Abstract:
A method for linearizing optical transmission systems that includes an optical linearizer connected to the output of the optical transmitter. From the output, which includes a modulated signal and a transmitter distortion, the linearizer interacts with the wavelength chirping (dλ c ) of the transmitter output. More specifically, the linearizer is characterized by a wavelength dependent optical transfer curve F(λ) that utilizes dλ c  to induce a compensation distortion. Further, the optical transfer curve F(λ) has a reference wavelength (λ p ) and an operating point wavelength offset Δλ b . In operation, (λ p +Δλ b ) of the optical transfer curve F(λ) is aligned with (λ c ) of the output to establish an effective value for the compensation distortion. This compensation distortion is then added with the transmitter distortion to cancel the transmitter distortion from the modulated signal; to thereby linearize the output.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention pertains generally to optical transmission systems. More particularly, the present invention pertains to devices and methods for optically linearizing the nonlinear distortions that are inherently introduced into signals produced within the optical transmission system. The present invention is particularly, but not exclusively, useful as a signal processor that can be incorporated into a fiber optic transmission system to optically compensate for the second and/or third order distortions that are produced in the system.  
         BACKGROUND OF THE INVENTION  
         [0002]    In a conventional fiber optic transmission system, an electrical information signal is used to modulate the intensity of an optical transmitter. The resultant modulated signal is then transmitted over a distance through an optical fiber. After passing through the optical fiber, the modulated signal is converted back into an electrical signal by an optical receiver. It is well known that the information carried on such a modulated signal may be either in a digital, an analog or a mixed signal format. For several reasons, such as an enhanced multiplexing capability, there is an increasing interest in delivering digital information via optical fibers in an analog format. Fiber optic transmission systems, however, are susceptible to degrading distortions which can significantly affect the quality of the communications.  
           [0003]    Laser diodes are well known devices that are now commonly used for transmitting signals with an analog format over a fiber optic transmission system. Laser diodes, however, like all other analog optical transmitters, have nonlinear transmission responses. Unfortunately, the nonlinearites introduced by the transmitters are often aggravated by the optical fiber, or by certain other optical components in the system. It happens that these nonlinear responses are predominantly second-order distortions and third- order distortions (distortions that can create spurious frequencies that fall within the bandwidth of interest). Obviously, it is desirable that these distortions be removed from transmitted signals.  
           [0004]    Heretofore, several electronic methods have been disclosed for the purpose of linearizing the outputs of laser diode transmitters. More specifically, these methods have been directed toward linearizing laser diodes when they are used in fiber optic analog transmission systems. In general, these methods have tended to include the use of predistortion circuits that intentionally generate distorted signals having second-order or third-order distortions. Typically, the distorted signals are generated with the same amplitude as the distortions generated in the system, but they have an opposite phase. Thus, when added together, the distortions generated by the predistortion circuits are intended to cancel the distortions that are introduced into the system by the laser diode transmitter. Predistortion circuits in general are limited in bandwidth due to the state of the art electronic circuit limitation.  
           [0005]    In addition to predistortion circuits, it is known that other linearization schemes can be fabricated in several ways. For example, known linearization schemes include: 1) cancellation by complimentary outputs; 2) push-pull operations with wavelength division multiplexing; and 3) the use of Fabry-Perot devices. These linearization schemes have, however, been susceptible to system degradation for several reasons. Specifically, scheme 1, as mentioned above, suffers from the need for two stable transmission fibers and scheme 2 suffers from electronic component bandwidth limitation. Furthermore, scheme 3 suffers from instability due to the difficulty in maintaining precise wavelength alignment between the laser diode and the Fabry-Perot.  
           [0006]    In light of the above, it is an object of the present invention to provide an optical apparatus for linearizing the output of an optical transmitter. Another object of the present invention is to provide an apparatus for linearizing the output of an optical transmitter that can be effectively wavelength (e.g. temperature) tuned for proper operation. Yet another object of the present invention is to provide an apparatus for linearizing an optical transmission system with selected optical devices that can have either linear or nonlinear wavelength dependent optical responses. Still another object of the present invention is to provide an apparatus for linearizing an optical transmission system that is simple to use, is relatively easy to manufacture, and is cost effective.  
         SUMMARY OF THE PREFERRED EMBODIMENTS  
         [0007]    In accordance with the present invention, a communications apparatus for linearizing the output of an optical transmitter (such as a DFB laser diode), includes an optical device (such as a fused fiber WDM coupler). Specifically, the optical device is connected to receive the output of the optical transmitter. It happens that the output from the optical transmitter will include a modulated signal, as well as second and third order distortions (hereinafter sometimes collectively referred to as a “transmitter distortion”). Importantly, the transmitter output also includes a characteristic wavelength “chirping”. In accordance with the present invention, this “chirping,” together with the desired transmitter output, is used as an input by the optical device, to optically generate nonlinear distortion signals (hereinafter sometimes collectively referred to as “compensation distortions”) that will compensate the transmitter distortion. Accordingly, the compensation distortions can be added to the output of the optical transmitter to cancel the transmitter distortions (second and/or third order distortions) in the output.  
           [0008]    Technically, the modulated signal that is transmitted by the transmitter (e.g. laser diode) will have a center emission wavelength (λ c ) and a characteristic wavelength chirping (dλ c ). Further, the optical device (e.g. coupler) will include components for establishing a predetermined, wavelength dependent, normalized optical transfer curve F(λ). Specifically, this optical transfer curve F(λ) is fabricated to accommodate the operating condition of the optical transmitter. In particular, the optical transfer curve F(λ) of the optical device is designed to have a reference wavelength (λ p ), a slope determinant wavelength spacing (Δλ w ), and an operating point wavelength offset (Δλ b ) that are all based on the known operating conditions of the transmitter.  
           [0009]    In their connection with each other, the optical device and the optical transmitter can be individually or collectively wavelength (e.g. temperature) tuned. Preferably, an operating temperature for the optical transmitter (or optical device) can be established which will align (λ c ) of the transmitter with (λ p +Δλ b ) of the optical device. Regardless how the operating temperature is established, when the system is tuned, an operating point can be established on the optical transfer curve F(λ) that will interact with the wavelength chirping (dλ c ) from the transmitter in a specified manner. Preferably, this operating point is established on the optical transfer curve F(λ) where λ p +Δλ b =λ c . Thus, the purpose here is to use F(λ) to optically induce a compensation distortion from the wavelength chirping (dλ c ) that will substantially compensate the transmitter distortions (second and/or third order distortions) that are introduced by the transmitter. Once the compensation distortions have been induced by the optical device (e.g. coupler), linearization of the optical transmitter (e.g. laser diode) is accomplished by adding the compensation distortion to the output of the transmitter. Stated differently, the compensation distortion is added to the output of the optical transmitter to cancel the transmitter distortion from the modulated signal in the output. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]    The novel features of this invention, as well as the invention itself, both as to its structure and its operation, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similar reference characters refer to similar parts, and in which:  
         [0011]    [0011]FIG. 1 is a schematic drawing of a fiber optic transmission system incorporating an optical linearizer in accordance with the present invention;  
         [0012]    [0012]FIG. 2 illustrates various exemplary optical transfer curves F(λ) that can be incorporated in an optical linearizer in accordance with the present invention;  
         [0013]    [0013]FIG. 3 is an optical transfer curve F(λ) showing a chirped wavelength input (dλ c ) interacting with the optical transfer curve F(λ) to create modulations (dF) to induce compensation distortions that are useful for linearizing the output of an optical transmitter;  
         [0014]    [0014]FIG. 4A is a graph showing empirical results for suppression of second order distortions as a function of the operating point wavelength of an optical linearizer;  
         [0015]    [0015]FIG. 4B is a graph showing a comparison between simulation results and experimental data for a specific operating condition of the present invention;  
         [0016]    [0016]FIG. 5 is a graph showing empirical results for suppression of third order distortions as a function of a slope determinant wavelength spacing of an optical linearizer;  
         [0017]    [0017]FIG. 6A is a schematic drawing of an embodiment for a fiber optic transmission system which incorporates feedback control; and  
         [0018]    [0018]FIG. 6B is a schematic drawing of an alternate embodiment of the system shown in FIG. 6A. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0019]    Referring initially to FIG. 1, a fiber optic transmission system in accordance with the present invention is shown and is generally designated  10 . As shown, the system  10  includes an optical transmitter  12  that is connected with an isolator  14  that is, in turn, connected with an optical linearizer  16 . An optical fiber  18  then interconnects the optical linearizer  16  with an optical detector  20 . As intended for the system  10  of the present invention, communications data is generated by a signal source  22  and is used to modulate the optical transmitter  12 . The communications data from signal source  22  may be in a digital, an analog, or a mixed format. In any event, the isolator  14  (which is optional) is positioned to prevent optical back reflection into the transmitter  12 . The modulated signal of the output of optical transmitter  12  is then fed into the optical linearizer for subsequent transmission through the optical fiber  18  to the optical detector  20 . A receiver  24  that is connected to the optical detector  20  provides an output of the received communications data.  
         [0020]    For purposes of the present invention, the optical transmitter  12  is preferably a laser diode of a type well known in the pertinent art, such as a DFB laser diode. It is to be appreciated, however, that the optical transmitter  12  can be a direct modulated laser diode, an electro-absorption modulator, or a Mach-Zehnder modulator, all of which are well known in the art. Importantly, in all cases, the output of the optical transmitter  12  at λ c  may have an analog modulation format that is sinusoidal in nature. It is also important to recognize that, in all cases, the output of the optical transmitter  12  will include more than just the modulated signal that is to be transmitted over the system  10 . Specifically, in addition to the modulated signal, the output of optical transmitter  12  will include optical distortions (second and/or third order) and it will have a “chirping” (dλ c ) that is characteristic of the optical transmitter  12 . For the system  10 , a bias control  26  can be used to influence the content of the output from the optical transmitter  12  (e.g. minimizing the third order distortions), while a wavelength control  28  is used to establish (tune) the center emission wavelength (λ c ). In a manner well known in the pertinent art, wavelength control  28  can be tuned in several ways, such as by temperature tuning, voltage tuning, current tuning or mechanical tuning.  
         [0021]    The optical linearizer  16  of the present invention is preferably an optical device of a type that is well known in the pertinent art, such as a fused fiber WDM coupler. The optical linearizer  16 , however, may alternatively be any well known type of optical device with a wavelength dependent transfer function that may include wavelength dependent absorptive (or gain) materials, electro-absorption semiconductor waveguides, fiber Bragg-gratings, wavelength dependent coupling interleavers, Mach-Zehnder waveguide modulators, acoustic-optical tunable filters, tapered fiber filters, thin film filters or arrayed waveguide grating (AWG) filters. Importantly, the system  10  can use these types of devices for the optical linearizer  16  either individually or in combination with each other. Importantly, regardless of the type device that is used for the linearizer  16 , the optical linearizer  16  is fabricated to have a specific optical transfer curve F(λ). Because the optical linearizer  16  is a wavelength dependent device, it can be tuned like the optical transmitter  12 . For the optical linearizer  16 , this tuning is accomplished by the operation control  30 .  
         [0022]    [0022]FIG. 2 shows various types of exemplary optical transfer curves that can be fabricated for the optical linearizer  16 . Specifically, the optical linearizers  16   a ,  16   b  and  16   c  are shown with respective optical transfer curves F 1 (λ), F 2 (λ) and F 3 (λ) that may be controlled (tuned) by respective operation controls  30   a ,  30   b  and  30   c . It is to be appreciated that the optical linearizers  16   a ,  16   b  and  16   c  are only exemplary, and that they may be used either individually or collectively in the system 10, as required. Further, these linearizers  16   a ,  16   b  and  16   c  all function substantially in the same way. The functionality of the linearizers  16   a ,  16   b  and  16   c , and their interaction with the optical transmitter  12  will, perhaps, be best appreciated with reference to FIG. 3.  
         [0023]    [0023]FIG. 3 shows an optical transfer curve F(λ) that is typical of one that can be fabricated for a fused fiber WDM coupler type optical linearizer  16 . As shown, the optical transfer curve F(λ) is characterized by a reference wavelength (λ p ) and a slope determinant wavelength spacing (Δλ w ). Also, FIG. 3 shows a typical operating point  32  for the optical linearizer  16  that is identified by the wavelength offset Δλ b . For the optical transfer curve F(λ) shown in FIG. 3, the slope of the curve will change as the operating point  32  is changed. This, of course, need not always be so (e.g. linearizer  16   b  in FIG. 2). Nevertheless, for the optical transfer curve F(λ) shown in FIG. 3, both the reference wavelength (λ p ), and a slope determinant wavelength spacing (Δλ w ), can be fabricated for the optical transfer curve F(λ). The coupler operating point offset (Δλ b ) can then be established (tuned) on optical transfer curve F(λ) by the operation controller  30 . Preferably, this is done by temperature tuning.  
         [0024]    Still referring to FIG. 3, it will be appreciated that the operating point  32  should be established where λ c =λ p +Δλ b . Accordingly, when the wavelength chirped dλ c  from the optical transmitter  12  is fed into the optical linearizer  16 , the interaction of the wavelength chirped dλ c  at the operating point  32  of the optical transfer curve F(λ) results in an output having modulations (dF). FIGS. 4A and 5 respectively show graphs  34 ,  36  that present empirical data for the suppression of optical distortions in a system  10 . Further, FIG. 4B shows a comparison  34 ′ between an empirical simulation and experimental data obtained for a suppression of optical distortions similar to those shown for the graph  34  of FIG. 4A. Specifically, these graphs  34 ,  36  indicate there is an identifiable operating point wavelength offset Δλ b , and an identifiable slope determinant wavelength spacing (Δλ w ) for each optical linearizer  16  that will induce a modulation (dF) which will effectively suppress transmitter distortions (second and/or third order) that are introduced into the system  10 .  
         [0025]    Several alternate embodiments of the system  10  are envisioned for the present invention. For example, one alternate embodiment (FIG. 6A) shows a system  10 A wherein closed loop feedback control is provided for the local optical transmitter  12 . On the other hand, another alternate embodiment (FIG. 6B) shows a system  10 B wherein closed loop feedback control is provided to achieve nonlinear distortion suppression of the whole system, including distortions induced by fiber transmission (optical fiber  18 ) and detection (optical detector  20 ) and any other optical components in the system  10 .  
         [0026]    In FIG. 6A, it is seen that the system  10 A provides for transmission of a pilot tone  38  through the transmitter  12 , linearizer  16  and optical fiber  18 . An optical coupler  40  then directs the output from the optical linearizer  16  (including the pilot tone  38 ) to a local optical detector  42  which, in turn, passes the output to an analyzer  44 . The analyzer  44  then analyzes the second and/or third order distortions of the pilot tone  38  and uses this analysis to appropriately and separately readjust the bias control  26  and the wavelength control  28 . Thus, local feedback control can be established for the optical transmitter  12 .  
         [0027]    For another alternate embodiment of the present invention, shown as the system  10 B in FIG. 6B, the pilot tone  38  is passed through distortion filters  46  after it has passed completely through the optical fiber  18  and the optical detector  20 . The filtered pilot tone  38  is then transmitted via an optical transmitter  48  through an optical fiber  18  to the optical detector  50 . Again, the analyzer  44  analyzes the second and third order distortions of the pilot tone  38  and uses this analysis to appropriately and separately readjust the bias control  26  and the wavelength control  28 . Alternatively, after the pilot tone  38  has passed completely through the optical fiber  18 , a localized feedback loop around a linearizer  16  can be accomplished at the input to an optical detector  20 .  
       OPERATION  
       [0028]    Generally, the wavelength dependency of an optical linearizer  16  can be represented by a normalized optical transfer curve F(λ). Mathematically, this transfer curve F(λ) can be expressed in Taylor series around the center emission wavelength λ c  of the transmitter:  
           F (λ)= F   0 (λ c )+ F   1 (λ−λ c )+ F   2 (λ−λ c ) 2 /2 +F   3 (α−λ c ) 3 /6+ . . .  
           +F   n (λ c )(λ−λ c ) n   /n!+ . . .    (Eq. 1) 
         [0029]    where F n =d n F(λ)/dλ n  with λ=λ c . Further, the modulated wavelength λ(t) (i.e. modulated signal output) of the optical transmitter  12  can be expressed as λ(t) =λ c +dλ c (t). For the present invention, in response to the transfer curve F(λ), the transmitter chirping dλ c  creates a modulated linearizer output (dF) shown in FIG. 3. Thus, the output of the optical linearizer  16  can be expressed as:  
           P   out ( t ,λ)= P   TR ( t )·α·F(λ)  (Eq. 2) 
         [0030]    where P out  is the output of the optical linearizer  16 , P TR  is the output of the transmitter, and α is the optical insertion loss of the optical linearizer  16 .  
         [0031]    In the specific case where the optical transmitter  12  is a DFB laser diode, the transmitter chirping dλ c  under single tone modulation can be expressed as:  
           dλ   c (t)=−η FM ·m·( l   b   −l   th ) sin (ω· t )·λ c   2   /C   (Eq. 3) 
         [0032]    where C is the light speed, η FM  is the FM response of the laser, l b  is the laser bias current, l th  is the laser threshold current, m is the optical modulation depth, and ω is the modulation angular frequency. Combining Equations (1) to (3), we can obtain the modulated linearizer output from P(λ) due to laser chirping as:  
           P   out ( t ,λ)= P   TR ( t )·α·{F 0 (λ c )+ F   1 ·(λ m ·sin (ω· t ))+F 2 ·(λ m ·sin (ω· t )) 2 /2+ 
           F   3 ·(λ m ·sin (ω· t )) 3 /6+ . . . }  (Eq. 4) 
         [0033]    where λ m =−η FM ·i b ·(λ c ) 2 /C and i b =m·(l b −i th ).  
         [0034]    When the optical transmitter is a laser diode the output P TR  can be modeled from the laser diode&#39;s nonlinear L-l curve, using a Taylor expansion as:  
           P   TR (l) P   LD (l b )+ h 1·( l−l   b )+ h 2·( l−l   b ) 2 /2 !+h 3·( l−l   b ) 3 /3!+ . . .   (Eq. 5) 
         [0035]    where hn=(d n P LD (l)/dl n ) at l=l b , and l is the laser diode driving current. Let l =l b +m·(l b −l th ) sin (ω·t) and i b =m·(l b −l th ), then the modulated laser diode output is  
           P   TR ( t )= P   LD ( l   b )+ h 1·( i   b · sin (ω· t ))+ h 2·( i   b · sin (ω· t )) 2 /2 +h 3·( i   b · sin (ω· t )) 3 /6+ . . .   (Eq. 6) 
         [0036]    Combining Equations (4) and (6), we can derive the second and third order compensation distortion contents after the output of the optical linearizer  16  as:  
                 P       o                 u                 t     ,     2      n                 d         ≈     α   ·     i   b   2     ·     cos        (     2   ·   ω   ·   t     )       ·     {         -   h2     ·       [         F   0          (     λ   c     )       +       F   2     ·       (       η     F                 M       ·       λ   c   2     /   C       )     2     ·       i   b   2     /   4         ]     /   4       +       [                h1   +     h3   ·       i   b   2     /   8         ]     ·       [                    F   1     ·     (       η     F                 M       ·       λ   c   2     /   C       )       +       F   3     ·       (       η     F                 M       ·       λ   c   2     /   C       )     3     ·       i   b   2     /   8         ]     /   2       -       [                    P   LD          (     I   b     )       +     h2   ·       i   b   2     /   4         ]     ·     F   2     ·         (       η     F                 M       ·       λ   c   2     /   C       )     2     /   4         }              
        and           (     Eq   .              7     )                 P       o                 u                 t     ,     3      r                 d         ≈     α   ·     i   b   3     ·     sin        (     3   ·   ω   ·   t     )       ·       {           -   h3     /   24     ·     [         F   0          (     λ   c     )       +       F   2     ·       (       η     F                 M       ·       λ   c   2     /   C       )     2     ·       i   b   2     /   4         ]       +       h2   /   8     ·     [                    F   1     ·     (       η     F                 M       ·       λ   c   2     /   c       )       +       F   3     ·       (       η     F                 M       ·       λ   c   2     /   C       )     3     ·       i   b   2     /   8         ]       -       [                h1   +     h3   ·       i   b   2     /   8         ]     ·     F   22     ·         (       η     F                 M       ·       λ   c   2     /   C       )     2     /   8       +       [                    P   LD          (     I   b     )       +     h2   ·       i   b   2     /   4         ]     ·     F   3     ·         (       η     F                 M       ·       λ   c   2     /   C       )     3     /   24         }     .               (     E                   q   .              8       )                               
 
         [0037]    The second order distortion terms in Equation (6) primarily consist of a combination of the second order distortion P out,2nd,LD  originated from the laser diode transmitter, second order distortion P out,2nd,LD{circle over (X)}linearizer  due to the mixing of the first order laser output with the first order chirping-modulated linearizer output, and the second order chirping-modulated linearizer output P out,2nd,linearizer . According to Equation (7) with proper λ c  and optical linearizer function F(λ), the second order distortion P out,2nd,LD  can be suppressed or compensated primarily by P out,2nd,LD{circle over (X)}linearizer  and P out,2nd,linearizer . Similarly, the third order distortion can be suppressed by proper λ c  and F(λ).  
         [0038]    The generality of this approach can be demonstrated using a few illustrative examples. For an optical linearizer with linear wavelength attenuation relationship, such as the linearizer  16   b  shown in FIG. 2, i.e., F n≧2 =0, the second order distortion can be suppressed if F 1 =h2·F 0 (λ c )·C/(2·h1·η FM ·λ c   2 ) and the third order distortion can be suppressed if F 1 =h3·F 0 (λ c )·C/(3·h2·η FM ·λ c   2 ), where F 1  is the slope of the normalized transfer curve at λ c . For an optical linearizer using fused fiber WDM coupler with an optical transfer curve F(λ) as shown in FIG. 3, this transfer function F(λ) can be expressed as:  
           F(λ)=[ 1+ cos (π·(Δλ b   +dλ)/Δλ   w )]/2  (Eq. 9) 
         [0039]    where Δλ w  is the fused fiber WDM coupler slope determinant wavelength spacing (i.e. the WDM coupler channel spacing), dλ c  is the wavelength chirping of the optical transmitter  12 , and Δλ b  is the coupler operating point offset. According to FIG. 3, we have Δλ b =λ c −λ p  where λ p  is the reference wavelength of the coupler. Using Equations (3), (7), (8) and (9), the second and third order distortions can be approximated as:  
                 P     out   ,     2      nd         ≈         α   ·     i   b   2     ·     cos        (     2   ·   ω   ·   t     )       ·     {         -   h2     ·       [     1   +     cos        (     π   ·       Δλ   b     /     Δλ   w         )         ]     /   8       -     h1   ·     sin        (     π   ·       Δλ   b     /     Δλ   w         )       ·     (     π   /   2     )     ·     (       λ   c   2     /   C     )     ·       (       η     F                 M       /     Δλ   w       )     /   2       +         P   LD          (     I   b     )       ·     cos        (     π   ·       Δλ   b     /     Δλ   w         )       ·       [     π   ·     (       λ   c   2     /   C     )     ·       η     F                 M       /     Δλ   w         ]     2             ]        8       }           (     Eq   .              10     )                 P     out   ,     3      rd         ≈     α   ·     i   b   3     ·       sin        (     3   ·   ω   ·   t     )       /   2     ·       {           -   h3     /   24     ·     [     1   +     cos        (     π   ·       Δλ   b     /     Δλ   w         )         ]       -       h2   /   4     ·     sin        (     π   ·       Δλ   b     /     Δλ   w         )       ·     (     π   /   2     )     ·     (       λ   c   2     /   C     )     ·     (       η     F                 M       /     Δλ   w       )       +     h1   ·     cos        (     π   ·       Δλ   b     /     Δλ   w         )       ·         [     π   ·     (       λ   c   2     /   C     )     ·       η     F                 M       /     Δλ   w         ]     2     /   8       +         P     L                 D            (     I   b     )       ·     sin        (     π   ·       Δλ   b     /     Δλ   w         )       ·         [     π   ·     (       λ   c   2     /   C     )     ·       η     F                 M       /     Δλ   w         ]     3     /   24         }     .               (     Eq   .              11     )                               
 
         [0040]    In light of the above, compensation distortion suppressions with a fused fiber WDM coupler can be examined using laser diode parameters where h1≈0.36 mW/mA, h2≈ 1 . 5 · 10   −4  mW/mA 2 , and h3≈4·10 −6  mW/mA 3 . Assuming l b −l th =60 mA, m=13%, λ c =1310 nm, η FM =100 MHz/mA, optical losses of 4.6 dB, laser output power of 22 mW, 0.85 mA/mW detector responsivity, no additional distortions after fiber transmission/detection and no distortion compensation from the optical linearizer  16 , the detected fundamental signal is −18 dBm, the second order harmonic is −79 dBm, and the third order harmonic is −103 dBm. The above distortions all originate from the optical transmitter  12 . With optical linearizer parameters Δλ w =3 nm and Δλ b =0.65 nm, the detected fundamental signal is −19 dBm, the second order harmonics is −120 dBm, and the third order harmonics is −104 dBm. The second order distortion is suppressed by 40 dB after optical compensation, with an additional optical loss of 0.5 dB due to coupler offset from the coupler maximum transmission point. With Δλ w =3 nm, FIG. 4 shows the second order suppression as a function of Δλ b . According to FIG. 4, a compensation suppression of more than 20 dB can be achieved when Δλ b  various from 0.6 to 0.7 nm. With optical linearizer  16  having Δλ w =0.47 nm and no offset (Δλ b =0 nm), the detected fundamental signal is −18 dBm, the second order harmonics is −77 dBm, and the third order harmonics is −140 dBm. The third order distortion is suppressed by 37 dB after optical compensation. With Δλ b =0 nm, FIG. 5 shows the third order suppression as a function of Δλ w . According to FIG. 5, a compensation suppression more than 20 dB can be achieved when Δλ w varies from 0.45 to 0.49 nm. It is also possible that with a single optical linearizer  16 , we can simultaneously suppress both second and third order distortions. A simulation with the optical linearizer Δλ w =0.45 nm and Δλ b =0.02 nm yields a detected fundamental signal of −18 dBm, the second order distortions of −107 dBm, and the third order distortions of −123 dBm. In this case, 20 dB or more suppression is simultaneously obtained for both second and third order distortion. To confirm the theory, FIG. 4B is included to show the second order distortion suppression obtained by empirical simulation in comparison with experimental data where h1 ˜0.15 mW/mA, h2=−0.7×10 −4  mW/mA 2 , λ c =1313 nm, η FM =270 MHz/mA, and Δλ w =5.5 nm.  
         [0041]    In the specific case where the optical linearizer  16  is a fused fiber WDM coupler, it can be appreciated with reference to from FIGS. 3 and 4, that λ c  needs to be aligned to λ p +Δλ b  with certain degree of accuracy to achieve good compensation distortion suppression. Given a specified operation condition for the optical transmitter  12 , Δλ w , and Δλ b  can be estimated for optimum performance. Knowing λ c , a fused fiber WDM coupler can be fabricated with a reference wavelength λ p =λ c −Δλ b  and the desired slope determinant wavelength spacing Δλ w . The small offset between λ c  and λ p +Δλ b  can then be minimized by temperature tuning the laser diode (optical transmitter  12 ) and/or the fused fiber WDM coupler (optical linearizer  16 ). If we consider the specific case wherein the optical linearizer is a fused fiber WDM coupler, the temperature sensitivity of the coupler (optical linearizer  16 ) may be around 0.01 nm/° C. and the sensitivity of the DFB laser diode (optical transmitter  12 ) may be around 0.1 nm/° C. The stability of a good laser diode temperature controller can be better than 0.1° C., which corresponds to wavelength stability on the order between 0.01 to 0.001 nm.  
         [0042]    While the particular Optical Linearizer for Fiber Communications as herein shown and disclosed in detail is fully capable of obtaining the objects and providing the advantages herein before stated, it is to be understood that it is merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended to the details of construction or design herein shown other than as described in the appended claims.