Methods and apparatus for recovering first and second transmitted optical waves from a polarization multiplexed optical wave

1. A method of recovering first and second transmitted optical waves from a polarization multiplexed optical wave, the first and second transmitted optical waves having orthogonal polarization states, the method comprising:

at an optical receiver, measuring an electrical field of the polarization multiplexed optical wave;

determining, from the measured electrical field, a plurality of polarization states of the polarization multiplexed optical wave;

estimating, from the plurality of polarization states, a transform that aligns the orthogonal polarization states of the first and second transmitted optical waves with respect to principal axes of the optical receiver; and

recovering the first and second transmitted optical waves by applying the transform to one of i) the polarization multiplexed optical wave and ii) the measured electrical field of the polarization multiplexed optical wave.

2. The method of claim 1 , wherein the transform is applied to the polarization multiplexed optical wave by altering the polarization state of the polarization multiplexed optical wave.

3. The method of claim 1 , wherein:

measuring the electrical field of the polarization multiplexed optical wave comprises determining a Jones vector that describes the polarization multiplexed optical wave; and

the transform is applied to the measured electrical field of the polarization multiplexed optical wave by applying the transform to the Jones vector.

4. The method of claim 3 , wherein estimating the transform comprises estimating a birefringence matrix and a rotation matrix.

5. The method of claim 1 , further comprising:

splitting first and second received optical waves from the polarization multiplexed optical wave, the first and second received optical waves having orthogonal polarization states, wherein:

measuring the electrical field of the polarization multiplexed optical wave comprises determining a Jones vector that contains the electrical fields of the first and second received optical waves; and

the transform is applied to the measured electrical field of the polarization multiplexed optical wave by applying the transform to the Jones vector.

6. The method of claim 1 , wherein estimating the transform comprises:

fitting a plane in Stokes' space to the plurality of polarization states; and

identifying a normal to the plane, the normal containing the center of the Poincaré sphere; and

determining a transform that aligns the normal with respect to the principal axes of the optical receiver.

7. A method of recovering a transmitted optical wave, the method comprising:

at an optical receiver, measuring an electrical field of a received optical wave;

determining, from the measured electrical field, at least one polarization state of the received optical wave;

estimating, from the at least one polarization state of the received optical wave, a transform that aligns a polarization state of the transmitted optical wave with respect to a principal axis of the optical receiver; and

recovering the transmitted optical wave by applying the transform to one of i) the received optical wave and ii) the measured electrical field of the received optical wave.

8. The method of claim 7 , wherein the transform is applied to the received optical wave by altering the polarization state of the received optical wave.

9. The method of claim 7 , wherein:

measuring the electrical field of the received optical wave comprises determining a Jones vector that describes the received optical wave; and

the transform is applied to the measured electrical field of the received optical wave by applying the transform to the Jones vector.

10. The method of claim 9 , wherein estimating the transform comprises estimating a birefringence matrix and a rotation matrix.

11. The method of claim 7 , further comprising:

splitting the received optical wave into first and second received optical waves, the first and second received optical waves having orthogonal polarization states, wherein:

measuring the electrical field of the received optical wave comprises determining a Jones vector that contains the electrical fields of the first and second received optical waves; and

the transform is applied to the measured electrical field of the received optical wave by applying the transform to the Jones vector.

12. Apparatus for recovering first and second transmitted optical waves from a polarization multiplexed optical wave, the first and second transmitted optical waves having orthogonal polarization states, the apparatus comprising:

an optical receiver configured to receive the polarization multiplexed optical wave and measure an electrical field of the polarization multiplexed optical wave; and

a control system configured to i) determine, from the measured electrical field, a plurality of polarization states of the polarization multiplexed optical wave, ii) estimate, from the plurality of polarization states, a transform that aligns the orthogonal polarization states of the first and second transmitted optical waves with respect to principle axes of the optical receiver, and iii) apply the transform to one of A) the polarization multiplexed optical wave and B) the measured electrical field of the polarization multiplexed optical wave.

13. The apparatus of claim 12 , wherein the receiver comprises a polarization diverse heterodyne receiver using a pair of 90° optical hybrids.

14. The apparatus of claim 12 , further comprising a polarization controller, the polarization controller configured to receive and alter the polarization state of the polarization multiplexed optical wave; wherein the control system is configured to apply the transform to the polarization multiplexed optical wave by configuring the polarization controller to apply the transform to the polarization multiplexed optical wave.

15. The apparatus of claim 12 , wherein the control system determines a polarization state of the polarization multiplexed optical wave by determining Stokes' parameters for the polarization state of the polarization multiplexed optical wave.

16. The apparatus of claim 15 , wherein the control system estimates the transform by:

fitting a plane in Stokes' space to the plurality of polarization states; and

identifying a normal to the plane, the normal containing the center of the Poincaré sphere; and

determining a transform that aligns the normal with respect to the principal axes of the optical receiver.

17. A heterodyne polarimeter, comprising:

a polarization beam splitter configured to split an input optical wave into first and second optical waves having orthogonal polarization states;

a pair of 90° optical hybrids, each 90° optical hybrid having a local oscillator input and an optical input configured to receive a respective one of the first and second optical waves, and each 90° optical hybrid having at least two optical outputs;

a set of detectors, each of the detectors configured to receive at least two optical waves from the optical outputs of the pair of 90° optical hybrids, and each of the detectors configured to produce electrical in-phase and quadrature signals for reconstructing an electrical field of the first and second optical waves, the electrical field being offset by an unknown phase of the local oscillator; and

a processing system configured to determine a polarization state of the input optical wave, the polarization state being independent of the phase of the local oscillator.