Learning outcomes of the course unit
The course aims to provide the main tools to analyze and design modern optical communication systems. Strictly speaking, the course would like to give knowledge and understanding about:
- linear effects in an optical fiber.
- nonlinear effects in an optical fiber.
- investigation of the trasmission/amplification/detection of an optical signal.
- the basic principles of a numerical simulation of an optical link.
Applying the knowledge and the understanding mentioned above, the student should be able to:
- analyze the main distortions of an optical link.
- analyze the main sources of noise that impact the bit error rate of an optical digital transmission.
- find strategies to cope with the above problems
- describe the optical channel by theoretical models in different cases.
- implement numerical algorithms for the analysis of nonlinear systems.
suggested basic knowledge of Digital Communications and Signal Processing.
Course contents summary
Introduction, motivations, state of the art.
Brief introduction of single mode fibers.
Group velocity dispersion.
Principles of Photodetection.
Nonlinear Schroedinger Equation.
Self phase modulation.
Cross phase modulation.
Four wave mixing.
Parametric gain and modulation instability.
Polarization Mode Dispersion.
Advanced modulation formats and optical coherent detection.
Introduction, Brief history of optical communications.
Ray optics. Snell's law. Total reflection. Single-mode fibers (overview).
Group velocity dispersion (GVD). Rigorous proof of GVD using Maxwell's equations. Attenuation. Group delay. Gaussian pulses. Dispersion length. Anomalous and normal dispersion. GVD in presence of signal's chirp. Instantaneous frequency. GVD in presence of signal chirp. Third order dispersion. Eye closure penalty in presence of GVD. Memory of GVD.
Erbium doped fiber amplifier (EDFA). Cross sections. Propagation equation and Rate equations. Reservoir. Amplified spontaneous emission (ASE) noise. Noise figure of an EDFA. Friis's formula.
Photo-detectors: photo-diode. Quantum efficiency. Responsivity. P-i-n photodiode. Avalanche photo-diode (APD). Poisson statistics. Shot noise. Optical Receivers.
Bit error rate (BER) for on-off keying (OOK) transmission. Quantum limit. Sensitivity power. Thermal noise. Gaussian approximation and Personick's formula. Gaussian approximation with APD. Power budget. Relation between Sensitivity penalty and Eye closure penalty for PIN and APD. Case with GVD. Signal to spontaneous and spontaneous to spontaneous noise beat. BER with ASE noise: Gaussian approximation. Comparison of noise variances.
Optical signal to noise ratio (OSNR). Marcuse's formula. Exercises.
Noise figure of optical amplifiers measured in the electrical domain. OSNR budget. Distributed amplification.
Nonlinear Schroedinger equation (NLSE). Reasons for the cubic nonlinear effect. Self Phase Modulation (SPM). Comparison between temporal/frequency vision of SPM/GVD. Wave breaking (WB).
Amplifier chains: limitations of ASE noise and nonlinear Kerr effect. Inhomogeneous amplifier chains. Lagrange multipliers method.
Solitons. Proof of fundamental soliton. Notes on Higher order solitons and Dark solitons. Numerical examples of soliton propagation. Solitons problems. Solitons and ASE: sliding filters.
Wavelength division multiplexing (WDM) systems. NLSE with separate fields. Cross-phase modulation (XPM) and four wave mixing (FWM). XPM filter. Walk-off coefficient.
Split-step Fourier method (SSFM). Formal solution using operators. Non commutative operators. SSFM with symmetrized and asymmetric step: accuracy. Choice of the step: constant step, step based on the nonlinear phase criterion, step based on the local error. Richardson extrapolation. Local error method: choice of the step size. Block diagram of the local error method. The Matlab programming language. Software Optilux. Examples.
Regular perturbation (RP) analysis of NLSE. FWM with CW signals. FWM efficiency. Phase matching coefficient.
Gaussian Noise (GN) model.
Modulation instability (MI). Optical parametric amplifier (OPA). Bandwidth and frequency of maximum gain of an OPA. Notes on Two pumps OPA.
Raman amplification. Memory induced by Raman effect. SPM, XPM and FWM in presence of Raman. Raman impact on XPM. Raman amplification: pump-signal case.
Polarization of light. Birefringence. Degree of polarization (DOP). Input/output relation with birefringence. Polarization mode dispersion (PMD): first order model.
Advanced modulation formats. Phase modulator and Mach Zehnder (MZ) modulator. Return to zero(RZ) pulses and its variants. Duobinary transmission. Differential phase shift keying (DPSK).
Coherent detection. Optical hybrid. Polarization division multiplexing (PDM). Digital signal processing (DSP). Electronic dispersion compensation of GVD. Electronic dispersion compensation of PMD: constant modulus algorithm (CMA). Phase estimation: Viterbi & Viterbi algorithm. Cross polarization modulation (XpolM). Nonlinear threshold (NLT) of optical links. Digital back-propagation (DBP) algorithm. Polarization switched quadrature phase shift keying (PS-QPSK).
Slides of the course are available.
Reading of the following books is suggested:
G. P. Agrawal, "Fiber-optic communication Systems", 3rd ed., Wiley, 2002;
G. P. Agrawal, "Nonlinear Fiber Optics", Academic Press
Further scientific papers will be indicated during the course.
Lessons given mainly by blackboard but also by video. There will be some lessons in the computer lab.
Assessment methods and criteria
The exam consists in an oral examination and in an individual project (max 4 pages) regarding the study of an optical link by simulation. The project is evaluated in terms of correctness, completeness, clarity of exposition, bibliography.
An intermediate test will be given during the course.
During the course a numerical simulator of optical links will be introduced