In the present thesis work, we have developed two different experimental setups for the optical detection of the OH radical in discharges at atmospheric pressure. The first one allows us to improve the time-resolved broad-band absorption spectroscopy. The main advances of the new set up are a better collimation of the UV light and a novel gating scheme. They both significantly reduce the interference of the plasma-induced emission on the absorption measurement. The second setup is dedicated to an improved laser induced fluorescence experiment, which takes advantage of a novel multi-transition excitation scheme. This permits the simultaneous measurements of both the OH density and its ground state rotational temperature. In addition, we have developed a new rate-equation model to rationalize LIF spectra, by taking into account the electronic quenching, the vibrational and rotational energy transfers, and the spatial profile of the laser beam. Finally, the electrical power dissipated in the discharge was accurately measured.

The thesis is divided into two topics: silicon nanocrystals based light emitting devices and erbium doped silicon nanocrystals devices. I have studied silicon nanocrystals based devices. Here I have demonstrated the role of the different injection mechanisms in determining the efficiency of the device. I have studied single and multilayer structures, both in diode or transistor configurations. Lastly, the time dependence of the electroluminescence has been studied, clarifying the role of bipolar or unipolar injection in these structures. On the second part of my thesis, I have studied Er and silicon nanocrystals co-doped devices. Firstly, the study was aimed at the understanding of the efficiency of the electrical pumping of Er ions. Then, integrated optical cavities were designed and fabricated and their optoelectronic properties measured. Here I built a specific set-up in order to measure at the same time the optical and electronic properties of active devices on wafer. Unfortunately, the measurements demonstrated that many nonlinear loss mechanisms set in when the devices are heavily injected with current. Therefore, despite the optical cavities are of high qualities, the system did not show any laser emission. On the other hand, I have demonstrated a fully integrated system where the Er doped injection device pumps a waveguide and the emission is then extracted through a grating. Last result was the experimental verification of the existence of intermediate band states through which the silicon nanocrystals to Er energy transfer occurs.

The contents of the present thesis can be divided into three parts. The first three chapters introduce the general context in which this work was developed: the social impact, the motivations and the key concepts of our research field. In particular, in Chapter 1 we discuss about the energy issue, focusing on the problem of sustainability of the energy sources. Through an analysis of updated energy and population statistics, we come to the conclusion that solar energy is the most environmentally, economically and socially sustainable energy source. Then, in Chapter 2 we present the basics of photoelectrochemical water splitting, as a possible strategy of solar hydrogen production. This discussion is inserted in the more general topic of artificial photosynthesis toward solar fuel generation. In view of the experimental work presented in this thesis, we put attention on semiconductor-based photoelectrochemical water splitting and on heterogeneous catalysis with inorganic catalytic materials. More specifically, we propose physical vapor deposition techniques as synthetic methods suitable for the industrial production of thin films for photoelectrochemical applications. In Chapter 3 we introduce the fundamentals of physical vapor deposition techniques (namely, radiofrequency magnetron sputtering, electron-beam deposition and pulsed laser deposition). The second part highlights some fundamental mechanisms that are relevant in the pulsed laser ablation of metals. In particular, we review our recent results on the modeling of liquid nanodroplet formation in the nanosecond laser ablation of pure metals. Chapter 4 develops a simplified model of phase explosion, based on the theory of homogeneous boiling. Through a continuum approach, we describe the liquid nanoparticle formation in a metastable liquid metal, whose temperature is constant over time and space. The results of our computational simulations are presented here for a set of seven metals (Al, Fe, Co, Ni, Cu, Ag and Au), commonly used in pulsed laser deposition. Our modeling was further improved, taking into account a more realistic spatial and temporal dependence of the temperature. In Chapter 5 we design a simulation of the nanosecond laser ablation of aluminum, which considers phase explosion and vaporization mechanisms. A nanosecond Gaussian-shaped laser pulse was assumed and the spatial gradient of the temperature was calculated according to the heat conduction equation. In this way, space–time resolved homogeneous boiling was studied and the size distribution of the produced liquid nanodroplets is presented. After this long digression on the fundamentals of laser ablation mechanisms, we return to focus on the application of physical vapor deposition techniques to the synthesis of solid-state thin layers for photoelectrochemical water splitting. This third part is composed of three chapters, each one dealing with a different physical vapor deposition technique. Chapter 6 presents the synthesis and characterization of tin-doped hematite through radiofrequency magnetron sputtering. That study allowed us to shed some light on the effect of tin doping on the structural, optical and electrochemical properties of hematite. Indeed, tin-doped hematite was studied as a photoanodic material in some considerable experimental works, but the employed techniques made difficult to decouple the effect of the dopant from other structural and morphological features. Chapters 7 and 8 present the results of our work on the pulsed laser deposition and electron-beam deposition of water oxidation catalysts, respectively. In particular, Chapter 7 proposes the synthesis of a porous amorphous iron oxide catalyst employed to functionalize hematite photoanodes. The small-scale nanostructuring obtained through pulsed laser deposition allowed minimizing some issues such as the parasitic light absorption. In Chapter 8 we characterize pure and binary metal oxide thin films based on Fe, Co and Ni, deposited through electron-beam deposition. In our investigation of the electrocatalytic performance of these water oxidation catalysts, NiFe2Ox results as the most active material, in agreement with recent literature.

Random numbers are fundamental elements in different fields of science and technology such as computer simulation like Monte Carlo-method simulation, statistical sampling, cryptography, games and gambling, and other areas where unpredictable results are necessary. Random number generators (RNG) are generally classified as “pseudo”-random number generators (PRNG) and "truly" random number generators (TRNG). Pseudo random numbers are generated by computer algorithms with a (random) seed and a specific formula. The random numbers produced in this way (with a small degree of unpredictability) are good enough for some applications such as computer simulation. However, for some other applications like cryptography they are not completely reliable. When the seed is revealed, the entire sequence of numbers can be produced. The periodicity is also an undesirable property of PRNGs that can be disregarded for most practical purposes if the sequence recurs after a very long period. However, the predictability still remains a tremendous disadvantage of this type of generators. Truly random numbers, on the other hand, can be generated through physical sources of randomness like flipping a coin. However, the approaches exploiting classical motion and classical physics to generate random numbers possess a deterministic nature that is transferred to the generated random numbers. The best solution is to benefit from the assets of indeterminacy and randomness in quantum physics. Based on the quantum theory, the properties of a particle cannot be determined with arbitrary precision until a measurement is carried out. The result of a measurement, therefore, remains unpredictable and random. Optical phenomena including photons as the quanta of light have various random, non-deterministic properties. These properties include the polarization of the photons, the exact number of photons impinging a detector and the photon arrival times. Such intrinsically random properties can be exploited to generate truly random numbers. Silicon (Si) is considered as an interesting material in integrated optics. Microelectronic chips made from Si are cheap and easy to mass-fabricate, and can be densely integrated. Si integrated optical chips, that can generate, modulate, process and detect light signals, exploit the benefits of Si while also being fully compatible with electronic. Since many electronic components can be integrated into a single chip, Si is an ideal candidate for the production of small, powerful devices. By complementary metal-oxide-semiconductor (CMOS) technology, the fabrication of compact and mass manufacturable devices with integrated components on the Si platform is achievable. In this thesis we aim to model, study and fabricate a compact photonic quantum random number generator (QRNG) on the Si platform that is able to generate high quality, "truly" random numbers. The proposed QRNG is based on a Si light source (LED) coupled with a Si single photon avalanche diode (SPAD) or an array of SPADs which is called Si photomultiplier (SiPM). Various implementations of QRNG have been developed reaching an ultimate geometry where both the source and the SPAD are integrated on the same chip and fabricated by the same process. This activity was performed within the project SiQuro—on Si chip quantum optics for quantum computing and secure communications—which aims to bring the quantum world into integrated photonics. By using the same successful paradigm of microelectronics—the study and design of very small electronic devices typically made from semiconductor materials—, the vision is to have low cost and mass manufacturable integrated quantum photonic circuits for a variety of different applications in quantum computing, measure, sensing, secure communications and services. The Si platform permits, in a natural way, the integration of quantum photonics with electronics. Two methodologies are presented to generate random numbers: one is based on photon counting measurements and another one is based on photon arrival time measurements. The latter is robust, masks all the drawbacks of afterpulsing, dead time and jitter of the Si SPAD and is effectively insensitive to ageing of the LED and to its emission drifts related to temperature variations. The raw data pass all the statistical tests in national institute of standards and technology (NIST) tests suite and TestU01 Alphabit battery without a post processing algorithm. The maximum demonstrated bit rate is 1.68 Mbps with the efficiency of 4-bits per detected photon. In order to realize a small, portable QRNG, we have produced a compact configuration consisting of a Si nanocrystals (Si-NCs) LED and a SiPM. All the statistical test in the NIST tests suite pass for the raw data with the maximum bit rate of 0.5 Mbps. We also prepared and studied a compact chip consisting of a Si-NCs LED and an array of detectors. An integrated chip, composed of Si p+/n junction working in avalanche region and a Si SPAD, was produced as well. High quality random numbers are produced through our robust methodology at the highest speed of 100 kcps. Integration of the source of entropy and the detector on a single chip is an efficient way to produce a compact RNG. A small RNG is an essential element to guarantee the security of our everyday life. It can be readily implemented into electronic devices for data encryption. The idea of "utmost security" would no longer be limited to particular organs owning sensitive information. It would be accessible to every one in everyday life.

The laser, whose name stands for Light Amplification by Stimulated Emission of Radiation, in less than a century has became a fundamental tool in several applications and technological processes, such as metrology, telecommunications, medicine and industry, because of their peculiar properties. More in details, they are spatially and temporally coherent, they exhibit a low divergence and can offer high power density and monochromaticity. The work of this thesis can be placed within the framework of laser assisted industrial processes. Material processing exploits the interaction between a high power laser beam and the matter. The interaction happens in the surface of the material where the extreme heat transferred by the laser source can cause a local phase change, without affecting in a significant way the bulk properties of the treated medium. Typically high brightness laser sources are used. The most used solution is represented by fiber lasers. In the last years the research moved towards the semiconductor laser sources because of the numerous advantages that they o↵er with respects to the other types of sources, like a higher conversion efficiency, a smaller size and the possibility of a mass production. Nevertheless, the maximum output power that can be extracted from a single diode laser is relatively small. The adopted strategies for power scaling rely on beam combining. Here we propose a novel architecture for the implementation of passive coherent beam combining, into a single resonant cavity. The main block of the scheme is an Interferometric Semiconductor Amplifier (ISA). In an ISA, the optical amplifier is placed in one arm of a Mach-Zehnder Interferometer. A sequence of ISA, placed into a common resonant cavity, is used for the power scaling. The theoretical model is presented, and the experimental results are discussed.

My research in these three years has been mainly focused on the characterization of structural and optical properties of three kinds of Si-based materials and devices. The first one is the study of SiOC thin films, carried within the TMR-POLYCERNET project financed by the European community. The scientific objective of this project is to create molecularly-tailored, nanostructured SiOC ceramics with unusual multifunctional properties, including photoluminescence. In addition these novel, polymer-derived ceramics, or PDCs, will have high resistance to oxidation, degradation, corrosion and deformation at temperatures above 1400°C. The aim of our work is focused on the optical characterization of PDCs. The PDCs are constituted from polymeric precursors which can be tailored and designed at the molecular level. These multifunctional properties are then carried over into the ceramic phase by self-assembly and controlled pyrolysis. Thus, these novel materials are apparently polymer-like in their structure (for example, they are seemingly amorphous but contain nanodomains) but have the chemical, mechanical and functional properties of high temperature ceramics. The photoluminescence will be the most important property that will be studied and optimized. The specific objective of this work is to optimize chemistry and processing to achieve bright emission and high external quantum efficiency in high-quality thin film. In the second chapter of the thesis, starting from a brief description of SiOC glasses and the sol-gel process to introduce our work, we explained how the thin films were prepared and characterised. A study on the absorption coefficient of the films is reported, in order to compare it with results in literature of similar samples. The major part of this chapter was focalized on our work on the photoluminescence of the films. At high annealing temperature, we observed a very high yellow luminescence from the films, most notably due to the presence of SiC nanoclusters and C clusters in our samples. A well detailed discussion on the origin of the strong emission is reported. A study of the effects of Boron addition on the photoluminescence of our thin films was also effectuated and by comparing the evolution of the B-free (SiOC) and B-containing samples (SiBOC), the important role of boron in promoting the evolution of nanostructure in our thin films is described. Finally, to have an idea of the potential of our films, their external quantum efficiency (E.Q.E.) was measured. A detailed description of the measurement technique is reported and the results are compared with Si-nc samples whose EQE is well-known. Very high EQE were found for TH films pyrolysed at 1200 °C (11.5 %) and THDH2 films pyrolysed at 1200 °C (5%). These external quantum efficiency values are very promising and make SiOC a very interesting material for LED applications. Another part of the work was devoted to the study of Si-based waveguides, and more particularly Silicon on Insulator (SOI) waveguides and Slot SOI waveguides. This work was carried out within the European project PHOLOGIC. The general objective of the PHOLOGIC project is to explore the mass-manufacturing feasibility of Silicon Nanocrystals inside SiO2 matrix in terms of CMOS technology compatibility for a highly scalable photonic logic gate structure. A XOR gate was chosen as functional validation device. The third and fourth chapters of this thesis are dedicated to this work. In the third chapter, we characterized various building blocks like splitters, MMI and bends made in Silicon on Insulator technology. The loss figures found for these building blocks were useful as a benchmark for further development of silicon microphotonics components and circuits on SOI platform like photonic crystals and ring resonators. In effect, the results of this chapter are basic to the development of the SCISSOR structures based on SOI technology, described in chapter five. In the fourth chapter, we studied nano-Si slot waveguides. Horizontal slot waveguides filled with Si-nc have been realized and characterized in terms of propagation losses as a function of the layer deposition conditions (i.e. Si excess and annealing temperature). We were able to reach propagation losses as low as 3 dB/cm which is the best result reported so far for slot waveguides of very small width (50 nm). We presented also experimental results of resonant optical cavities such single and double ring resonators coupled to the horizontal slot waveguides with very high quality factors. The importance of this works relies on the fact that by optimizing the annealed SRSO (i.e. Si-nc) in the slot, we have significantly reduced the propagation losses and at the same time we can add new functionalities related to the Si-nc optical properties (i.e. light emission and/or non-linear optical effects). Finally, a one-dimensional photonic crystal structure based on horizontal slot waveguide with a photonic band gap around 1.55 μm has also been designed and optically characterized. Finally, the last part of this thesis will be devoted to the characterization of Silicon on Insulators Multi-Resonators. This work is a continuation of the study of SOI building blocks described above, and was carried within the European project WADIMOS. The main goal of the WADIMOS project is to build a complex photonic interconnect layer incorporating multi-channel microsources, microdetectors and different advanced wavelength routing functions directly integrated with electronic driver circuits. Our work in this project is to test innovative optical waveguide division multiplexing circuits based on coupled ring resonators. In the last part of this thesis, we will characterize various coupled ring/disks resonators structures, from simple double coupled rings until eight coupled ring SCISSOR. In the last chapter, we measured and compared the characteristic of the light propagation of different connection geometries for sequences of microrings (or microdisks) resonators. In this work, we studied various configurations of coupled disk/ring resonators. With these various structures, we observed the differences in the transmission spectrum between rings and disks resonators, we noticed the whispering gallery modes and the effect of the gap in the CRIT effect for a serially double-disks resonator. On a first time, we studied the serially coupled configuration CROW where each ring resonator is coupled to one another. For this structure, we restrict our attention to two ring/disk based units. We observed the differences in the transmission spectrum between rings and disks resonators and we noticed the whispering gallery modes and the effect of the gap in the electromagnetically induced transparency effect for a serially double-disks resonator. The second configuration that was studied is the SCISSOR configuration. In this case, all resonators are coupled to both the input and drop port waveguides. We characterized the behaviour of complex eight-resonators SCISSOR devices in the case of microdisks and microrings resonators. In order to facilitate the characterization of these complex structures, a new set-up was also build up, which allowed us to study the scattered light of the resonators from the top as a function of the wavelength. Finally, with this technique, for the first time, we demonstrated the presence of EIT-like band even in complex structures. Extremely small differences between adjacent rings can give rise to the appearance of EIT states, delocalized over only few rings and with a great Q-factor and strong out-of-plane scattering.

The work in this thesis has been centred on the light emitting properties of silicon nanocrystals and the possible applications of this particular material platform to various topics ranging from bio-imaging to erbium ion sensitization. Silicon nanocrystals as bio-imaging agent have been investigated by employing colloidal dispersion of individual silicon nanocrystals where surface properties could be controlled to a great extent. By using a suitable functionalization scheme, high quality hydrophilic luminescent nanoparticles were produced. Using the improvements in the physical coating, bio-imaging on living cells (in vitro) was demonstrated showing that silicon nanocrystals have a great potential in bio-imaging and offer a promising alternative to commonly used fluorescence dyes. A part from being good light emitters, silicon nanocrystals could also amplify the light. This is a reason why the part of the work in this thesis has been dedicated to the investigation of silicon nanocrystals as a gain material. While most of the studies on this topic are concentrated on the nanocrystal surface as a driving mechanism behind the optical amplification, the work presented in this thesis concerns the study of a zero phonon (direct) optical transition as a possible source of optical amplification in this material system. To this scope, investigation of the dynamics of the system on a nanosecond time-scale and under high excitation conditions has been employed. Additional insight on ultrafast dynamics has been obtained by using optical cavities in the form of optically active free-standing micro-disk resonators. Finally, in the last part of this thesis a study of Er3+-doped Silicon-Rich-Oxide (SRO) materials and Er3+-doped SRO based devices is presented. This part of the work differs from the rest of the work reported in this thesis as is not focused on the light emitting properties of silicon nanocrystals but mostly on their non-radiative process engineering (energy transfer to erbium ions). Er3+ doped SRO opens the route towards compact waveguide amplifiers and lasers and allows for the possibility of electrical injection schemes, which are not realizable in standard erbium amplifiers used in EDFA for telecom applications. To that end, novel opto-electronic structures were proposed, modeled and manufactured and preliminary results of their performance were presented. The sensitization mechanism between silicon nanoparticles and erbium ions was studied and its complex nature was illustrated. Although, the acquired knowledge of physics involved was not sufficient for formulation of a complete working theory of the energy transfer process, some important physical aspects of this process have been elucidated paving the way towards its complete understanding.

In principle, the lattice of elementary propositions of a generic quantum system admits a representation in real, complex or quaternionic Hilbert spaces as established by Solèr’s theorem (1995) closing a long standing problem that can be traced back to von Neumann’s mathematical formulation of quantum mechanics. However up to now there are no examples of quantum systems described in Hilbert spaces whose scalar field is different from the set of complex numbers. We show that elementary relativistic systems cannot be described by irreducible strongly-continuous unitary representations of SL(2, C) on real or quaternionic Hilbert spaces as a consequence of some peculiarity of the generators related with the theory of polar decomposition of operators. Indeed such a ”naive” attempt leads necessarily to an equivalent formulation on a complex Hilbert space. Although this conclusion seems to give a definitive answer to the real/quaternionic-quantum-mechanics issue, it lacks consistency since it does not derive from more general physical hypotheses as the complex one does. Trying a more solid approach, in both situations we end up with three possibilities: an equivalent description in terms of a Wigner unitary representation in a real, complex or quaternionic Hilbert space. At this point the ”naive” result turns out to be a definitely important technical lemma, for it forbids the two extreme possibilities. In conclusion, the real/quaternionic theory is actually complex. This improved approach is based upon the concept of von Neumann algebra of observables. Unfortunately, while there exists a thorough literature about these algebras on real and complex Hilbert spaces, an analysis on the notion of von Neumann algebra over a quaternionic Hilbert space is completely absent to our knowledge. There are several issues in trying to define such a mathematical object, first of all the inability to construct linear combination of operators with quaternionic coeffients. Restricting ourselves to unital real *-algebras of operators we are able to prove the von Neumann Double Commutant Theorem also on quaternionc Hilbert spaces. Clearly, this property turns out to be crucial.

Realizzazione di un sistema in concentrazione: inseguitore, ottica primaria, ricevitore. Al fine di massimizzare la potenza elettrica trasferita al carico, è stata posta particolare attenzione al tipo di connessioni fra le celle che costituiscono l'array.

The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on the introduction of the bundle of affine scalars over the configuration manifold, is then presented. The analysis includes a revisitation of Pontryagin Maximum Principle and of the Erdmann-Weierstrass corner conditions, a local interpretation of Pontryagin's equations as dynamical equations for a free (singular) Hamiltonian system and a generalization of the classical criteria of Legendre and Bliss for the characterization of the minima of the action functional to the case of piecewise-differentiable extremals with asynchronous variation of the corners.