Next: Previous years Up: Lezioni Previous: Lezioni
Each lecture is 2 hours.
Introduction, presentation of the course, motivations. A Brief history of optical communications.
Notes: References can be found within the slides, available at Elly.
Supplementary reading: An interesting analysis of the market of optical communications can be found in [Win17,Des06]. An introduction to the history of optical communications can be found in [Win18,Agrbase]. A very good analysis of optical communications with emphasis to channel capacity can be found in [Ess10]. A list of the main companies in optical communications is in [Ecocex]. A list of the main Italian companies is in [ListITA]. Seldom, conferences on optical communications have a special web-page for job positions. See for instance [OFCjobs].
Notation.
Optical Modulators. ITU-T grid. Terminology: Super-channel, elastic networking, Nyquist transmission. Review of fundamentals of digital communications. Real lasers. Phase Modulator. Mach Zehnder modulator. Non-return to zero (NRZ) on-off keying (OOK) modulation. Return to zero (RZ) carving. Carrier suppressed RZ. Phase shift keying. Binary phase shift keying with phase modulator or Mach Zehnder modulator. I/Q modulators. Quadrature phase shift keying (QPSK) and quadrature amplitude modulation (QAM). Polarization division multiplexing (PDM). Single-modulator trick in experiments.
Notes: The optical modulators are described in the book [Seimetz]. A good comparison of modulation formats is in [Win06,Big04]. Other references are included in the slides.
Supplementary reading: Other information on optical modulators can be found in [Binh]. Further information are in [Win18].
Models of light. Ray optics. Fermat's principle. Snell's law. Total reflection. The 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). Examples.
Notes: The principles of ray optics can be found in [Alb05] and [Saleh,Agrbase]. A rigorous proof of GVD can be found in [AgrNL,Agrbase]. The factor 1/2 from bandpass to lowpass signals is described in [Proakis].
Supplementary reading: The carrier and envelope delay theory can be found in ``Carrier and envelope delay'' in [Carlson] and in Wikipedia.
The rigorous derivation of propagation equation by using Maxwell's equations. Analysis of the approximations made in the derivation.
Notes: For the rigorous proof of GVD see [AgrNL].
Supplementary reading: For a general description of Maxwell's equation see [Saleh]. A more rigorous proof of GVD (and nonlinear Kerr effect) using the multiple scales approach can be found in [Men99,Men06]. A list of the main optical fibers can be found in [Cisco].
Linear Schrödinger equation. Unit of measure of electric field. Attenuation. Group delay. Dispersion length. Impact of GVD over a Gaussian pulse. Power and phase of Gaussian pulse impaired by GVD.
Notes: GVD is described in [Alb05] and [Agrbase,AgrNL].
Supplementary reading: Other details can be found in [Saleh]. I suggest to revise the main relationships of Fourier transform, for instance by looking at the Wikipedia page of Fourier transform.
Impact of GVD over a Gaussian pulse. Instantaneous frequency. Anomalous and normal dispersion. Dispersion Management (DM). Dispersion map. GVD in presence of signal's chirp. Third-order dispersion.
Notes: GVD and GVD-chirp interaction are described in [Alb05] and [Agrbase,AgrNL].
Supplementary reading: Other details about GVD can be found in [Saleh].
Eye closure penalty (ECP) in presence of GVD. Fourier transform induced by strong GVD.
Notes: details can be found in [Alb05]. The Fourier transform induced by GVD is an approximation also called by the alternative names: stationary phase approximation, far field approximation, saddlepoint method, Fresnel diffraction.
Supplementary reading: Fresnel diffraction is discussed in [Saleh].
Memory of GVD.
Erbium doped fiber amplifier (EDFA). Cross sections. Propagation equation for the photon flux over distance.
Notes: details can be found in [Alb05]. A good book on EDFA is [Becker].
Supplementary reading: A discussion about the cross sections is in [Saleh]. The models of the EDFA are in [Sal90,Sun96].
Reservoir. Rate equations. Gain saturation. Amplified spontaneous emission (ASE) noise.
Notes: details can be found in [Alb05]. A detailed description of the reservoir is in [Alb98].
Supplementary reading: A discussion about the cross sections is in [Saleh]. The models of the EDFA are in [Sal90,Sun96].
Amplified spontaneous emission (ASE) noise. Noise figure of an EDFA: definition. Excess noise figure. Optical signal to noise ratio (OSNR). OSNR in transparent links. Friis's formula. Dual stage amplification: evaluation of noise figure.
Notes: details can be found in [Alb05]. For the noise figure definition see [Hau98].
Supplementary reading: For the zero-point energy and the Casimir effect take a look at Wikipedia. General discussions on OSNR can be found in [Agrbase].
Dual stage amplification: evaluation of noise figure. Comparison of single-, dual-stage amplification and dispersion uncompensated.
Exercises on OSNR evaluation.
Notes: details can be found in [Alb05].
Supplementary reading: General discussions on OSNR can be found in [Agrbase].
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).
Notes: details can be found in [Alb05]. The property that one photon contributes to one charge to the net current is described in [Saleh] in section 17.1 ``Properties of semiconductor photo-detectors''.
Supplementary reading: A more general discussion about photo-diodes can be found in [Alexander] and [Agrbase].
Poisson statistics. Poisson counting process.
Shot noise. Power spectral density (PSD) of shot noise.
Bit error rate (BER) for on-off keying (OOK) transmission. Optical receivers. Matched filter with Poisson arrivals. Quantum limit.
Notes: Details can be found in [Alb05]. Quantum limit is also discussed in [Agrbase].
Supplementary reading: An alternative proof of Campbell's theorem can be found in [Saleh]. Other details about BER can be found in [Saleh].
Quantum limit.
Bit error rate (BER) for on-off keying (OOK) transmission. Thermal noise. Gaussian approximation. Comparison between shot noise and thermal noise. Sensitivity power. Eye closure penalty vs. sensitivity penalty.
Notes: details can be found in [Alb05] and [Agrbase].
Supplementary reading: other details about BER can be found in [Saleh].
BER with ASE noise. Variance of signal/spontaneous beating noise. Spontaneous-spontaneous beat noise: motivations for Gaussian approximation. Comparison between true probability density function (PDF) and Gaussian approximation and motivations for the match.
Notes: details can be found in [Alb05]. The BER in direct detection is also discussed in [Agrbase].
Supplementary reading: More complete methods to evaluate the BER without the Gaussian approximation can be found in [Hum91,For00].
Exercises on BER, OSNR, sensitivity penalty.
Notes: I suggest to design a sketch of the power profile along distance, whenever possible.
Supplementary reading: No supplementary reading.
Exercises on IM-DD detection.
Polarization of light: ellipse of polarization, Jones formalism and Stokes formalism. Poincaré sphere. Examples of Stokes vectors over the Poincarč sphere. Linear description of birefringence.
Notes: A good book on PMD is [Damask].
Supplementary reading: Basic ideas of birefringence are discussed in [AgrNL].
Polarization maintaining fiber (PMF). Motion along distance. Motion along frequency. Polarization mode dispersion (PMD). Differential group delay (DGD). Principal states of polarization (PSP).
Overview of statistics of differential group delay (DGD). Outage probability.
Notes: A good book on PMD is [Damask].
Supplementary reading: A nice tutorial on PMD is [Gor00]. Many other details on polarization effects are discussed in the course ``Polarized fiber optic transmission''.
Proof of NLSE. Reasons of the nonlinear term. Nonlinear length.
Notes: The reference book for nonlinear effects is [AgrNL].
Supplementary reading: A rigorous proof of NLSE can be found in [Men06,Men99].
Self phase modulation (SPM). Comparison between temporal interpretation of SPM and frequency interpretation of GVD. SPM in frequency domain. SPM with sinusoidal power. Bandwidth enlargement due to SPM.
Notes: SPM is well described in [AgrNL].
Supplementary reading: SPM induces chirp, see [And92].
Inhomogeneous amplifier chains. Lagrange multipliers method. Best amplifiers gain in inhomogeneous chains.
Solitons. Proof of fundamental soliton.
Notes: details about solitons can be found in [AgrNL].
Supplementary reading: The inhomogeneous amplifier chains are described in [Mec98].
Solitons. Proof of fundamental soliton. Scaling properties of solitons. Pills on dark solitons and problems of solitons. Sliding filters.
Notes: details about solitons can be found in [AgrNL].
Supplementary reading: Further details on solitons can be found in [Agr11]. A reference book on solitons in the Unipr library is [Hasegawa].
Wavelength division multiplexing (WDM).
NLSE with separate fields. Comparison of unique and separate fields equations. Cross-phase modulation (XPM) and four wave mixing (FWM).
Notes: For cross-channel effects see [AgrNL].
Supplementary reading: Unique and separate fields are described in [Ros15].
Intra- and inter-channel GVD. XPM with inter-channel GVD: probe/pump case. XPM filter for single fiber. Walk-off coefficient. Frequency response of XPM filter. Comparison of SPM and XPM.
Notes: XPM without intra-channel GVD is discussed in [Kaz96].
Supplementary reading: An improved version of the XPM filter is discussed in [Bel98,BelVar98]. XPM impact on ASE noise without intra-channel GVD is discussed in [Ho04]. XPM in hybrid systems is discussed in [Alb09]. An alternative derivation of the XPM filter can be found in [Car99].
XPM with multiple spans. Examples.
Four wave mixing (FWM). Regular perturbation (RP) method to approximate the solution of the NLSE. FWM with CW signals. FWM efficiency.
Notes: FWM can be found in [AgrNL].
Supplementary reading: An alternative derivation of the XPM filter can be found in [Car99]. The RP method is discussed in [Van02].
Four wave mixing (FWM). Kernel of FWM. Phase matching coefficient. Examples of FWM. FWM in multiple spans. Pills on parametric amplification.
Notes: FWM can be found in [AgrNL].
Supplementary reading: The RP method is discussed in [Van02].
Split-step Fourier method (SSFM). Formal solution using operators. Scaling properties of SSFM error. Asymmetric and symmetrized SSFM. SSFM with effective length. Block diagram of asymmetric SSFM.
Notes: SSFM can be found in [AgrNL].
Supplementary reading: The SSFM step size is analyzed in [Sin03].
Step choice of SSFM: walk-off criterion. Nonlinear phase criterion.
Coherent detection: motivations. 3 dB optical coupler. Differentially coherent detection: differential phase shift keying (DPSK). Differential quadrature phase shift keying (DQPSK). Comparison OOK/DPSK, DPSK/DQPSK.
Notes: SSFM can be found in [AgrNL]. The step size is analyzed in [Sin03]. A detailed bibliography of coherent detection can be found into the slides.
Supplementary reading: The adaptive method based on the local error is described in [Feldman]. An extension of the method of the nonlinear phase including GVD is described in [Zha08]. An analysis of the spurious resonances induced by a constant step is shown in [Bos00].
Historical background of coherent detection. Comparison between coherent and differentially coherent detection. Optical hybrid. Detection of in-phase and quadrature components. Polarization division multiplexing (PDM). Polarization diversity receiver. Digital signal processing: static equalization of GVD, clock recovery.
Notes: A detailed bibliography of coherent detection can be found into the slides.
Supplementary reading: Coherent detection is a hot topic, hence I suggest to take a look at the most recent scientific articles.
Digital signal Processing (DSP). Dynamic channel equalization: data-aided and blind algorithms. Constant modulus algorithm (CMA). Carrier phase estimation: Viterbi & Viterbi algorithm, blind-phase search. Frequency estimation. Example of real experiments.
Notes: A detailed bibliography can be found into the slides.
Supplementary reading: Coherent detection is a hot topic, hence I suggest to take a look at the most recent scientific articles.
The Matlab programming language.
Notes: A Matlab primer is [Sig93]. Free versions of Matlab are Octave and SciLab.
Supplementary reading: An advanced tutorial of Matlab is [Ack03]. A collection of general purpose Matlab functions can be found at Matlab-File-Exchange.
With Octave a graphical user interface may be useful, e.g., gnuplot (in wikipedia at the voice Octave there is an exhaustive list of alternatives). The basic toolboxes of Matlab are available in Octave at Octave-Forge. Some useful code lines regarding saving the body of a Matlab file into a variable can be found in the forum of the Optical Communications course at Moodle, (search in the forum for 'thisfile').
Software Optilux. Examples. Discretization of a signal in the time and frequency domain.
Notes: Optilux can be downloaded at OptiluX.
Supplementary reading:
I suggest to keep update Optilux with
Subversion, both
for Windows and Linux. More instructions available on Elly.
For old computer architectures, I suggest to compile the mex
files inside Optilux (e.g., run the function comp_mex.m
in the Optilux_files directory). In this case, under Linux
it may be useful the installation of the package build-essential.
Block diagram of RP1 and comparison with SSFM. Gaussian Noise (GN) model. Best power using the GN model. Application of the GN model: best SNR, scaling of SNR. Constrained Performance. Constrained performance: scaling of nonlinear asymptote with the number of spans. Reach.
Notes: The Gaussian noise model for the signal to noise ratio can be found in [Alb11]. The scaling laws of the SNR can be found in [Alb12].
Supplementary reading: Further details on the GN model can be found in [Pog14,Pog11] and [Car12].
Laboratory experience. Introduction to the laboratory. Safeguards. Measure of fiber attenuation.
Notes: see the slides on Elly.
Supplementary reading: see the slides on Elly.
Software Optilux. Examples.
Notes: Optilux can be downloaded at OptiluX.
Supplementary reading:
I suggest to keep update Optilux with
Subversion, both
for Windows and Linux. More instructions available on Elly.
For old computer architectures, I suggest to compile the mex
files inside Optilux (e.g., run the function comp_mex.m
in the Optilux_files directory). In this case, under Linux
it may be useful the installation of the package build-essential.
Maximum reach with GN model. Tolerance to errors and implications in optical link design. Reconfigurable optical add and drop multiplexer (ROADM). Power setup in a network.
Cross-polarization modulation. (XPolM). Comparison XPolM-XPM. XPolM motion over the Poincaré sphere.
Manakov equation. XPolM as a FWM combination.
Digital back-propagation (DBP). Zero-forcing behavior of DBP. Impact of nonlinear signal noise interaction (NSNI) on DBP performance.
Notes: The Gaussian noise model for the signal to noise ratio can be found in [Alb11]. The scaling laws of the SNR can be found in [Alb12]. A detailed bibliography about XPolM and DBP can be found into the slides.
Supplementary reading: Further details on the GN model can be found in [Pog11] and [Car12].
Paolo 2019-09-10