Learning objectives
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 transmission/amplification/detection of an optical signal.
- the basic principles of a numerical simulation of an optical link.
With such a knowledge 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 a digital transmission by means of fiber optics.
- 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.
Prerequisites
suggested basic knowledge of Digital Communications, Signal Processing and electro-magnetic waves.
Course unit content
Introduction, motivations, state of the art.
Brief introduction of single mode fibers.
Group velocity dispersion.
Optical Transmitters.
Optical Amplifiers.
Principles of Photo-detection.
Performance Evaluation of optical communication systems.
Birefringence and polarization mode dispersion.
Nonlinear effects in optical fibers:
- Self phase modulation.
- Cross phase modulation.
- Four wave mixing.
- Cross polarization Modulation.
- Modulation Instability
Optical Solitons.
Numerical simulation of optical communication systems.
Gaussian noise model.
Raman Effect.
Digital Back propagation..
Full programme
Introduction, Brief history of optical communications.
Ray optics. Snell's law. Total reflection. Single-mode fibers (overview).
Optical modulators. ITU-T grid. Review of digital communications and lasers. Return to zero formats. Phase modulation by Mach Zehnder modulators. In-phase/quadrature optical modulators.
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. Optical signal to noise ratio (OSNR). Exercises.
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.
Marcuse's formula. Exercises.
Noise figure of optical amplifiers measured in the electrical domain.
Polarization of light. Birefringence. Stokes formalism. Poincaré sphere. Review of unitary and Hermitian matrices. Polarization mode dispersion (PMD). Differential group delay. Principal states of polarization.
Coherent detection. Optical coupler. Differentially coherent detection: DPSK. Optical hybrid. Balanced detector. Polarization division multiplexing. Digital signal processing at the receiver. Electronic compensation of GVD and PMD. Carrier phase and frequency recovery.
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. 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. Applications of 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. Pump-signal case.
Cross polarization modulation (XpolM). Comparison XPM vs. XPolM. Digital back-propagation (DBP) algorithm. Impact of optical noise on DBP performance.
Bibliography
Slides of the course are available at Elly web site.
Supporting books are the following:
G. P. Agrawal, "Fiber-optic communication Systems", 3rd ed., Wiley, 2002;
G. P. Agrawal, "Nonlinear Fiber Optics", Academic Press
Supporting scientific papers are indicated at:
http://www.tlc.unipr.it/serena/CO/lezioni.html
Teaching methods
Lessons given mainly by blackboard but also by video.
Some exercises will be solved during the lectures.
Some lessons will be given 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.
A mid term exam will be given during the course.
Other information
During the course a numerical simulator of optical links will be introduced
