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Lecture VII

Lecture VII. The Theory of Polarization ch. 14 – part 5 “Notes” . Statistical Models in Optical Communications. Vector algebra in Dirac notation. Vector algebra in Dirac notation. Column:. Row:. Outer Product:. Inner Product:. Coherency matrix .

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Lecture VII

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  1. Lecture VII • The Theory of Polarization • ch. 14 – part 5 “Notes” Statistical Models in Optical Communications

  2. Vector algebra in Dirac notation

  3. Vector algebra in Dirac notation Column: Row: OuterProduct: InnerProduct: Coherency matrix

  4. Math background - square bra-ket notation for column and row vectors (I) A “bra” is a row - (the complex transpose of the corresponding ket) A “ket” is a column A “bra-ket” is an inner product

  5. Math background - square bra-ket notation for column and row vectors (II) A “ket-bra” is an outer product Unit vectors

  6. Math background - square bra-ket notation for column and row vectors (III)

  7. Jones polarization calculus

  8. Introduction to polarization (I) Z-propagating beam For a monochromatic beam the corresponding real vector field is Jones polarization vector • The state of polarization may be described in terms of this ellipse as follows: • The orientation in space of the plane of the ellipse • The orientation of the ellipse in the plane, • its shape and the sense in which it is described • The size of the ellipse • The absolute temporal phase

  9. Introduction to polarization (II) a b Absolute amplitudes and absolute phases are of secondary interest, just the amplitude ratio and the phase difference counts. Hence the relevant information is embedded in the phasors ratio: Change of basis to e.g. to circular – corresponds to bilinear transformation in the complex plane.

  10. Jones polarization vectors and matrices

  11. Jones polarization vectors and matrices (II)

  12. Jones polarization vectors and matrices (III)

  13. Jones polarization vectors and matrices(IV)

  14. Jones polarization vectors and matrices (V)

  15. Jones polarization vectors and matrices(VI) 0 1

  16. The coherency matrix

  17. The Coherency Matrix Jones vector E E MUTUAL INTENSITIES INTENSITIES Coherency matrix (D=2) (optical polarization theory) Correlation/covariance matrix (statistics) Density matrix (quantum mechanics) Coherency matrix E E E

  18. The coherency matrix (II)

  19. The coherency matrix (III)

  20. The coherency matrix (IV)

  21. The coherency matrix (V)

  22. The coherency matrix (VI)

  23. The coherency matrix(VII)

  24. The coherency matrix(VIII)

  25. The coherency matrix (IX)

  26. The coherency matrix (X)

  27. The coherency matrix(XII)

  28. The coherency matrix (XII)

  29. The degree of polarization

  30. The degree of polarization (I) correlation coeff.

  31. The degree of polarization (II)

  32. The degree of polarization (III)

  33. The degree of polarization (IV)

  34. The degree of polarization (V)

  35. The degree of polarization (VI)

  36. The degree of polarization (VII)

  37. The degree of polarization (VIII)

  38. The degree of polarization (IX)

  39. The degree of polarization (X)

  40. The degree of polarization (XI)

  41. The degree of polarization (XII)

  42. The Stokes parameters

  43. phasor of x-pol. phasor of y-pol. SOP descriptions Polarization ellipse Poincare sphere cc circ. pol. 135lin-pol. y-pol. ellipt. pol. Jones polarization vector 45lin-pol. x-pol. ccc circ. pol.

  44. The four Stokes parameters Total power SAME SOP Power imbalance Interferometric terms many  one Jones vector one one

  45. Coherency matrixStokes parameters (D=2) Stokes parameters …in terms of coherency matrix Jones vector Coherency matrix in terms of Jones vector elements

  46. The Stokes Parameters vs. the coherency matrix

  47. The Poincare sphere (I)

  48. The Poincare sphere (II)

  49. The Poincare sphere (III)

  50. The Poincare sphere radius

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