Abstract:
An apparatus and method for measuring optical signal-to-noise ratio in optical communications includes (1) a variable optical band-pass filter (VOBPF) that passes the amplified output beam when the beam wavelength is the same as the passing wavelength of the VOBPF; (2) a 1×4 beam distributor for distributing the passing beam of the VOBPF into four streams; (3) a measuring device for measuring Stokes parameters S 0 , S 1 , S 2 , S 3  from the four distributed beams; (4) a calculating device for calculating the optical signal power by finding the power of the polarized component of the amplified output beam from the Stokes parameters S 1 , S 2 , and S 3 ; (5) a calculating device for calculating the noise power by finding the power of the noise included in the amplified output beam from Stokes parameter S 0  and the optical signal power; and (6) a dividing device for calculating the ratio          Power                 of                 Optical                 Signal       Power                 of                 Noise                             
     at the passing wavelength.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to optical communications, and more particularly relates to an apparatus and a method for measuring optical signal-to-noise ratio in optical communications. An optical amplifier is a device to amplify optical signals without photo-electric/electric-photo conversion, and does not depend on the transmission speed or the transmission format of optical signals. A conventional optical transmitter amplifies the signals after photo-electric conversion, and reproduces optical signals with electric-photo conversion. The optical amplifier is substituted for the conventional optical transmitter. In particular, the optical amplifier can simultaneously amplify many optical signals of different wavelengths in a wide band, and the optical amplifier plays an important role in Wavelength Division Multiplexing (WDM) optical communications. In order to increase the transmitting capacity, several channels of optical signals are multiply divided with different wavelengths in WDM 
     2. Description of the Related Art 
     The optical amplifier produces not only the amplified optical signals but also the noise of wide wavelength band. Even though optical filters are used to remove the noise included in the output beam of the optical amplifier, the noise of same wavelengths of the signals can not be eliminated. Optical signal-to-noise ratio, the power of the optical signals divided by the power of the corresponding noise, is used as a standard for a transmitting quality of optical communication network. And it is necessary to monitor the optical signal-to-noise ratio at optical lines or at optical nodes for optical communication network management. 
     FIG. 1 is a power spectrum of the output beam when the optical amplifier amplifies the multiplexed signals without optical filters in WDM optical communications. The spectrum is taken from a conventional spectrum analyzer. As mentioned above, the optical signal-to-noise ratio is the value of the power of the optical signals divided by the power of the corresponding noise. However, the noise can not be measured directly since the noise are detected with the optical signals as shown in FIG.  1 . 
     FIG. 2 is a graph to explain how to measure the optical signal-to-noise ratio of output signals shown in FIG.  1 . In order to measure the ratio, first take a power spectrum of the multiplexed signals amplified with the optical amplifier. From the obtained spectrum, find A, the peak power of the Optical Signal  1 , and measure a, b, the neighboring noise power. Calculate (a+b)/2, the average noise-power, and assume it as the noise power at the wavelength of the Optical Signal  1 . Then, the optical signal-to-noise ratio of the Optical Signal  1  is obtained using EQUATION 1.                Optical  Signal-to-noise  ratio
    of  the  Optical  Signal  1     =       A   -       (     a   +   b     )     /   2           (     a   +   b     )     /   2               [     EQUATION                 1     ]                                
     Similarly, the ratio of the Optical Signal  2 , and Signal  3  can be obtained. 
     However, in some cases, it is impossible to measure the optical signal-to-noise ratio with the above method in FIG.  2 . FIG. 3 explains these cases, and shows another power spectrum of the output beam when optical filters are used to remove the noise in WDM optical communications. According to the method in FIG. 2, the power (a, b) of noise nearby the peak wavelength should be known in order to measure the optical signal-to-noise ratio. In cases of FIG. 3, the method in FIG. 2 can not be used since the noise is not easily distinguishable from the optical signals. 
     FIG. 4 is a block diagram to solve the problems, and shows a device to measure the optical signal-to-noise ratio using a polarization controller and a linear polarizer (LP). The optical signal-to-noise ratio in FIG. 3 can be measured with the instruments in FIG.  4 . The device ( 400 ) for measuring the optical signal-to-noise ratio shown in FIG. 4 is published in &#39;98 European Conference on Optical Communication, p. 549-550, 1998&#39; with the title of “Optical Signal-to-Noise Ratio Measurement in WDM Networks Using Polarization Extinction” by M. Rasztovits-Wiech, M. Danner, and W. R. Leeb. 
     In optical communications, laser diodes are generally used as a light source. The polarization state of the output beam from a laser diode is 100% linearly polarized, and the optical signals are still 100% polarized even though the polarization state is changed as the signals traveling the optical fiber. On the other hand, the noise from an optical amplifier is 100% unpolarized since the noise consists of the randomly occurred lights of all polarization states. 
     Therefore, the power of the interested noise can be measured when the amplified optical signals are eliminated using a polarization controller ( 401 ) and a LP ( 402 ). The polarization controller controls the polarization of the input beam, and the LP passes only the component of the light coincide with the polarization axis. The 100% polarized optical signals can be completely eliminated; the polarization controller ( 401 ) can control the polarization state of the optical signals even after the signals traveled the optical fiber, and the controller changes the polarization of the optical signals orthogonal to the polarization axis of the LP ( 402 ). However, the power of the noise passing through a LP ( 402 ) always reduces to the half since the noise consists of the lights of all polarization states. 
     Referring FIG. 4, the output beam (shown in FIG. 1) of the optical amplifier is inputted into the polarization controller ( 401 ). Adjust the polarization controller to maximize the power of the optical signals passing through the LP ( 402 ) and the variable optical band-pass filter, VOBPF ( 403 ) at the photo detector ( 404 ), and measure the maximum value. Then, readjust the polarization controller to minimize the power at the photo detector ( 404 ), and measure the minimum value. Repeat the process for the full spectrum range by changing the passing wavelength of the VOBPF ( 403 ). 
     FIG.  5 ( a ) is a spectrum of the output beam in FIG. 1 when the power at the photo detector ( 404 ) in FIG. 4 is maximized, and FIG.  5 ( b ) is another spectrum when the power is minimized. In FIG.  5 ( a ), the peak power is the sum of the power, D, of the optical signals and the half, d, of the noise power, while the power in FIG.  5 ( b ) is the half of the original noise. Then, the optical signal-to-noise ratio of the Optical Signal  1  is obtained using EQUATION 2.                Optical  Signal-to-noise  ratio
    of  the  Optical  Signal  1     =       D   -   d       2   ×   d               [     EQUATION                 2     ]                                
     Similarly, the ratio of the Optical Signal  2 , and Signal  3  can be obtained. 
     FIG.  6 ( a ) is a spectrum of the output beam in FIG. 3 when the power at the photo detector ( 404 ) in FIG. 4 is maximized, and FIG.  6 ( b ) is another spectrum when the power is minimized. In FIG.  6 ( a ), the peak power is the sum of the power, E, of the optical signals and the half, e, of the noise power, while the power in FIG.  6 ( b ) is the half of the original noise. Therefore, the optical signal-to-noise ratio of the Optical Signal  1  is obtained using EQUATION 3.                Optical  Signal-to-noise  ratio
    of  the  Optical  Signal  1     =       E   -   e       2   ×   e               [     EQUATION                 3     ]                                
     Similarly, the ratio of the Optical Signal  2 , and Signal  3  can be obtained. 
     However, the preceding method shown in FIG. 4 needs to adjusts the polarization controller ( 401 ) to find the maximum and the minimum of the optical power at the photo detector ( 404 ) for each given wavelength. And the method has two major problems; (1) long operation time to measure the optical signal-to-noise ratio, and (2) a complicated active control circuit to handle the polarization controller ( 401 ). 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide an apparatus and a method for measuring the optical signal-to-noise ratio using Stokes parameters in optical communications. The present invention can solve the above mentioned problems. 
     In accordance with an aspect of the present invention there are provided an apparatus and a method for measuring the optical signal-to-noise ratio in optical communications. The apparatus according to the invention comprises (1) a VOBPF passing the amplified output beam when the beam wavelength is same as the passing wavelength of the VOBPF; (2) a 1×4 beam distributor distributing the passing beam of the VOBPF into four streams; (3) a measuring means of Stokes parameters S 0 , S 1 , S 2 , S 3  from the four distributed beams; (4) a calculating means of the optical signal power finding the power of the polarized component of the amplified output beam from the Stokes parameters S 1 , S 2 , S 3 ; (5) a calculating means of the noise power finding the power of the noise included in the amplified output beam from Stokes parameter S 0  and the optical signal power; and (6) a dividing means calculating the          Power                 of                 Optical                 Signal       Power                 of                 Noise                            
     of the passing wavelength from the optical signal power and the noise power. The apparatus according to the invention measures the          Power                 of                 Optical                 Signal       Power                 of                 Noise                            
     for the whole spectrum range by changing the passing wavelength of the VOBPF, and eventually find the optical signal-to-noise ratio of an optical signal by searching the peak from the measured          Power                 of                 Optical                 Signal       Power                 of                 Noise                            
     graph. 
     In a preferred apparatus, the measuring means of Stokes parameters S 0 , S 1 , S 2 , S 3  further comprises (1) 0° linear polarization means detecting the power of 0° linear polarization component (PX) from the first distributed beam; (2) 90° linear polarization means detecting the power of 90° linear polarization component (PY) from the second distributed beam; (3) 45° linear polarization means detecting the power of 45° linear polarization component (P45) from the third distributed beam; (4) circular polarization means detecting the power of right-hand circular polarization component (PRCP) from the forth distributed beam; and (5) a Stokes parameter calculating means finding Stokes parameters S 0 , S 1 , S 2 , S 3  from the measured power PX, PY, P45, PRCP 
     In a more preferred apparatus, the circular polarization means further comprises (1) a λ/4 retarder making the phase difference between the two orthogonal beams with 0° and 90° linear polarization become λ/4 by retarding the phase of the input beam, and (2) a 45° LP passing only the 45° linear polarization component after the λ/4 retarder. 
     In another more preferred apparatus, the Stokes parameter calculating means further comprises (1) a first adder finding Stokes parameter S 0  by adding the power PX and PY; (2) a second adder finding Stokes parameter S 1  by subtracting the power PY from PX; (3) a first multiplier multiplying the power P45 by 2; (4) a third adder finding Stokes parameter S 2  by subtracting Stokes parameter S 0  from the output of the first multiplier, 2P45; (5) a second multiplier multiplying the power PRCP by 2; and (6) a fourth adder finding Stokes parameter S 3  by subtracting Stokes parameter S 0  from the output of the second multiplier, 2PRCP. 
     In another preferred apparatus, the VOBPF can be embodied with a Fabry-Perot variable filter, an integrated optic device with lattices, or a multi-layered thin film. 
     A method for measuring the optical signal-to-noise ratio in optical communications according to the invention comprises following 8 steps. (1) A first step where the amplified output beam passes through the VOBPF with the starting wavelength; (2) a second step where the passing beam of the first step is distributed into four streams; (3) a third step where obtain Stokes parameters S 0 , S 1 , S 2 , S 3  from the four distributed beams; (4) a fourth step where find the optical signal power by calculating the power of the polarized component of the amplified output beam from the Stokes parameters S 1 , S 2 , S 3 ; (5) a fifth step where find the power of the noise included in the amplified output beam from Stokes parameter S 0  and the optical signal power; (6) a sixth step where calculate          Power                 of                 Optical                 Signal       Power                 of                 Noise                            
     of the passing wavelength from the optical signal power and the noise power; (7) a seventh step where measure          Power                 of                 Optical                 Signal       Power                 of                 Noise                            
     for the whole spectrum range by repeating the process from the second step to the sixth step for the each passing wavelength of the VOBPF; and (8) a eighth step where find the optical signal-to-noise ratio of an optical signal by searching the peak from the measured          Power                 of                 Optical                 Signal       Power                 of                 Noise                            
     graph. 
     In a preferred method, the third step further comprises (1) a first sub-step where detect the power PX, PY, P45, PRCP; and (2) a second sub-step where calculate Stokes parameters S 0 , S 1 , S 2 , S 3  from the measured power PX, PY, P45, PRCP. 
     In a more preferred method, the second sub-step further comprises following four steps. (1) Finding Stokes parameter S 0  by adding the power PX and PY; (2) finding Stokes parameter S 1  by subtracting the power PY from PX; (3) finding Stokes parameter S 2  by subtracting Stokes parameter S 0  from 2P45; and (4) finding Stokes parameter S 3  by subtracting Stokes parameter S 0  from 2PRCP. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Exemplary embodiments of the present invention will be described in conjunction with the drawings in which: 
     FIG. 1 is a power spectrum of the output beam when the optical amplifier amplifies the multiplexed signals without optical filters in WDM optical communications, taken from a conventional spectrum analyzer; 
     FIG. 2 is a graph to explain how to measure the optical signal-to-noise ratio of output signals shown in FIG. 1; 
     FIG. 3 is another power spectrum of the output beam when optical filters are used to remove the noise in WDM optical communications; 
     FIG. 4 is a block diagram to show a conventional device to measure the optical signal-to-noise ratio using a polarization controller and a linear polarizer; 
     FIG.  5 ( a ) is a spectrum of the output beam in FIG. 1 when the power at the photo detector ( 404 ) in FIG. 4 is maximized; 
     FIG.  5 ( b ) is another spectrum of the output beam in FIG. 1 when the power at the photo detector ( 404 ) in FIG. 4 is minimized; 
     FIG.  6 ( a ) is a spectrum of the output beam in FIG. 3 when the power at the photo detector ( 404 ) in FIG. 4 is maximized; 
     FIG.  6 ( b ) is another spectrum of the output beam in FIG. 3 when the power at the photo detector ( 404 ) in FIG. 4 is minimized; 
     FIG. 7 is a block diagram of the apparatus ( 700 ) for measuring optical signal-to-noise ratio according to the present invention; 
     FIG.  8 ( a ) and ( b ) show power spectra of the amplified output beam when optical filters are used in WDM optical communications, taken from a conventional spectrum analyzer; 
     FIG.  9 ( a ) shows the wavelength dependence of the measured Stokes parameters S 0 , S 1 , S 2 , S 3  when the output beam of FIG.  8 ( b ) is inputted into the VOBPF ( 701 ) in FIG. 7; 
     FIG.  9 ( b ) shows the wavelength dependence of the noise power in addition to Stokes parameter S 0 ; 
     FIG.  10 ( a ) shows the wavelength dependence of the polarized beam power and the noise power; 
     FIG.  10 ( b ) shows the wavelength dependence of the            Power                 of                 Polarized                 beam       Power                 of                 noise       ;                          
     and 
     FIG. 11 is a flow chart of the method for measuring the optical signal-to-noise ratio according to the present invention. 
    
    
     EXPLANATIONS FOR MAIN SYMBOLS IN THE DRAWINGS 
       700 : Block diagram of the apparatus for measuring optical signal-to-noise ratio 
       701 : Variable Optical Band-Pass Filter (VOBPF) 
       702 : 1×4 Beam Distributor 
       703 : 0° Linear Polarizer (LP) 
       704 : 90° LP 
       705 ,  707 : 45° LP 
       706 : λ/4 Retarder 
       708 ,  709 ,  710 ,  711 : Photo Detector 
       713 ,  714 ,  716 ,  718 ,  720 : Adder 
       715 ,  717 : Multiplier 
       719 : Signal Processor 
       721 : Divider 
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     The present invention will be better understood with regard to the following description, appended claims, and accompanying figures. 
     FIG. 7 is a block diagram of the apparatus ( 700 ) for measuring optical signal-to-noise ratio according to the present invention. The apparatus of the invention composes a VOBPF ( 701 ), an 1×4 beam distributor( 702 ), 4 linear polarizers ( 703 ,  704 ,  705 ,  707 ), λ/4 retarder ( 706 ), 4 photo detectors ( 708 ,  709 ,  710 ,  711 ), 5 adders ( 713 ,  714 ,  716 ,  718 ,  720 ), 2 multipliers ( 715 ,  717 ), a signal processor ( 719 ), and a divider ( 721 ). 
     The VOBPF ( 701 ) passes the amplified output beam whose wavelength is same as the selected passing wavelength of the VOBPF. The 1×4 beam distributor ( 702 ) distributes the passing beam of the VOBPF into four streams, and the distributed beams are guided into the 0°, 90°, 45° LP ( 703 ,  704 ,  705 ), and the λ/4 retarder ( 706 ). The 0° LP ( 703 ) passes only the 0° linear polarization beam, the 90° LP ( 704 ) passes only the 90° linear polarization beam, and the 45° LP ( 705 ) passes only the 45° linear polarization beam. Only the beam of right-hand circular polarization passes through λ/4 retarder ( 706 ) and 45° LP ( 707 ). The photo detectors ( 708 ,  709 ,  710 ,  711 ) measure the power, (PX/4, PY/4, P45/4, PRCP/4) of the corresponding polarization components. The Stokes parameters S 0 /4, S 1 /4, S 2 /4, S 3 /4 can be calculated from the measured the power (PX/4, PY/4, P45/4, PRCP/4) with the adders ( 713 ,  714 ,  716 ,  718 ) and the multipliers ( 715 ,  717 ). 
     With the calculated Stokes parameters (S 1 /4, S 2 /4, S 3 /4) the signal processor ( 719 ) produces                S   1   2     +     S   2   2     +     S   3   2         4     ,                                    Power                 of                 Polarized                 beam     4     .                           
     In other words, the signal processor ( 719 ) gives the            Power                 of                 Optical                 Signal     4     .                          
     The          Power                 of                 Noise     4                          
     is obtained from the Stokes Parameter S 0  and          Power                 of                 Optical                 Signal     4                          
     by the adder ( 720 ), and the divider ( 721 ) finally gives the            Power                 of                 Optical                 Signal       Power                 of                 Noise       .                          
     The Stokes parameters S 0 , S 1 , S 2 , S 3  are defined as follow: 
     S 0 =Sum of the polarized beam power and the unpolarized beam power, 
     S 1 =PX (Power of 0° linear polarization component)−PY (Power of 90° linear polarization component), 
     S 2 =P45 (Power of +45° linear polarization component)−P−45 (Power of −45° linear polarization component), 
     S 3 =PRCP (Power of right-hand circular polarization component)−PLCP (Power of left-hand circular polarization component). 
     Since each of (0° linear polarization and 90° linear polarization), (+45° linear polarization and −45° linear polarization), and (right-hand circular polarization and left-hand circular polarization) is a complete orthogonal set, the following equations hold: 
     [EQUATION 3] 
     
       
           S   0 = PX+PY=P 45 +P −45 =PRCP+PLCP   
       
     
     
       
           S   1 = PX−PY=PX −( S   0 − PX )=2 PX−S   0   
       
     
     
       
           S   2 = P 45 −P −45 =P 45−( S   0 − P 45)=2 P 45 −S   0   
       
     
     
       
           S   3 = PRCP−PLCP=PRCP −( S   0 − PRCP )=2 PRCP−S   0   
       
     
     The optical signals are 100% polarized, and the noise from the amplifier is 100% unpolarized. Therefore, the optical signal-to-noise ratio can be obtained using EQUATION 4: 
     [EQUATION 4] 
     
       
         Power of Optical Signal=Power of the polarized component={square root over ( S   1   2 + S   2   2 + S   3   2 )} 
       
     
     
       
         Power of Noise=Power of the unpolarized beam=Total Power−Power of Optical Signal= S   0 −{square root over ( S   1   2 + S   2   2 + S   3   2 )} 
       
       
         
           
              
             
               
                 
                   
                     
                       ∴ 
                       
                           
                       
                        
                       
                         signal-to-noise  ratio 
                       
                     
                     = 
                     
                       
                         Power 
                          
                         
                             
                         
                          
                         of 
                          
                         
                             
                         
                          
                         Optical 
                          
                         
                             
                         
                          
                         Signal 
                       
                       
                         Power 
                          
                         
                             
                         
                          
                         of 
                          
                         
                             
                         
                          
                         Noise 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                     
                       
                         
                           
                             S 
                             1 
                             2 
                           
                           + 
                           
                             S 
                             2 
                             2 
                           
                           + 
                           
                             S 
                             3 
                             2 
                           
                         
                       
                       
                         
                           S 
                           0 
                         
                         - 
                         
                           
                             
                               S 
                               1 
                               2 
                             
                             + 
                             
                               S 
                               2 
                               2 
                             
                             + 
                             
                               S 
                               3 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
                 
         
             
         
      
     
     This process to find the power of the optical signal from Stokes parameters can be found in “Principles of Optics Electromagnetic Theory of Propagation, Interference and Diffraction of Light” by Max Born and Emil Wolf, 6th Ed., PERGAMON PRESS, pp. 554-555 and in Hewlett Packard Product Note 8509-1, “Polarization Measurement of Signals and Components”, pp 5. 
     Now the apparatus of the invention has the following functions. First, set the passing wavelength of the VOBPF ( 701 ) to the starting wavelength of the output beam spectrum. Then, only the beam whose wavelength is same as the passing wavelength of the VOBPF passes through the VOBPF ( 701 ), and reaches to the 1×4 beam distributor ( 702 ). The passing beam is distributed into four streams by the 1×4 beam distributor ( 702 ), and the distributed beams are guided to 0° LP ( 703 ), 90° LP ( 704 ), 45° LP ( 705 ), and λ/4 retarder ( 706 ). 
     Only the 0° linear polarization component passes through the 0° LP ( 703 ), and reaches to the photo detector ( 708 ). Thus, the output value of the photo detector ( 708 ) is PX/4 of the output beam passing the VOBPF ( 701 ). Similarly, the output value of the photo detector of  709  and  710  are PY/4 and P45/4 of the output beam passing the VOBPF ( 701 ), respectively. 
     The λ/4 retarder ( 706 ) retards the phase of 90° linear polarization component, and makes the phase difference with 0° linear polarization component become λ/4. Therefore, the right-hand circular polarization component is changed into the 45° linear polarization component at the λ/4 retarder ( 706 ), and guided to the 45° LP ( 707 ). Accordingly, only the right-hand circular polarization component passes through the λ/4 retarder ( 706 ) and 45° LP ( 707 ), and reaches to the photo detector ( 711 ). Thus, output value of the photo detector ( 711 ) is PRCP/4 of the output beam passing the VOBPF ( 701 ). 
     S 0 /4 is obtained by the adder ( 713 ) adding the PX and the PY. S 1 /4 is obtained by the adder ( 714 ) subtracting the PY from the PX. S 2 /4 is obtained by the multiplier ( 715 ) multiplying 2 with the P45/4, and by the adder ( 716 ) subtracting the S 0 /4 from the P45/2. S 3 /4 is obtained by the multiplier ( 717 ) multiplying 2 with the PRCP/4, and by the adder ( 718 ) subtracting the S 0 /4 from the PRCP/2. 
     The signal processor ( 719 ) produce the          Power                 of                 Polarized                 beam     4                          
     from the calculated Stokes parameters (S 1 /4, S 2 /4, S 3 /4). The Power of Polarized Beam (i.e., Power of Optical Signal) is {square root over ( S   1   2 + S   2   2 + S   3   2 )} as in EQUATION 4. The          Power                 of                 Noise     4                          
     is obtained by the adder ( 720 ) subtracting the          Power                 of                 Polarized                 beam     4                          
     from the S 0 /4. Thus, the Power of Noise is S 0 −{square root over ( S   1   2 + S   2   2 + S   3   2 )} as in EQUATION 4. Finally, the          Power                 of                 Optical                 Signal       Power                 of                 Noise                            
     is obtained by the divider ( 721 ) dividing the          Power                 of                 Optical                 Signal     4                          
     by the            Power                 of                 Noise     4     .                          
     Repeat the process to find the optical signal-to-noise ratio        (     =       Power                 of                 Optical                 Signal       Power                 of                 Noise         )                          
     increasing the passing wavelength of the VOBPF ( 701 ) by one unit for each step until the passing wavelength becomes the last wavelength for the spectrum. And find the optical signal-to-noise ratio of an optical signal in WDM optical communications by searching the peak from the measured          Power                 of                 Optical                 Signal       Power                 of                 Noise                            
     graph. 
     FIG.  8 ( a ) and ( b ) show power spectra of the amplified output beam when optical filters are used in WDM optical communications, taken from a conventional spectrum analyzer. In FIG.  8 ( a ), there are no optical signals, and only the noise from the amplifier passes through optical filters. This kind of spectrum shows up when the background noise passes through optical filters. On the other hand, in FIG.  8 ( b ), there are optical signals whose wavelength peak position coincides with the left broad peak of the passing curve for the optical filters. The optical signal power is 9.66 times greater than the corresponding noise power, and the optical signal-to-noise ratio in this case is 9.85 dB (=10 log 10 9.66). 
     FIG.  9 ( a ) shows the wavelength dependence of the measured Stokes parameters S 0 , S 1 , S 2 , S 3  when the output beam of FIG.  8 ( b ) is inputted into the VOBPF ( 701 ) in FIG.  7 . And FIG.  9 ( b ) shows the wavelength dependence of the noise power in addition to Stokes parameter S 0 . 
     FIG.  10 ( a ) shows the wavelength dependence of the polarized beam power and the noise power, and FIG.  10 ( b ) shows the wavelength dependence of the            Power                 of                 Polarized                 beam       Power                 of                 noise       .                          
     As shown in FIG.  10 ( b ), the peak value is about 10 dB, and it coincides with the value (9.85 dB) at FIG.  8 ( b ). 
     Obviously, the above mentioned procedure can be applied in order to measure the optical signal-to-noise ratio for the output beam of FIG. 1, where the optical amplifier amplifies the multiplexed signals without optical filters in WDM optical communications. 
     FIG. 11 a is flow chart of the method for measuring the optical signal-to-noise ratio according to the present invention. First, set the passing wavelength of the VOBPF ( 701 ) to the starting wavelength of the output beam spectrum (S 101 ). Distribute the beam passing the VOBPF ( 701 ) into four streams (S 102 ). Detect the power PX, PY, P45, PRCP from the distributed beam (S 103 ). Find Stokes parameters S 0 , S 1 , S 2 , S 3  from the measured power PX, PY, P45, PRCP (S 104 ). Calculate the polarized beam power, {square root over ( S   1   2 + S   2   2 + S   3   2 )} from Stokes parameters S 1 , S 2 , S 3  (S 105 ). Calculate the noise power subtracting the polarized beam power from S 0  (S 106 ). Divide the polarized beam power by the noise power (S 107 ). Compare the current passing wavelength of the VOBPF ( 701 ) and the last wavelength of the output beam spectrum (S 108 ). If the current passing wavelength of the VOBPF ( 701 ) is not greater than the last wavelength of the spectrum, increase the passing wavelength by one unit (S 109 ), and go to the step of S 102 . If the current passing wavelength of the VOBPF ( 701 ) is greater than the last wavelength of the spectrum, measure the optical signal-to-noise ratio of an optical signal by searching the peak from the results of the step of S 107  (S 101 ). This peak value is the desired optical signal-to-noise ratio. 
     The apparatus according to the present invention produces the following effects: First, since we measure the optical signal-to-noise ratio using Stokes parameters of the output beam without the polarization controller and the complicated active circuit to handle the controller, we can quickly measure the optical signal-to-noise ratio. Second, we can measure the optical signal-to-noise ratio more accurately with a simple hardware. 
     While the foregoing invention has been described in terms of the embodiments discussed above, numerous variations are possible. Accordingly, modifications and changes such as those suggested above, but not limited thereto, are considered to be within the scope of the following claims.