Abstract:
Apparatus and methods for polarimetric measurements across a spectral range, such as determining the polarimetric state across a wavelength band in a wavelength-division multiplexed fiber optic channel. A variable phase delay is introduced between orthogonal polarization components in an incident light. The resulting intensity changes are used to compute parameters indicative of the polarimetric state of the light. These measurements may be used, for example, for polarimetric imaging, polarimetric component characterization, and measuring polarization states in a fiber link.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]    The present application claims the benefit of co-pending provisional application Serial No. 60/312,288, filed on Aug. 14, 2001, the entire disclosure of which is incorporated by reference as if set forth in its entirety herein. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    The invention relates to the field of optical measurement systems and, in particular, to apparatus and methods for measurements of polarimetric state.  
         BACKGROUND OF THE INVENTION  
         [0003]    A polarimeter may be used to measure the electric field orientation, i.e., the polarization, of light. Elliptical polarization, depicted in FIG. 1, is the most general case for a completely polarized beam, with the electric field vector tracing an ellipse in transverse coordinates as the light propagates. Linear and circular polarization are degenerate cases of elliptical polarization, with the electric field vector describing a line or circle with propagation, respectively, instead of an ellipse.  
           [0004]    A polarization state may also be described using a Stokes vector S. This formalism assumes that the light&#39;s intensity is measured through a 50 percent transmitting filter (defined to be I 0 ), a perfect horizontal linear polarizer (defined to be I 1 ), a perfect linear polarizer with its transmission axis at 45 degrees from the horizontal axis (defined to be I 2 ), and a perfect right circular polarization filter (defined to be I 3 ). Then, the vector S may be expressed as:  
             S   =       [           S   0               S   1               S   2               S   3           ]     =           2        I   0                   2        I   1       -     2        I   0                     2        I   2       -     2        I   0                     2        I   3       -     2        I   0                         (     Eq   .              1     )                               
 
           [0005]    The individual Stokes parameters S i  have their own physical significance. S 0  is the total intensity and is typically normalized to one. The parameters S 1  through S 3  measure the degree of horizontal linear polarization versus vertical linear polarization, +45 degrees linear polarization versus −45 degrees linear polarization, and left circular polarization versus right circular polarization, respectively.  
           [0006]    Measurements of a light&#39;s polarimetric state have several practical applications. Polarimetric imaging—the imaging of a scene according to the polarization content of the light it emits or reflects—can facilitate object and scene recognition. Measuring the polarimetric state of a beam of light travelling through a medium permits the characterization of the medium in terms of power loss, reflectance, and other characteristics. Then, measured transmission impairments in the medium can be countered by polarization scrambling and launch-polarization control. As a fiber in a dense-wavelength division multiplexing (DWDM) system may contain a large number of independent wavelength channels, each with a finite bandwidth, it is also desirable to have a multichannel polarimeter to simultaneously determine the polarization state of each DWDM wavelength channel in a spectral waveband.  
           [0007]    Prior art solutions for measuring the polarimetric state of light typically require control over the light source, altering the light emitted by the light source in a way that facilitates the measurement of its polarimetric state. However, it is typically infeasible to alter the operation of a light source in an optical system that is currently in service (e.g., transmitting voice data) without taking the system off-line, losing data or transmission capacity. A need therefore exists for apparatus and methods capable of determining the polarization parameters of light without directly controlling the source of the light.  
         SUMMARY OF THE INVENTION  
         [0008]    The present invention provides apparatus and methods for polarimetric measurements across a spectral range. In accord with the present invention, a phase delay is introduced between orthogonal polarization components in an incident light signal. The resulting intensity changes are used to compute parameters indicative of the polarimetric state of the light, as discussed in greater detail below. These measurements may be used, by way of example, for polarimetric imaging, polarimetric component characterization, and determining the polarimetric state across one or more wavelength bands in a wavelength division multiplexed (WDM) fiber optic channel  
           [0009]    In one aspect, the present invention provides an apparatus for polarimetric state measurement across a spectral range. In one embodiment, the apparatus comprises a phase modifier and a polarization state detector. The phase modifier receives incident light having a plurality of polarization components and provides a dithered light, and the polarization state detector receives the dithered light and determines a polarization state thereof. The phase modifier provides the dithered light by introducing a variable phase delay between two orthogonal components of the incident light. The phase modifier may receive the incident light through free space, through an optical fiber, or from a collimator. The introduced phase delay may be continuous and varying with time or a set of discrete phase steps.  
           [0010]    In one embodiment, the phase modifier comprises an optical rotator and a variable retarder. The optical rotator rotates the semi-major axis of the incident light by an angle θ and the variable retarder introduces the variable phase delay between the two orthogonal polarization components. In one version of this embodiment, the angle θ assumes at least two different values. Suitable optical rotators include Faraday rotators and combinations of waveplates, such as free-space birefringent crystals, waveguide devices, or fiber squeezers. Suitable phase retarders include fixed-axis liquid crystal retarders, spatially-dithering mirrors, and variable retardance waveplates (such as waveguides and fiber squeezers).  
           [0011]    In a further embodiment, the apparatus includes a beam splitter, which receives the incident light and splits the incident light into two orthogonal polarization components. The beam splitter may be a polarizing beam splitter. The apparatus further includes a beam combiner that receives the two orthogonal polarization components and provides a combined light. The beam combiner may comprise a polarization beamsplitter, two quarterwave plates and two mirrors, where the quarterwave plates each rotate its respective polarization component and the mirrors each receive its respective rotated polarization component and reflect it.  
           [0012]    In one embodiment, the polarization state detector comprises a polarizer and an electro-optic detector. In another embodiment, the polarization state detector comprises a polarizer, one of a demultiplexer and a spectrograph for receiving the dithered light, and a plurality of electro-optic detectors. In a third embodiment, the polarization state detector comprises a polarizer, a tunable filter, and an electro-optic detector.  
           [0013]    In another aspect, the present invention provides a method for polarimetric state measurement across a spectral range. In one embodiment, the method operates on light having a plurality of polarization components. A variable phase delay is introduced between a first orthogonal pair of polarization components, and parameters associated with the light are then measured. A variable phase delay is introduced between a second orthogonal pair of polarization components, and parameters associated with the light are then measured. The polarization state of the light is determined based on these measurements. The variable phase delay may be a discrete delay profile or a continuous periodic delay profile, such as a sinusoidal profile ranging from 0 and 2π radians.  
           [0014]    In one embodiment, parameters associated with the light are measured by generating an interference pattern using the light after the introduction of the variable phase delay, and measuring the intensity of the interference pattern to provide a set of intensity values. First and second sets of intensity values can be decomposed into constant, cosine, and sine component values. The constant, cosine, and sine component values can be used to compute the aforementioned Stokes parameters, for example, such that S 1 /S 0 =−C θ2 , S 2 /S 0 =C θ1 / 2, S 3 /S 0 =−S θ1 /2, and S 0   2 =S 1   2 +S 2   2 +S 2   3 .  
           [0015]    The foregoing and other features and advantages of the present invention will be made more apparent from the description, drawings, and claims which follow.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0016]    The advantages of the invention may be better understood by referring to the following description taken in conjunction with the accompanying drawings in which:  
         [0017]    [0017]FIG. 1 illustrates the variation in the electric field of an elliptically polarized light propagating through space;  
         [0018]    [0018]FIG. 2 illustrates a first embodiment of a polarimetric measuring apparatus in accord with the present invention;  
         [0019]    [0019]FIG. 3 depicts an embodiment of the incident light source  200  of FIG. 2;  
         [0020]    [0020]FIGS. 4 and 5 illustrate embodiments of the phase modifier  204  of FIG. 2;  
         [0021]    [0021]FIG. 6 shows an embodiment of the polarization state detector  208  of FIG. 2;  
         [0022]    [0022]FIG. 7 illustrates a second embodiment of a polarimetric measuring apparatus in accord with the present invention; and  
         [0023]    [0023]FIG. 8 is a flowchart presenting an embodiment of a method for measuring polarization state in accord with the present invention; 
     
    
       [0024]    In the drawings, like reference characters generally refer to corresponding parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed on the principles and concepts of the invention.  
       DETAILED DESCRIPTION OF THE INVENTION  
       [0025]    In brief overview, Applicants&#39; invention provides apparatus and methods for measuring the polarimetric state (i.e., the polarization parameters) of light across a spectral waveband. A variable phase delay is introduced between orthogonal polarization components of the incident light. After introducing the delay, the orthogonal polarization components are interfered to form an interference pattern. Measurements of the resulting interference pattern are used to compute the polarization parameters of the incident light across various spectral bands.  
         [0026]    [0026]FIG. 2 illustrates a first embodiment of the present invention having a light source  200 , a phase modifier  204 , and a polarization state detector  208 . The phase modifier  204  receives light having a plurality of polarization components from the incident light source  200 . The phase modifier  204  generates a dithered light by introducing a variable phase delay between two orthogonal polarization components of the incident light. The dithered light is received and measured by the polarization state detector  208 . These measurements provide sufficient data to permit the determination of the polarization state of the light source  200  in one or more spectral bands of interest. The light provided by the light source  200  may have a narrow or a wide spectral band. The spectral band of the light provided by the light source  200  may be substantially constant or it may vary with time.  
         [0027]    The phase modifier  204  receives the light from the light source  200  and introduces a phase delay between two arbitrary orthogonal polarization components of the light. The phase delay can vary continuously with time, such as a sine wave, or can be a series of discrete phase steps. Typically the phase delay is a periodic function, for example, a series of discrete phase steps that repeats itself every 2π radians. The polarization state detector  208  receives the dithered light after the introduction of the delay and performs sufficient measurements to permit the determination of the polarization state, as discussed in greater detail below.  
         [0028]    There are several suitable embodiments of the light source  200  for operation in accord with the present invention. One embodiment, illustrated in FIG. 3, consists of a light-emitting element  300  connected to a linkage  304 . The light-emitting element  300  may be, for example, a laser diode, a gas laser, a solid-state laser, an arc discharge, or a similar light source.  
         [0029]    The light-emitting element  300  serves as the source of the incident light, while the linkage  304  conveys the light between the light-emitting element  300  and the phase modifier  204 . Typical linkages  304  include, but are not limited to, an optical fiber, free space, or an optical fiber in combination with a collimator.  
         [0030]    [0030]FIG. 4 illustrates a first embodiment of the phase modifier  204 . In this embodiment, the phase modifier  204  includes an optical rotator  400  and a variable retarder  404  that are in optical communication. The optical rotator  400  receives the light from the light source  200  and rotates the semi-major axis of the incident light through an angle θ. The variable retarder  404  receives the rotated light and introduces a variable retardance between an arbitrary pair of orthogonal polarization components in the rotated light. The introduced retardance itself may be, for example, a value from a continuous time-varying function or a value from a set of discrete values.  
         [0031]    The optical rotator  400  is variable in the sense that its rotator angle θ can assume at least two values, i.e., θ 1  and θ 2 . Various optical equipment, either singly or in combination, may provide the functionality of optical rotator  400 . For example, in one embodiment, optical rotator  400  is a Faraday rotator. In another embodiment, optical rotator  400  is two sequential switchable waveplates (free space, waveguide, or fiber squeezer, for example) with fast axes at angles of 0° and θ/2° to the y-axis. Embodiments of the variable retarder  404  include a fixed-axis liquid crystal retarder, a spatially-dithering mirror, or a variable-retardance waveplate—in particular, free space, a waveguide, or a fiber squeezer.  
         [0032]    In some embodiments, the phase modifier  204  or the variable retarder  404  physically separate the incident light from light source  200  into its orthogonal polarization components before introducing the variable retardance, i.e., dithering the light. Embodiments that separate the light into its polarization components typically recombine the polarization components into a single beam after dithering.  
         [0033]    [0033]FIG. 5 illustrates a second embodiment of the phase modifier  204  that separates and recombines the orthogonal polarization components of the incident light. In this embodiment, the phase modifier  204  includes the optical rotator  400  and the variable retarder  404  discussed above, but also includes a beam splitter  500  and a beam combiner  504  in optical communication with the optical rotator  400  and the variable retarder  404 . The beam splitter  500  receives the light from the optical rotator  400  and splits it into orthogonal polarization components. While the beam is separated, the variable retarder  404  introduces a variable retardance between the components. Alternately, two separate variable retarders  404   1  and  404   2 , one for each orthogonal beam, may introduce retardances into the beams. The beam combiner  504  receives the dithered light and combines the polarization components into a single beam.  
         [0034]    Beam splitter  500  may be, for example, a polarizing beam splitter. In one embodiment, beam combiner  504  is a polarizing beamsplitter, a pair of quarterwave plates, and a pair of reflectors, with one quarterwave plate and one reflector in the path of each polarization component to rotate the component before recombination.  
         [0035]    In embodiments lacking beam splitter  500  and beam combiner  504 , the optical rotator  400  and variable retarder  404  provide similar functionality when the fast and slow axes of the variable retarder  404  are referenced to the x- and y-axes of the rotator  400 . This approach achieves a similar result because a constant phase shift of both polarization components has no effect on the resulting intensity patterns, whereas the relative phase difference, i.e., the retardance between the orthogonal polarization components, does affect the intensity measurements, as discussed further below.  
         [0036]    [0036]FIG. 6 illustrates an embodiment of the detector  208 . This embodiment includes a polarizer  600  in optical communication with a sensor  604 . The polarizer  600  is typically oriented at an angle between the orientations of the two orthogonal polarization components so that it interferes the orthogonal polarization components of the dithered beam. The result is an interference pattern that is suitable for measurement by sensor  604 . In one embodiment, polarizer  600  is a 45 degree linear polarizer.  
         [0037]    The form of sensor  604  may vary according to the desired measurement parameters. If the desired measurement parameter is the average polarization state across a waveband, then the sensor  604  may be, for example, a single electro-optic detector. If the desired measurement parameter is the polarization state among a set of bins contained in the waveband, then the sensor  604  may be, for example, a demultiplexer or spectrograph illuminating a series of detectors or a detector array. In this embodiment, the demultiplexer or spectrograph disperses the interfered beam across the detectors. The output of each detector then characterizes a narrow wavelength band within the larger waveband. For example, a 256-element array would allow for the polarimetric characterization of 256 spectral channels. In still another embodiment, the sensor  604  is a tunable filter in optical communication with a single electro-optic detector. In this embodiment, the frequency bins are sampled temporally rather than spatially. Suitable tunable filters include, but are not limited to, a scanning Fabry-Perot filter, a liquid crystal tunable filter, or a mechanically tuned linear variable filter.  
         [0038]    [0038]FIG. 7 illustrates a second embodiment of a polarimetric measuring apparatus in accord with the present invention. The optical rotator  400  receives the incident light from the light source  200  and rotates the semi-major axis through an angle θ. The incident light passes through the beam splitter  500  where it is split into two beams, transmitting E x  and reflecting E y . The variable retarder  404  introduces a variable phase dither—either continuous or discrete—into one of the separated beams. A quarterwave plate and reflector in each arm form a beam combiner  504 , as described above, which recombines the beams. The recombined beam passes through the polarizer  600  and produces an interference pattern. The interference pattern is dispersed across the sensor  604 , which in this embodiment consists of a multiplexer in optical communication with a detector array. The resulting intensity measurements of the interference pattern may be used to determine the polarimetric state of the spectral waveband that corresponds to the particular detector element in the array. In still another embodiment, a tunable filter and a single electro-optic detector are placed after the polarizer  600  to temporally sample different frequency bins.  
         [0039]    [0039]FIG. 8 illustrates measurement of polarization state in accord with the present invention. First, a polarization rotator is set to an angle θ 1 , e.g., 0 degrees. The incident light signal is received (Step  800 ), and then rotated through θ 1  (Step  804 ). A variable retarder is configured to introduce a sufficient range of phase delay between the orthogonal polarization components of the rotated light (Step  808 ). Typical ranges of phase delay include a continuous periodic delay profile, e.g., a sinusoid from 0 to 2π radians, or a set of several discrete delay steps, e.g., between 0 and 2π radians at π/2 intervals. While the delay is introduced, sensors measure the intensity of the interference pattern formed by the polarization components of the light (Step  812 ). Next, the phase rotator is reconfigured to rotate the polarization state of the light by an angle θ 2  around the optical axis (Step  816 ). Repeating Steps  808  and  812 , a variable phase delay is introduced (Step  820 ) and the resulting intensity pattern is measured (Step  824 ), as discussed above.  
         [0040]    Certain of the discrete phase delay settings with rotator setting θ 2  may collect identical information to other phase delay settings with rotator setting θ 1  and, therefore, do not need to be repeated. For example, if θ 1 =0° and θ 2 =45° with a phase delay of π/2 radians yield identical signals at the detectors, only measurements from one of the two cases need to be collected.  
         [0041]    Using these intensity measurements and knowledge of the parameters of the variable phase delay introduced between the orthogonal polarization components, the system computes the polarization parameters associated with the spectral band forming the interference pattern (Step  828 ). When θ 1  is 0° (for example) and the introduced phase delay is d, the expression for the measured intensity I 0  of the spectral component with frequency ω is:  
               I   0     =       I   0          {     1   +         2        E   x          E   y        cos                 ɛ     I        cos                   (        ω     )       -         2        E   x          E   y        sin                 ɛ     I        sin                   (        ω     )         }               (     Eq   .              2     )                               
 
         [0042]    where  
           I   0   ≡E   x   2   +E   y   2    (Eq. 3)  
         [0043]    is the incident flux entering the polarimeter.  
         [0044]    Similarly, when θ 2  is 45° (for example) and the introduced delay is d, the expression for the measured intensity I 45  of the spectral component with frequency ω is:  
               I   45     =       I   0          {     1   +           E   y   2     -     E   x   2       I        cos                   (        ω     )       -         2        E   x          E   y        sin                 ɛ     I        sin                   (        ω     )         }               (     Eq   .              4     )                               
 
         [0045]    Note that, per equations (2) and (4), for each frequency ω the signal is sinusoidal with delay d:  
           I   0   =I   0 {1 +C   0  cos( d ω)+ S   0  sin( d ω)}  (Eq. 2′)  
           I   45   =I   0 {1 +C   45  cos( d ω)+ S   45  sin( d ω)}  (Eq. 4′)  
         [0046]    where  
                 C   0     =         {       2        E   x          E   y        cos                 ɛ     I     }                     S   0       =     {     -       2        E   x          E   y        sin                 ɛ     I       }              
            C   45     =         {         E   y   2     -     E   x   2       I     }                     S   45       =     {     -       2        E   x          E   y        sin                 ɛ     I       }                 (     Eq   .              5     )                               
 
         [0047]    Knowing d, and ω, the sinusoidal signals I 0 (d) and I 45 (d) can be solved for the parameters C 0 , S 0 , I 0 , C 45 , and S 45 . Then, in one embodiment, the Stokes parameters for each wavelength of light in the source beam are computed from these parameters. For a Stokes vector S=[S 0 S 1 S 2 S 3 ] T , the Stokes parameters are given by:  
         
       S 
       0 
       =E 
       x 
       2 
       +E 
       y 
       2  
     
         
       S 
       1 
       =E 
       x 
       2 
       −E 
       y 
       2  
     
           S   2 =2 E   x   E   y  cos ε 
           S   3 =2 E   x   E   y  sin ε  (Eq. 6)  
         [0048]    Comparing (Eq. 5) and (Eq. 6), the following relationship may be obtained:  
                   S   1       S   0       =         -     C   45                         S   2       S   0         =       C   0     2              
              S   3       S   0       =       -       S   0     2       =         -       S   45     2                       S   0   2       =       S   1   2     +     S   2   2     +     S   3   2                     (     Eq   .              7     )                               
 
         [0049]    The method of FIG. 8 therefore yields a set of polarization parameters at each wavelength after two delay cycles. In other embodiments, polarimetric values other than Stokes parameters are determined using information obtained from measurements of the interference pattern. For example, the polarization state may be expressed in terms of a Degree of Polarization DOP, semi-major axis Θ, and an ellipticity ε, where  
               DOP   =         (       S   1   2     +     S   2   2     +     S   3   2       )       1   /   2         S   0         ,     Θ   =       1   2          arctan        (       S   2       S   1       )           ,     
          ɛ   =     Θ   =       1   2          arcsin        (       S   3         (       S   1   2     +     S   2   2     +     S   3   2       )       1   /   2         )                     (     Eq   .              8     )                               
 
         [0050]    Many alterations and modifications may be made without departing from the spirit and scope of the invention. Therefore, it is to be understood that these embodiments have been shown by way of example and should not be taken as limiting the invention, which is defined by the following claims. These claims are thus to be read as not only including literally what is set forth by the claims but also to include those equivalents which are insubstantially different, even though not identical in other respects to what is shown and described in the above illustrations.