Learning objectives
- Knowledge of the techniques and formalisms used for representing the polarization of light.
- Understanding linear propagation in fiber optics, with an emphasis on polarization related phenomena.
- Applying mathematical/geometrical tools for the description of light polarization, within the telecommunications context or other technological contexts.
- Ability to apply the techniques of propagation of polarized light, to evaluate distortions and penalties in telecom systems.
Prerequisites
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Course unit content
Summary
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Polarization of light; Fiber-optic propagation of polarized light; Polarization Mode Dispersion (PMD); PMD compensation techniques; Nonlinear propagation in fiber optic
Detailed Syllabus
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(BEWARE: what follows corresponds to the field "Programma esteso", in the italian text. The corresponding field, in the english text, although existing, is not visualized - for unknown reasons - in the corresponding web page)
Polarization of light
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Polarization-sensitive technological (and non-tech.) contexts;
Jones vectors and polarization ellipses;
ideal polarizers: the projector;
The Polarimeter: hardware scheme;
Stokes parameters and Pauli matrices;
Stokes vectors and the Poincaré sphere;
Orthonormality between states of polarization;
The Degree Of Polarization (DOP);
Relationship between Jones and Stokes vectors: the spin-vector;
Fiber-optic propagation of polarized light
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Vectorial Linear Schroedinger Equation (VLSE);
Vectorial propagation: the birefringence vector;
Beat length and correlation length;
(Hints on) Polarization Dependent Loss (PDL);
System matrix: Hermitian and unitary matrices;
Exponential forms for homogeneous fibers;
Pauli decomposition;
Equations of motion in Stokes space;
Polarization Mode Dispersion (PMD)
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The PMD vector "Omega";
Differential Group Delay (DGD) and Principal States of Polarization (PSP);
"1st-order" PMD and "all-order" PMD;
Photodetected current and depolarization: depolarization trace;
Photodetected current and "ghost pulses";
Eye Closure Penalty (ECP): generalized Chen's formula;
Statistical PMD: (hints on) stochastic models of birefringence;
PMD compensation techniques
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PMD compensation through “PSP transmission”;
1-stage and 2-stage compensators: spherical geometry;
3-stage and ideal multi-stage compensators;
PMD compensation in coherent systems: the Constant Modulus Algorithm (CMA);
Nonlinear propagation in fiber optic
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Vectorial Non-Linear Shroedinger Equation (VNLSE or CNLSE);
Kerr effect and its vectorial description;
Polarization mixing: the Manakov equation;
Cross-Polarization Modulation (XPolM);
Lossless Polarization Attraction (LPA) and the nonlinear lossless polarizer;
Full programme
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Bibliography
- Alberto Bononi, Armando Vannucci, "PMD: a Math Primer", technical report 14 july 2001, rev. 18/12/2008, available at the Faculty copying facility.
- Andrea Galtarossa, Curtis R. Menyuk, (Eds.), "Polarization Mode Dispersion", Ed. Springer (New York, USA), 2005, ISBN-10: 0-387-23193-5.
- Jay N. Damask, "Polarization Optics in Telecommunications", Ed. Springer (New York, USA), 2005, ISBN: 0-387-22493-9.
Teaching methods
- class lectures (34h), given by the teacher, with the aid of blackboard and overhead projector/PC (for showing software applications, figures, web pages).
- simulation laboratory (4h), using the open source simulator Optilux (University of Parma) for signal propagation in fiber optics.
- measurement laboratory (4h), using hardware instruments and devices.
Assessment methods and criteria
oral exam:
with reference to the contents of the lectures given during the course, the understanding level is evaluated, as well as the capability of analyzing and presenting the topics.
No homeworks or classworks are foreseen, during the course.
Other information
For this course, informations and materials are available on the LEA web-learning platform ( http://lea.unipr.it/course/view.php?id=393 )
