Patent Publication Number: US-2005129346-A1

Title: Dynamic polarization mode dispersion emulator

Description:
FIELD OF THE INVENTION  
      The present invention relates generally to emulators. More particularly, the present invention relates to polarization mode dispersion emulators suitable for testing of optical systems.  
     BACKGROUND OF THE INVENTION  
      Polarization mode dispersion is a non-linear phenomenon that causes optical pulses to broaden, particularly in high-speed optical systems (10 Gb/s and greater). This broadening means that pulses can overlap and cause transmitted information to be lost and system performance to be degraded. This is one of the greatest limitations in designing new high-speed systems.  
      Fiber can be field-tested for polarization mode dispersion to determine, how it will degrade system performance. However, field fiber polarization mode dispersion characterization is a time-consuming and expensive undertaking.  
      Emulation of polarization mode dispersion permits the behaviour of an optical field fiber to be recreated in a lab setting, thus permitting inexpensive lab testing of high-speed optical systems and polarization mode dispersion compensators. Many groups have demonstrated polarization mode dispersion emulators. These emulators rely on randomly varying the polarization state of light launched into polarizing maintaining fiber sections or birefringent crystals. However, polarization mode dispersion changes dynamically due to environmental and other conditions, resulting in state of polarization and differential group delay fluctuations in the time domain, and conventional polarization mode dispersion emulators do not take into account the true dynamic nature of polarization mode dispersion.  
      It is, therefore, desirable to provide a polarization mode dispersion emulator that can dynamically emulate polarization mode dispersion and facilitate more accurate and realistic test results.  
     SUMMARY OF THE INVENTION  
      It is an object of the present invention to obviate or mitigate at least one disadvantage of previous polarization mode dispersion emulators. In particular, it is an object of the present invention to provide a method for polarization mode dispersion emulation that models its true dynamic behaviour.  
      In a first aspect, the present invention provides a method of dynamic polarization mode dispersion emulation using an emulator setup having a birefringent section. The birefringent section has a corresponding polarization controller for controlling a polarization state determinant. The method consists of determining a previous polarization state determinant for the birefringent section; and determining an updated polarization state determinant for the birefringent section. The updated polarization state determinant for the birefringent section obeys a statistical probability distribution function for the dynamic behaviour of a desired fiber type, taking into account the previous polarization state determinant.  
      In a presently preferred embodiment, the statistical probability distribution function is a Gaussian probability distribution function, the Gaussian width of which is a user-specified dynamic input value corresponding to the dynamic behaviour of a field fiber, such as an aerial, buried, conduit, or submarine cable. Determining the updated polarization state determinant includes determining an updated differential group delay, or mode coupling angle, for the birefringent section, or more particularly, for wave plates associated with the polarization controller to change the differential group delay, or mode coupling angle, of the birefringent section to the updated differential group delay, or mode coupling angle.  
      In a further aspect, the present invention provides a polarization mode dispersion emulator for use with the above-described test setup. The emulator consists of a random distribution generator and a signal generator. The random distribution generator determines a random distribution of updated polarization state determinants for the polarization controller based on its current polarization state determinant, and obeying a statistical probability distribution function for the dynamic behaviour of a desired fiber type. The signal generator provides a signal to each polarization controller to effect a change of its polarization state determinant to its respective updated polarization state determinant.  
      In a presently preferred embodiment, the random distribution generator includes a pseudo-random number generator, and determines a random distribution of differential group delay values, or mode coupling angles, for the birefringent section that obey a Gaussian probability distribution function. The Gaussian width is determined by a user-specified dynamic input value that represents the dynamic behaviour of a field fiber, such as, an aerial, buried, conduit, or submarine cable. The signal generator generates control signals for controlling the birefringence of a plurality of wave plates, such as fiber squeezers, associated with the polarization controller.  
      Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      Embodiments of the present invention will now be described, by way of example only, with reference to the attached Figures, wherein:  
       FIG. 1  is schematic of a polarization mode dispersion emulation test setup and emulator according to the present invention;  
       FIG. 2  is a flow chart of an embodiment of the emulation method according to the present invention;  
       FIGS. 3   a  and  3   b  are histograms comparing state of polarization fit for model and emulator results for different values of a; and  
       FIGS. 4   a  and  4   b  are Maxwellian fits for classical emulator (a) and emulator and experimental field fiber fit (b). 
    
    
     DETAILED DESCRIPTION  
      Generally, the present invention provides a method and system for dynamically emulating polarization mode dispersion to facilitate testing of optical systems, and for modelling desired dynamic effects on polarization mode dispersion. The present invention permits polarization mode dispersion dynamics in aerial and other fiber to be modelled by an emulator controlling a test setup having polarization controllers for modifying the polarization of light launched into birefringent fiber sections. A polarization state determinant, such as differential group delay or mode coupling angle, is modified according to a statistical probability distribution function, such as a Gaussian probability distribution function, to dynamically model polarization mode dispersion. This is in contrast to previously known polarization mode dispersion emulators that randomly modify the polarization state determinants in uniform manner.  
      Referring to  FIG. 1 , the present invention uses a conventional emulation test setup  10  consisting of a number N of polarization controllers  12 , each having multiple wave plates. Randomly spliced birefringent, or polarization maintaining fiber, sections  14  are placed after each polarization controller  12 , such that the total differential group delay of the system can be changed by varying the birefringence of each wave plate. In the illustrated embodiment, five sets of polarization controllers and polarization maintaining fiber sections are shown. However, as will be understood by those of skill in the art, one or more sets can be used, as deemed appropriate for the desired emulation.  
      In a presently preferred embodiment, polarization controllers  12  each consist of four piezoelectric squeezers  16  orientated at fixed angles of 0°, +45°, 45° and 0° degrees that squeeze a length of optical fiber thus inducing birefringence, such as commercially available Acrobat™ polarization controllers available from Corning Inc. Each polarization maintaining fiber section  14  consists of a concatenation of birefringent fiber segments  18 . A laser source  20  is provided to launch light into the input of the series of polarization controllers  12  and polarization maintaining sections  14 , and a polarimeter  22  detects the resulting polarization at the output.  
      The emulator  24  of the present invention controls the operation of the polarization controllers  12  to modify the total differential group delay of the system  14  by modifying the birefringence of squeezers  16 . In operation, the polarization controllers  12  are constructed in such a way that, when certain voltages are applied, the state of polarization of light launched into their respective polarization maintaining fiber sections  14  is modified to an arbitrary point on the Pointcaré sphere. In the presently preferred embodiment, the squeezers  16  in each polarization controller  12  are controlled to randomly change a polarization state determinant of the length of fiber by squeezing the fiber and changing its birefringence. The maximum and minimum applied voltages on each squeezer  16  are calibrated to cause a 0 to 2π rotation of the state of polarization on the Poincaré sphere. The effect of these changes can be modelled by changing the differential group delay of the squeezer  16 , which is equivalent to changing the length of the polarization maintaining fiber section  14 . The differential group delay of a single polarization maintaining fiber section  14  scales linearly with its length. The squeezers  16  are allowed to randomly tune (squeeze) according to a statistical probability distribution function. This biases the squeezers  16  and models the desired dynamic polarization mode dispersion behaviour. By contrast, a conventional polarization mode dispersion emulator uses an evenly distributed (uniform) probability distribution function.  
      The emulator  24  generates appropriate control signals based upon the statistical probability distribution function, the current and previous differential group delay, of each polarization controller  12 , and a dynamic input value (a that is dependent on the dynamic characteristics of the actual fiber type being emulated. The dynamic input value can be selected by a user, generated by machine or retrieved from a lookup table, or other storage means.  
      Generally, as shown in  FIG. 1 , emulator  24  consists of a random distribution generator  26  for determining the random distribution of updated polarization state determinants for each polarization controller  12  based on its current polarization state determinant, and according to a random distribution obeying a statistical probability distribution function for dynamics of a desired fiber type. The emulator  24  also includes a signal generator  28  for generating a signal to the polarization controller  12  to effect a change of its polarization state determinant to its updated polarization state determinant.  
      In the presently. preferred embodiment of emulator  24 , a statistical distribution with memory, analogous to a “random walk” process, is used. This is implemented using a conditional probability distribution function based, for example, on a Gaussian distribution. In this case, the dynamic input value is equivalent to the Gaussian width. It is also filly contemplated that other statistical distributions, such as a Lorentzian distribution, are suitable depending on the data to be modelled, and the present invention is explicitly not limited to a Gaussian probability distribution function. In the presently preferred embodiment, emulator  24  uses a one-generation memory in which a current transition probability is a function only, of the previous value. A variation on this embodiment is to use a statistical distribution with a longer memory in which the current transition probability is a function of more than one previous generation of values.  
      To model dynamic state of polarization fluctuation for aerial fiber, it is assumed that the polarization controllers cause the differential group delay of each section to take a new value τ j  (t+Δt) after time increment Δt around its previous position τ j  (t). A Gaussian function is used because it has been found to accurately describe the random nature of an aerial fiber under expected atmospheric perturbations, such as wind. The Gaussian probability distribution can be described by the following conditional transition probability with periodic boundary condition τ j =mod(τ j , τ j2π )  
         P   ⁡     [         τ   j     ⁡     (       t     0   +       ⁢   Δ   ⁢           ⁢   t     )       |       π   j     ⁡     (     t   0     )         ]       =       1     σ   ⁢     π         ·     ⅇ       -       [         τ   j     ⁡     (     t   +     Δ   ⁢           ⁢   t       )       -       τ   j     ⁡     (   t   )         ]     2         σ   2               
 
 where σ is the width of the Gaussian probability density function and τ j2π  is the value of the differential group delay causing a 2π rotation on a Poincaré sphere. 
 
      According to the present invention, to emulate such a model, a pseudo-random number generator is used to generate suitable probability values. A single pseudo-random number generator is sufficient in the present embodiment to generate sufficient pseudo-random numbers to configure each squeezer  16  without significant delay. A Gaussian probability distribution function is used to determine how to change the pressure applied, and hence the differential group delay in the corresponding polarization maintaining fiber section  14 , for each of the squeezers  16 . Using the described test setup  10 , the mode coupling angles for each squeezer  16  axe constant, as determined by the physical makeup of the polarization controllers  12 . However, it is fully within the contemplation of the present invention that either the differential group delay or mode coupling angle can be held constant, or that both can be varied, depending on the type of polarization controller chosen for the test setup.  
      The Matlab™ source code found at Appendix A provides an example implementation of an algorithm according to the present embodiment that creates a distribution of random differential group delay values for generating suitable control signals to control the squeezers  16 . The created distribution obeys a particular Gaussian probability distribution function as specified by the dynamic input value (i.e. Gaussian width=“sigmaStep”). A flow chart, corresponding to the example implementation is illustrated in  FIG. 2 . As shown, the inputs are the current differential group delay “DGD”, the optical angular carrier frequency “Omega”, and a generated random, or pseudo-random, number. It is assumed that the transition has a short memory, i.e. it takes a new value based only on its current value. The time variable is implicit, not explicit. To account for a time evolution of At each of the orientation angles is permitted to update with every realization.  
      By manipulating the dynamic input value, representing the width of a Gaussian probability distribution function, the emulator of the present invention can be set to emulate the dynamics of different fiber types in varying conditions, for example aerial, buried, conduit, and undersea.  
      State of polarization and polarization mode dispersion measurements are taken at each time interval Δt. Correlation functions can be used to analyze the emulated state of polarization and polarization mode dispersion measurements. To analyze the state of polarization results, the angle between the Stokes Vectors with fixed separation time can be used: 
 
γ( t   0   , t )= arc  cos( {right arrow over (S)}   t0   ·{right arrow over (S)}   t0+t ) 
 
 where {right arrow over (S)} t0  corresponds to a normalized Stokes Vector at time t 0  and {right arrow over (S)} t0+t  refers to the same at time t 0 +t from the experimental state of polarization data For a fixed time delay t histograms can be generated. 
 
       FIGS. 3   a  and  3   b  shows state of polarization fits for model and emulator results for σ=0.01 and σ=0.075, which approximate to the dynamics of a buried fiber and a poor aerial fiber, respectively. The fits show high correlation for the buried fiber. The results are more de-correlated for the poor aerial fiber. This is likely due to the use of only five segments in the emulator setup. Increasing the N segments. would improve the correlations.  
       FIGS. 4   a  shows Maxwellian fits for classical emulator and experimental field fiber fit for an aerial fiber. Arclength curves were generated using the above formula The differential group delay curves shown in  FIG. 4   b  were generated. using a Maxwellian probability distribution function fit and an Aligent Polarimeter.  
      As will be apparent to those of skill in the art, the present invention accurately emulates dynamic polarization mode dispersion and allows system performance testing in the laboratory without the inconvenience and effort of field tests using real optical fiber. The dynamic polarization mode dispersion emulator can be used by optical systems designers to test systems with differing amounts of dynamic effects, and thus more accurately real world conditions under which different types of fibers operate. This permits more accurate polarization mode dispersion laboratory testing, particularly for high-speed optical systems. It also allows telecommunication companies to investigate the system impact of dynamic polarization mode dispersion. Fiber optic researchers can use the dynamic polarization mode dispersion emulator of the present invention to accurately model polarization mode dispersion in experimental settings.  
      The above-described embodiments of the present invention are intended to be examples only.. Alterations, modifications and variations may be effected to the particular embodiments by those of skill in the art without departing from the scope of the invention, which is defined solely by the claims appended hereto.  
      Appendix A:  
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                                          %   inputs:   last DGD = last calculated DGD value       %       sigmaStep = sigma step (const) (GAUSSIAN WIDTH)       %   output:   DGD = DGD value       %       %   note:   omega is Gaussian width (angular optical carrier frequency)               and is a static user input constant.                         oldTheta = ((lastDGD*omega)/2           R = rand(1) %create random value           if(R &gt; 0.5)                         newTheta = oldTheta +sigmaStep*erfinv(2*R−1)                         else                         newTheta = oldTheta − sigmaStep*erfinv(1−2*R)                         end                 % convert it to always be [0, 2pi]                         newTheta = mod(newTheta, 2*pi)                 % convert DGD value from [0, 2pi] to a ps DGD value                         DGD = 2*newTheta/omega