Abstract:
A compensation arrangement for addressing the problem of first-order and second-order polarization mode dispersion (PMD) in an optical fiber communication system includes separate, independent elements for each type of PMD. First-order PMD may be compensated using conventional techniques related to adjusting the transit time differential between the polarization states. The second-order polarization mode dispersion is compensated by recognizing the separate sources of second-order PMD (pulse broadening analogous to chromatic dispersion, additional pulse broadening due to optical filtering (narrowing), and coupling of a portion of the optical signal into the orthogonal polarization relative to the main pulse with a different transmit time. A chirped fiber grating with a variable temperature gradient, a complementary optical filter with variable spectral transmission and a polarizer, respectively, can be used to compensate for these three sources of second-order PMD.

Description:
TECHNICAL FIELD 
     The present invention relates to an arrangement for mitigating the effects of first- and second-order polarization mode dispersion (PMD) in optical fiber communication systems and, more particularly, to the recognition of the sources of second-order PMD and the provision of specific components that are capable of compensating for both first-order and second-order PMD. 
     BACKGROUND OF THE INVENTION 
     Polarization mode dispersion (PMD) occurs in an optical fiber as a result of a small residual birefringence that is introduced in the fiber core by asymmetric internal stress or strain as well as random polarization coupling due to external forces acting upon the fiber. In particular, PMD causes optical signal distortion as a function of time. Consequently, PMD may severely impair the transmission of a signal in an optical fiber network. Indeed, with the continued push to higher bit rates (i.e., greater than 2.5 Gb/s) in telecommunication systems, PMD is becoming a non-negligible propagation effect. So-called “single” mode fiber actually supports two modes, one for each polarization. Since in general the effective index of these two modes is not the same at any given point in a transmission system, there exists modal dispersion between the two polarizations (i.e., PMD). 
     It is well-known that PMD affects certain polarization components of an optical signal propagating through an optical fiber transmission line differently, such that differential time delays occur among the components as they travel through the fiber. These differential time delays may range from about 0.1 ps/(km) ½  for low-PMD optical fibers of modern manufacture to several ps/(km) ½  for single mode optical fibers of older manufacture. Disadvantageously, the differential time delay that may result over a “long distance” fiber optic link (for example, a 100 km terrestrial transmission system) may be more that 20 ps, with a 10 ps or greater delay associated with a transoceanic link employing state-of-the-art low-PMD optical fiber. 
     It is well-known that the differential time delay that might occur in a particular transmission fiber is not constant over time, but may vary as the physical environment of the fiber changes (e.g., temperature of the fiber, pressure upon the fiber). Thus, the statistics of time-dependent differential time delay caused by PMD in an optical fiber usually follows a Maxwellian distribution and, therefore, at any point in time, may be substantially lower to several times higher than its average (or mean) value. 
     Prior methods of dealing with signal impairments associated with PMD in an optical fiber include, for example: (1) electrical equalization of the signal distortion caused by PMD, as discussed in an article entitled “Experimental Equalization of Polarization Dispersion”, by M. A. Santoro et al., appearing in IEEE Photonic Technology Letters, Vol. 2, No. 8, 1990, beginning at page 591; and (2) electrical compensation of the differential time delay in the received electrical signals, as discussed in the article entitled “Polarization Mode Dispersion Compensation by Phase Diversity Detection”, by B. W. Hakki, appearing Photonic Technology Letters, Vol. 9, No. 1, 1997, beginning at page 121. Such prior methods also include optical compensation of the differential time delay before converting the optical signals into electrical signals, as discussed in the article “Automatic Compensation of First-Order Polarization Mode Dispersion in a 10-Gb/s Transmission System”, by F. Heismann et al, appearing in the Proceedings of ECOC &#39;98, September 1998. 
     While these methods are useful at addressing first-order effects, there remains in the art the need to address the impact of second-order polarization mode dispersion on optical fiber transmission systems. 
     SUMMARY OF THE INVENTION 
     The need remaining in the prior art is addressed by the present invention, which relates to an arrangement for mitigating the effects of first- and second-order-polarization mode dispersion (PMD) in optical fiber communication systems and, more particularly, to the recognition of the sources of second-order PMD and providing components that are capable of compensating for first-order and second-order PMD. 
     In accordance with the teachings of the present invention, first-order PMD compensation can be provided by any technique well-known in the art, such as by including a time delay arrangement that is controlled to adjust the propagation differential between the orthogonal polarization states. Second-order PMD is recognized in accordance with the present invention as associated with at least one of three distinct effects: (1) polarization dependent pulse broadening (analogous to chromatic dispersion); (2) additional pulse broadening (attributed to optical filtering); and (3) coupling of a portion of the optical signal into the orthogonal polarization (relative to the main pulse) with a different propagation time. Each one of these effects is increased when the spectral bandwidth of the optical signal is increased. In one embodiment of the present invention, therefore, second-order PMD can be minimized by minimizing the spectral bandwidth of the transmitted pulse. 
     In an alternative embodiment of the present invention, second-order PMD is compensated by including separate elements within the transmission system that address each of the three identified sources of second-order PMD mentioned above. For example, a chirped fiber grating with a variable temperature gradient can be used to compensate for the first type of pulse broadening that is akin to chromatic dispersion. An independent, complementary optical filter with variable spectral transmission can be inserted in the signal path to compensate for the additional pulse broadening. Lastly, an additional polarizer can be inserted in the transmission path to filter out the signal that has coupled into the unwanted polarization. 
     In accordance with the present invention, the various components used to provide the above-described compensation may be disposed in any suitable arrangement along the signal path. Additionally, one may sacrifice the degree of second-order compensation (if size or economy is an issue, for example) by eliminating one or two of the three separate components used for second-order PMD compensation. 
    
    
     Other and further aspects of the present invention will become apparent during the course of the following discussion and by reference to the accompanying drawings. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Referring now to the drawings, 
     FIG. 1 is a graph illustrating an initial Gaussian pulse at 1550 nm, and the same pulse after propagation through 300 km of standard single mode fiber; 
     FIG. 2 illustrates a conventional prior art fiber optic transmission path including an arrangement for providing first-order PMD compensation; 
     FIG. 3 illustrates an exemplary arrangement of the present invention capable of compensating for both first-order and second-order PMD; and 
     FIG. 4 is a graph illustrating both first-order and second-order PMD. 
    
    
     DETAILED DESCRIPTION 
     The following discussion of polarization mode dispersion will utilize a Gaussian pulse as an exemplary bit, where FIG. 1 shows both an initial Gaussian pulse and a dispersed pulse (the dispersion as a result of propagation through 300 km of standard single mode fiber). In order to better understand the effect of polarization mode dispersion on pulse propagation, it is helpful to first discuss propagation of a pulse in a fiber without any polarization effects at all. A Gaussian pulse is chosen as the desired waveform shape merely because of the simplification of the mathematics: Gaussian functions transform into Gaussian functions, and so conversion from the time domain to the frequency domain is trivial. When such a pulse propagates down a section of fiber. with chromatic dispersion, the pulse arrives as shown by the dotted line in FIG.  1 . The propagation is mathematically represented very simply: 
     
       
           E ( z )= e   βz   E (0), 
       
     
     where it will be recalled that β is defined as the propagation constant and can be expanded into:        β   =           n        (   ω   )          ω     c     =       -     β   0       +       β   1        δ                 ω     +       1   2          β   2        δ                   ω   2       +   …                              
     where β 1  is the inverse of the group velocity V g  and β 2  is proportional to the chromatic dispersion. At a distance z=L, the pulse peak arrives at time t max  defined as follows:          t   max     =         β   1        L     =     L     V   g                                
     with a maximum power, P max , reduced from the initial value P initial  to          P   max     =       P   initial         1   +         β   2   2          L   2         Δ                   t   4                                      
     and a characteristic pulse width Δt final , increased from the initial pulse width Δt initial  to          Δ                   t   final       =     Δ                   t   initial            1   +         β   2   2          L   2         Δ                   t   initial   4                                      
     For an exemplary 300 km span, the group delay t max  is approximately 1.5 ms. For a 10 Gbit pulse, Δt initial  is approximately 100 ps. In standard single mode fiber, β 2  is on the order of −25 ps 2 /km, giving a final pulse width of 125 ps. 
     As mentioned above, single mode fibers actually propagate two distinct modes, corresponding to the two orthogonal polarizations. The description of pulse propagation described thus far has not considered this fact and, indeed, a modification of equation (1) is required to account for both polarizations. In the case of only one mode, a scalar operator can be used to describe the system, as shown above. In the case of two modes, a 2×2 matrix operator is required. In the specific case of polarizations, this 2×2 matrix referred to as a “Jones” matrix, and the associated propagation equation is: 
     
       
           {overscore (E)} ( z )= Be   iβz   {overscore (E)} (0). 
       
     
     In this case, E represents the electrical is a Jones vector carrying the information for both polarizations, and B is the 2×2 Jones matrix. For the purposes of the present invention, it will be presumed that B exhibits negligible, or uncorrelated polarization dependent loss (PDL), meaning that B is unitary and can be completely described by one real amplitude and three real phases. Written explicitly:        B   =     [             r        (   ω   )                                      ϕ   1          (   ω   )                     -       1   -       r   2          (   ω   )                                            ϕ   3          (   ω   )                           1   -       r   2          (   ω   )                                          ϕ   2          (   ω   )                     r        (   ω   )                         (         ϕ   2          (   ω   )       +       ϕ   3          (   ω   )       -       ϕ   1          (   ω   )         )                 ]                            
     Without loss of generality, the basis system can be chosen as the launched mode and an orthogonal mode. This yields, for an optical signal centered at ω 0 ,            E        (     ω   ,              L     )       ≈       [                        (         r   1          (     ω   0     )       +       r   1   ′        δ                 ω     +       1   2          r   1   ″        δ                   ω   2         )                       (         ϕ   1          (     ω   0     )       +       ϕ   1   ′        δ                 ω     +       1   2          ϕ   1   ″        δ                   ω   2         )                       (         r   2          (     ω   0     )       +       r   2   ′        δ                 ω     +       1   2          r   2   ″        δ                   ω   2         )                       (         ϕ   2          (     ω   0     )       +       ϕ   2   ′        δ                 ω     +       1   2          ϕ   2   ″        δ                   ω   2         )                 ]     ×                           β                 L            E        (     ω   ,   0     )           ,                          
     where r 1 (ω) and r 2 (ω) are not independent, but are related by the unitary condition r 1   2 +r 2   2 =1. Note that this expansion of B has terms that are readily identifiable. The first and second derivatives of r are broadening terms, while the first derivative of φ is a change in the group velocity and the second derivative of φ equivalent to chromatic dispersion. Without any correction made to the effects of polarization mode dispersion within the fiber, all of these effects are present. In general, φ 1 ′ and φ 2 ′ are not equal. They translate to a difference in transit times for the two different output polarizations. This difference in transit time, usually measured in picoseconds (ps), is then defined as “first-order” polarization mode dispersion (PMD). 
     Since B is a standard 2×2 matrix, the eigenstates of the matrix can be determined for a given frequency ω 0 . By launching the eigenstate of B at frequency ω 0 , B is diagonalized at the center frequency. Keeping the lower order terms in r yields:          E        (     ω   ,   L     )       ≈       [             (     1   +       1   2          r   1   ″        δ                   ω   2         )                       (         ϕ   1          (     ω   0     )       +                  ϕ   1   ′        δ                 ω                +       1   2          ϕ   ″        δ                   ω   2         )                       (         -     r   1   ″            δ                 ω     )                       (         ϕ   2          (     ω   0     )       +       ϕ   2   ′        δ                 ω       )                 ]                                β                 L              E        (     ω   ,   0     )       .                              
     In this simplified form, it can be seen that to the first order, all the output is associated with a single polarization state, and that state is only delayed in time by the first order correction. All other terms in this expression are second-order in this expansion and will be discussed separately below. 
     FIG. 2 illustrates an exemplary prior art system including an optical delay section used to adjust the difference in transit times to overcome the presence of the first-order portion of the PMD. Referring to FIG. 2, an optical signal launched by a transmitter  10  propagates through an optical fiber transmission system  12 , which may include a number of amplifying devices  14  if the span is sufficiently long. At a predetermined distance from the transmitter (for example, 300 km), a first-order PMD compensator  16  may be disposed. As shown in FIG. 2, by the time an exemplary pulse reaches first-order PMD compensator  16 , the orthogonal polarizations may have a difference in transit times of Δτ. This difference is removed by first passing the pulses through a polarization controller  18 , which functions to align the polarization of the two distinct pulses with the subsequent beam splitter axes. The two orthogonal pulses next pass through a first polarization beam splitter  20  which functions to de-couple the two polarizations, sending a first polarization along signal path  22 , and the remaining polarization along signal path  24 . As shown in FIG. 2, signal path  24  is designed to exhibit an optical path length that is Δτ greater than signal path  22 . Therefore, when the two signals are re-combined in a second polarization beam splitter  26 , the additional delay associated with path  24  will result in the two polarizations essentially overlapping in time at the output of second polarization beam splitter  26 , effectively removing the presence of the first-order polarization mode dispersion. 
     While this arrangement is sufficient in removing most, if not all, of the first-order polarization mode dispersion, the effects of second-order PMD are still present. Realizing that r 1 ″ is negative by the above-defined unitary condition (see equation (9)), the effects of second-order PMD can be examined. First, upon inspect of the above simplification, it can be seen that the additional pulse broadening due to φ 1 ″ is of the well-known form associated with chromatic dispersion. In fact, upon detection it is difficult to discern if this particular broadening is due to chromatic dispersion or PMD Therefore, the second-order effect associated with this portion of the pulse broadening can be compensated by the same methods used to remove chromatic dispersion from optical transmission. Another second-order effect is additional pulse broadening due to optical filtering. That is, the power in the original signal has been reduced by the presence of r 1 ″. More particularly, the optical spectrum has been narrowed by a bandpass filter centered ω 0 . An independent, complementary filter can therefore be used to nullify this effect. Lastly, there is now power present in the orthogonal polarization, where this pulse has significantly different shape and is delayed with respect to the original pulse. The addition of a polarizer can be used to discard the unwanted polarization. 
     FIG. 3 illustrates an compensator of the present invention which provides both first-order and second-order polarization mode dispersion. The components associated with the provisioning of the first-order PMD compensation are identical to those shown in FIG.  2  and need not be reviewed. In accordance with the present invention, the various aspects of second-order polarization mode dispersion can be compensated by including additional elements, each element, associated with a separate source of second-order PMD. Referring to FIG. 3, a circulator  30  is shown as disposed beyond second polarization beam splitter  26  and functions to couple the optical signal into the components associated with second-order compensation. 
     In particular, circulator  30  and a chirped fiber grating  32  are shown in FIG.  3  and are used to remove the additional pulse broadening that appears identical to “chromatic” dispersion. Chirped fiber grating  32  exhibits a dispersion that can be controlled as a function of temperature and is therefore capable of providing a dynamic, adjustable dispersion compensation. One exemplary type of such a dynamic chirped fiber grating is disclosed in Ser. No. 09/183,048 and is herein incorporated by reference. 
     A variable spectral transmission optical filter  34  is disposed beyond grating  32  and functions to provide a “complement” to the filter causing the additional pulse broadening present in the second-order PMD. This variable width notch filter can be adjusted dynamically as the spectral width of the bandpass filter effect changes in the system. A polarization controller  37  is then used to maximize the power through a polarizer  36 , included to remove essentially all of the power that has been coupled into the unwanted component of the optical signal. It is to be understood that these three components of second-order PMD are independent and, as such, any one (or two) of the compensation elements can be eliminated while still providing a degree of second-order PMD compensation. Ideally, the order of these components is not fixed and they may, in general, be placed in any suitable sequence. However, the polarization dependent properties of particular components may suggest a preferred order to avoid polarization-dependent transmission. 
     It is to be understood that while Gaussian expressions were used to define the pulses discussed above, the results and conclusions concerning the B matrix are very general and can be used with any suitable amplitude-modulated format. In fact, it has been found that by using either duobinary or NRZ transmission, second-order PMD will be “automatically” reduced, since both of these schemes use relatively narrow spectral bandwidth signals. In general, the foregoing is merely illustrative of the principles of the present invention. Those skilled in the art will be able to devise numerous arrangements, which, although not explicitly shown or described herein, nevertheless embody those principles that are within the spirit and scope of the present invention.