As Tε[0,1] then according to Equations (9) and (10), R 1 ,R 2 ε[0,½]. In this case, the loss between input and output is optimized whereas add and drop ports encounter additional losses that are limited to 3 dB each, namely −10· 10  log(1−R2). 
   To illustrate the operation of the DGEF/ROADM, let us consider the following example, where T=½. 
   
     
       
             
           
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Transmission values between input/add port and output/drop port for 
             
             
               T = ½ (−3.0 dB), equivalent dB values are given in parentheses 
             
           
        
         
             
                 
               Output 
               Drop port 
             
           
        
         
             
                 
               φ = 0 
               φ = π 
               φ = 0 
               φ = π 
             
             
                 
             
             
               Input 
                  0 (−∞) 
                0.686 (−1.63) 
               0.547 (−2.62) 
               0.0161 (−17.9) 
             
             
               Add 
               0.547 (−2.62) 
               0.0161 (−17.9) 
                  0 (−∞) 
                0.205 (−6.88) 
             
             
               port 
             
             
                 
             
             
               Note: 
             
             
               insertion losses of the multiplexer and demultiplexer at the add and drop ports are disregarded. 
             
           
        
       
     
   
   When in equalizer mode, add port  421  and drop port  422  are idle, and the loss between input  101  and output  109  can be tuned by adjusting φ. The maximum and minimum losses attainable are −∞ dB and −1.63 dB, respectively. In add/drop mode, however, φ will be set to 0. In that case, full power blocking is achieved between input  101  and output  109 , and between add port  421  and drop port  422 , while power transfer is maximized from add port  421  to output  109  and from input  101  to drop port  409 . The values provided in hold for the ideal case. In a practical realization, however, manufacturing tolerances limit the dropped channel extinction ratio to about 30 dB in contrast to full extinction in the ideal case. 
     FIG. 5   a  depicts a block diagram of a dual-stage design of a combined DGEF/ROADM. By cascading two DGEF&#39;s from  FIG. 1  as is illustrated in  FIG. 5 , the required 40 dB is obtained. Each DGEF functions substantially the same as the DGEF described in  FIG. 1 .  FIG. 5   a  includes a first DGEF  100   b , a second DGEF  100   a , an optical multiplexer  510  and an optical demultiplexer  520 . 
   In the embodiment of  FIG. 5   a , the first DGEF  100   b  including a phase shifter  108   b  is cascaded with the second DGEF  100   a  including a phase shifter  108   a  through an optical connection between an output port  109   b  of the first DGEF  100   b  and an input port  101   a  of the second DGEF  100   a . This arrangement results in six available ports: optical input port  101   b , optical output port  109   a , optical add port  121   a , optical drop port  122   b , and two dummy optical ports ( 121   b ,  122   a ) that remain idle. 
   The input port  101   b  is for inputting an optical signal. The optical add port  121   a  is connected to an optical multiplexer  510  which allows for the addition of a plurality of channels. The optical multiplexer  510  functions substantially the same as the multiplexer  210  and  410  described above. The optical drop port  122   b  is connected to a demultiplexer  520  which allows for the dropping of a plurality of channels. The optical demultiplexer  520  functions substantially the same as the demultiplexer  220  and  420  described above. In an embodiment, both corresponding phase shifters ( 108   a ,  108   b ) will be adjusted simultaneously for each individual wavelength channel. The simultaneous adjustment of the phase shifters will limit the necessary control electronics of the system. Optionally, the phase shifter  108   a  or  108   b  can have an offset of 180 degrees predetermined phase shift at zero heating. 
   Some advantages of the embodiment of  FIG. 5   a  are double dropped channel extinction ratio; full add and drop port separation; east-west separability; and reduced losses between add port and output and between input and drop port. On the other hand, some drawbacks are double minimum loss between input and output in equalization mode; and double heater power consumption for controlling of the phase shifters. 
   The power transmission between the output port  109   a  and input port  101   b  of the dual-stage design is governed by the following equations: 
   
     
       
         
           
             
               
                 
                   
                     E 
                     OUT 
                   
                   / 
                   
                     E 
                     IN 
                   
                 
                 = 
                 
                   
                     
                       [ 
                       
                         R 
                         - 
                         
                           
                             ( 
                             
                               1 
                               - 
                               R 
                             
                             ) 
                           
                           ⁢ 
                           
                             ⅇ 
                             jϕ 
                           
                           ⁢ 
                           
                             T 
                           
                         
                       
                       ] 
                     
                     2 
                   
                   ⇒ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           
                             
                               P 
                               OUT 
                             
                             / 
                             
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                               IN 
                             
                           
                           = 
                           
                             
                               [ 
                               
                                 
                                   
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                                       - 
                                       
                                         
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                                           ) 
                                         
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                                           ⁡ 
                                           
                                             ( 
                                             ϕ 
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                           T 
                                         
                                       
                                     
                                     ] 
                                   
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                                   [ 
                                   
                                     
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                                       ) 
                                     
                                     ⁢ 
                                     
                                       sin 
                                       ⁡ 
                                       
                                         ( 
                                         ϕ 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       T 
                                     
                                   
                                   ] 
                                 
                               
                               ] 
                             
                             2 
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             
                               [ 
                               
                                 
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                                   2 
                                 
                                 + 
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         R 
                                       
                                       ) 
                                     
                                     2 
                                   
                                   ⁢ 
                                   T 
                                 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   
                                     R 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         R 
                                       
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                     cos 
                                     ⁡ 
                                     
                                       ( 
                                       ϕ 
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                     T 
                                   
                                 
                               
                               ] 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 11 
                 ) 
               
             
           
           
             
               
                 
                   
                     
                       
                         
                           
                             E 
                             DROP 
                           
                           / 
                           
                             E 
                             IN 
                           
                         
                         = 
                         
                           
                             E 
                             OUT 
                           
                           / 
                           
                             E 
                             ADD 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             j 
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     R 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         1 
                                         - 
                                         R 
                                       
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     ⅇ 
                                     jϕ 
                                   
                                   ⁢ 
                                   
                                     
                                       
                                         R 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             R 
                                           
                                           ) 
                                         
                                       
                                       ⁢ 
                                       T 
                                     
                                   
                                 
                               
                               ] 
                             
                           
                           ⇒ 
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           
                             P 
                             DROP 
                           
                           / 
                           
                             P 
                             IN 
                           
                         
                         = 
                         
                           
                             P 
                             OUT 
                           
                           / 
                           
                             P 
                             ADD 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             R 
                             ⁡ 
                             
                               ( 
                               
                                 1 
                                 - 
                                 R 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   [ 
                                   
                                     1 
                                     + 
                                     
                                       
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                                         ⁡ 
                                         
                                           ( 
                                           ϕ 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         T 
                                       
                                     
                                   
                                   ] 
                                 
                                 2 
                               
                               + 
                               
                                 
                                   [ 
                                   
                                     
                                       sin 
                                       ⁡ 
                                       
                                         ( 
                                         ϕ 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       T 
                                     
                                   
                                   ] 
                                 
                                 2 
                               
                             
                             } 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             R 
                             ⁡ 
                             
                               ( 
                               
                                 1 
                                 - 
                                 R 
                               
                               ) 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               1 
                               + 
                               T 
                               + 
                               
                                 2 
                                 ⁢ 
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     ϕ 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   T 
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 12 
                 ) 
               
             
           
           
             
               
                 
                   
                     E 
                     DROP 
                   
                   / 
                   
                     E 
                     ADD 
                   
                 
                 = 
                 
                   
                     0 
                     ⇒ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         P 
                         
                           
                               
                           
                           ⁢ 
                           DROP 
                         
                       
                       / 
                       
                         P 
                         
                           
                               
                           
                           ⁢ 
                           ADD 
                         
                       
                     
                   
                   = 
                   0 
                 
               
             
             
               
                 ( 
                 13 
                 ) 
               
             
           
           
             
               
                 R 
                 = 
                 
                   
                     
                       
                         T 
                       
                       
                         1 
                         + 
                         
                           T 
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     or 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       T 
                     
                   
                   = 
                   
                     R 
                     
                       1 
                       - 
                       R 
                     
                   
                 
               
             
             
               
                 ( 
                 14 
                 ) 
               
             
           
         
       
     
   
   For the example case T=½, the transmission values at the extremes are summarized in Table 2. 
   
     
       
             
           
             
             
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Transmission values of the dual-stage concept between input/add port 
             
             
               and output/drop port for T = ½ (−3.0 dB), equivalent dB values 
             
             
               are given in parentheses 
             
           
        
         
             
                 
               Output 
               Drop port 
             
           
        
         
             
                 
               φ = 0 
               φ = π 
               φ = 0 
               φ = π 
             
             
                 
                 
             
           
        
         
             
               Input 
                  0 (−∞) 
                0.471 (−3.27) 
               0.707 (−1.51) 
               0.0208 (−16.8) 
             
             
               Add 
               0.707 (−1.51) 
               0.0208 (−16.8) 
                  0 (−∞) 
                  0 (−∞) 
             
             
               port 
             
             
                 
             
             
               Note: 
             
             
               insertion losses of the multiplexer and demultiplexer at the add and drop ports are disregarded. 
             
           
        
       
     
   
     FIG. 5   b  depicts a block diagram of an alternative dual-stage design of a combined DGEF/ROADM. This variation will reduce the power consumption. The embodiment of  FIG. 5   b  is substantially the same as  FIG. 5   a  except the second DGEF  100   a  is replaced by a third DGEF  100   c . The variation of  FIG. 5   b  is that the phase shifters  108   c  are located on the lower arm  504   c  thereby leaving arm  503   c  as a simple waveguide. In this embodiment, the output is located at port  122   c  instead of  109   c . It is an optional mode of operation to adjust the power level with only phase shifter  108   b  in this embodiment. 
     FIG. 5   c  depicts a block diagram of an alternative dual-stage design of a combined DGEF/ROADM. The embodiment of  FIG. 5   c  is another variation based on  FIG. 5   b  where the two DGEFs are cascaded with a waveguide between ports  122   b  and  121   c . The add multiplexer  510   d  substantially similar to the add multiplexer  510  is connected to port  101   c . The drop multiplexer  520   d  which functions substantially similar to drop multiplexer  520  is connected to port  109   b . In this embodiment, an optional mode of operation includes using only phase shifter  108   c  to adjust the power. Another way of looking at the embodiment of  FIG. 5   c  is that  FIG. 5   b  and  FIG. 5C  are reciprocals of each other. Specifically, the output and input are interchanged and add and drop are switched. 
     FIG. 6  depicts a block diagram of a combined DGEF/ROADM. The embodiment of  FIG. 6  is another way to reach the required dropped channel extinction ratio. In the embodiment as shown in  FIG. 6 , the combined DGEF/ROADM comprises a counter-clockwise circulator  650 , a first polarization beam splitter (PBS)  660 , polarization rotators  670 , a fifth coupler  643 , a sixth coupler  644 , a seventh coupler  664 , an eighth coupler  663 , a second PBS  640 , a clockwise circulator  630 , an optical multiplexer  610  for adding a plurality of optical channels and an optical demultiplexer  620  for dropping a plurality of optical channels. 
   An output  609 , an input  601 , and the first polarization beam splitter (PBS)  660  are connected in that order to a counter-clockwise circulator  650 . The input is sent to the first PBS. The PBS splits the received optical signal into two signals separated by 90 degrees and transmits them to the seventh  664  and eighth  663  couplers. The signals received from the seventh and eighth couplers are combined and sent to the counter-clockwise circulator to the output  609 . 
   The upper left port of the seventh coupler  664  is connected through fiber  662  to the left port of the first PBS, and the upper right port of the eighth coupler  663  through fiber  661  is connected to the right port of the first PBS. The upper left port of the eighth coupler  663  and the upper right port of the seventh coupler  664  are connected by an upper arm  680 . The lower left port of the eighth coupler  663  and the lower right port of the seventh coupler  664  are connected by a lower arm  685  that includes a multiplexer  674 , demultiplexer  673  and polarization rotators  670 . The lower arm  685  functions similarly to the lower arm  104  of  FIG. 1  except the signals are controlled by rotating the polarization instead of shifting the phase. 
   The fifth coupler  643  has 4 ports. The upper left port is a dummy port. The lower left port is connected to the second PBS  640 . The upper right port of the fifth coupler  643  is connected to the lower left port of the seventh coupler  664 . The lower right port of the fifth coupler  643  is connected via fiber  645  to the lower left port of the sixth coupler  644 . 
   The sixth coupler  644  functions substantially the same as the fifth coupler  643 . In addition to the fiber connection of the fifth coupler  643  via the lower left port, the upper left port is connected to the lower right port of eighth coupler  663 . The lower right port of the sixth coupler is a dummy port. The upper right port of the sixth coupler  644  is connected to the second PBS  640  via fiber  642 . 
   The second PBS  640  has 3 ports. The left port of the second PBS  640  is connected to the fifth coupler  643  by fiber  641 , and the sixth coupler  644  is connected to the right port of the second PBS through fiber  642  as described above. The left and right ports of the second PBS are separated by 90 degrees. For signals received from the clockwise circulator  630  at the second PBS, two signals will be transmitted on the right and left ports separated by 90 degrees. Similarly, the signals received from the fibers will be combined and transmitted from the third port of the PBS to the clockwise circulator  630  to be circulated for dropping channels at demultiplexer  620 . 
   The clockwise circulator  630  circulates the signals from the multiplexer  610  for adding optical channels, third port of the second PBS  640 , and the demultiplexer  620  for dropping channels, respectively. The clockwise circulator  630  therefore allows for the add channels at the multiplexer  610  to be transmitted to the third port of the second PBS  640  and the signals at the third port of the second PBS  640  to be circulated to the drop ports of the demultiplexer  620 . 
   The design as indicated in  FIG. 6  results in the separation of the add signals from the multiplexer  610  and input  601  into two orthogonally polarized signals that counter-propagate through the structure of  FIG. 6 . After propagation, parts of the signals will be recombined by the PBS&#39;s  640 ,  660  and appear via the optical circulators  630 ,  650  at the output  609  and/or drop ports  620 , respectively, depending on the applied polarization rotation at the polarization rotators  640 . 
   Signals leaving from one PBS at either polarization are blocked by the same PBS after propagation through the structure, and directed to the output  609  or drop port  621  by the other PBS. However, when polarization rotation is applied, the signals are divided over both the output  609  and drop  621  port. Coupling of the orthogonal polarization states to the +45 and −45 degree angles with respect to the horizontal axis of the waveguides is chosen to assure polarization independent behavior of the design. In theory, any two angles with a difference of 90 degrees are permitted. 
   Introducing vector notation for the electrical field of the optical signals, the operation of the DGEF/ROADM from  FIG. 6  can now be described by the following equations: 
   
     
       
         
           
             
               
                 
                   
                     E 
                     -&gt; 
                   
                   OUT 
                 
                 = 
                 
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             R 
                             1 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           Θ 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           E 
                           -&gt; 
                         
                         IN 
                       
                     
                     ⇒ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         P 
                         OUT 
                       
                       / 
                       
                         P 
                         IN 
                       
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             R 
                             1 
                           
                         
                         ) 
                       
                       2 
                     
                     ⁢ 
                     T 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         sin 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         Θ 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 15 
                 ) 
               
             
           
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               E 
                               -&gt; 
                             
                             DROP 
                           
                           ❘ 
                           
                             
                               E 
                               -&gt; 
                             
                             OUT 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               
                                 
                                   R 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       R 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     R 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 
                                   cos 
                                   ⁡ 
                                   
                                     ( 
                                     Θ 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   T 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     
                                       - 
                                       1 
                                     
                                   
                                   
                                     0 
                                   
                                 
                                 
                                   
                                     0 
                                   
                                   
                                     j 
                                   
                                 
                               
                               ] 
                             
                             ⁢ 
                             
                               
                                 E 
                                 -&gt; 
                               
                               IN 
                             
                           
                           ❘ 
                           
                             
                               
                                 E 
                                 -&gt; 
                               
                               ADD 
                             
                             ⇒ 
                           
                         
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         
                           
                             P 
                             DROP 
                           
                           / 
                           
                             P 
                             IN 
                           
                         
                         = 
                         
                           
                             P 
                             OUT 
                           
                           / 
                           
                             P 
                             ADD 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               R 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   R 
                                   1 
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   
                                     R 
                                     2 
                                   
                                 
                                 ) 
                               
                               ⁡ 
                               
                                 [ 
                                 
                                   1 
                                   + 
                                   
                                     
                                       cos 
                                       ⁡ 
                                       
                                         ( 
                                         Θ 
                                         ) 
                                       
                                     
                                     ⁢ 
                                     
                                       T 
                                     
                                   
                                 
                                 ] 
                               
                             
                             2 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 16 
                 ) 
               
             
           
           
             
               
                 
                   
                     E 
                     -&gt; 
                   
                   DROP 
                 
                 = 
                 
                   
                     
                       
                         
                           jR 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               R 
                               2 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           Θ 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           T 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 1 
                               
                             
                             
                               
                                 
                                   - 
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           E 
                           -&gt; 
                         
                         ADD 
                       
                     
                     ⇒ 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         P 
                         DROP 
                       
                       / 
                       
                         P 
                         ADD 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           R 
                           1 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               R 
                               2 
                             
                           
                           ) 
                         
                       
                       2 
                     
                     ⁢ 
                     T 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         sin 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         Θ 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 17 
                 ) 
               
             
           
           
             
               
                 
                   R 
                   1 
                 
                 = 
                 
                   
                     
                       
                         T 
                       
                       
                         1 
                         + 
                         
                           T 
                         
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     or 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       T 
                     
                   
                   = 
                   
                     
                       R 
                       1 
                     
                     
                       1 
                       - 
                       
                         R 
                         1 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 18 
                 ) 
               
             
           
           
             
               
                 
                   R 
                   2 
                 
                 = 
                 
                   
                     
                       
                         
                           1 
                           - 
                           
                             T 
                           
                         
                         
                           2 
                           - 
                           
                             T 
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       or 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     - 
                     
                       T 
                     
                   
                   = 
                   
                     
                       R 
                       2 
                     
                     
                       1 
                       ⁢ 
                       
                           
                       
                       - 
                       
                           
                       
                       ⁢ 
                       
                         R 
                         2 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 19 
                 ) 
               
             
           
         
       
     
   
   In the equations above (15 through 17), Θ represents the angle of polarization rotation. The electrical fields and respective optical powers are defined as 
   
     
       
         
           
             
               
                 
                   
                     
                       E 
                       -&gt; 
                     
                     X 
                   
                   ≡ 
                   
                     [ 
                     
                       
                         
                           
                             E 
                             
                               X 
                               , 
                               
                                 - 
                                 45 
                               
                             
                           
                         
                       
                       
                         
                           
                             E 
                             
                               X 
                               , 
                               
                                 + 
                                 45 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
                 , 
                 
                   
                     
                       P 
                       X 
                     
                     ≡ 
                     
                       
                          
                         
                           
                             E 
                             -&gt; 
                           
                           X 
                         
                          
                       
                       2 
                     
                   
                   = 
                   
                     
                       
                          
                         
                           E 
                           
                             X 
                             , 
                             
                               - 
                               45 
                             
                           
                         
                          
                       
                       2 
                     
                     + 
                     
                       
                          
                         
                           E 
                           
                             X 
                             , 
                             
                               + 
                               45 
                             
                           
                         
                          
                       
                       2 
                     
                   
                 
                 , 
               
             
             
               
                 ( 
                 20 
                 ) 
               
             
           
         
       
     
   
   where E X,−45  and E X,+45  are the electrical fields of the respective −45° and +45° polarization states. 
   An advantage is the additional dropped channel extinction of about 20 dB (cross talk between the two states of polarization at the PBS). The major drawback to be mentioned is the additional 6 dB loss between input and output in DGEF mode. For the situation T=½, the transmission values at the extremes are summarized in Table 3. 
   
     
       
             
           
             
             
             
           
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               Transmission values of the polarization-based concept between 
             
             
               input/add port and output/drop port for T = ½ (−3.0 dB), 
             
             
               equivalent dB values are given in parentheses 
             
           
        
         
             
                 
               Output 
               Drop port 
             
           
        
         
             
                 
               Θ = 0 
               Θ = π/2 
               Θ = 0 
               Θ = π/2 
             
             
                 
                 
             
           
        
         
             
               Input 
                  0 (−∞) 
               0.172 (−7.66) 
               0.547 (−2.62) 
                0.188 (−7.27) 
             
             
               Add 
               0.547 (−2.62) 
               0.188 (−7.27) 
                  0 (−∞) 
               0.0513 (−12.9) 
             
             
               port 
             
             
                 
             
             
               Note: 
             
             
               insertion losses of the multiplexer and demultiplexer at the add and drop ports, PBS&#39;s, and circulators are disregarded. 
             
           
        
       
     
   
     FIG. 7  depicts a block diagram illustrating a general approach for realization of polarization insensitive DGEF/ROADM designs. Depending on the chip technology used, the designs depicted in  FIG. 2  thru  FIG. 5  can be polarization sensitive. The embodiment shown in  FIG. 7  is a polarization insensitive arrangement. 
   The embodiment of  FIG. 7  includes an optical multiplexer  610 , an optical demultiplexer  620 , a counter-clockwise circulator  650 , a clockwise circulator  630 , a third PBS  760 , a fourth PBS  740 , and a DGEF/ROADM block  750 . The DGEF/ROADM block  750  could comprise any one of the embodiments of  FIG. 2 ,  FIG. 3 ,  FIG. 4 , or  FIG. 5  without the optical multiplexer ( 210 ,  410 ,  510 ) and optical demultiplexer ( 220 ,  420 ,  520 .) The DGEF/ROADM block includes input, output, add and drop ports that correspond to those ports in  FIG. 2 ,  FIG. 3 ,  FIG. 4 , and  FIG. 5 . The orthogonal polarizations of the PBS&#39;s ( 740 ,  760 ) are coupled to the same axis of the waveguides. 
   The counter-clockwise circulator  650  of  FIG. 7  functions substantially the same as the counter-clockwise circulator of  FIG. 6 . The third PBS  760  is connected to the counter-clockwise circulator in  FIG. 7 . The input signal  601  is circulated to the third PBS  760 . The third PBS  760  splits the input  601  signal received at the first circulator  650  and propagates two orthogonal polarized signals on two fibers  661 ,  662 . Fiber  661  connects the right port of the third PBS  760  to the output of the DGEF/ROADM block  750 . Fiber  662  connects the left port of the third PBS  760  to the input of the DGEF/ROADM block  750 . The signals received by the third PBS  760  from the DGEF/ROADM  750  are combined and circulated to the output  609 . 
   The clockwise circulator  630  of  FIG. 7  functions substantially the same as the clockwise circulator in  FIG. 6 . It receives a WDM signal including a plurality of optical signals that is multiplexed by the optical multiplexer  610  of  FIG. 7  that functions substantially the same as the multiplexer  610  in  FIG. 6 . That WDM signal is passed clockwise to the fourth PBS  740  which splits that signal into two orthogonal polarized signals on two fibers  641 ,  642 . Fiber  641  connects the left port of the fourth PBS  740  to the add port of the DGEF/ROADM block  750 . Fiber  642  connects the right port of the fourth PBS  740  to the drop port of the DGEF/ROADM block  750 . The signals that are received by the fourth PBS  740  is combined and circulated to the demultiplexer  620  of  FIG. 7  that functions substantially the same as the demultiplexer  620  of  FIG. 6  where the signal is demultiplexed to drop the desired channels. 
   An alternative to polarization diversity to achieve polarization insensitivity is to use a half-wave plate inserted in the center of the DGEF chip. 
   While the foregoing is directed to various embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof. As such, the appropriate scope of the invention is to be determined according to the claims, which follow.