- Introducció
Photonic systems are powerful test-beds for the investigation of complex dynamics emerging from
delays in feedback or coupling. The aim of this thesis was to study two relevant properties of photonic
delay systems with direct applications in current information processing and encryption systems:
consistency and unpredictability. We characterized the ability of laser systems with delay to exhibit, on
the one hand, reliable complex dynamics when an external stimulus is applied, and on the other hand,
unpredictable complex behavior, depending on the operating conditions. Consistency properties have
been studied as a necessary condition for the implementation of Reservoir Computing schemes. The
property of unpredictability has been exploited in the application of random bit generation.
- Contingut de la investigació
For the characterization of the consistency properties, we used three different experiments based on a
semiconductor laser systems with delay that followed the drive-response scheme. Through the analysis
of the responses to a repeated drive, a consistent or inconsistent behavior can be identified.
In the first setup, we investigated consistency of a semiconductor laser to its own time-delayed feedback,
so that the drive was the self-generated complex signal, and the response system was the semiconductor
laser itself. A high accuracy in the repetition of the drive was achieved with the design of a fiber-optic
setup with two feedback loops. This allowed us the extraction of measures like the sub-Lyapunov
exponent.
We extended the study to the use of a semiconductor laser system with excitability properties subject to electrical input pulse trains. Here, two different pulse trains modulating the pump current of the laser
were used as drives, while the semiconductor laser with delayed feedback operating in the chaotic
regime of Low Frequency Fluctuations acted as response system. The purpose of this experiment was to
study the possibility and requirements to induce a consistent response, particularly the power drop-out,
with the injection of a short pulse.
To complement the investigations on consistency, the last drive-response scheme used
was an electro-optic intensity oscillator driven by 3 scalar signals: an harmonic waveform, a sequence of
pulses, and recorded time-traces from the autonomous dynamics. Under certain conditions, the response
system can show hysteresis and coexistence of multistable states.
We introduced new tools to quantify consistency and identified common features of the setups
investigated. Our study showed that when the autonomous dynamics were periodic or period doubled, a
consistent response was obtained independent of the drive. In cases of bistable dynamics, new sorts of
consistency were discovered, like reproducible time-position transitions between the two states.
The last Chapter of this thesis was devoted to the use of the unpredictable dynamics for the generation of
random bits. A semiconductor laser with polarization rotated feedback was utilized to provide chaos
characterized by randomness-like features, including a flat broad spectrum, suppression of the delay
echoes of the autocorrelation function and no recurrences in the temporal oscillations. Nevertheless, we
found that other factors like the data acquisition and the postprocessing of the signal also affected the
randomness of the finally generated bits. The validity of our guidelines was proven with our random bit
generator, enhancing its generation rate up to 160Gbit/s.
- Conclusió
With this work, we explored the emerging complex behavior in laser systems with delay. In particular,
we characterized their ability to display a consistent behavior, and deterministic chaos that can lead to
unpredictable dynamics. We introduced new tools and measures to quantify consistency, and guidelines
for an optimum performance of a random bit generator. Altogether, our results represent a significant
contribution to the areas where these two properties play a role, such as information processing and
secure optical communications.
Contents:
Resumen vii
Summary ix
List of publications xiii
1 Introduction 1
1.1 Delay systems 2
1.2 Photonic delay systems 3
1.2.1 Photonic delay systems in the drive-response scheme 3
1.3 About Consistency 4
1.3.1 Applications of consistency 5
1.4 About Unpredictability 6
1.4.1 Applications of unpredictable dynamics 7
1.5 Overview of this Thesis 8
2 Concepts and tools 11
2.1 Consistency and Generalized Synchronization 11
2.2 Tools to measure consistency 13
2.2.1 The sub-Lyapunov exponent 13
2.2.2 Inter- and intra-correlations 15
2.2.3 Review of the consistency measures 19
2.3 Tools to measure unpredictability 21
3 Consistency of a laser to time delayed feedback 23
3.1 Introduction 23
3.2 Experimental implementation 24
3.2.1 Dynamical performance 26
3.3 Quantifying consistency from experimental data 29
3.3.1 Consistency correlation 29
3.3.2 Sub-Lyapunov exponents from transverse distribution functions 33
3.4 Sub-Lyapunov exponent in numerical simulations 39
3.5 Summary and conclusions 41
4 Consistency of a laser system to input pulse trains 43
4.1 Introduction 43
4.2 Experimental realization 44
4.2.1 A study at slow timescales 48
4.3 Influence of the history of pulses 48
4.3.1 Consistency for a bimodal distribution of drive pulses 51
4.4 Influence of the inter-pulse intervals 54
4.4.1 Consistency for a uniform distribution of drive pulses 55
4.5 Filtering the responses 58
4.6 Summary and conclusions 59
5 Consistency of an electro-optic intensity oscillator 61
5.1 Introduction 61
5.2 Experimental realization 62
5.2.1 Methodology 64
5.3 Dynamics without modulation 65
5.3.1 Changing : from fixed point to chaos 65
5.3.2 Changing and 0: the bifurcation diagrams 66
5.4 Consistency with an external drive 71
5.4.1 Harmonic drive 72
5.4.2 Pseudo-random pulse distribution 74
5.4.3 Recorded time traces 77
5.5 Summary and conclusions 83
6 Random bit generation with a chaotic laser 87
6.1 What are random numbers? 88
6.1.1 Types of random bit generators 89
6.1.2 Why a random bit generator based on a semiconductor laser? 89
6.2 Experimental implementation 90
6.3 Dynamical properties for a good Random Bit Generator 91
6.3.1 RF power spectrum 92
6.3.2 Autocorrelation conditions 93
6.3.3 Systematic study of the AC properties 96
6.3.4 Role of noise 97
6.4 Acquisition conditions 97
6.4.1 Sampling rate and data acquisition . 99
6.5 Postprocessing 100
6.6 Assessing the randomness 102
6.7 Generation of random bit sequences 105
6.8 Interplay of postprocessing and sampling rate 106
6.9 Optimizing the bit generation rate 108
6.9.1 Extension to 16-bit digitization 110
6.9.2 Information Theoretic limits 110
6.10 Discussion 112
6.11 Summary 115
7 Conclusions and future work 117
7.1 Conclusions 117
7.2 Future work 119
Bibliography 121
| Identifer | oai:union.ndltd.org:TDX_UIB/oai:www.tdx.cat:10803/378032 |
| Date | 16 December 2015 |
| Creators | Oliver Andreu, Neus |
| Contributors | Fischer, Ingo, Mirasso, Claudio R. (ponent), Universitat de les Illes Balears. Departament de Física |
| Publisher | Universitat de les Illes Balears |
| Source Sets | Universitat de les Illes Balears |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis, info:eu-repo/semantics/publishedVersion |
| Format | 60 p., application/pdf |
| Source | TDX (Tesis Doctorals en Xarxa) |
| Rights | ADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel·lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant als continguts de la tesi com als seus resums i índexs., info:eu-repo/semantics/openAccess |
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