Characterization of second-order PMD in chirped fiber Bragg gratings

1. GPIB Vectra PC and Monitor Controller PC running instrument control software Tunable laser GPIB CFBG HP 8509B Polarization State Analyzer S3 RCP LVP L -45 S0’ m00 m01 m02 m03 S0 S1’ = m10 m11 m12 m13 S1 S2’ m20 m21 m22 m23 S2 S3’ m30 m31 m32 m33 S3 LHP L +45 S2 S1 LCP 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 1940’s 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 2EoxEoycosδ S3 2EoxEoysinδ total intensity amount of LHP or LVP Incident Stokes vector Amount of RCP or LCP amount of linear L+45 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)