Characterization of second-order PMD in chirped fiber Bragg gratings

1
Characterization of second-order PMD in chirped
fiber Bragg gratings
C. Miscisin, R. Saperstein, K. Tetz, and Y.
Fainman
Background
Experimental Set-Up

• Chirped Fiber Bragg gratings (CFBGs) are useful
  for Fiber Optic Communications and Optical Signal
  Processing
• CFBGs can be used for dispersion compensation in
  long haul fiber optic transmission systems
• Each wavelength is reflected at a different
  location along the fiber canceling pulse spread
  caused by chromatic dispersion
• However, CFBGs suffer from severe 2nd order
  polarization mode dispersion (PMD)
• Each spectral component of light receives an
  independent polarization rotation
• If this 2nd order PMD can be characterized,
  then it can be compensated.

Stokes Polarization Parameters
Poincaré Sphere
Mueller Matrix Formalism

• In 1852, Sir George Gabriel Stokes discovered
  that the polarization behavior of light could be
  represented in terms of real observables, he
  developed a mathematical statement that could
  represent fully, partially, and even un-polarized
  light.
• The Stokes polarization parameters can be
  obtained by direct measurement of the time
  averaged intensity of a lightwave that has passed
  through a retarder and a polarizer in sequence.

• Around 1890 Henri Poincaré discovered that the
  polarization ellipse could be represented on a
  complex plane and that this plane could be
  projected onto a sphere.
• Six basis polarization states have Stokes
  vectors which define the 3D axes of the Poincaré
  sphere .

• In the early 1940s Hans Mueller became the
  first person to describe polarizing components in
  terms of matrices.
• To derive a Mueller matrix for a polarization
  altering device, for a single wavelength of
  light, we have four equations and sixteen
  unknowns.
• Using four of the six basis polarization states
  the calculation of a Mueller matrix is simplified.

I(0,0) I(90,0) I(0, 0) - I(90,0)
2I(45,0) I(0,0) I(90,0)
2I(45,90) I(0,0) I(90,0)
S0 Eox2 Eoy2 S1 Io Eox2 -
Eoy2 S2 2EoxEoycosd S3
2EoxEoysind
total intensity
amount of LHP or LVP
Incident Stokes vector
Amount of RCP or LCP
amount of linear L45 or L-45
(retardation, orientation of polarizer)
Experiment
Resultant Stokes vector
Mueller matrix describing a polarization altering
device

• A Mueller matrix is derived for each wavelength
• Polarization measurements were taken every ¼
  wavelength from 1535nm to 1565nm
• Polarization states resulting from the input of
  each basis polarization for the specified range
  of wavelengths are displayed below
• Stokes polarization parameters and their
  locations on the Poincaré sphere

Linear 45o Polarized Light (L45)
Linear Horizontally Polarized Light (LHP)
Linear Vertically Polarized Light (LVP)
Right Circularly Polarized Light (RCP)