Abstract:
A directly modulated optical transmitter for use with a fiber optical communications system operating in the 1550 nm wavelength band exhibits very low chirp. The chirp inherently present in a directly modulated laser is cancelled by a phase modulator which optically modulates the directly modulated laser light beam by applying a 180° phase delay to a split-off portion of the input radio frequency signal. This provides a low cost transmitter capable of operating in the 1550 nm band and with laser chirp effectively cancelled or substantially reduced, thereby avoiding distortions due to laser chirp interactions with the downstream optical fiber.

Description:
FIELD OF THE INVENTION 
       [0001]    This invention relates to optical transmission systems, for instance those using a laser or laser diode to transmit optical (light) signals over optical fibers and in particular to such a system using a directly modulated laser in the transmitter. 
       DESCRIPTION OF RELATED ART 
       [0002]    Directly modulating the analog output signal intensity of a light emitting laser diode (LED) or semiconductor laser or other type of laser with an electrical signal is well known in the field. Typically this is used for transmitting optical analog signals such as voice and video, such as cable television, on optical fibers. Although such analog transmission techniques have the advantage of substantially smaller bandwidth requirements than digital transmission, such as digital pulse code modulation, or analog or pulse frequency modulation, such use of amplitude modulation tends to suffer from noise and nonlinearity of the optical transmitter. 
         [0003]    Exemplary types of analog signals thereby transmitted are analog video signals which carry information in amplitude modulation (AM) format and specifically AM-VSB (AM-Vestigial Side Band) format. In order to transmit multiple video signals, such AM-VSP signals are up-converted to specific frequency. The collection of such signals is referred to as a composite signal and occupies a typical (radio frequency—RF) frequency range from 54 MHz to 1 GHz. Carrying such signals over fiber optic cables with the required linearity typically requires special transmitters. 
         [0004]    The transmitters are classified into direct modulation or external modulation type. Direct modulation transmitters are of the type where the input composite radio frequency analog (electrical) signal changes the optical output power of the laser or laser diode by changing its bias current in proportion to the instantaneous amplitude of the composite signal. Externally modulated transmitters use another device known as the modulator to perform the modulation function on the optical (light) signal from the laser. In such transmitters the laser bias current is normally held constant. Instead, the analog RF electrical signal, which is the information,to be transmitted, is applied to the electrical input terminal of the modulator, also known as an electro-optic modulator. Such an electro-optic modulator is an optical device in which a single controlled element displaying electro-optic effect is used to electrically modulate a beam of light, typically laser light. The modulation may be imposed on the phase, frequency, amplitude or direction of the modulated light beam. Typically a nonlinear optical material is used in the optic modulator and is, for instance, a crystal such as lithium niobate. The most common type of electro-optic modulator includes such a crystal whose refractive index is a function of the strength of the local electric field. Thus, if the lithium niobate crystal is exposed to an electric field, light travels more slowly through it. However the phase of light leaving the crystal is directly proportional to the length of time it takes the light to pass through it. Therefore the phase of the laser light beam exiting the modulator is controlled by changing the strength of the electric field in the crystal by the applied analog RF (electrical) signal. 
         [0005]    Both types of modulation have advantages and disadvantages. The externally modulated transmitter has the advantage of low chirp, where chirp is an abrupt undesirable change in the laser beam&#39;s center wavelength caused by laser instability. This chirp is typically caused by variations in the applied bias current, which is inherent in a directly modulated laser. Hence externally modulated lasers usually have a low chirp since there is typically little change in the bias current. Externally modulated lasers also have relatively little signal-to-noise degradation even though the length of the optical fiber which the transmitter is driving may vary. The laser itself need not be particularly linear in operation and external modulators operate well at the 1550 nm optical wavelength, which is standard for optical transmission networks. Externally modulated transmitters are more complex, expensive and have lower modulation depth (are less linear) than directly modulated transmitters. Also, suppression of stimulated Brillouin scattering (SBS) is difficult. SBS is a well-known distortion in optical signals. 
         [0006]    In contrast, directly modulated lasers are less complex, less costly, and more linear in operation. Disadvantageously, heretofore they do not work well at the 1550 nm optical wavelength. They do work well at the 1310 nm wavelength, however optical amplifiers for 1310 nm light are generally not commercially available, making 1310 nm difficult to use. 
         [0007]    The issue with chirp is that it interacts with the dispersion in the optical fiber to produce undesirable distortions, primarily CSO (Composite Second Order) distortions, that fall in band in multi-octave (wideband) systems such as cable television. Because of these various advantages and disadvantages, typically directly modulated lasers heretofore have been used almost exclusively at the 1310 nm optical wavelength where standard fiber has no dispersion. Conversely, for a system using 1550 nm wavelength, the transmitters are currently almost all the externally modulated type since the optical fiber has large amounts of dispersion in that wavelength. 
         [0008]    The present inventor determined it would be advantageous to have an optical transmitter which is directly modulated with the attendant advantages and which operates at the 1550 nm optical wavelength without suffering from excessive chirp. 
         [0009]    A directly modulated laser system is shown in lannelli US 2006/0210282A1, published Sep. 21, 2006, incorporated by reference herein in its entirety. This shows in  FIG. 2  (see also present  FIG. 1 ) a block diagram of a directly modulated laser transmitter  100  with an external cavity laser which does operate in the 1530-1570 nm wavelength range. lannelli shows the RF electrical signal at terminal  101  is applied to directly modulate laser  102 , whose output beam  110  is carried by fiber to be incident on phase modulator  109 , and passed into fiber optic link  113  via optical amplifier  112 . A split off part of the RF electrical signal is applied to attenuator  104 , tilt circuit  106 , and phase delay circuit  107 , to drive phase modulator  109 . SBS suppression tone generator  108  is also provided. The phase delay is only 0° to −10°, see paragraph 49, to maximize the CSO which is a property of the optical fiber span, rather than only the laser. In addition to being limited to the external cavity type laser, it appears that chirp correction here would be inadequate for a directly modulated laser (e.g., DFB) which generally requires more chirp correction. 
       SUMMARY 
       [0010]    In accordance with the invention, there is provided a directly modulated optical transmitter operating at the 1550 nm optical wavelength band (extending for instance from 1530 run to 1570 nm but not so limited) that exhibits very low chirp in the transmitter and is suitable for use in optical fiber networks. While it is recognized, as pointed out above, that directly modulated laser systems inherently produce chirp, which is an unwanted modulation (change) of the laser optical wavelength, the present optical transmitter overcomes this by canceling the chirp induced by the directly modulated laser itself by means of a phase modulator which optically modulates a phase of the light beam output from the directly modulated laser. The chirp is canceled by use of a combination of an integrator, electrical delay element, and an electrical amplifier, which receive a portion of the RF signal also used to drive the laser, and which apply an approximately 180° phase delay and the resulting electrical signal is then used to drive the phase modulator to offset or cancel the chirp induced by the laser itself. 
         [0011]    In one embodiment, the transmitter includes a plurality of directly modulated lasers, each outputting light as a different wavelength, e.g., in the 1550 nm band, and each driven by two radio frequency (RF) signals, one being, e.g., a common analog composite RF signal and the other being, e.g., a QAM (quadrature amplitude modulation) signal, the information content of which differs for each laser, thereby also supporting what is called in the cable television field narrowcasting of the QAM signals. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]      FIG. 1  shows a prior art directly modulated transmitter. 
           [0013]      FIG. 2  shows a block diagram of a transmitter in accordance with this disclosure. 
           [0014]      FIG. 3  shows another transmitter in accordance with this disclosure. 
           [0015]      FIGS. 4-10  show performance of the  FIG. 2  transmitter graphically. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0016]      FIG. 2  shows in a block diagram an optical transmitter in accordance with this disclosure. The various components are each of standard type, commercially available, and well known in the field. The remainder of the system, including the fiber optic span and the optical receiver, are also conventional as in  FIG. 1 . Hence  FIG. 2  (unlike  FIG. 1 ) only shows the transmitter. As shown, there is input terminal  10  to which is applied a composite RF (electrical) signal such as a cable television signal, which may include many channels of analog cable television transmissions or other types of signals, including for instance a QAM signal. The composite RF signal may be an analog video signal or a digital video signal such as QAM (Quadrature Amplitude Modulation). Thus the present apparatus is suitable for use with digital signals also. The input composite RF electrical signal is applied to a radio frequency splitter tap coupler  12  which is a standard device. The RF splitter/RF coupler  12  passes the bulk of the signal on, via for instance a coaxial cable or similar transmission line  14 , to a conventional directly modulated laser  18 . Thus the RF signal applied on line  14  directly modulates the bias current of the laser  18  such as part no. CQF-935 from JDSU Company via the power supply (not shown) of laser  18 . The directly modulated laser  18  which is for instance a semiconductor laser, laser diode or other type of laser, such as a direct feedback laser, all commercially available, outputs a beam of coherent light  24  having a center wavelength in the 1550 nm band typically into a short length of optical fiber. This optical beam  24  may be incident on a collimating lens (not shown) if needed. Beam  24  then passes via optical fiber into a phase modulator  26  which is a standard type device as described above. An exemplary phase modulator is available from General Photonics Inc., for instance their part number LPM-001. A variety of similar devices are available from other vendors. The resulting phase modulated optical signal (coherent light beam)  30  is then emitted from the phase modulator and coupled to the fiber optic span which is ultimately in communication with a suitable optical receiver, not shown, as in  FIG. 2 . 
         [0017]    Referring back to RF splitter/RF coupler  12 , the smaller part of the electrical RF signal is applied to an integrator component  32  which is a two port network having particular transfer characteristics in one embodiment across the frequency band 50 to 1000 MHz. The transfer characteristics of the network are empirically derived to provide the optimum cancellation of the chirp in that frequency band. The electrical output signal of the network is then applied to a gain amplifier  36 . The optimum gain of this amplifier is achieved using attenuators and coaxial cables of varied delays. The resulting amplified/attenuated and delayed signal (in other words, phase altered) is applied to an input terminal of a conventional diplexer  40  which is a type of signal combiner. Applied to the other input terminal of diplexer  40  is a SBS tone suppression signal applied from the SBS tone generator  46  which is for instance an oscillator coupled to a narrow band amplifier from Sirenza Inc. This phase adjusting signal with the added SBS tone suppression is applied by diplexer  40  to the electrical input terminal  50  of phase modulator  26  to drive the phase modulator. The mathematical derivation supplied below shows that the FM signal in the laser output signal (the chirp) is canceled in the modulator when the delays, amplitudes, and phases are matched. 
         [0018]    This transmitter has the advantages of being lower cost than a typical externally modulated transmitter, having a higher modulation depth than an externally modulated transmitter, and having a very high SBS threshold that allows high optical power signal (e.g., more than 23 dBm) to be inserted into a 25 kilometer long span of standard optical fiber. 
         [0019]    Note that in accordance with this invention the chirp suppression is of the chirp actually induced by the frequency excursions of the laser  18  caused by the applied AM RF signal. This chirp is advantageously canceled or reduced. Typically the amount of phase delay provided by the amplifier  36  is approximately 180° so as to cause full cancellation of the amplitude of the chirp caused by the laser  18 . This the cancellation effect is provided by the electrical signal at electrical input terminal  50  of the phase modulator  26  being identical in amplitude and having a 180° phase differential from the chirp present (in optical form) in the optical signal  24 . Hence typically the amplifier  36  provides an approximately 180° phase differential. The amplitudes of the two signals are matched while finding the best cancellation of the CSO distortion across the frequency band, e.g. 50 to 1000 MHz. 
         [0020]    It is understood that the present method and apparatus are suitable also for carrying microwave signals as well as for very high-speed digital signals. In one embodiment the phase modulator may include the laser in a single package as an integrated device. 
         [0021]    The following describes in more detail operation of the  FIG. 2  transmitter. The input RF signal at terminal  10  is a composite of several frequencies and is represented as s(t). 
         [0000]    
       
         
           
             
               
                 
                   
                     s 
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       n 
                     
                      
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             
                               ω 
                               i 
                             
                              
                             t 
                           
                           + 
                           
                             ϕ 
                             i 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where ω i  and φ i  are the various RF (e.g. CATV) frequencies and the phases respectively. This composite signal is used to directly modulate laser  18  which also produces laser chirp. By directly modulating the laser  18 , the light intensity of beam  24  from the laser is modulated. However due to the chirp, the laser frequency is also modulated. This leads to the undesirable frequency deviation of the carrier (RF) which is proportional to that of the input information signal at terminal  10 . This signal is represented as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     I 
                     = 
                     
                       
                         
                           I 
                           0 
                         
                          
                         
                           ( 
                           
                             1 
                             + 
                             
                               m 
                               * 
                               
                                 s 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                       
                       * 
                       
                         cos 
                          
                         
                           [ 
                           
                             
                               
                                 ω 
                                 c 
                               
                                
                               t 
                             
                             + 
                             
                               
                                 k 
                                 f 
                               
                                
                               
                                 
                                   ∫ 
                                   
                                     - 
                                     ∞ 
                                   
                                   t 
                                 
                                  
                                 
                                   
                                     s 
                                      
                                     
                                       ( 
                                       τ 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     τ 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   I 
                   = 
                   
                     
                       
                         I 
                         0 
                       
                        
                       
                         ( 
                         
                           1 
                           + 
                           
                             m 
                             * 
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   1 
                                 
                                 n 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         ω 
                                         i 
                                       
                                        
                                       t 
                                     
                                     + 
                                     
                                       ϕ 
                                       i 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     * 
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             
                               ω 
                               c 
                             
                              
                             t 
                           
                           + 
                           
                             
                               k 
                               f 
                             
                              
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   1 
                                 
                                 n 
                               
                                
                               
                                 
                                   sin 
                                    
                                   
                                     ( 
                                     
                                       
                                         
                                           ω 
                                           i 
                                         
                                          
                                         t 
                                       
                                       + 
                                       
                                         ϕ 
                                         i 
                                       
                                     
                                     ) 
                                   
                                 
                                 
                                   ω 
                                   i 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where k f  is the frequency modulation factor. This modulated light is passed through the phase modulator  26 . As this light passes through the optical fiber (the laser  18  pigtail which is the laser output port and the phase modulator  26  input optical fiber) it accumulates some delay. The phase modulator  26  modulates the phase of the carrier with the signal that is applied to it at terminal  50 . The signal that is applied to the phase modulator at terminal  50  follows an electrical path through electrical components  32 ,  36 ,  40  and hence acquires some delay. Thus a differential delay between the two signals paths is established. This differential delay is labeled τ diff . Then equations 2 and 3 modify as follows: 
         [0000]    
       
         
           
             
               
                 
                   I 
                   = 
                   
                     
                       
                         I 
                         0 
                       
                        
                       
                         ( 
                         
                           1 
                           + 
                           
                             m 
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                               s 
                                
                               
                                 ( 
                                 t 
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                         ) 
                       
                     
                     * 
                     
                       cos 
                        
                       
                         [ 
                         
                           
                             
                               ω 
                               c 
                             
                              
                             t 
                           
                           + 
                           
                             
                               k 
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                              
                             
                               
                                 ∫ 
                                 
                                   - 
                                   ∞ 
                                 
                                 t 
                               
                                
                               
                                 
                                   s 
                                    
                                   
                                     ( 
                                     τ 
                                     ) 
                                   
                                 
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                                    
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                           + 
                           
                             
                               k 
                               p 
                             
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                               s 
                                
                               
                                 ( 
                                 
                                   t 
                                   - 
                                   
                                     τ 
                                     diff 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         I 
                         = 
                           
                          
                         
                           
                             
                               I 
                               0 
                             
                              
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   m 
                                   * 
                                   
                                     
                                       ∑ 
                                       
                                         i 
                                         = 
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                                       n 
                                     
                                      
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           
                                             
                                               ω 
                                               i 
                                             
                                              
                                             t 
                                           
                                           + 
                                           
                                             ϕ 
                                             i 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
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                           * 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         ω 
                                         c 
                                       
                                        
                                       t 
                                     
                                     + 
                                     
                                       
                                         k 
                                         f 
                                       
                                        
                                       
                                         
                                           ∑ 
                                           
                                             i 
                                             = 
                                             1 
                                           
                                           n 
                                         
                                          
                                         
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 
                                                   
                                                     ω 
                                                     i 
                                                   
                                                    
                                                   t 
                                                 
                                                 + 
                                                 
                                                   ϕ 
                                                   i 
                                                 
                                               
                                               ) 
                                             
                                           
                                           
                                             ω 
                                             i 
                                           
                                         
                                       
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       k 
                                       p 
                                     
                                      
                                     
                                       
                                         ∑ 
                                         
                                           i 
                                           = 
                                           1 
                                         
                                         n 
                                       
                                        
                                       
                                         cos 
                                          
                                         
                                           [ 
                                           
                                             
                                               
                                                 ω 
                                                 i 
                                               
                                                
                                               
                                                 ( 
                                                 
                                                   t 
                                                   - 
                                                   
                                                     τ 
                                                     diff 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                             + 
                                             
                                               ϕ 
                                               i 
                                             
                                           
                                           ] 
                                         
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Eq. 5 shows the carrier 
         [0000]    
       
         
           
             cos 
              
             
               ( 
               
                 
                   
                     ω 
                     c 
                   
                    
                   t 
                 
                 + 
                 
                   
                     k 
                     f 
                   
                    
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       n 
                     
                      
                     
                       
                         sin 
                          
                         
                           ( 
                           
                             
                               
                                 ω 
                                 i 
                               
                                
                               t 
                             
                             + 
                             
                               ϕ 
                               i 
                             
                           
                           ) 
                         
                       
                       
                         ω 
                         i 
                       
                     
                   
                 
                 + 
                 
                   
                     k 
                     p 
                   
                    
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       n 
                     
                      
                     
                       cos 
                        
                       
                         [ 
                         
                           
                             
                               ω 
                               i 
                             
                              
                             
                               ( 
                               
                                 t 
                                 - 
                                 
                                   τ 
                                   diff 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             ϕ 
                             i 
                           
                         
                         ] 
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
         [0000]    has two associated terms which have to be cancelled to cancel the original chirp generated by the laser. This cancellation is possible only if the term 
         [0000]    
       
         
           
             
               k 
               f 
             
              
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 n 
               
                
               
                 
                   sin 
                    
                   
                     ( 
                     
                       
                         
                           ω 
                           i 
                         
                          
                         t 
                       
                       + 
                       
                         ϕ 
                         i 
                       
                     
                     ) 
                   
                 
                 
                   ω 
                   i 
                 
               
             
           
         
       
     
         [0000]    and the term 
         [0000]    
       
         
           
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 n 
               
                
               
                 
                   k 
                   p 
                 
                  
                 
                     
                 
                  
                 
                   cos 
                    
                   
                     [ 
                     
                       
                         
                           ω 
                           i 
                         
                          
                         
                           ( 
                           
                             t 
                             - 
                             
                               τ 
                               diff 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         ϕ 
                         i 
                       
                     
                     ] 
                   
                 
               
             
             ) 
           
         
       
     
         [0000]    are identical in amplitude and have a 180 degree phase differential. In order to achieve this, the electrical signal before being applied to the phase modulator  26  is passed through an integrator  32  and an amplifier  36  that causes a 180 degree phase differential. Equation 5 would then become 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         I 
                         = 
                           
                          
                         
                           
                             
                               I 
                               0 
                             
                              
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   m 
                                   * 
                                   
                                     
                                       ∑ 
                                       
                                         i 
                                         = 
                                         1 
                                       
                                       n 
                                     
                                      
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           
                                             
                                               ω 
                                               i 
                                             
                                              
                                             t 
                                           
                                           + 
                                           
                                             ϕ 
                                             i 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           * 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         ω 
                                         c 
                                       
                                        
                                       t 
                                     
                                     + 
                                     
                                       
                                         k 
                                         f 
                                       
                                        
                                       
                                         
                                           ∑ 
                                           
                                             i 
                                             = 
                                             1 
                                           
                                           n 
                                         
                                          
                                         
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 
                                                   
                                                     ω 
                                                     i 
                                                   
                                                    
                                                   t 
                                                 
                                                 + 
                                                 
                                                   ϕ 
                                                   i 
                                                 
                                               
                                               ) 
                                             
                                           
                                           
                                             ω 
                                             i 
                                           
                                         
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       k 
                                       p 
                                     
                                      
                                     
                                       
                                         ∑ 
                                         
                                           i 
                                           = 
                                           1 
                                         
                                         n 
                                       
                                        
                                       
                                         
                                           sin 
                                            
                                           
                                             [ 
                                             
                                               
                                                 
                                                   ω 
                                                   i 
                                                 
                                                  
                                                 
                                                   ( 
                                                   
                                                     t 
                                                     - 
                                                     
                                                       τ 
                                                       diff 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                               + 
                                               
                                                 ϕ 
                                                 i 
                                               
                                             
                                             ] 
                                           
                                         
                                         
                                           ω 
                                           i 
                                         
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    First, the amplitudes of the two terms 
         [0000]    
       
         
           
             
               k 
               f 
             
              
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 n 
               
                
               
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         
                           
                             ω 
                             i 
                           
                            
                           t 
                         
                         + 
                         
                           ϕ 
                           i 
                         
                       
                       ) 
                     
                   
                   
                     ω 
                     i 
                   
                 
                  
                 
                     
                 
                  
                 and 
                  
                 
                     
                 
                  
                 
                   k 
                   p 
                 
                  
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       1 
                     
                     n 
                   
                    
                   
                     
                       sin 
                        
                       
                         [ 
                         
                           
                             
                               ω 
                               i 
                             
                              
                             
                               ( 
                               
                                 t 
                                 - 
                                 
                                   τ 
                                   diff 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             ϕ 
                             i 
                           
                         
                         ] 
                       
                     
                     
                       ω 
                       i 
                     
                   
                 
               
             
           
         
       
     
         [0000]    should match so they are balanced. The second term critical for cancellation is the differential delay between the two signal paths. If τ diff ≠0 then the two terms in equation 6 associated with the carrier add to a term that has a frequency dependence in cancellation. The differential delay τ diff  is adjusted to zero by making the electrical path lengths traversed by the two electrical signals the same. When perfect cancellation is thus achieved the final signal optical before launching into the fiber span would have the following form: 
         [0000]    
       
         
           
             
               
                 
                   I 
                   = 
                   
                     
                       
                         I 
                         0 
                       
                        
                       
                         ( 
                         
                           1 
                           + 
                           
                             m 
                             * 
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   1 
                                 
                                 n 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         ω 
                                         i 
                                       
                                        
                                       t 
                                     
                                     + 
                                     
                                       ϕ 
                                       i 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     * 
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             ω 
                             c 
                           
                            
                           t 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0022]    A multi-tone analysis in parallel to the foregoing follows. The input RF signal at terminal  10  is a composite of several frequencies and is represented as s(t). 
         [0000]        s ( t )=cos(ω 1   t )+cos(ω 2   t )   (1) 
         [0000]    where ω 1  and ω ’ are two frequencies. For simplicity we have made their arbitrary phases φ 1  and φ 2  as zeros. This signal is used to directly modulate a laser  18  which also produces laser chirp. By directly modulating the laser  18  the light intensity out of the laser is modulated. However due to the chirp, the laser frequency is also modulated. This leads to the frequency deviation of the carrier which is proportional to the information signal. This signal is represented as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     I 
                     = 
                     
                       
                         
                           I 
                           0 
                         
                          
                         
                           ( 
                           
                             1 
                             + 
                             
                               m 
                               * 
                               
                                 s 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                           
                           ) 
                         
                       
                       * 
                       
                         cos 
                          
                         
                           [ 
                           
                             
                               
                                 ω 
                                 c 
                               
                                
                               t 
                             
                             + 
                             
                               
                                 k 
                                 f 
                               
                                
                               
                                 
                                   ∫ 
                                   
                                     - 
                                     ∞ 
                                   
                                   t 
                                 
                                  
                                 
                                   
                                     s 
                                      
                                     
                                       ( 
                                       τ 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     τ 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   I 
                   = 
                   
                     
                       I 
                       0 
                     
                      
                     
                       { 
                       
                         1 
                         + 
                         
                           m 
                           * 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       cos 
                                        
                                       
                                         ( 
                                         
                                           
                                             ω 
                                             1 
                                           
                                            
                                           t 
                                         
                                         ) 
                                       
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     cos 
                                      
                                     
                                       ( 
                                       
                                         
                                           ω 
                                           2 
                                         
                                          
                                         t 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                       } 
                     
                     * 
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             
                               ω 
                               c 
                             
                              
                             t 
                           
                           + 
                           
                             
                               k 
                               f 
                             
                              
                             
                               [ 
                               
                                 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           ω 
                                           1 
                                         
                                          
                                         t 
                                       
                                       ) 
                                     
                                   
                                   
                                     ω 
                                     1 
                                   
                                 
                                 + 
                                 
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           ω 
                                           2 
                                         
                                          
                                         t 
                                       
                                       ) 
                                     
                                   
                                   
                                     ω 
                                     2 
                                   
                                 
                               
                               ] 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where k f  is the frequency modulation factor. This modulated light is passed through the phase modulator  26 . As this light passes through the fiber (laser  18  pigtail and phase modulator  26  input fiber) it accumulates some delay. The phase modulator  26  modulates the phase of the carrier with the signal that is applied to it. The signal that is applied to the phase modulator  26  follows an electrical path through electrical components  32 ,  36 ,  40  and hence acquires some delay. Thus a differential delay between the two signals paths is established. This differential delay is labeled τ diff . Then equations 2 and 3 modify as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         I 
                         = 
                           
                          
                         
                           
                             
                               I 
                               0 
                             
                              
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   m 
                                   * 
                                   
                                     s 
                                      
                                     
                                       ( 
                                       t 
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                           * 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           cos 
                            
                           
                             [ 
                             
                               
                                 
                                   ω 
                                   c 
                                 
                                  
                                 t 
                               
                               + 
                               
                                 
                                   k 
                                   f 
                                 
                                  
                                 
                                   
                                     ∫ 
                                     
                                       - 
                                       ∞ 
                                     
                                     t 
                                   
                                    
                                   
                                     
                                       s 
                                        
                                       
                                         ( 
                                         τ 
                                         ) 
                                       
                                     
                                      
                                     
                                        
                                       τ 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   k 
                                   p 
                                 
                                  
                                 
                                   s 
                                    
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       
                                         τ 
                                         diff 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         I 
                         = 
                           
                          
                         
                           
                             I 
                             0 
                           
                            
                           
                             { 
                             
                               1 
                               + 
                               
                                 m 
                                 * 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 
                                                   ω 
                                                   1 
                                                 
                                                  
                                                 t 
                                               
                                               ) 
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           cos 
                                            
                                           
                                             ( 
                                             
                                               
                                                 ω 
                                                 2 
                                               
                                                
                                               t 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                             } 
                           
                           * 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         ω 
                                         c 
                                       
                                        
                                       t 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         k 
                                         f 
                                       
                                        
                                       
                                         [ 
                                         
                                           
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     1 
                                                   
                                                    
                                                   t 
                                                 
                                                 ) 
                                               
                                             
                                             
                                               ω 
                                               1 
                                             
                                           
                                           + 
                                           
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     2 
                                                   
                                                    
                                                   t 
                                                 
                                                 ) 
                                               
                                             
                                             
                                               ω 
                                               2 
                                             
                                           
                                         
                                         ] 
                                       
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       k 
                                       p 
                                     
                                      
                                     
                                       [ 
                                       
                                         
                                           
                                             
                                               
                                                 cos 
                                                  
                                                 
                                                   ( 
                                                   
                                                     
                                                       ω 
                                                       1 
                                                     
                                                      
                                                     
                                                       { 
                                                       
                                                         t 
                                                         - 
                                                         
                                                           τ 
                                                           diff 
                                                         
                                                       
                                                       } 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                               + 
                                             
                                           
                                         
                                         
                                           
                                             
                                               cos 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     2 
                                                   
                                                    
                                                   
                                                     { 
                                                     
                                                       t 
                                                       - 
                                                       
                                                         τ 
                                                         diff 
                                                       
                                                     
                                                     } 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Eq. 5 shows the carrier 
         [0000]    
       
         
           
             cos 
              
             
               ( 
               
                 
                   
                     ω 
                     c 
                   
                    
                   t 
                 
                 + 
                 
                   
                     k 
                     f 
                   
                    
                   
                     [ 
                     
                       
                         
                           sin 
                            
                           
                             ( 
                             
                               
                                 ω 
                                 1 
                               
                                
                               t 
                             
                             ) 
                           
                         
                         
                           ω 
                           1 
                         
                       
                       + 
                       
                         
                           sin 
                            
                           
                             ( 
                             
                               
                                 ω 
                                 2 
                               
                                
                               t 
                             
                             ) 
                           
                         
                         
                           ω 
                           2 
                         
                       
                     
                     ] 
                   
                 
                 + 
                 
                   
                     k 
                     p 
                   
                    
                   
                     [ 
                     
                       
                         
                           
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   
                                     ω 
                                     1 
                                   
                                    
                                   
                                     { 
                                     
                                       t 
                                       - 
                                       
                                         τ 
                                         diff 
                                       
                                     
                                     } 
                                   
                                 
                                 ) 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             cos 
                              
                             
                               ( 
                               
                                 
                                   ω 
                                   2 
                                 
                                  
                                 
                                   { 
                                   
                                     t 
                                     - 
                                     
                                       τ 
                                       diff 
                                     
                                   
                                   } 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               ) 
             
           
         
       
     
         [0000]    has two associated terms which have to be cancelled to cancel the original chirp generated by the laser. This cancellation is possible only if the term 
         [0000]    
       
         
           
             
               k 
               f 
             
              
             
               [ 
               
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         
                           ω 
                           1 
                         
                          
                         t 
                       
                       ) 
                     
                   
                   
                     ω 
                     1 
                   
                 
                 + 
                 
                   
                     sin 
                      
                     
                       ( 
                       
                         
                           ω 
                           2 
                         
                          
                         t 
                       
                       ) 
                     
                   
                   
                     ω 
                     2 
                   
                 
               
               ] 
             
           
         
       
     
         [0000]    and the term k p [cos(ω 1 {t−τ diff })+cos(ω 2 {t−τ diff })] are identical in amplitude and have a 180 degree phase differential. In order to achieve this, the signal before being applied to the phase modulator  26  is passed through an integrator  32  and an amplifier  36  that causes a 180 degree phase differential. Equation 5 would then become 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         I 
                         = 
                           
                          
                         
                           
                             I 
                             0 
                           
                            
                           
                             { 
                             
                               1 
                               + 
                               
                                 m 
                                 * 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 
                                                   ω 
                                                   1 
                                                 
                                                  
                                                 t 
                                               
                                               ) 
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           cos 
                                            
                                           
                                             ( 
                                             
                                               
                                                 ω 
                                                 2 
                                               
                                                
                                               t 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                             } 
                           
                           * 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         ω 
                                         c 
                                       
                                        
                                       t 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         k 
                                         f 
                                       
                                        
                                       
                                         [ 
                                         
                                           
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     1 
                                                   
                                                    
                                                   t 
                                                 
                                                 ) 
                                               
                                             
                                             
                                               ω 
                                               1 
                                             
                                           
                                           + 
                                           
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     2 
                                                   
                                                    
                                                   t 
                                                 
                                                 ) 
                                               
                                             
                                             
                                               ω 
                                               2 
                                             
                                           
                                         
                                         ] 
                                       
                                     
                                     - 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       k 
                                       p 
                                     
                                      
                                     
                                       [ 
                                       
                                         
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 
                                                   ω 
                                                   1 
                                                 
                                                  
                                                 
                                                   { 
                                                   
                                                     t 
                                                     - 
                                                     
                                                       τ 
                                                       diff 
                                                     
                                                   
                                                   } 
                                                 
                                               
                                               ) 
                                             
                                           
                                           
                                             ω 
                                             1 
                                           
                                         
                                         + 
                                         
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 
                                                   ω 
                                                   2 
                                                 
                                                  
                                                 
                                                   { 
                                                   
                                                     t 
                                                     - 
                                                     
                                                       τ 
                                                       diff 
                                                     
                                                   
                                                   } 
                                                 
                                               
                                               ) 
                                             
                                           
                                           
                                             ω 
                                             2 
                                           
                                         
                                       
                                       ] 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0023]    The differential delay τ diff  is adjusted to zero by making the electrical path lengths traversed by the two signals the same. This reduces equation 6 as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         I 
                         = 
                           
                          
                         
                           
                             I 
                             0 
                           
                            
                           
                             { 
                             
                               1 
                               + 
                               
                                 m 
                                 * 
                                 
                                   [ 
                                   
                                     
                                       
                                         
                                           
                                             cos 
                                              
                                             
                                               ( 
                                               
                                                 
                                                   ω 
                                                   1 
                                                 
                                                  
                                                 t 
                                               
                                               ) 
                                             
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           cos 
                                            
                                           
                                             ( 
                                             
                                               
                                                 ω 
                                                 2 
                                               
                                                
                                               t 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   ] 
                                 
                               
                             
                             } 
                           
                           * 
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           cos 
                            
                           
                             ( 
                             
                               
                                 
                                   
                                     
                                       
                                         ω 
                                         c 
                                       
                                        
                                       t 
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         k 
                                         f 
                                       
                                        
                                       
                                         [ 
                                         
                                           
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     1 
                                                   
                                                    
                                                   t 
                                                 
                                                 ) 
                                               
                                             
                                             
                                               ω 
                                               1 
                                             
                                           
                                           + 
                                           
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     2 
                                                   
                                                    
                                                   t 
                                                 
                                                 ) 
                                               
                                             
                                             
                                               ω 
                                               2 
                                             
                                           
                                         
                                         ] 
                                       
                                     
                                     - 
                                     
                                       
                                         k 
                                         p 
                                       
                                        
                                       
                                         [ 
                                         
                                           
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     1 
                                                   
                                                    
                                                   t 
                                                 
                                                 ) 
                                               
                                             
                                             
                                               ω 
                                               1 
                                             
                                           
                                           + 
                                           
                                             
                                               sin 
                                                
                                               
                                                 ( 
                                                 
                                                   
                                                     ω 
                                                     2 
                                                   
                                                    
                                                   t 
                                                 
                                                 ) 
                                               
                                             
                                             
                                               ω 
                                               2 
                                             
                                           
                                         
                                         ] 
                                       
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0024]    Now balancing the amplitude factors such that k f  and k p  are identical leads to equation 8. 
         [0000]        I=I   0 [1+ m *{cos(ω 1   t )+cos(ω 2   t )}]*cos(ω c   t )   (8) 
         [0025]    This intensity modulated signal is now launched into the fiber span. Since the laser chip is cancelled, the distortions due to the laser chirp interaction with fiber dispersion can be avoided. 
         [0026]      FIG. 3  shows an extension of the  FIG. 2  transmitter. The  FIG. 3  transmitter supports in this example, as does the  FIG. 2  transmitter, transmission of the composite analog RF signal input on terminal  10  in a frequency range (which is exemplary) of 50 MHz to 550 MHz. Note that elements in  FIG. 3  which are the same as in  FIG. 2  are similarly labeled in terms of reference numbers. Additionally, the  FIG. 3  transmitter has provisions for input of multiple QAM (quadrature amplitude modulation) RF signals each having differing information content in the exemplary bandwidth of 550 MHz to 1 GHz. These are applied respectively on terminals  56   a - 56   d , so here there (as an example) are four such different QAM signals applied. These are what is called in the cable television field narrowcast signals. Each input narrowcast RF signal is applied to an adder (or combiner) respectively  60   a - 60   d , each operating in the electrical domain, which in turn is respectively coupled to the input port of lasers  54   a - 54   d . As shown, each of these lasers outputs light at a different wavelength in the 1550 nm band, here designated λ 1 , λ 2 , λ 3  and λ 4 , respectively. (There is no requirement of using this particular illustrative combination of composite and QAM input RF signals.) 
         [0027]    The optical signals output from lasers  54   a - 54   d  are each applied to an input port of a conventional DWD (dense wavelength division) multiplexer (or other suitable multiplexer) operating of course in the optical domain, which outputs a combined optical signal on its output port  68 , and which in turn is coupled to the optical input port of phase modulator  50 . This configuration successfully suppresses the laser chirp of all four lasers simultaneously and thus reduces the CSO degradation of broadcast signals (e.g. 50 to 550 MHz frequencies) carried by the four lasers. Note that again here only one phase modulator  50  is shared by all of these various input RF signals. This is an advantage because it economizes on component count, and hence reduces cost. (Note that the phase modulators are typically one of the relatively more expensive components of such transmitters.) Multiple transmitters of the type of  FIG. 2  or  FIG. 3  can each drive a single fiber span of a length of 30 Km. Typically each transmitter in such an arrangement has its own unique set of optical wavelengths. 
         [0028]    The  FIG. 3  transmitter allows multiple signals with unique content in the 550 MHz to 1 GHz frequency range to be carried on a single optical fiber. This arrangement will for instance quadruple the capacity of a fiber optic cable. By operating in the 1550 nm wavelength band, the well known crosstalk problems that limit wavelength division multiplexing (both coarse wavelength division multiplexing and dense wavelength division multiplexing) at other wavelengths are minimized. Also, optical signals at the 1550 nm band can be amplified by conventional EDFAs (erbium doped fiber amplifiers), further reducing system costs. This technique is not limited to the 1550 nm band. A similar technique can be used to transmit multiple DWDM signals in the 1310 nm band. However adequate care should be taken in choosing the DWDM wavelengths in the 1310 nm band. The wavelengths can be placed below, at, or above the dispersion null point which is 1312±6 nm for a single mode fiber. When DWDM signals are placed at the dispersion null point, the FWM (four wave mixing) nonlinearity can be significant. In addition, Raman crosstalk will extend to higher RF frequencies because of the low dispersion, but its magnitude can be limited by choosing smaller wavelength spacing. Since this is well known in optics, the only other option is to place the DWDM wavelengths above or below the dispersion null point. Thus multiple wavelengths can be placed in the 1280 to 1300 nm band or the 1318 to 1332 nm band. In either case, there will be some crosstalk due to a) very low fiber dispersion, b) lower mode field diameter of the fiber at 1310 nm, and c) the need to launch high per wavelength power into the fiber to compensate for higher fiber loss at 1310 nm. This will permit use of this DWDM technique in the 1310 nm band (1270 to 1350 nm), but with some severe limitations on distance, power, number of wavelengths, etc. 
         [0029]      FIGS. 4-10  show exemplary performance of the transmitter of  FIG. 2  under various test conditions and as compared to prior art systems.  FIG. 4  shows along the horizontal axis the frequency in megahertz of the input composite (RF) signal, and the amount of CSO (composite second order) distortion expressed in decibels (dB) along the vertical axis. In general in these graphs the higher up along the vertical axis, the better is the distortion performance, except for  FIGS. 6 ,  7 ,  9 , and  10 . In  FIG. 4  the key at the bottom of the figure shows the various plots. The first plot labeled “CSO-Laser dBC” is the optical signal output strength at the laser itself, which is the directly modulated laser  18  in  FIG. 2 . The next plot is the signal strength level (in the optical domain) at the end of a 50 kilometer long optical span designated “uncompensated”. This is the prior art of  FIG. 1 . The next plot is also for the 50 kilometer span, designated “compensated”, which corresponds to the transmitter of  FIG. 2 , the compensation being due to the presence of the integrator, variable delay, gain circuitry, diplexer, and SBS tone generator for providing the compensation. As shown, this is a significantly better signal than along the same length of optical fiber span uncompensated. The last two plots shown are for respectively the signal strength on a 25 long kilometer span uncompensated, and on a 25 long kilometer span compensated or in accordance with  FIG. 2 . As shown for both the 50 kilometer and the 25 kilometer distances, the compensated present transmitter provides better performance then the uncompensated prior art transmitter. 
         [0030]      FIG. 5  shows plots using the same key legends as in  FIG. 4 , with the vertical axis here showing minimum degradation in the CTB (composite triple beat) distortion with and without the present type of transmitter having compensation. CTB is well known in the field and also expressed here in dB. Again, the present compensated transmitter provides better performance along both the 50 kilometer span and the 25 kilometer span than does the (prior art) uncompensated transmitter. 
         [0031]      FIG. 6  shows along the vertical axis the residual CSO (composite second order) distortion achieved with the present transmitter of  FIG. 2  at different optical (laser output) power levels as applied to a 25 long kilometer optical fiber span. The various “launch” optical powers shown are 7.5, 16, 13 and 18 dBM. As shown at all of these power levels, the amount of residual CSO is roughly the same, with approximately the same shape to each curve. The CSO degradation with fiber span length is severe for the high frequency channels. The approach disclosed here perfectly cancels the effect of fiber dispersion. Since the chirp is canceled, the CSO improvements are effective for all span lengths, i.e. the approach is not fiber distance dependent. Another measure of the effectiveness of the cancellation scheme is the amount of CSO degradation left uncompensated.  FIGS. 6 and 10  show the effectiveness of the present scheme over frequencies of 50 to 550 MHz. Also these figures show the cancellation at different optical powers. This shows that the linear effects of the laser chirp and fiber dispersion are canceled. The CSO due to non-linear effects such as SPM (self-phase modulation), which change dramatically due to the optical launch power, plays a much smaller role in signal degradation. 
         [0032]      FIG. 7  is a plot similar to that of  FIG. 6 , but rather then being tested on a 25 long kilometer span here, the span is 50 kilometers long. The launch powers are the same as in  FIG. 6 . Again, in this case all four plots are very close, indicating approximately the same level of performance at each optical power. 
         [0033]      FIG. 8  is a plot similar to that of  FIG. 4 , except that a different type of laser is used. The laser used in the  FIG. 8  test is one with a lower chirp than that of the  FIG. 4  test. Note that the shapes of the plots are roughly the same as in  FIG. 4 , although the amount of CSO compensation is slightly higher at all frequencies than in  FIG. 4 . 
         [0034]      FIG. 9  shows a plot similar to that of  FIG. 6 , but again with a lower chirp laser used. Again, the plot is roughly the same shape as in  FIG. 6 . 
         [0035]      FIG. 10  corresponds to  FIG. 7  in showing the residual CSO achieved with the present transmitter at different optical powers, but again with the lower chirp laser. Here the shape of the plot is slightly different than in  FIG. 7  and the amount of residual CSO is generally somewhat less. 
         [0036]    This description is illustrative and not limiting; further modifications will be apparent to those skilled in the art in light of this disclosure and are intended to fall within the scope of the appended claims.