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
- 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 distortions
- describe the optical channel by theoretical models in different cases.
- write a numerical algorithm simulating the propagation of a signal
within an optical fiber.
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, presentation of the course, motivations. Brief history of
Ray optics. Fermat's principle. Snell's law. Total reflection. Numerical
aperture of an optical fiber. Multi-mode fibers. Problems of multi-mode
fibers. Single-mode fibers (overview). V-number (overview). Systems
theory approach to the optical fiber. Phase delay and group delay. Group
velocity dispersion (GVD). Propagation constant beta. Delay between two
frequencies induced by GVD. Conversion from beta2 to dispersion
GVD: examples. Waveguide and material dispersion. Rigorous proof of
GVD using Maxwell's equations.
Attenuation. Group delay. Impact of GVD over a Gaussian pulse.
Dispersion length. Anomalous and normal dispersion. GVD in presence of
signal's chirp. Instantaneous frequency.
GVD in presence of signal chirp. Best chirp using Heisenberg's principle.
Matched filter interpretation of GVD with chirp. Third order dispersion.
Eye closure penalty in presence of GVD.
Chen's formula for the GVD induced eye closure penalty. Fourier
transform induced by strong GVD. de Bruijn sequences. Memory of GVD.
Erbium doped fiber amplifier (EDFA). Cross sections. Propagation
equation for the photon flux over distance. Rate equation in time.
Reservoir. State model interpretation of reservoir. Small signal gain. Gain
Propagation equation with gain saturation. Fixed output power of an
EDFA in saturation. Reservoir dynamics with modulated signals. Amplified
spontaneous emission (ASE) noise. Noise figure of an EDFA: definition.
Friis's formula. Excess noise figure. Dual stage amplification: evaluation
of noise figure.
Photo-detectors: photo-diode. Quantum efficiency. Responsivity. Reasons
for photo-current: electron-holes contributions to current. P-i-n junction.
Junction capacity. Photo-diode bandwidth.
Avalanche photo-diode (APD).
Poisson statistics. Poisson counting process. Shot noise. Campbell's
theorem with proof. Power spectral density (PSD) of shot noise. PSD with
A P D .
Optical receivers. Matched filter. Amplifiers for the photo-current: low
impedance, high impedance, trans-impedance. Bit error rate (BER) for onoff
keying (OOK) transmission. Quantum limit. Sensitivity power. Thermal
noise. Gaussian approximation and Personick's formula.
Gaussian approximation. Q-factor. Gaussian approximation with APD.
Optimal multiplication factor with APD. Power budget.
Relation between Sensitivity penalty and Eye closure penalty for PIN and
APD. Case with GVD using Chen's formula. Exercise regarding the
amount of chirp yielding a given sensitivity penalty. Pre-amplified
receivers. Signal to spontaneous and spontaneous to spontaneous noise
BER with ASE noise: Gaussian approximation. Isserlis's formula. Average
and variance of signal/spontaneous, spontaneous/spontaneous, shot,
thermal noise. Comparison of noise variances.
Optical signal to noise ratio (OSNR). Comparison signal/spontaneous,
spontaneous/spontaneous. Marcuse's formula. Pre-amplified receivers:
comparison with quantum limit. Exercises.
Bergano's method to estimate BER. Threshold error using the Gaussian
Nonlinear Schroedinger equation (NLSE). Reasons for the cubic nonlinear
effect. Self Phase Modulation (SPM). Comparison between temporal
interpretation of SPM and frequency interpretation of GVD.
Comparison between temporal interpretation of SPM and frequency
interpretation of GVD. SPM with sinusoidal power. Bandwidth
enlargement induced by SPM. Wave breaking (WB). Impact of chirp
induced by SPM and GVD over a Gaussian pulse.
Noise figure of optical amplifiers measured in the electrical domain.
OSNR budget. Distributed amplification. Amplifier chains: limitations of
ASE noise and nonlinear Kerr effect. Inhomogeneous amplifier chains.
Part of the course is written in lecture notes.
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 mainly with blackboard but also by a video projector. In particular, some examples of numerical simulation will be provided.
Assessment methods and criteria
The exam consists in an oral examination and in an individual project (4
pages) regarding the study of an optical link by simulation. The project is
evaluated in terms of correctness, completeness, clarity of exposition,
During the course a numerical simulator of optical links will be introduced