Calculation of distributed birefringence and polarization mode dispersion from waveguide scatter with full polarization state optical frequency domain reflectometry

1. A method for determining birefringence of a waveguide segment at a particular location along the waveguide, where the waveguide has a first index of refraction for a first polarization state and a second, different index of refraction for a second polarization state that is substantially orthogonal to the first polarization state, the method comprising:

coupling light with a first polarization state into the waveguide;

detecting, at a polarization diverse receiver, first polarization state back scatter reflections associated with the waveguide segment corresponding to a first set of polarization state values;

generating first polarization state back scatter data associated with the first polarization state back scatter reflections;

coupling light with a second polarization state into the waveguide that is substantially orthogonal to the light with the first polarization state;

detecting, at a polarization diverse receiver, second polarization state back scatter reflections associated with the waveguide segment corresponding to a second set of polarization state values different from the first set of polarization state values;

generating second polarization state back scatter data associated with the second polarization state back scatter reflections;

determining a spectral response based on the first polarization state back scatter data and the second polarization state back scatter data;

computing a correlation based on the spectral response;

determining the birefringence of the waveguide segment at the particular location along the waveguide based on the correlation; and

using the determined birefringence to characterize the waveguide segment.

2. The method in claim 1 , further comprising:

forming a matrix based on the first polarization state back scatter data and the second polarization state back scatter data, and

computing a spectral response for each component of the matrix.

3. The method in claim 2 , further comprising:

computing a spectral amplitude function based on the spectral responses computed for components, and

calculating an autocorrelation of the spectral amplitude function.

4. The method in claim 3 , further comprising:

determining a spectral shift from a main autocorrelation peak to a side autocorrelation peak, the spectral shift corresponding to the birefringence of the waveguide segment, and

determining the birefringence of the waveguide segment at the particular location along the waveguide based on the spectral shift.

5. The method in claim 3 , wherein the matrix is a 2×2 matrix having four matrix components, the method further comprising:

combining the four matrix components;

determining a combined spectral amplitude function determined from the combined four matrix components, and

calculating the autocorrelation of the combined spectral amplitude function.

6. The method in claim 3 , wherein the matrix is a 2×2 matrix having two 1×2 vectors, the method further comprising:

rotating the 2×2 matrix until one of the rotated 1×2 vectors represents light polarized in the fast polarization mode and the other of the rotated 1×2 vectors represents light polarized in the slow polarization mode.

7. The method in claim 6 , further comprising:

storing in memory one or more rotation angles associated with the rotating of the 2×2 matrix, and

using the one or more rotation angles to characterize the waveguide segment.

8. The method in claim 6 , further comprising:

combining the one rotated 1×2 vector and the other rotated 1×2 vector to produce a combined result,

computing a fast spectral amplitude function and a slow spectral amplitude function based on the combined result.

9. The method in claim 8 , further comprising:

computing a cross-correlation of the fast spectral amplitude function and the slow spectral amplitude function;

determining a spectral shift of a cross-correlation peak from zero; and

determining the birefringence of the waveguide segment at the particular location along the waveguide based on the spectral shift.

10. The method in claim 1 , wherein the coupling includes scanning the waveguide with a tunable laser, wherein light from the laser is reflected as a result of Rayleigh scattering in the waveguide and corresponds to the scatter reflections.

11. The method in claim 1 , further comprising:

determining a birefringence value for each of multiple waveguide segments along the waveguide, and

combining the birefringence values for the multiple waveguide segments to form a birefringence distribution over the length of the waveguide.

12. The method in claim 1 , further comprising determining strain or temperature based on the determined birefringence or discriminating between strain and temperature based on the determined birefringence.

13. The method in claim 1 , further comprising determining local curvature or bending based on the determined birefringence.

14. The method in claim 1 , further comprising determining pressure based on the determined birefringence.

15. The method in claim 1 , further comprising determining magnetic or electric field strength based on the determined birefringence.

16. An optical apparatus for determining birefringence of a waveguide segment at a particular location along the waveguide, comprising:

a light source to couple light with a first polarization state into the waveguide and to couple light with a second polarization state into the waveguide, wherein the second polarization state is substantially orthogonal to the first polarization state;

optical detection circuitry configured to:

detect first polarization state back scatter reflections associated with the waveguide segment corresponding to a first set of polarization state values and generate first polarization state back scatter data associated with the first polarization state back scatter reflections, and

detect second polarization state back scatter reflections associated with the waveguide segment corresponding to a second set of polarization state values different from the first set of polarization state values and generate second polarization state back scatter data associated with the second polarization state back scatter reflections;

processing circuitry configured to:

determine a spectral response based on the first polarization state back scatter data and the second polarization state back scatter data;

compute a correlation based on the spectral response;

determine the birefringence of the waveguide segment at the particular location along the waveguide based on the correlation; and

use the determined birefringence to characterize the waveguide segment.

17. The optical apparatus in claim 16 , wherein the optical apparatus includes an optical vector analysis network comprising:

a launch conditioning network, coupled to the light source, including a first light path and a second light path, where the second light path is delayed with respect to the first light path, and a polarization controller to ensure light in the first light path is substantially orthogonal to light in the second light path; and

a measurement interferometer to combine the light from first and second paths in the launch conditioning network with light reflected from the waveguide,

wherein the optical detection circuitry includes a polarization diverse receiver, coupled to the measurement interferometer, to separately detect the first polarization state back scatter data and the second polarization state back scatter data.

18. The optical apparatus in claim 16 , wherein the light source is configured to couple light with the first polarization state into the waveguide during a first time period and to couple light with the second polarization state into the waveguide during a second time period, and

wherein the optical apparatus includes an optical backscatter reflectometer network comprising:

a polarization controller to switch between two orthogonal polarization launch states for the first and second time periods; and

a measurement interferometer to combine the light from the polarization controller with light reflected from the waveguide,

wherein the optical detection circuitry includes a polarization diverse receiver, coupled to the measurement interferometer, to separately detect the first polarization state back scatter data and the second polarization state back scatter data.

19. The optical apparatus in claim 16 , wherein the processing circuitry is configured to:

form a matrix based on the first polarization state back scatter data and the second polarization state back scatter data, and

compute a spectral response for each component of the matrix.

20. The optical apparatus in claim 19 , wherein the processing circuitry is configured to:

compute a spectral amplitude function based on the spectral responses computed for components, and

calculate an autocorrelation of the spectral amplitude function.

21. The optical apparatus in claim 20 , wherein the processing circuitry is configured to:

determine a spectral shift from a main autocorrelation peak to a side autocorrelation peak, the spectral shift corresponding to the birefringence of the waveguide segment, and

determine the birefringence of the waveguide segment at the particular location along the waveguide based on the spectral shift.

22. The optical apparatus in claim 20 , wherein the matrix is a 2×2 matrix having four matrix components, and wherein the processing circuitry is configured to:

combine the four matrix components;

determine a combined spectral amplitude function determined from the combined four matrix components, and

calculate the autocorrelation of the combined spectral amplitude function.

23. The optical apparatus in claim 20 , wherein the matrix is a 2×2 matrix having two 1×2 vectors, and wherein the processing circuitry is configured to:

rotate the 2×2 matrix until one of the rotated 1×2 vectors represents light polarized in the fast polarization mode and the other of the rotated 1×2 vectors represents light polarized in the slow polarization mode.

24. The optical apparatus in claim 23 , wherein the processing circuitry is configured to:

store in memory one or more rotation angles associated with the rotating of the 2×2 matrix, and

use the one or more rotation angles to characterize the waveguide segment.

25. The optical apparatus in claim 23 , wherein the processing circuitry is configured to:

combine the one rotated 1×2 vector and the other rotated 1×2 vector to produce a combined result,

compute a fast spectral amplitude function and a slow spectral amplitude function based on the combined result.

26. The optical apparatus in claim 25 , wherein the processing circuitry is configured to:

compute a cross-correlation of the fast spectral amplitude function and the slow spectral amplitude function;

determine a spectral shift of a cross-correlation peak from zero; and

determine the birefringence of the waveguide segment at the particular location along the waveguide based on the spectral shift.

27. The optical apparatus in claim 16 , wherein the processing circuitry is configured to:

determine a birefringence value for each of multiple waveguide segments along the waveguide, and

combine the birefringence values for the multiple waveguide segments to form a birefringence distribution over the length of the waveguide.

28. An optical apparatus for determining polarization mode dispersion for a waveguide segment at a particular location along the waveguide, comprising:

a light source to couple light with a first polarization state into the waveguide and to couple light with a second polarization state into the waveguide, wherein the second polarization state is substantially orthogonal to the first polarization state;

optical detection circuitry configured to:

detect first polarization state back scatter reflections associated with the waveguide segment corresponding to a first set of polarization state values and generate first polarization state back scatter data associated with the first polarization state back scatter reflections, and

detect second polarization state back scatter reflections associated with the waveguide segment corresponding to a second set of polarization state values different from the first set of polarization state values and generate second polarization state back scatter data associated with the second polarization state back scatter reflections;

processing circuitry configured to:

determine a time delay domain response based on the first polarization state back scatter data and the second polarization state back scatter data;

compute a correlation based on the time delay domain response;

determine a time delay associated with the polarization mode dispersion of the waveguide segment at the particular location along the waveguide based on the correlation; and

use the time delay associated with the polarization mode dispersion to characterize the waveguide segment.

29. The optical apparatus in claim 28 , wherein:

the time delay domain response is a time domain polarization state averaged amplitude function,

the correlation is an autocorrelation, and

the processing circuitry is configured to determine the time delay associated with the polarization mode dispersion based on a separation between a center peak and a side band resulting from the autocorrelation.

30. The optical apparatus in claim 28 , wherein:

the time delay domain response is a time domain transfer function,

the correlation is a cross-correlation, and

the processing circuitry is configured to determine the time delay associated with the polarization mode dispersion based on a separation between zero and a side band resulting from the cross-correlation.