Abstract:
The required penalty in the optical signal-to-noise ratio induced by nonlinear effects in an optical communication system is reduced by specific expedients. The communication system is operated and is adapted to be operated in a pseudo-linear regime. Further, an optical phase conjugator is employed with a suitable dispersion map. This combination yields a desirable improvement in the required penalty in the optical signal-to-noise ratio due to nonlinear effects.

Description:
FIELD OF THE INVENTION  
         [0001]    This invention relates to optical communication and in particular to optical communication in which nonlinear optical effects are significant.  
         ART BACKGROUND  
         [0002]    In optical communication systems a signal is 1) launched on an optical line or path, 2) optically amplified periodically (discrete amplification and/or distributed Raman amplification) along the line, 3) optically reshaped and/or retimed for further transmission and 4) received and converted into a signal in electronic form. (Reshaping is defined as any process that is optical and by which the optical signal is transformed such that after transformation the variation in amplitude among signal portions corresponding to a code level (e.g. 0 or 1 in the case of binary code) is reduced and retiming is defined as any process that reduces the variation of any individual coded level of a signal at optimum sampling time used to detect a bit such that the overall bit error rate for bits at such level is minimized.) Thus the line is defined by a series of segments with each segment attached at each end to a device i.e. amplifier (discrete amplifier or a pump for a distributed amplifier), transmitter, multiplexers, demultiplexers, filters, wavelength converters, dispersion compensators, receiver, retimer, switch, add-drop multiplexers, cross connects, modulator, or reshaper. For example, in FIG. 1 segment  7  has a reshaper and erbium-doped fiber amplifier (EDFA) attached to its end points; segment  8  has an EDFA at its end points; segment  9  an EDFA and Raman amplifier pump; while segment  10  has a Raman pump and transmitter at its end points.  
           [0003]    The signal injected into the line is substantially affected by its propagation along the line. Both linear and nonlinear phenomena contribute to this change in the signal. A significant contributor to such linear effects is chromatic dispersion. That is, different wavelengths of light travel along the line at different speeds. Since no pulse of light is perfectly monochromatic, all pulses will be broadened as they traverse the line because the longer wavelength components will travel along the line at a different speed from the shorter wavelength components. Accordingly, an injected narrow pulse will be received at the end of a segment as a broadened pulse with longer wavelengths on one side of the broadened pulse and shorter wavelengths on the other. The properties of the segment determine whether the longer wavelengths, or shorter wavelengths, travel faster.  
           [0004]    Nonlinear effects also influence injected pulses. For nonlinear effects the intensity of the signal affects the speed at which different parts of the signal propagates and/or causes interactions (e.g. exchanges of intensity) between portions e.g. pulses, of the injected signal. In single frequency channel communication systems such interactions are significant and occur between pulses while in multichannel communication systems where a plurality of signals are injected each within a different wavelength range, such interactions both between frequency channels and within a signal frequency channel are quite significant.  
           [0005]    The result of these linear and nonlinear effects is that one pulse upon propagation overlaps with another by spreading of the pulse over the other and/or pulse distortion is induced by transfer of energy from one pulse to another. Accordingly either a slower bit rate (greater pulse spacing) or a shorter transmission distance between reshaping and/or retiming must be used to prevent loss of information. Slowing of the bit rate or more frequent amplification is not desirable due to the associated increase of capital costs of the system.  
           [0006]    A variety of expedients have been developed to reduce the consequences of such linear and nonlinear phenomena. For example, dispersion compensators have been inserted into optical systems to mitigate linear effects. After chromatic dispersion is introduced by propagation of an optical signal through all or part of a line, the signal is transmitted through a fiber coil that introduces dispersion opposite in sign to that accumulated in the line. For example, a segment or series of segments of the line speeds up (or slows down) the shorter wavelengths relative to the longer while the coil slows down (or speeds up) the shorter relative to the longer wavelengths. As a result, the chromatic dispersion of the line is offset and thus, in essence, removed.  
           [0007]    Other innovations have reduced signal degradation associated with nonlinear effects. In one particularly important approach the optical fiber (denominated TrueWave® by OFS Fitel, Inc.) of the line is configured to have a non-negligible dispersion e.g. 5 psec/(nm·km) rather than manufactured to minimize such dispersion. While the introduced dispersion is corrected after propagation as previously discussed, it helps reduce nonlinear effects. By purposefully introducing chromatic dispersion signal pulses in different channels (and thus different wavelengths) are caused to traverse the line at different speeds. The pulses from different channels, thus, acquire different phases during propagation resulting in phase mismatch among channels that mitigates four-wave mixing (a nonlinear effect). Accordingly the nonlinear interaction between these pulses is limited.  
           [0008]    Despite the improvement due to TrueWave® fiber, the high bit rates (greater than 2.5 gigabits per channel) now being employed or now contemplated has increased the possibility of encountering increased power (more pulses per unit time). Additionally the desire to increase span distances between amplifiers has made use of increased power appealing. Increased power however, as previously discussed, leads to more pronounced problems involving nonlinear effects.  
           [0009]    Further inventive approaches have been developed to address these difficulties at high bit rates. As discussed in Kaminow, I., et.al. (2000)  Optical Fiber Telecommunications  IV B, Chapter 6, Academic Press, New York, pages 232-304, ISBN 80-12-395173-9; dispersion mapping is one such approach. In one embodiment rather than launching narrow pulses, optical signals are processed so that they have, when injected, the same pulse broadening as a narrow pulse would have if it had undergone substantial linear dispersion. The configuration of the signal corresponding to a particular level of dispersion applied to a narrow pulse is adjusted periodically throughout the line. For example, FIG. 2 is illustrative of a dispersion map. The map is a graph of position along the line versus the waveform of the signal at this position as represented by the degree of cumulative dispersion produced by linear effects required to produce such waveform when applied to a signal with narrow pulses. Thus, the map at  6  in FIG. 2 shows a cumulative dispersion of −800 psec/nm upon injection.  
           [0010]    In the example of FIG. 2 the injected signal having −800 psec/nm cumulative dispersion, is very broad, rapidly changes configuration until it has sharp pulses at zero cumulative dispersion (point  21  in FIG. 2), and further rapidly changes configuration until it again is quite broad at +800 psec/nm (point  22  in FIG. 2). Because of the rapid changes in configuration the induced phase change is averaged over the entire pulse in a uniform manner, and thus significant distortion of each pulse is avoided. The linear dispersion is adjusted using dispersion compensators typically at each point of amplification (indicated in FIG. 2 by  17 ) to produce the desired dispersion to reduce nonlinear effects. Because of this averaging and intensity mitigation, nonlinear effects as previously discussed, are reduced. The particular dispersion map employed depends on the specific properties of the line, the bit rate, and the power of the injected pulse. (See Kaminow supra, Chapter 6 for a discussion of the considerations involved in choosing a dispersion map.)  
           [0011]    An alternate expedient has been employed to continue the drive towards reducing the penalty in required optical signal-to-noise ratio introduced due to nonlinear effects. (Referred to for purposes of this invention as required OSNR penalty.) In this regard a particular system including an optical phase conjugator (OPC) has been described. (See Brener, I. et.al. “Cancellabon of all Kerr Nonlinearites in Long Fiber Spans Using a LiNbO 3  Phase Conjugator and Raman Amplificabon,” Optical Fiber Communication Conference 2000 postdeadline paper PD  33 - 1 .) An OPC also has the property of reversing the sign of the cumulative dispersion of a signal associated with linear effects (e.g. +800 psec/nm becomes −800 psec/(nm) and exchanging the longer wavelengths of the pulse with the shorter wavelengths. Thus, as shown in FIG. 3, the shorter wavelengths,  41 , and the longer wavelengths,  42 , of a pulse are interchanged as shown in FIG. 4. The field generated by distorting effects leading to distortion is phase conjugated (part of the phase linear in distance along the line undergoes a sign change) by the OPC. Upon propagation over a second segment of a line because of the conjugation, such distortion is gradually but increasingly mitigated. The power distribution has an effect on the extent of this mitigation. (The power distribution is the graph of the total power of the signal, versus position along the line.) An asymmetric power profile with an OPC has been considered and viewed as disadvantageous especially compared to a symmetric or nearly symmetric power distribution (as produced by employing distributed Raman amplification). As previously discussed, the amplitude of nonlinear effects is dependent on signal intensity. In the case that the intensity distribution along the line is symmetric or nearly symmetric around the OPC, the penalty associated with nonlinear effects generated in the segment following the OPC offsets the nonlinear effects produced in the segment before the OPC.  
           [0012]    The use of OPCs has also been employed in other manners to reduce distortion. Specifically, in a soliton transmission system, it is possible to position an OPC so that timing jitter due to noise is significantly reduced. (See Smith, N.J. (1997) “Soliton Transmission Using Periodic Dispersion Compensation,” Journal of Lightwave Technology, 15(10),  1808  for a description of such approach.)  
           [0013]    Despite all such improvements, it is always desirable to reduce further the required OSNR penalty introduced by a segment or series of segments and thus allow higher pulse rates and/or greater signal intensities.  
         SUMMARY OF THE INVENTION  
         [0014]    The penalty associated with nonlinear effects is reduced while not substantially affecting those associated with linear effects by the practice of the invention. Significantly, this result is accomplished without ensuring that the power profile is symmetric on either side of an OPC. It is possible for the power profile to be symmetric or asymmetric around the position of the OPC. In particular at least one OPC is employed somewhere within a series of segments. However, the OPC should be used in conjunction with a particular class of dispersion maps in a pseudo-linear operating regime. For operation in a pseudo-linear regime three criteria are satisfied. First, the bit rate should be 20 gigabits/sec or greater for at least one channel. Second, somewhere within a series of segments being improved, the temporal full width at half maximum (FWHM) of a pulse becomes 2/B where B is the bit rate. For example, 1/B is 25 psec for a bit rate of 40 gigabits per second. Third, in the series of segments to be improved the power for at least one channel having a bit rate of at least 20 gigabits per second reaches at least one tenth the power launched from the transmitter that is the source of signals for that channel in the segment. The dispersion map employed is also significant. For the series of segments being improved, the dispersion map is configured so that the absolute value of the ratio between a) the sum of positive dispersions at half points and b) the sum of the negative dispersion at half points, is in the range 0.5 to 2.0 preferably 0.8 to 1.25, most preferably 0.9 to 1.1. (The half point, Zo for a segment is the point Zo along the segment where ∫o Zo γ(z)P(z)dz equals ∫ Zo   L γ(z)P(z)dz. (P(z) is the function of signal power versus position in a segment, L is the length of the segment, and γ(z) is a coefficient as defined in Kaminow supra, page 248 equation 6.25 which states that γ equals n 2 ω 0 /(cA eff ) where n 2  is the Kerr nonlinear refractive index coefficient of the fiber, A eff  is the effective mode area of the fiber, ω 0  is the angular frequency of transmitted light and c is the speed of light in vacuum.) That is, as shown in FIG. 5 the area  72  under the curve,  74 , P(Z) (with the assumption for purposes of this illustration that γ(z) is constant for all z), on the left of dotted line  75  is equal to the area,  73 , under the curve to the right of  75 . The OPC should be positioned within the segment or series of segments to be improved, for example at a position between the half point positions corresponding to negative dispersion and half points corresponding to positive dispersion. Some dispersion maps are configured to provide low magnitude excursions of the cumulative pulse dispersion from zero. In these maps, the cumulative dispersion at half point positions of segments is kept below a preselected maximum value. The preselected maximum values in picoseconds per nanometer are less than about 16,000 to 32,000 times the inverse of the bit rate in gigabits per second. At bit rates of 40 gigabits per second, the preselected maximum values are less than about 400 to 800 picoseconds per nanometer. Additionally, it is desirable for the OPC to be positioned alone or in combination with dispersion compensators so that the magnitude of the cumulative dispersion due to linear effects in the presence of the OPC at the end of the line before reshaping or retiming is adjusted, for example, by using a compensator to have a cumulative dispersion less than or equal to about 250 psec/nm.  
           [0015]    To avoid substantially affecting dispersion due to linear effects it is possible to place the OPC(s) in the line so that the dispersion map is not altered. For example, if the desired dispersion map is shown in FIG. 6, it is possible for the waveform at 86 to encounter an OPC. The OPC reverses the sign of the cumulative dispersion without the need for a dispersion compensation and the signal configuration is changed from point  86  to point  89 . Similarly by placing the OPC at point  82  where dispersion due to linear effects is zero, the conjugation due to an OPC leaves the dispersion map unchanged.  
           [0016]    The invention provides the potential for increasing bit rate and/or increasing injected signal power through use of at least one appropriately positioned OPC without the necessity for adjusting the power distribution along the line by, for example, distributed Raman amplification. (Nevertheless, use of Raman amplification with the invention is not precluded.) An OPC is a well studied device (see Fisher, Robert A. (1995).  Optical Phase Conjugation . San Diego, Academic Press.) and does not substantially complicate the system construction. Additionally, the positive consequences associated with choice of a suitable dispersion map and dispersion compensators are not compromised. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0017]    [0017]FIG. 1 is illustrative of an optical communication system and its relationship to the invention;  
         [0018]    [0018]FIGS. 2 through 4 exemplify concepts associated with optical communication and their use in the invention;  
         [0019]    [0019]FIGS. 7, 8 and  9  relate to the concept of half point and dispersion map ratio;  
         [0020]    [0020]FIG. 10 demonstrates effects associated with optical phase conjugators; and  
         [0021]    [0021]FIG. 11 is illustrative of systems relating to the invention 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0022]    As discussed the invention is applicable both to single and multiple optical communication systems. For the purposes of this invention a system includes a system portion, i.e. a series of at least two adjacent segments. The primary elements of a segment are optical fiber waveguides. Other devices such as amplifiers, filters, wavelength converters, dispersion compensators, retimers, reshapers, multiplexers, demultiplexers, add-drop multiplexers, cross-connects, receivers, switches, modulators and transmitters define the end point of a segment but are not considered part of the segment. For example, such devices are not parts of segments for purposes of determining the ratio of dispersion at half points.  
         [0023]    As discussed, the invention is effective for system portions operating in a pseudo-linear regime. For a system portion to be considered operating in such regime the following criteria should be satisfied: 1) the pulse bit rate should be 20 gigabits/sec or greater for at least one channel, 2) somewhere within the system portion the FWHM of a signal pulse is 2/B and 3) in the system portion the power of at least one channel of the signal with bit rate greater than 20 gigabits/sec reaches at least one tenth the power launched from the transmitter that is the source of the channel for that system portion. A system portion is considered as a pseudo-linear regime system portion if for such series of segments all three criteria are satisfied. In this regard, a series of segments is that which forms a string of adjacent segments. Thus, in FIG. 1, segments  12 ,  7 ,  8 ,  9 ,  11  form a series of segments as does  8 ,  9 , and  10 ,  9 ,  8 ,  7 . Analogously the system portion is configured to operate in a pseudo-linear regime if the segments and the devices in the optical path connecting segments are configured so that it is possible to satisfy the three requisite criteria. So as shown in FIG. 11( a ) the system portion in one embodiment involves an ERDA,  134  and  136 , an OPC,  135 , and a reshaper/retimer,  137  in the optical path with segments  131 ,  132  and  133  where the device  134 ,  135 ,  136 , and  137  are configured for the pseudo-linear regime. Similarly FIG. 11( b ) shows the system with Raman pumps for some amplification.  
         [0024]    The dispersion map within a pseudo-linear regime over at least one system portion should satisfy a certain criterion. In particular for such a region the absolute value of the ratio between 1) the sum of positive dispersions at half points and (2) the sum of negative dispersions at half points, is in the range 0.5 to 2.0. (The absolute value of this ratio for this invention is denominated the dispersion map ratio). So, for example, in FIG. 7 amplification occurs at points  97  whose segments are denoted  91 ,  92 ,  93 , and  94 . The half points are the points  96 . Thus the dispersion map ratio is the absolute value of the ratio between the sum of the dispersion at points  103  and  104  to the sum at points  101  and  102 . The procedure for determining the dispersion map ratio in a region having distributed Raman amplification would be the same except the power graph would probably look more like that of FIG. 9 where Raman pumps are located at points  111 , the segments are  112 ,  113 ,  114 , and  115 , and the half points are at  116 . The evolution of the signal power P(z) in a Raman amplifier is obtained by calculation as described in accordance with published procedures. In particular this calculation is described in Essiambre, R.-J. et.al. “Design of Bidirectionally Pumped Fiber Amplifiers Generating Double Rayleigh Backscattering.” IEEE Photonics Technology Letters, 14(7), 914-916 (2002). Computer programs suitable for performing such calculations include VPI Systems Incorporated™ transmission suite software such as VPI Transmission Maker. (Cruz Plaza, 943. Holmdel Road, Holmdel, N.J. 07733), and RSoft Corporation amplifier and transmission software (Ossining, N.Y., USA). The technology used to produce the OPC is generally not critical. Typically, an OPC is formed in a crystal of periodically poled lithium niobate as described in Fejer, M. M. et.al. IEEE Journal of Quantum Electronics, 28, 2631 (1992). The OPC generally is pumped in the wavelength range 1500 nm to 1650 nm. Other OPC devices such as semiconductor optical amplifiers are described in Girardin, et.al. “Low-Noise and Very High-Efficiency Four-Wave Mixing in 1.5-mm-Long Semiconductor Optical Amplifiers,” IEEE Photonics Technology Letters, 9(6) 746 (1997).  
         [0025]    An OPC also inverts the channels of a multichannel system around a frequency associated with the pump source frequency of the OPC. (For devices whose operation is based on a four-wave mixing mechanism or cascaded three-wave mixing the signal frequency is mirrored around the pump frequency. For devices whose operation is based on a three-wave mixing mechanism without cascading, the signal frequency is mirrored around half the pump frequency. See Chou, M. H. et.al. “1.5-pm-Band Wavelength Conversion Based on Cascaded Second-Order Nonlinearity in LiNbO 3  Waveguides,” IEEE Photonics Technology Letters, 11, 653 (1999) for a description of devices whose operation is based on a cascaded three-wave mixing mechanism.) Therefore as shown in FIG. 10, channels  121 ,  122 , and  123  having frequencies as shown before traversing the OPC would have corresponding frequencies  125 ,  126 , and  127  after traversing the OPC assuming the pump for the OPC is at frequency  124 . As a result, the frequency order of the channels is reversed and the channel frequencies are changed. If these changes are unacceptable a configuration that does not cause such a reversal is useful. Such a configuration is described in U.S. application Ser. No. ______ (Chowdhury 6-9) filed concurrently by Aref Chowdhury and Rene&#39; Essiambre with this application whose disclosure is hereby incorporated by reference in its entirety. In such embodiment involving the invention of this application the pump wavelength of the OPCs employed are chosen as described therein to avoid the channel reversal consequences discussed.  
         [0026]    Generally it is convenient to locate the OPC at, for example, a segment end point so that access to the line is easily achieved. It is often convenient to locate an optical phase conjugator at one of these positions on the dispersion map. It is possible to use more than one OPC such as at position  86  and  83  in FIG. 6 with the dispersion map continuing to repeat the pattern beyond  83 . Nevertheless the OPCs should be configured, if necessary with other optical devices, such that the desired dispersion map is not compromised. Again, as shown in FIG. 6, it is possible to position an OPC so that it encounters the waveform at  86 , since a property of the OPC is that it reverses the sign of the cumulative dispersion. Thus an OPC will provide the change from point  86  to point  89  on the dispersion map. As a result a dispersion compensator at these points is not necessary to achieve the desired dispersion map.  
         [0027]    It is possible to position OPCs in other configurations and still not disturb the desired dispersion map. For example, if the OPC is placed at point  82  where the cumulative dispersion is zero the OPC causes, no change of the cumulative dispersion occurs and the map is undisturbed. Similarly it is possible to position the OPC at a non-zero cumulative dispersion position and bring the reversal of the cumulative dispersion produced by the OPC back to its original value using a dispersion compensator. Thus if an OPC is placed at position having −20 psec/nm level of cumulative dispersion is inverted to +20 psec/nm and a dispersion compensator would be needed to bring the level back to −20 psec/nm.  
         [0028]    As with other optical communication systems, the optical elements comprising the line are advantageously chosen so that the magnitude of cumulative dispersion, is compensated such that the signal before reshaping and/or retiming has a value less than 250 psec/nm. As discussed, various forms of amplification are employable. Both discrete amplifiers such as erbium-doped fiber amplifiers (EDFAs) and continuous amplification as achieved with distributed Raman amplification are acceptable. It is acceptable for all amplifiers in the system to be discrete amplifiers such as EDFAs, to be distributed Raman amplifiers, or a combination of both. The power profile relative to the OPC position is not critical to the invention.