Abstract:
Method and apparatus for transmitting a light signal in an optical transmission system is described. In an example, an optical transmission link includes an input port and an output port. The optical transmission link is configured to propagate optical pulses from the input port to the output port. Information is encoded using phase relationships between adjacent ones of the optical pulses. A phase conjugator is disposed between the input port and the output port. The phase conjugator is positioned to reduce phase variance of the optical pulses at the output port.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention generally relates to optical communication systems and, more particularly, to reducing phase jitter in an optical communication system.  
           [0003]    2. Description of the Related Art  
           [0004]    In the propagation of optical pulses in ultra-long haul (ULH) applications, such as transoceanic transmission, numerous parameters associated with such transmission limit the capacity of the optical fiber cable system through which the optical pulses are transmitted. Pulse timing jitter is a major limitation to the maximum reach of ULH on-off transmission systems. For single-channel systems, a significant source of timing jitter is attributed to contributions from transmitter and receiver electronics, acoustic interaction effects, or especially, in the case of soliton transmission, to the Gordon-Haus effect. The Gordon-Haus effect is caused by the interaction of soliton pulses with amplifier spontaneous emission (ASE) noise present along the transmission medium. For multi-channel wavelength division multiplexed (WDM) systems, timing jitter is increased significantly by inter-channel soliton collisions. This collision-induced (CI) timing jitter is the dominant impairment of WDM soliton systems. Thus the search continues for other transmission formats that are less susceptible to timing jitter.  
           [0005]    One such transmission format that has attracted attention is a differential-phase-shift-keyed (DPSK) modulation format. In a DPSK system (as well as other phase-shift keying (PSK) modulation formats, such as quadrature phase-shift keying (QPSK)), information is encoded using phase differences between neighboring optical pulses (e.g., solitons). For PSK systems, however, the error-free transmission distance is limited by phase jitter, in which power shifts caused by ASE are converted into phase shifts by self-phase modulation (SPM). It is thus desirable to provide a practical and cost effective method and apparatus for reducing phase jitter in an optical communication system.  
         SUMMARY OF THE INVENTION  
         [0006]    These and other deficiencies of the prior art are addressed by the present invention of a method and apparatus for transmitting a light signal in an optical transmission system. In one embodiment, an optical transmission link includes an input port and an output port. The optical transmission link is configured to propagate optical pulses from the input port to the output port. Information is encoded using phase relationships between adjacent ones of the optical pulses. A phase conjugator is disposed between the input port and the output port. The phase conjugator is positioned to reduce phase variance of the optical pulses at the output port. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]    So that the manner in which the above recited features of the present invention are attained and can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof which are illustrated in the appended drawings.  
         [0008]    It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments.  
         [0009]    [0009]FIG. 1 is a block diagram depicting an exemplary embodiment of an optical transmission system in accordance with the invention;  
         [0010]    [0010]FIG. 2 is a block diagram depicting another embodiment of an optical transmission system in accordance with the invention;  
         [0011]    [0011]FIG. 3 is a block diagram depicting yet another embodiment of an optical transmission system in accordance with the invention;  
         [0012]    [0012]FIG. 4 is a graph depicting an exemplary phase variance versus distance for the optical transmission system of FIG. 1; and  
         [0013]    [0013]FIG. 5 is a graph depicting an exemplary phase variance versus distance for the optical transmission system of FIG. 2. 
     
    
     DETAILED DESCRIPTION  
       [0014]    A method and apparatus for reducing phase jitter in an optical communications system is described. One or more aspects of the invention are related to reducing phase jitter in a single channel differential-phase-shift-keyed (DPSK) optical transmission system exhibiting constant dispersion. Those skilled in the art will appreciate, however, that the invention may be used to reduce phase jitter in other types of phase-shift-keyed (PSK) optical transmission systems, such as multi-channel (e.g., WDM) and/or dispersion managed (DM) PSK systems.  
         [0015]    [0015]FIG. 1 is a block diagram depicting an exemplary embodiment of an optical transmission system  100  in accordance with the invention. The optical transmission system  100  comprises a transmitter  102 , an optical transmission link  150 , and a receiver  104 . The transmitter  102  illustratively comprises a laser source  106 , a pulse generator  110 , a pulse modulator  112 , a data source  108 , and a differential encoder  114 . The laser source  102  operates in a continuous wave (CW) mode to produce light at a predefined transmission wavelength. The light generated by the laser source  102  is coupled to the pulse generator  110  to generate a pulse train. For example, a train of optical pulses (e.g., solitons) may be produced having a repetition rate of 10 GHz and a duty cycle of 33% (pulse full width half maximum (FWHM) of 33 ps).  
         [0016]    The pulse modulator  112  modulates the optical pulse train in accordance with an output of the differential encoder  114 . The differential encoder  114  encodes data from the data source  108  using the phase of the optical pulses of the pulse train. For example, every ‘0’ in the data may be represented by a shift in the relative phase of two adjacent optical pulses of π radians, and every ‘1’ in the data may be represented by a shift in the relative phase of two adjacent optical pulses of 0 radians (i.e., DPSK modulation). The output of the pulse modulator  112  is launched into the optical transmission link  150 .  
         [0017]    The optical transmission link  150  includes a section  116 , a phase conjugator (PC)  118 , and a section  120 . The phase conjugator  118  divides the optical transmission link  150  such that the section  116  has a length z 1  and the section  120  has a length z 2 . Each of the sections  116  and  120  may include one or more spans  124  of predefined length (e.g., 100 km). Each of the spans  124  may include an optical fiber  126  and an amplifier  128 . In one embodiment, the optical transmission link  150  may exhibit constant dispersion (CD). As such, the optical fiber  126  of a given span  124  may be anomalous optical fiber. In another embodiment, the optical transmission link  150  may exhibit dispersion management (DM). In such an embodiment, each of the spans  124  may further comprise a dispersion compensating fiber (DCF)  130 . The amplifier  128  of each of the spans  124  may be an erbium doped fiber amplifier (EDFA), Raman amplifier, or like type optical amplifiers, or any combination thereof. The phase conjugator  118  may be a parametric amplifier or like type phase conjugation device known in the art. At the output of the phase conjugator  118 , the spectrum of the optical pulse train becomes a mirror image of the spectrum at the input of the phase conjugator  118 . In other words, the optical channel undergoes a spectral inversion. Operation of the phase conjugator  118  is well-known in the art.  
         [0018]    As described above, the main impairment of PSK optical transmission systems is phase jitter, in which power fluctuations caused by amplifier noise are converted into phase fluctuations by self-phase modulation (SPM). For purposes of clarity by example, the effects of phase jitter within a single-channel soliton transmission system is illustrated below. Notably, provided that the overall length, z, of the optical transmission link  150  is much longer that the dispersion length, the soliton condition is maintained adiabatically and the growth of the normalized soliton power- and phase-perturbations is governed approximately by the following correlation equations:  
         d z           p 2           =σ p ,   (1)  
         d z           pφ         ={overscore (γ)}         p 2           ,   ()  
           d   z           φ 2           =σ φ +2{overscore (γ)}           p φ         ,   (3)  
         [0019]    where d z  indicates a derivative with respect to z,                     denotes an ensemble average,          p2          is the power variance,          φ 2            is the phase variance,          pφ          is the correlation between power and phase, σ p  is the strength of noise-induced power kicks, σ φ ≈σ p /4 is the strength of noise-induced phase kicks, and {overscore (γ)} is the effective nonlinearity coefficient. Formulas for these quantities are stated in C. J. McKinstrie and C. Xie, “Phase Jitter in Single-Channel Soliton Systems with Constant Dispersion”, IEEE Journal of Selected Topics in Quantum Electronics, vol. 8, no. 3, May/June 2002, which is incorporated by reference herein in its entirety. The noise-induced power and phase kicks are attributable to amplifier noise within the system  100 .  
         [0020]    Let z 0  be the initial soliton position and let z 1  be any subsequent position. Then, integrating Equations (1) through (3) yields the following:  
                   〈     p   2     〉     1     =         〈     p   2     〉     0     +       σ   p          z   1           ,           (   4   )                     〈     p                 φ     〉     1     =         〈     p                 φ     〉     0     +         〈     p   2     〉     0            γ   _     ·     z   1         +         σ   p            γ   _     ·     z   1   2         2         ,           (   5   )                   〈     φ   2     〉     1     =         〈     φ   2     〉     0     +     2          (     p                 φ     )     0            γ   _     ·     z   1         +         〈     p   2     〉     0              γ   _     2     ·     z   1   2         +       σ   φ          z   1       +           σ   p              γ   _     2     ·     z   1   3         3     .               (   6   )                               
 
         [0021]    Suppose that the input solitons are unperturbed. Then Equations (4) through (6) are consistent with the standard results that the power variance grows with increasing z, and the phase variances grows (asymptotically) as z 3 /3. As is apparent to those skilled in the art, the rapid growth of the phase variance limits the transmission distance of a DPSK system.  
         [0022]    Returning to system  100  of FIG. 1, Equations (4) through (6) apply to the section  116  having a length z 1  (where the initial position, z 0 , is the start of the optical transmission link  150 ). The phase conjugator  118  has no effect on the power and phase variances, but changes the sign of the correlation between power and phase. Equations (4) through (6) also apply to the section  120  having a length z 2 , provided that the subscripts 0 and 1 are changed to 1 and 2, respectively. It follows from these observations that:  
                   〈     p   2     〉     2     =       σ   p          (       z   1     +     z   2       )         ,           (   7   )                     〈     p                 φ     〉     2     =       σ   p            γ   _          [           (       z   1     +     z   2       )     2     2     -     z   1   2       ]           ,           (   8   )                   〈     φ   2     〉     2     =         σ   φ          (       z   1     +     z   2       )       +       σ   p                γ   _     2          [           (       z   1     +     z   2       )     3     3     -     2        z   1   2          z   2         ]       .                 (   9   )                               
 
         [0023]    As apparent from Equation (9), the phase conjugator  118  does not affect the growth of phase perturbations that are driven (directly) by phase kicks. The phase conjugator  118  does have an effect, however, on phase perturbations that are driven (indirectly) by power kicks.  
         [0024]    Notably, in one embodiment, the phase conjugator  118  is symmetrically placed (“symmetric PC configuration”) within optical transmission link  150  (i.e., z 1 =z 2 ). In such an embodiment, the output phase variance of the optical transmission link  150  (i.e.,          φ 2             2 ) is proportional to z 3 /12, where z=z 1 +z 2  is the total length of the optical transmission link  150 . Thus, in the symmetric PC configuration, the phase variance is reduced by a factor of four. Suppose that phase jitter in the system  100  begins to cause errors at a critical distance z c  along the optical transmission link  150 . Then, by symmetrically placing the phase conjugator  118  along the optical transmission link  150 , the maximal transmission distance of the system  100  is increased by a factor of 1.59.  
         [0025]    In another embodiment, the phase conjugator  118  may be asymmetrically placed (“asymmetric PC configuration”) along optical transmission link  150  (i.e., z 1 ≠z 2 ). Let x=z 1 /z, then z 2 /z=1-x. Thus, the phase variance          φ 2             2  may be represented by the following:  
                   〈     φ   2     〉     2     =       (         σ   p            γ   _     ·     z   3         3     )          v        (   x   )           ,           (   10   )                               
 
         [0026]    where  
           v ( x )=1−6 x   2 (1- x ),   (11)  
         [0027]    A standard minimization calculation shows that the optimal value of x is ⅔ and the corresponding minimal value of v is {fraction (1/9)}. As such, the optimal lengths of the sections  116  and  120  are z 1 =2z/3 and z 2 =z/3, for which the minimal phase variance is proportional to z 3 /27. Thus, in the asymmetric PC configuration, the output phase variance may be reduced by a factor of nine and the maximal transmission distance of the system  100  may be increased by a factor of 2.08.  
         [0028]    It is clear from Equation (9) that the output phase variance of the optical transmission link  150  depends on the nonlinear phase-shift coefficient {overscore (γ)}z. Consequently, the phase variance of system  100  may be further reduced using post transmission nonlinear phase-shift compensation. Notably, in another embodiment, a nonlinear phase-shift compensator (NPSC)  122  is coupled to the optical transmission link  150  before the receiver  104 . Suppose that each soliton is subject to a compensating phase shift that is proportional to its power (φ c =κp). Then the compensated correlation equations are as follows:  
                   p 2             c =         p 2           ,   (12)  
                     p φ           c =           p φ         +κ           p   2           ,   (13)  
                   φ 2             c =         φ 2           +2κ           p φ         +κ 2             p   2           .   (14)  
         [0029]    The optimal phase-shift coefficient is thus:  
               κ   c     =     -         〈     p                 φ     〉       〈       p                2     〉       .               (   15   )                               
 
         [0030]    The minimal phase variance is shown by:  
                 〈     φ   2     〉     c     =       〈     φ   2     〉     -           〈     p                 φ     〉     2       〈       p                2     〉       .               (   16   )                               
 
         [0031]    Equations (15) and (16) apply to any system without a phase conjugator, or with one or more phase conjugators along the optical transmission link.  
         [0032]    If the correlation between phase and power is greater than zero (i.e., there is no phase conjugator), then κ&lt;0. If such a negative phase-shift is required, the NPSC  122  may be produced by cascaded quadratic processes or may be a phase modulator. If the correlation between phase and power is greater than zero, as it is in the system  100  having the phase conjugator  118  and z 2 &lt;0.29z, then κ&gt;0. If such a positive phase-shift is required, the NPSC  122  may be a section of highly nonlinear fiber (HNF).  
         [0033]    In the symmetric PC configuration, the NPSC  122  reduces the phase variance of the system  100  by an additional factor of four (a total factor of 16). In the asymmetric PC configuration, the NPSC  122  reduces the phase variance of the system  100  by an additional factor of 12/11 (a total factor of 108/11). The performance improvements associated with on (a)symmetrically-placed phase conjugator, with and without an NPSC, are summarized in Table 1. In the column headings, S, A, and NC are abbreviations for symmetric PC configuration, asymmetric PC configuration, and NPSC, respectively.  
                                                             TABLE 1                                   1 S   1 S + NC   1 A   1 A + NC                                        Jitter reduction   4.00   16.0   9.00   9.82           Range extension   1.59   2.52   2.08   2.14                      
 
         [0034]    [0034]FIG. 4 is an exemplary graph  400  illustrating the phase variances as functions of distance for the system of FIG. 1. In this example, the system  100  is configured as follows: The fiber dispersion, loss, and nonlinearity coefficients are −0.3 ps 2 /km, 0.21 dB /km, and 1.7/km-W, respectively. The total length of the optical transmission link 150 is 9.0 million meters (Mm). Fiber loss is compensated by uniformly-distributed Raman amplification, for which the spontaneous-emission factor is 1.1. The soliton full-width at half-maximum is 30 ps and the associated peak power was 0.60 mW. Solving the NS equation numerically for an ensemble of approximately 10 4  solitons yields the graph  400 .  
         [0035]    Notably, an axis  402  represents phase variance, and an axis  404  represents distance in Mm. A curve 406 represents the phase variance without the presence of a phase conjugator. A curve  408  represents the phase variance with an asymmetrically placed phase conjugator (i.e., the section  116  has a length of z 1 =2z/3 and the section  120  has a length of z 2 =z/3, where z is the total length). A curve  410  represents the phase variance with a symmetrically placed phase conjugator (i.e., z 1 =z 2 ). As shown, the output phase variance of the system  100  is reduced by using the phase conjugator  118  in both an asymmetric and a symmetric position along the optical transmission link  150 .  
         [0036]    [0036]FIG. 2 is a block diagram depicting another embodiment of the optical transmission system  100  in accordance with the invention. Elements of FIG. 2 that are the same or similar to elements of FIG. 1 are designated with identical reference numerals and are described in detail above. In the present embodiment, the optical transmission link  150  comprises two phase conjugators  208  and  210 . The phase conjugators  208  and  210  divide the optical transmission link  150  into a section  202  having a length z 1 , a section  204  having a length z 2 , and a section  206  having a length z 3 . Extending the derivation of Equations (7) through (9) yields the following:  
                   〈       p                2     〉     3     =       σ   p          (       z   1     +     z   2     +     z   3       )         ,           (   17   )                     〈     p                 φ     〉     3     =       σ   p            γ   _          [           (       z   1     +     z   2     +     z   3       )     2     2     -       (       z   1     +     z   2       )     2     +     z   1   2       ]           ,           (   18   )                   〈     φ   2     〉     3     =       σ   p          γ   _            {           (       z   1     +     z   2     +     z   3       )     3     3     -       2        [         (       z   1     +     z   2       )     2     -     z   1   2       ]       ·     z   3       -     2        z   1   2          z   2         }     .               (   19   )                               
 
         [0037]    In one embodiment, the phase conjugators  208  and  210  are symmetrically placed along the optical transmission link  150  and are separated by equal distances (i.e., z 1 =z 2 =z 3 =z/3) (“symmetric and equal PC configuration”). As such, the phase variance at the output of the optical transmission link (i.e.,          φ 2             3 ) is proportional to z 3 /27. That is, the output phase variance is reduced by a factor of nine. In another embodiment, the phase conjugators  208  and  210  are symmetrically place along the optical transmission link  150 , but are separated by unequal distances (e.g., z 1 =z 3 =z/4 and z 2 =z/2, although other section lengths may be employed) (“symmetric and unequal PC configuration”). In this embodiment, the phase variance at the output of the optical transmission link is proportional to z 3 /48. That is, the output phase variance is reduced by a factor of 16.  
         [0038]    In yet another embodiment, the phase conjugators  208  and  210  may be asymmetrically placed along the optical transmission link  150 . The optimal section lengths are z 1 =z 2 =2z/5 and z 3 =z/5, although other section lengths may be employed. Such a configuration yields a phase variance at the output of the optical transmission link  150  that is proportional to z 3 /75. That is, the output phase variance is reduced by a factor of 25. As with the embodiment shown in FIG. 1, the NPSC  122  may be used to further reduce the phase variance. The performance improvements are summarized in Table 2, where SE and SU are abbreviations for symmetric and equal PC configuration and symmetric and unequal PC configuration, respectively.  
                                                                         TABLE 2                                   2 SE   2 SE + NC   2 SU   2 SU + NC   2 A   2 A + NC                                    Jitter   9.00   36.0   16.0   16.0   25.0   25.8       reduction       Range   2.08   3.30   2.52   2.52   2.92   2.95       extension                  
 
         [0039]    [0039]FIG. 5 is an exemplary graph  500  illustrating the phase variances as functions of distance for the system of FIG. 2. In this example, the system  100  is configured as follows: The fiber dispersion, loss, and nonlinearity coefficients are −0.3 ps 2 /km, 0.21 dB/km, and 1.7/km-W, respectively. The total length of the optical transmission link  150  is 9.0 million meters (Mm). Fiber loss is compensated by uniformly-distributed Raman amplification, for which the spontaneous-emission factor is 1.1. The soliton full-width at half-maximum is 30 ps and the associated peak power was 0.60 mW. Solving the NS equation numerically for an ensemble of approximately 10 4  solitons yields the graph  500 .  
         [0040]    Notably, an axis  502  represents phase variance, and an axis  504  represents distance in Mm. A curve  506  represents the phase variance without the presence of a phase conjugator. A curve  508  represents the phase variance with two symmetrically placed phase conjugators separated by unequal distances (e.g., z 1 =z 3 =z/4 and z 2 =z/2). A curve  512  represents the phase variance with two symmetrically placed phase conjugators separated by equal distances (i.e., z 1 =z 2 =z 3 =z/3). A curve  510  represents the phase variance with two asymmetrically placed phase conjugators (e.g., z 1 =z 2 =2z/5 and z 3 =z/5). As shown, the output phase variance of the system  100  of FIG. 2 is reduced by using the phase conjugators  208  and  210  in both asymmetric and symmetric positions along the optical transmission link  150 .  
         [0041]    [0041]FIG. 3 is a block diagram depicting yet another embodiment of the optical transmission system  100  in accordance with the invention. Elements of FIG. 3 that are the same or similar to elements of FIG. 1 are designated with identical reference numerals and are described in detail above. In the present embodiment, the optical transmission link  150  comprises n−1 phase conjugators  302   1  through  302   n−1  (collectively referred to as phase conjugators  302 ) that divide the optical transmission link  150  into n sections  304   1  through  304   n  (collectively referred to as sections  304 ). The sections  304   1  through  304   n  have lengths of z 1  through z n , respectively. As apparent from the embodiments of FIGS. 1 and 2, the performance of the system  100  depends upon the number of phase conjugators used along the optical transmission link. In the present embodiment, the cumulative length of the optical transmission link  150  is defined as  
         x   n     =       ∑     i   =   1     n                     z   n                             
 
         [0042]    and the squared length is defined as  
           y   n   2     =       ∑     i   =   1     n                         (     -   1     )       n   -   i            x   i   2           ,                         
 
         [0043]    where n is the number of sections  304 . Since y 2   n+1 =x 2   n+1 −y 2   n , one can show that  
                     〈       p                2     〉     n       σ   p       =     x   n       ,           (   20   )                       〈     p                 φ     〉     n         σ   p          γ   _         =         x   n   2     2     -     y     n   -   1       ,   2           ,           (   21   )                     〈     φ   2     〉     n         σ   p            γ   _     2         =         x   n   3     3     -     2          ∑     i   =   1       n   -   1                         y   i   2            z     i   +   1       .                     (   22   )                               
 
         [0044]    For symmetrically placed phase conjugators  302  of equal separation, the phase variance may be represented as follows:  
                     〈     φ   2     〉     n         σ   p            γ   _     2          z   3         =       1     3        n   2         -     1     4        n   2             ,           (   23   )                               
 
         [0045]    where the first term on the right side applies to systems without an NPSC, and both terms on the right side apply to systems with an NPSC. For symmetrically placed phase conjugators  302  of unequal separation, the phase variance may be represented as follows:  
                   〈     φ   2     〉     n         σ   p            γ   _     2          z   3         =       1     12          (     n   -   1     )     2         -         [     1   +       (     -   1     )     n       ]       32          (     n   -   1     )     4         .               (   24   )                               
 
         [0046]    With symmetrically placed phase conjugators  302  of unequal separation, NPSC is only possible for even n (odd n−1), and its effectiveness decreases rapidly as n increases. For asymmetric systems, which are obtained by removing the last half-sections from the corresponding symmetric systems of equal separation, the phase variance may be represented as follows:  
                   〈     φ   2     〉     n         σ   p            γ   _     2          z   3         =       1     3          (       2      n     -   1     )     2         -       1     4          (       2      n     -   1     )     4         .               (   25   )                               
 
         [0047]    In asymmetric systems, NPSC is always possible, but its effectiveness decreases rapidly as n increases.  
         [0048]    For large values of n, symmetrically placed phase conjugators  302  of equal separation and compensated with an NPSC  122 , symmetrically placed phase conjugators  302  of unequal separation, and asymmetrically placed phase conjugators  302  all perform comparably well. Let z i  denote the length of a typical section between phase conjugators  302 . Then in each case considered, the reduced phase variance associated with the power kicks is of order σ p ({overscore (γ)}z i ) 2 z, whereas the phase variance associated with the phase kicks is σ φ z.  
         [0049]    While the foregoing is directed to the illustrative embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.