CA2490592A1 - Method for increasing accuracy of measurement of mean polarizaton mode dispersion - Google Patents

Method for increasing accuracy of measurement of mean polarizaton mode dispersion Download PDF

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Publication number
CA2490592A1
CA2490592A1 CA002490592A CA2490592A CA2490592A1 CA 2490592 A1 CA2490592 A1 CA 2490592A1 CA 002490592 A CA002490592 A CA 002490592A CA 2490592 A CA2490592 A CA 2490592A CA 2490592 A1 CA2490592 A1 CA 2490592A1
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CA
Canada
Prior art keywords
mode dispersion
polarization mode
group delay
frequency
differential group
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Granted
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CA002490592A
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French (fr)
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CA2490592C (en
Inventor
Mikhail Boroditsky
Mikhail Brodsky
Nicholas J. Frigo
Peter Magill
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AT&T Corp
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AT&T Corp
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/30Testing of optical devices, constituted by fibre optics or optical waveguides
    • G01M11/33Testing of optical devices, constituted by fibre optics or optical waveguides with a light emitter being disposed at one fibre or waveguide end-face, and a light receiver at the other end-face
    • G01M11/336Testing of optical devices, constituted by fibre optics or optical waveguides with a light emitter being disposed at one fibre or waveguide end-face, and a light receiver at the other end-face by measuring polarization mode dispersion [PMD]
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/30Testing of optical devices, constituted by fibre optics or optical waveguides
    • G01M11/33Testing of optical devices, constituted by fibre optics or optical waveguides with a light emitter being disposed at one fibre or waveguide end-face, and a light receiver at the other end-face
    • G01M11/331Testing of optical devices, constituted by fibre optics or optical waveguides with a light emitter being disposed at one fibre or waveguide end-face, and a light receiver at the other end-face by using interferometer
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B10/00Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/25Arrangements specific to fibre transmission
    • H04B10/2507Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion
    • H04B10/2569Arrangements specific to fibre transmission for the reduction or elimination of distortion or dispersion due to polarisation mode dispersion [PMD]

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.

Claims (33)

1. A method for measuring a true mean differential group delay (.tau.) of at least one length of optical fiber comprising the steps of:
measuring a mean square differential group delay (.tau.2)B averaged over a finite bandwidth B of the source using a polarization mode dispersion measurement apparatus;
calculating a root mean square differential group delay in accordance with and applying a systematic correction factor a to to calculate (.tau.), the application of a minimizing a systematic error caused by the finite bandwidth B of the source, where .tau. is in units of second, B in units of radian/second.
2. The method of Claim 1, further including the step of applying the systematic correction factor a in accordance with:
where .pi. is substantially equal to 3.14159 and (.tau.) is in units of second, (.tau.)B is in units of second2.
3. The method of Claim 2, wherein the finite bandwidth B is much greater than the inverse of the root mean square differential group delay :
further wherein E is defined by the following equation:
where B is in units of radian/second, and .tau.and are in units of second.
4. The method of Claim 1, wherein the polarization mode dispersion measurement apparatus used to measure the mean square differential group delay (~2)B comprises a time-domain measurement apparatus.
5. The method of Claim 4, wherein the time-domain measurement apparatus is an interferometric device.
6. The method of Claim 1, wherein the polarization mode dispersion measurement apparatus used to measure the mean square differential group delay (~2)B comprises a frequency-domain measurement apparatus.
7. The method of Claim 6, wherein the frequency-domain measurement apparatus is a polarimeter.
8. The method of Claim 7, further comprising the step of applying one of a Jones Matrix Eigenanalysis, Poincare Sphere Analysis, and Miiller Matrix Method to calculate the mean square differential group delay (~2)B
9. The method of Claim 1, wherein the at least one length of optical fiber is an optical fiber link in an optical telecommunication network.
10. The method of Claim 1, wherein the at least one length of fiber is an optical fiber route in an optical telecommunication network.
11. A method for measuring a mean differential group delay (~) of at least one length of optical fiber, comprising the steps of characterizing a polarization mode dispersion vector as a function of frequency using a frequency-domain polarization mode dispersion measurement apparatus;
calculating a second-order polarization mode dispersion vector ~~~ as a function of frequency by calculating a derivative with respect to frequency of the polarization mode dispersion vector;

calculating a mean of a square root of a magnitude of the second-order polarization mode dispersion vector ~~~ to obtain a first result, according to , wherein ~~~~~
represents the magnitude of the second-order polarization mode dispersion vector; and multiplying a proportionality coefficient A2 of the second-order polarization mode dispersion vector ~~~, by the first result to calculate the mean differential group delay (~) in accordance with the following equation:
where ~ and (~) are in units of second2, ~~~~ is in units of second, .omega.
is in units of radian/second, and A2 is dimensionless.
12. The method of Claim 11, wherein A2 is substantially equal to 1.37.
13. The method of Claim 11, wherein the frequency-domain polarization mode dispersion measurement apparatus is one of a polarimetric device and a Fixed Analyzer device.
14. The method of Claim 11, wherein the at least one length of fiber is a single fiber link.
15. The method of Claim 11, wherein the at least one length of fiber is a fiber route.
16. A method for measuring a mean differential group delay (~) of at least one length of fiber, comprising the steps of:
measuring a magnitude of a polarization mode dispersion vector ~~~~ as a function of frequency, using a frequency-domain polarization mode dispersion measurement apparatus the magnitude of the polarization mode dispersion vector ~~~~ being a scalar differential group delay;
calculating a frequency derivative of the scalar differential group delay from the magnitude of the polarization mode dispersion vector, the frequency derivative of the scalar differential group delay being a scalar second-order polarization mode dispersion function;

calculating a first result, according to , where ¦.tau.¦ is in units of second and .omega. is a frequency in units of radian/second; and multiplying a proportionality coefficient B2 by the first result to calculate the mean differential group delay, in accordance with the following equation:

where B2 is dimensionless, .tau. and are in units of second, .omega. is in units of radian/second, and is in units of second2.
17. The method of Claim 16, wherein B2 is substantially equal to 2.64.
18. The method of Claim 16, wherein the frequency-domain polarization mode dispersion measurement apparatus comprises one of a polarimetric device and a Fixed Analyzer device.
19. The method of Claim 16, wherein the at least one length of optical fiber is a single optical fiber link.
20. The method of Claim 16, wherein the at least one length of optical fiber is an optical fiber route.
21. A method for measuring a mean square differential group delay .tau.2 RMS
of at least one length of optical fiber, comprising the steps of:
measuring a polarization mode dispersion vector as a function of frequency, using a frequency-domain polarization mode dispersion measurement apparatus;
calculating a second-order polarization mode dispersion vector ~.omega. as a function of frequency by calculating a derivative of the polarization mode dispersion vector with respect to frequency .omega.;
calculating the mean of the magnitude of the second-order polarization mode dispersion vector ¦~.omega.¦ to obtain a first result, according to ; and multiplying a proportionality coefficient A1 by the first result to calculate the mean square differential group delay, in accordance with the following equation:
where A1 is dimensionless, ¦~.omega.¦ is in units of second2 and .TAU.2 RMS is in units of second2.
22. The method of Claim 21, wherein A1 is substantially equal to 2.02.
23. The method of Claim 21, wherein the frequency-domain polarization mode dispersion measurement apparatus comprises one of a polarimetric device and a Fixed Analyzer device.
24. The method of Claim 21, wherein the at least one length of optical fiber is a single optical fiber link.
25. The method of Claim 21, wherein the at least one length of optical fiber is an optical fiber route.
26. A method for measuring a mean square differential group delay .TAU.2 RMS
of at least one length of optical fiber, comprising the steps of:
measuring a magnitude of a polarization mode dispersion vector as a function of frequency using a frequency-domain polarization mode dispersion measurement apparatus, the magnitude of the polarization mode dispersion vector being a scalar differential group delay;
calculating a frequency derivative of the scalar differential group delay from the magnitude of the polarization mode dispersion vector, the frequency derivative of the scalar differential group delay being a scalar second-order polarization mode dispersion function;
calculating a first result, according and multiplying a proportionality coefficient B1 by the first result to calculate the mean square differential group delay, in accordance with the following equation:

(25) where B1 is dimensionless, and in units of second2.
27. The method of Claim 26, wherein B1 is substantially equal to 6.80.
28. The method of Claim 26, wherein the frequency-domain polarization mode dispersion measurement apparatus comprises one of a polarimetric device and a Fixed Analyzer device.
29. The method of Claim 26, wherein the at least one length of optical fiber is a single optical fiber link.
30. The method of Claim 26, wherein the at least one length of optical fiber is an optical fiber route.
31. A method for measuring a mean polarization mode dispersion of at least one length of optical fiber, using a source of bandwidth B, comprising the steps of:
collecting polarization mode dispersion data as a function of frequency from a frequency-domain polarization mode dispersion measurement apparatus;
extracting one of a vector and a scalar frequency-dependent function from the polarization mode dispersion data, by applying a frequency-domain polarization mode dispersion technique, the one of the vector and the scalar function being one of a first-order and a second-order polarization mode dispersion function;
applying a systematic correction to the one of the vector and the scalar frequency-dependent function, the systematic correction minimizing a systematic error caused by bandwidth B; and wherein applying the systematic correction results in a derivation of one of a mean differential group delay and a mean square differential group delay .TAU.2 RMS.
32. A method of measuring a mean differential group delay of a length of optical fiber comprising the steps of:
deriving a first mean in accordance with equation (21) and Claim 11;

deriving a second mean in accordance with equation (26) and Claim 16;
deriving a linear equation of the first mean and the second mean to calculate a combined mean , wherein a sum of coefficients of the linear equation is substantially equal to one.
33. A method of measuring a mean square differential group delay .tau.2 RMS of a length of optical fiber comprising the steps of:
deriving a first mean square differential group delay .tau.2 RMS in accordance with equation (20) and Claim 21;
deriving a second mean square differential group delay .tau.2 RMS in accordance with equation (25) and Claim 26;
deriving a linear equation of the first mean square differential group delay .tau.2 RMS and the second mean square differential group delay .tau.2 RMS to calculate a combined mean square differential group delay .tau.2 RMS, wherein a sum of coefficients of the linear equation is substantially equal to one.
CA002490592A 2003-12-29 2004-12-21 Method for increasing accuracy of measurement of mean polarizaton mode dispersion Expired - Fee Related CA2490592C (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US10/747,804 US7292322B2 (en) 2003-12-29 2003-12-29 Method for increasing accuracy of measurement of mean polarization mode dispersion
US10/747,804 2003-12-29

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US (4) US7292322B2 (en)
EP (1) EP1551118B1 (en)
JP (1) JP2005195598A (en)
CA (1) CA2490592C (en)
DE (1) DE602004028563D1 (en)
HK (1) HK1073736A1 (en)

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Publication number Publication date
EP1551118A2 (en) 2005-07-06
CA2490592C (en) 2010-01-12
DE602004028563D1 (en) 2010-09-23
US20110051126A1 (en) 2011-03-03
US7956993B2 (en) 2011-06-07
US7292322B2 (en) 2007-11-06
US20080007719A1 (en) 2008-01-10
EP1551118A3 (en) 2006-07-26
EP1551118B1 (en) 2010-08-11
JP2005195598A (en) 2005-07-21
US7852467B2 (en) 2010-12-14
US20100134788A1 (en) 2010-06-03
HK1073736A1 (en) 2005-10-14
US20050140965A1 (en) 2005-06-30

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