POLARIZED FIBER OPTIC TRANSMISSION
Learning outcomes of the course unit
- 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.
There are no strict prerequisites, to follow this Coursem besides some basic knowledge in Electromagnetics and Linear Algebra, assumed to have been acquired during the Bachelor Degree.
However, despite this course appears in the first year of the Course Catalogue, it is perfectly adequate to take it in parallel with the "Optical Communications" course, placed at the second (and last) year.
Course contents summary
- Polarization of light.
- Fiber-optic propagation of polarized light.
- Polarization Mode Dispersion (PMD) and PMD compensation techniques.
- Formalisms to represent polarized optical signals and polarization-sensitive optical systems.
A detailed outline of each single lecture follows (an asterisk is placed before some 'keywords' of this course):
PFOT-lecture01: General informations on this course, bibliographic references, teaching and assessment methods, course outline.
*Polarization of light.
Use of EM polarization in radio and oprtical communications (hints).
Historical perspective on fiber optic transmission, in the last thirty years (brief hints): transmission speed, main impairments and enabling techniologies.
PFOT-lecture02: Uniform plane wave (TEM) approximation. Vectorial representation of the Electromagnetic (EM) field (hints): optical frequencies, optical bandwidth and complex envelope.
Polarization representation: case of a continuous monochromatic wave (CW). Lissajous curves.
*Jones vectors and polarization ellipses:
implicit and parametric forms; phase-difference "phi"; degenerate cases; handedness: right- and left-handed polarizations; conventions.
PFOT-lecture03: Special States Of Polarization (SOP): LH, LV, L+45, L-45, RHC, LHC; unitmagnitude Jones vectors and corresponding angles (\chi, \phi). Inner product in C2: norm, orthogonality. More general polarizations: linear SOPs and elliptic SOPs with zero azimuth.
*Orthonormality between states of polarization.
Azimuth and ellipticity of a SOP (\theta, \epsilon) formalism.
Software “Polarization Tutor” (HP): use and check of theoretical results.
PFOT-lecture04: *Fiber-optic propagation of polarized light.
The fiber as a (2x2) MIMO system: transfer matrix. The Engineer's approach to the "fiber-system". Delay: variations of refractive index; chromatic dispersion and birefringence; causes. Attenuation (Loss): measurements in dB. Experimental results on attenuation: linear dependence on fiber length; propagation windows and historical perspective; independence of SOP.
*Hints on Polarization Dependent Gain/Loss (PDG/PDL):
PFOT-lecture05: Transfer matrix of a "birefringent" lossy fiber.
Propagation in a "homogeneous fiber with H/V birefringence" (diagonal \beta): example with a monochromatic diagonal input SOP. SOP evolution:
Polarization eigenstates (for a homogeneous H/V fiber).
*Polarization Mode Dispersion (PMD):
pulse broadening and intersymbol interference.
*Differential Group Delay (DGD).
Birefringence axes (and birefringence "strength"). Generalization of results for any homogeneous fiber.
Factorization of losses: lossless transfer matrix: adjpoint matrix; unitarity.
PFOT-lecture06: Different approaches to optical propagation: geometric optics, wave optics, Maxwell's equations, quantum optics. Examples of application. Physics approach to optical transmission: Maxwell's equations and constituent relations of matter. The case of Silica (SiO2): structure and aggregation forms. Differential operators ("nabla") and vector properties. Helmholtz equation: uniform planar wave (TEM) and monochromatic solution; wavefronts. Electric susceptibility in optical fibers: physical assumptions and mathematical consequences; peculiarities of the PFOT course (inhomogeneous matrix vs homogeneous scalar).
PFOT-lecture07: Formulation in the "omega" domain, with "narrowband" modulated fields (complex envelopes). Slowly Varying Envelope Approximation (SVEA). SVEA hypothesis and paraxial optics.
Passband propagation equation and effects of electric susceptibility: attenuation and phase/polarization distortion. System matrices: general, diagonal and degenerate cases.
*Vectorial Linear Schroedinger Equation (VLSE):
solution in the homogeneous case and corresponding transfer matrix.
VLSE for a lossless fiber: conservation of energy. "beta" (local) matrix and "T" (global) matrix.
*System matrix: Hermitian and unitary matrices.
PFOT-lecture08: *The Polarimeter: hardware scheme;
*Ideal polarizers: the projector;
Hermitian and idempotent transfer matrix. SOP measurement and field intensity. Output currents from a Polarimenter. Pauli matrixes and identit
- Alberto Bononi, Armando Vannucci, "PMD: a Math Primer", technical report 14 july 2001, rev. 18/12/2008, available at the Faculty copying facility.
- Jay N. Damask, "Polarization Optics in Telecommunications", Ed. Springer (New York, USA), 2005, ISBN: 0-387-22493-9. Available at the Biblioteca Politecnica (reference ELE2/731).
- Serge Huard, "Polarization of Light", Ed. J.Wiley&sons, 1997, ISBN: 0-471-96536-7. Available at the Biblioteca Politecnica (reference BIE2/446).
- Andrea Galtarossa, Curtis R. Menyuk, (Eds.), "Polarization Mode Dispersion", Ed. Springer (New York, USA), 2005, ISBN-10: 0-387-23193-5. Available at the Biblioteca Politecnica (reference ELE2/730).
- class lectures (36h), 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 (2h), using hardware instruments and devices.
Assessment methods and criteria
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.
At the Student discretion, a project/case-study can be undertaken by the Student alone or within a small group, to deepen the analysis of a specific topic, agreed with the Teacher.
No homeworks or classworks are foreseen, during the course.
A midterm multiple-choice test is foreseen during the 'spring session' (right after Easter Holidays).