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  Method for increasing accuracy of measurement of mean polarization mode dispersionUSPTO Application #: 20080007719Title: Method for increasing accuracy of measurement of mean polarization mode dispersion Abstract: The present invention provides a method for increasing the accuracy of measurement of mean differential group delay (DGD) from the polarization mode dispersion (PMD) in optical fiber. The method includes a systematic correction to mean-square DGD measured with any conventional mean to minimize systematic error caused by finite source bandwidth. The method further includes a systematic correction to the measurement of mean DGD and mean square DGD from statistics of the second-order PMD (SOPMD) obtained with frequency domain PMD-measuring apparatus. The probability density function (PDF) of either the vector or scalar SOPMD is applied, depending on which quantity is measured. The systematic correction is made to minimize the systematic error in estimating mean DGD, caused by finite source bandwidth, to achieve a two-fold reduction of the measurement variance equivalent to doubling the source bandwidth. (end of abstract) Agent: At&t Corp. - Bedminster, NJ, US Inventors: Mikhail Boroditsky, Mikhail Brodsky, Nicholas J. Frigo, Peter Magill USPTO Applicaton #: 20080007719 - Class: 356073100 (USPTO) The Patent Description & Claims data below is from USPTO Patent Application 20080007719. Brief Patent Description - Full Patent Description - Patent Application Claims
CROSS-REFERENCE TO RELATED APPLICATION [0001] This application is a divisional of U.S. application Ser. No. 10/747,804 filed Dec. 29, 2003, which is incorporated herein by reference. FIELD OF THE INVENTION [0002] The invention relates to the field of high-speed optical telecommunication systems, and more particularly to a method for increasing the accuracy of the measurement of mean polarization mode dispersion in optical fiber. BACKGROUND OF THE INVENTION [0003] The optical waveguides or fibers used to transmit signals in optical telecommunication systems are characterized, in part, by the vector property of polarization mode dispersion (PMD). Polarization mode dispersion occurs as a result of birefringence in the fiber, which may be caused by physical asymmetry in the fiber construction itself, or by stress, strain, or other external forces imposed on the fiber. In addition, random polarization coupling can occur, giving rise to a time-varying statistical factor. Optical fibers display an anisotropy in the refractive index, which will vary as a function of position and time. Consequently, components of an optical signal that differ in polarization will propagate at different velocities, resulting in a differential group delay (DGD) between the components, and causing significant broadening of the optical pulses propagating along long lengths of fiber. [0004] The PMD is fully characterized by a vector quantity {right arrow over (.tau.)}(.omega.) where the DGD is the magnitude of the vector |{right arrow over (.tau.)}(.omega.)|. As shown in FIG. 1, the DGD is generally designated as .tau. 10. Any state of polarization (SOP) can be resolved into directional components along two orthogonal principal states of polarization (PSP) 12, 14. The DGD or .tau. 10 then represents the separation in time between fast PSP 12 and slow PSP 14, after traversing a length of optical fiber 16. For each optical frequency or wavelength propagating in a fiber, there always exists two PSPs, such that the pulse spreading due to the first-order PMD vanishes if only one PSP is excited. The PMD is typically characterized in terms of an average DGD corresponding to different frequencies, and is independent, to first order, of wavelength, temperature, and external perturbations. In low mode coupled fiber, this measure of DGD averaged over a large range of optical frequencies is fairly constant over time, but in high mode coupled fibers, for example, in long fiber spans, the frequency-averaged DGD varies randomly in time, due to the combined effects of the variations in birefringence and random polarization mode coupling along the fiber length. This statistical variation in DGD lends itself to characterization of the DGD in terms of a statistical figure of merit, mean DGD. [0005] Higher orders of the polarization mode dispersion also exhibit statistical properties. The effect of second-order polarization mode dispersion (SOPMD) 18 is shown in FIG. 1. The SOPMD is the first derivative of the PMD with respect to frequency, representing the change in the PMD as a function of frequency. The SOPMD, therefore, additionally characterizes the overall pulse spreading due to the frequency-dependence of the PMD and the spectral bandwidth of the injected optical pulse 19. [0006] The polarization mode dispersion of a fiber is unlike most other sources of degradation in an optical telecommunication system, in its dependence on both time and frequency. Conventional methods for characterizing the full PMD vector over a frequency range, well known by those skilled in the art, include the Poincare Sphere Analysis (PSA), the Jones Matrix Eigenvalue (JME), Muller Matrix Method (MMM), Fixed Analyzer and interferometric techniques. These methods provide a measure of mean DGD and root mean square (RMS) DGD, which is calculated from the set of frequency-dependent DGD values. It is then commonly assumed by those skilled in the art that the statistical DGD follows a Maxwellian distribution, so that a true mean DGD <.tau.>, determined by averaging the DGD values obtained for a number of fibers over a bandwidth B of optical frequencies, can be estimated by multiplying the measured RMS DGD .tau. 2 B by a factor of 8 3 .times. .pi. . [0007] The fundamental problem in accurately evaluating a statistical limitation to an estimation of the mean DGD of a fiber, in order to find a more precise measurement of the mean DGD, was first recognized in a paper by N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, entitled "How Accurately Can One Measure a Statistical Quantity Like Polarization-Mode Dispersion?" IEEE Photon. Tech. Lett., Vol. 12, pp. 1671-1673 (August 1996), which is incorporated herein by reference. The accuracy of mean DGD estimation does improve as the mean is taken over a larger spectral bandwidth (approaching the ideal theoretical case where B.fwdarw..infin.). However, contrary to the statistical requirement that each of the measurements used to calculate an average be independent, the DGD at nearby wavelengths are not frequency independent. Gisin et al. demonstrated that this frequency dependence resulted in lower uncertainty in the mean DGD (around 9%) for larger PMD on the order of 1 picosecond (ps) e.g., as compared to a 28% uncertainty in mean DGD measurement when the PMD is smaller (on the order of 0.1 ps). The uncertainty in mean DGD measurement increases with decreasing source bandwidth. Gisin et al. demonstrated that the same level of uncertainty is intrinsic to all measurement techniques that average the DGD over wavelength. [0008] The mathematical formalism was developed further by M. Shtaif and A. Mecozzi, "Study of the Frequency Autocorrelation of the Differential Group Delay in Fibers with Polarization Mode Dispersion," IEEE Photon. Tech. Lett., Vol. 25, pp. 707-709 (May 2000), which is incorporated herein by reference. In measurements of the frequency autocorrelation of the DGD, the square DGD, and orientation of the PMD vector, Shtaif et al. showed that all corresponding correlation bandwidths are comparable. Shtaif et al. also showed that all statistical properties of the PMD characterizing the fiber under test are uniquely defined by the mean DGD. [0009] Polarization mode dispersion (PMD) is recognized as a potentially limiting impairment for high-speed long-haul optical transmission. Moreover, precise measurement of the true mean differential group delay (DGD) of individual fiber links and whole fiber routes is important for accurate estimation of service outage probabilities. Since PMD varies with time, as well as with frequency, measurements of the mean frequency-averaged DGD of the same fiber taken at different times may differ from each other and from the true value of mean DGD for a given fiber. For DGD values in the usual range of interest, and within the optical bandwidths of commercially available equipment, the variance of DGD measurements is approximately inversely proportional to the optical bandwidth of the optical source used for the measurement. In other words, an accurate measurement of the mean DGD of low birefringence fiber is limited by the optical bandwidth of the source used for the measurement. [0010] The need for precise PMD characterization will increase as the high-speed networks of the future employ very low PMD fibers. There exists a need, therefore, for more precise measurement of the mean DGD of individual fiber links and whole fiber routes than is presently provided by conventional methods. SUMMARY OF THE INVENTION [0011] The present invention, which addresses the needs unmet by conventional methods, relates to methods of improving accuracy of measuring a differential group delay (DGD) in an optical fiber link and in a whole optical fiber route. [0012] A method of the present invention for measuring a true mean differential group delay of at least a length of optical fiber includes the initial step of measuring a mean square differential group delay averaged over a finite spectral bandwidth B of a source, using a polarization mode dispersion measurement apparatus. A root mean square differential group delay is then calculated in accordance with .tau. 2 B and a systematic correction factor .epsilon. to the conventional method of estimating true mean <.tau.> from the measured root mean square differential group delay .tau. 2 B is applied. The systematic correction factor .epsilon. minimizes a systematic error caused by the finite spectral bandwidth of the source. [0013] Preferably, the systematic correction factor .epsilon. is applied to the mean square differential group delay in accordance with .tau. = 8 3 .times. .pi. .times. .tau. 2 B + c , to obtain the true mean differential group delay <.tau.>. In the regime where .tau..sub.RMSB>>1, <.tau.> is calculated according to: .tau. = 8 3 .times. .pi. .times. .tau. 2 B + 8 9 .times. 2 .times. 1 B , ( 16 .times. .times. a ) .times. .times. and .times. .times. ( 16 .times. b ) in other words, .times. .times. is .times. .times. 8 9 .times. 2 .times. 1 B . [0014] This method, which is applied directly to a measured mean square differential group delay, may be applied to measurements taken using time-domain techniques with an apparatus such as an interferometer. This method may also be applied to measurements taken using frequency-domain techniques, such as Jones Matrix Eigenanalysis, Poincare Sphere Analysis, and Muller Matrix Method using an apparatus, for example, including a polarimeter. The method may be used for measuring the mean differential group delay through a single optical fiber link, or an entire optical fiber route. [0015] In another embodiment of the method of the present invention, a method for measuring a mean differential group delay of at least one length of optical fiber, includes an initial step of characterizing a polarization mode dispersion vector as a function of frequency using a frequency-domain polarization mode dispersion measurement apparatus. The method further includes calculating a second-order polarization mode dispersion vector as a function of frequency {right arrow over (.tau.)}.sub..omega. from the polarization mode dispersion vector, and calculating a mean of the square root of a magnitude of the second-order polarization mode dispersion vector |{right arrow over (.tau.)}.sub..omega.| to obtain a first result, according to .tau. _ .omega. 1 / 2 . The first result is multiplied by a proportionality coefficient A.sub.2 to calculate the mean differential group delay, in accordance with the following equation: A 2 .times. .tau. _ .omega. 1 / 2 = .tau. . ( 21 ) [0016] Preferably, the proportionality coefficient A.sub.2 is obtained from the probability density function of the second-order polarization mode dispersion vector. Most preferably, A.sub.2 is substantially equal to 1.37. [0017] A further embodiment of the method of the present invention provides a method for measuring a mean differential group delay of a length of optical fiber, including an initial step of measuring a magnitude of a polarization mode dispersion vector as a function of frequency, using a frequency-domain polarization mode dispersion measurement apparatus, where the magnitude of the polarization mode dispersion vector is a scalar differential group delay. The method further includes calculating a frequency-derivative of the scalar differential group delay, the frequency derivative being a scalar second-order polarization mode dispersion function. The method further includes calculating a first result, according to d .tau. _ d .omega. 1 / 2 , and multiplying a proportionality coefficient B.sub.2 by the first result. The mean differential group delay is calculated, therefore, in accordance with the following equation: B 2 .times. d .tau. _ d .omega. 1 / 2 = .tau. . ( 26 ) [0018] Preferably, B.sub.2 is obtained from the probability density function of the scalar second-order polarization mode dispersion function. Most preferably, B.sub.2is substantially equal to 2.64. [0019] Yet another embodiment of the present invention provides a method for measuring a mean square differential group delay .tau..sub.RMS.sup.2 of a length of optical fiber, including an initial step of characterizing a polarization mode dispersion vector as a function of frequency using a frequency-domain polarization mode dispersion measurement apparatus. Additionally, a second-order polarization mode dispersion vector is calculated as a function of frequency {right arrow over (.tau.)}.sub..omega. from the polarization mode dispersion vector. The method further includes calculating a mean of the magnitude of the second-order polarization mode dispersion vector |{right arrow over (.tau.)}.sub..omega.| to obtain a first result, according to The first result is multiplied by a proportionality coefficient A.sub.1 to calculate the mean square differential group delay, in accordance with the following equation: A 1 .times. .tau. _ .omega. = .tau. RMS 2 . ( 20 ) [0020] Preferably, A.sub.1 is obtained from the probability density function of the second-order polarization mode dispersion vector. Most preferably, A.sub.1 is substantially equal to 2.02. Continue reading... Full patent description for Method for increasing accuracy of measurement of mean polarization mode dispersion Brief Patent Description - Full Patent Description - Patent Application Claims Click on the above for other options relating to this Method for increasing accuracy of measurement of mean polarization mode dispersion patent application. ###  How KEYWORD MONITOR works... a FREE service from FreshPatents1. Sign up (takes 30 seconds). 2. Fill in the keywords to be monitored. 3. Each week you receive an email with patent applications related to your keywords. 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