Abstract:
The polarization of the lightwave at the input to a heterodyne receiver can be determined by measurements of the amplitude of electrical signals without the need for phase measurements. This allows more accurate measurements of the polarization in the presence of noise and allows a determination of the degree of polarization of the lightwave.

Description:
BACKGROUND OF INVENTION  
       [0001]     The polarization state of a lightwave may be determined by detecting the optical power transmitted through specific polarization filters. Conventional polarimeters typically measure the optical powers P 0 −P 3  to determine the Stokes parameters S 0 −S 3 . Hence, S 0 −S 3  are given by: 
 
S 0 =P 0    (1) 
 
 S   1 =2 P   1   −P   0    (2) 
 
 S   2 =2 P   2   −P   0    (3) 
 
 S   3 =2 P   3   −P   0    (4) 
 
 From the Stokes parameters the degree of polarization, p, may be calculated:  
             p   =         (       S   1   2     +     S   2   2     +     S   3   2       )         S   0               (   5   )             
 
  FIG. 1   a  shows conventional space-division polarimeter  100  where the lightwave on input  101  is split into four separate lightwaves and the resulting lightwaves are processed in parallel. The lightwave on output  102  passes through linear horizontal polarizer  115  and provides P 1 . The lightwave on output  103  passes through linear  45  degree polarizer  120  and provides P 2 . The lightwave on output  104  passes through quarter-wave plate  125  and linear  45  degree polarizer to provide P 3  which is a measure of circularly polarized light. Quarter-wave plate  125  transforms the circularly polarized portion of the input lightwave to a linear 45 degree lightwave which is passed through linear  45  degree polarizer  130 . The lightwave on output  105  passes out directly to provide P 0 , which is proportional to the total power. Hence, the degree of polarization is determinable from measurements performed by polarimeter  100  using equations (1)-(5). 
 
         [0002]     Some heterodyne optical receivers, such as the Agilent Technologies 81910A and 83453A, may be configured to measure the polarization of the received optical field. In these polarization resolving heterodyne optical receivers, the phase difference between two electrical signals coming from the receiver must be measured to determine the polarization of the received optical field. This phase measurement can be difficult, in particular if the electrical signals contain significant noise. Additionally, the measurements from these heterodyne optical receivers do not allow a determination of the degree of polarization. Hence, it would be desirable to have a heterodyne optical receiving system which overcomes these difficulties and provides the data normally supplied by a conventional polarimeter.  
       SUMMARY OF INVENTION  
       [0003]     In accordance with the invention, the polarization of the lightwave at the input to a heterodyne receiver can be determined by measurements of the amplitude of electrical signals without the need for phase measurements. This allows more accurate measurements of the polarization in the presence of noise and allows a determination of the degree of polarization of the lightwave. All of the polarization resolving receivers may be balanced receivers to reduce the intensity noise.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0004]      FIG. 1   a  shows a simplified drawing of a prior art polarimeter.  
         [0005]      FIG. 1   b  shows the concept of a polarization-resolving heterodyne receiver in accordance with the invention.  
         [0006]      FIGS. 2   a - b  show alternative positions for placing a polarization synthesizer or waveplate in accordance with the invention.  
         [0007]      FIG. 3  shows an embodiment in accordance with the invention.  
         [0008]      FIG. 4  shows an embodiment in accordance with the invention.  
         [0009]      FIG. 5  shows an embodiment in accordance with the invention of a polarization resolving receiver.  
         [0010]      FIG. 6  shows an embodiment in accordance with the invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0011]      FIG. 1   b  shows the concept of a polarization-resolving heterodyne receiver in accordance with the invention. Swept local oscillator reference source  175  provides a reference signal proportional to cos ω 1 t having a definite linear polarization while the input signal is proportional to x(t)cos ω 2 t with an unknown polarization. The typically radio frequency output from receiver  185  is proportional to 2x(t)cos θ cos(ω 1 −ω 2 )t where θ is the angle between the signal input and the reference signal polarization. The amplitude of the signal detected by receiver  185  is proportional to 2x(t)cos θ which is equivalent to the output of an input signal passed through a polarizer positioned at an angle θ to the polarization of the input signal.  
         [0012]     In accordance with the invention a polarization synthesizer or waveplate may be placed in the signal path or in the local oscillator path as shown in  FIGS. 2   a  and  2   b,  respectively. The two situations may be examined using a Jones matrix analysis.  
         [0013]     Case  1  shown in simplified form in  FIG. 2   a  assumes polarization synthesizer  201  or waveplate  201  is in signal path  205 . Case  2  shown in simplified form in  FIG. 2   b  assumes polarization synthesizer  201  or waveplate  201  is in local oscillator path  206 . Taking J S  to represent the Jones matrix for polarization synthesizer  201  in signal path  205  with the signal represented by S and J L  to represent the Jones matrix for polarization synthesizer  201  in local oscillator path  206  with the local oscillator represented by L. Coupler  207  combines signal path  205  and local oscillator path  206 . The heterodyne intensity signal R 1 , measured by receiver  210  in case  1  may be written in Jones matrix formalism as: 
 
 R   1   =L   T   [J   S   S]*+[J   S   S]   T   L*    (6) 
 
 where T denotes the matrix transpose and * denotes the complex conjugate. Similarly, the heterodyne intensity signal R 2  measured by receiver  210  in case  2  may be written in Jones matrix formalism as: 
 
 R   2   =[J   L   L]   T   S+S   T   [J   L   L]*    (7) 
 
 Setting R 1=R   2  provides the result that in order for the intensities to be equal: 
 
J L =J S − 1    (8) 
 
 Hence, if a polarization resolving heterodyne receiver is constructed using a polarization synthesizer in local oscillator path  206 , the result is equivalent to having the polarization synthesizer in signal path  205  provided that Eq. (8) is satisfied. 
 
         [0014]      FIG. 3  shows an embodiment in accordance with the invention. Typically, swept narrow linewidth optical source  310  is used to provide the swept local oscillator reference source needed for a heterodyne system. Optical source  310  connects to polarizer  320  by single mode optical fiber  315 . Polarizer  320  connects to four way splitter  335  by polarization maintaining optical fiber  325 . Four way splitter  335  splits the reference lightwave four ways into polarization maintaining fibers  345 ,  346 ,  347  and  348 . Polarization maintaining fibers  345 ,  346 ,  347  and  348  connect four way splitter  335  to single polarization receiver  360 , single polarization receiver  365 , single polarization receiver  370  and polarization diversity receiver  375 , respectively. An input signal lightwave enters four way splitter  340  on single mode optical fiber  330  and the signal lightwave is split four ways into single mode fibers  351 ,  352 ,  353  and  354 . Single mode fiber  353  couples through quarter waveplate  355 . Single mode fibers  351 ,  352 ,  353  and  354  are also connected to single polarization receiver  360 , single polarization receiver  365 , single polarization receiver  370  and polarization diversity receiver  375 , respectively, as shown in  FIG. 3 . Note that receivers  360 ,  365 ,  370  and  375  may be balanced receivers to reduce intensity noise.  
         [0015]     Polarizer  320  receives the reference lightwave from optical source  310  and ensures that the reference lightwave entering polarization maintaining optical fiber  325  is linearly polarized and is properly aligned with the polarization direction of polarization maintaining optical fiber  325 . Polarization of the reference lightwave is maintained after splitting by four way splitter  335  into polarization maintaining optical fibers  345 ,  346 ,  347  and  348 . Polarization maintaining optical fiber  345  is typically oriented such that the linear polarization of the reference lightwave entering single polarization receiver  360  is 0 degrees. Polarization maintaining optical fiber  346  is typically oriented such that the linear polarization of the reference lightwave entering single polarization receiver  365  is 45 degrees. Polarization maintaining optical fiber  347  is typically oriented such that the linear polarization of the reference lightwave entering single polarization receiver  370  is 45 degrees. Quarter wave retarder  355  converts the circularly polarized part of the signal lightwave entering single polarization receiver  370  on single mode optical fiber  353  into 45 degree linearly polarized light prior to reception by single polarization receiver  370 . Hence, the polarization of the signal lightwave entering single polarization receiver  370  is 45 degrees. Single polarization receivers  360 ,  365  and  370  function as polarization sensitive optical heterodyne receivers that convert the input lightwaves into electrical representations. The electrical signal output is related to the intensity of the component of the input signal lightwave polarized in the direction of the reference lightwave. Therefore, the electrical output of single polarization receivers  360 ,  365  and  370  provides measurements of P 1 , P 2  and P 3 , respectively.  
         [0016]     Polarization diversity receiver  375  functions as a coherent receiver that converts the input lightwaves into electrical representations. The electrical signal output is related to the total intensity of the input signal lightwave. Therefore, the electrical output of polarization diversity receiver  375  provides a measurement of P 0 .  
         [0017]      FIG. 4  shows an embodiment in accordance with the invention. Swept narrow linewidth optical source  410  provides the swept local oscillator reference source needed for a heterodyne system. Optical source  410  connects to polarizer  420  by single mode optical fiber  415 . Polarizer  420  connects to three way splitter  435  by polarization maintaining optical fiber  425 . Three way splitter  435  splits the reference signal lightwave three ways into polarization maintaining fibers  445 ,  446  and  448 . Polarization maintaining optical fibers  445  and  446  connect three way splitter  435  to polarization resolving receiver  480 , single polarization receiver  465  and single polarization receiver  470 , respectively. Polarization maintaining optical fiber  448  connects to single mode optical fiber  449  via quarter wave retarder  455 . Single mode optical fiber  449  connects quarter wave retarder  455  to single polarization receiver  470 . Alternatively, quarter wave retarder  455  may be placed in the input signal path between single mode fiber  453  and receiver  470 . An input signal lightwave enters three way splitter  440  on single mode optical fiber  430  and the signal lightwave is split three ways into single mode fibers  451 ,  452  and  453 . Single mode fibers  451 ,  452  and  453  are also connected to polarization resolving receiver  480 , single polarization receiver  465  and single polarization receiver  470 . Note that receivers  480 ,  465  and  470  may be balanced receivers to reduce intensity noise.  
         [0018]     Polarizer  420  receives the reference lightwave from optical source  410  and ensures that the reference lightwave entering polarization maintaining optical fiber  425  is linearly polarized and is properly aligned with the polarization direction of polarization maintaining optical fiber  425 . Polarization of the reference lightwave is maintained after splitting by three way splitter  435  into polarization maintaining optical fibers  445 ,  446  and  448 . Polarization maintaining optical fiber  445  is oriented such that the linear polarization of the reference lightwave entering polarization resolving receiver  480  is 45 degrees. Polarization maintaining optical fiber  446  is oriented such that the linear polarization of the reference lightwave entering single polarization receiver  465  is 45 degrees. Polarization maintaining optical fiber  448  is connected to quarter wave retarder  455  . Quarter wave retarder  455  converts the linearly polarized reference lightwave coming from polarization maintaining optical fiber  448  to circularly polarized light that passes to single polarization receiver  470  on single mode optical fiber  449 . Single polarization receivers  465  and  470  function as polarization sensitive optical heterodyne receivers that convert the input lightwaves into electrical representations. The electrical signal output is related to the intensity of the component of the input signal lightwave polarized in the direction of the reference lightwave. The electrical output of single polarization receivers  465  and  470  corresponds to P 2  and P 3 , respectively, and provides measurements of P 2  and P 3 .  
         [0019]     Polarization resolving receiver  480  provides two outputs x and y proportional to the input lightwave polarized in the x direction and the input lightwave polarized in the y direction.  FIG. 5  shows an embodiment in accordance with the invention of polarization resolving receiver  480  of  FIG. 4 . Polarizing beam splitter  530  splits the incoming lightwave from swept narrow linewidth optical source  410  which has a 45 degree polarization into two equal components that mix with the input lightwave from single mode fiber  451 . The input signal is polarized with an unknown angle θ with respect to polarizing beam splitter  530  and is split as cos θ (x direction) and sin θ (y direction). Because the reference lightwave from swept narrow linewidth optical source  410  is polarized at 45 degrees, the reference lightwave is equally divided between photodetectors  545  and  550 . Squaring and summing the electrical output from photodetectors  545  and  550  in digital processor  499  produces a signal that is independent of the unknown angle θ and taking the square root gives total power P 0 . The signal in the x direction is proportional to the power in the 0 degree polarization direction and is scaled to P 1  by scaler  490 . Determining P 0 , P 1 , P 2  and P 3  allows calculation of the Stokes parameters and characterization of the degree of polarization of the input signal.  
         [0020]      FIG. 6  shows an embodiment in accordance with the invention using polarization synthesizer  630 . The embodiment shown in  FIG. 6  reduces the number of receivers required to one by introducing polarization synthesizer  630 . Swept narrow line width optical source  610  is coupled to polarizer  620  by single mode fiber  615 . Polarizer  620  is coupled to polarization synthesizer  630  by polarization maintaining fiber  605 . Typically, for the output of a polarization synthesizer to be known and well-defined, it is necessary to have a well-defined input polarization which is accomplished by using polarization maintaining fiber  605  to couple polarizer  620  to polarization synthesizer  630 . Polarization synthesizer  630  is coupled to polarization resolving receiver  660  via single mode fiber  640 . Polarization resolving receiver  660  is similar to polarization resolving receiver  480  shown in  FIG. 5  and has an x and y component output. Polarization resolving receiver  660  is typically a balanced receiver. Polarization resolving receiver  660  is also coupled to receive input signal  651 . Polarization resolving receiver  660  functions as a coherent receiver that converts the input lightwaves into electrical representations. In this embodiment, four separate measurements are made at each optical frequency—one measurement for each of the four settings of the polarization synthesizer of 0 degrees for P 1 , 45 degrees for P 2 , circular polarization for P 3  and 90 degrees for √{square root over ((P 0   2 −P 1   2 ))}, each measurement yielding an x and y component. This allows determination of the degree of polarization and the Stokes parameters S 0 −S 3  for input signal  651 , typically performed by a digital processor (not shown).  
         [0021]     While the invention has been described in conjunction with specific embodiments, it is evident to those skilled in the art that many alternatives, modifications, and variations will be apparent in light of the foregoing description. Accordingly, the invention is intended to embrace all other such alternatives, modifications, and variations that fall within the spirit and scope of the appended claims.