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Generalized Talbot effect theory and application to advanced optical wave processing.


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Romero Cortés, Luis (2018). Generalized Talbot effect theory and application to advanced optical wave processing. Thèse. Québec, Doctorat en télécommunications, Université du Québec, Institut national de la recherche scientifique, 275 p.

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The capability to generate precisely-timed periodic trains of optical pulses has pushed forward many fields of science and technology. Periodic optical waves are key to disciplines such as optical communications and computing, optical signal processing, sensing, spectroscopy, nonlinear and quantum optics, and many others. Periodic optical waveforms can be generated through electro-optical means, external modulation of continuous-wave lasers, and through mode-locking, perhaps one of the most significant recent advances in optical science and technology. Mode-locking is the process by which the different longitudinal modes oscillating in a laser cavity are tightly locked in phase, giving rise to the repetitive emission of a light pulse, i.e., a periodic pulse train. The spectrum of such a signal is a collection of equally-spaced discrete frequency components, known as a frequency comb for the characteristic comb-like shape of its power spectrum. Currently, optical frequency combs are the most precise man-made clocks in history. These signals are used in a myriad of fundamental and applied disciplines, and they are the key enabling factor of many scientific and technological fields, ranging from high-resolution spectroscopy of molecules and atoms, to next-generation optical communication systems and the astronomical search for exo-planets. The separation between adjacent frequency components of a frequency comb, known as the free spectral range (FSR), is the inverse of the repetition period of the corresponding pulse train in the time domain representation of the signal. This is a fundamental parameter from an application viewpoint. Not only most applications of periodic optical signals require their periodicity to be fixed with precision (for instance, the rate at which information is transmitted in a telecommunication system, and processed in a computing system, is strongly related to the pulse period of the clock signal), but distinct applications require fundamentally different orders of magnitude. As an example, typical atomic and molecular spectroscopy applications require combs with FSR values in the MHz regime, while astronomical spectrographic measurements, as well as applications aimed at arbitrary waveform generation and processing, are performed with frequency combs in the GHz regime. Conventional, well-established approaches for periodicity control through manipulation of pulse trains and frequency combs include spectral amplitude filtering and temporal pulse picking (or time gating). The main drawback of these approaches is their low energy efficiency, as they rely on directly discarding signal energy. Additionally, these methods suffer from practical implementation shortcomings. The amplitude filtering method needs high-finesse filters, with tight design and operational requirements (e.g., precise spectral alignment between the filter and the comb), in order to achieve signals with high quality. Similarly, the imperfect suppression of undesired pulses in pulse picking techniques results in spectral line-to-line amplitude fluctuations of the obtained comb. The relatively low extinction ratio of current electro-optic intensity modulators often forces to use optical gates based on nonlinear effects (incurring in even higher energy inefficiency), or optical switches based on semiconductor optical amplifiers and acousto-optic modulators (with typically low operation speeds). Precise timing between the pulse train and the pulse picking gate also becomes a critical factor for a correct pulse suppression. Another fundamental metric for the applicability of periodic optical waveforms is related to their noise content. Indeed, our ability to detect signals or events and to extract information contained therein is ultimately limited by the strength of said signal and that of the noise content of the measurement. Noise is ubiquitous, and its origin mechanisms are often random and difficult to control. In the particular case of periodic optical signals, the aforementioned techniques for periodicity control typically result in the degradation of the signal-to-noise ratio of the waveform of interest. This is mainly due to the fact that a large amount of energy from the input signal is deliberately thrown away (e.g., in the form of line suppression by spectral amplitude filtering of frequency combs, or pulse rejection by temporal amplitude gating of pulse trains). Versatile methods to control the pulse period of optical trains and the FSR of frequency combs with high energy efficiency and low signal degradation based on passive, linear processes are highly desired. Periodicity control methods for optical signals based on phase-only manipulations – temporal phase modulation and/or spectral phase filtering – are particularly attractive solutions to the problem, as these techniques recycle the energy of the input signal, rather than discarding part of it, redistributing it to form the desired output signal. Several techniques for periodicity control through phase-only manipulations have been proposed. In particular, an important set of these techniques relies on periodic phase transformations based on the theory of Talbot self-imaging. Realizations of Talbot phenomena have been reported across several observation domains, including time and frequency (for pulse trains and frequency combs respectively), and although the phenomenon has been extensively studied, a description that unifies its manifestations across all observation domains is still missing. The main goal of this dissertation is to propose a universal method for arbitrary, energy-preserving control of the period of repetitive optical signals, through the development of a unified mathematical description of the Talbot effect in Fourier-dual representation domains of waves. Such a generalization of the phenomenon is presented in Chapter 3, followed by the formulation of the aforementioned universal periodicity control model. Chapters 4 and 5 present experimental demonstrations of arbitrary, energy-preserving control of the repetition period of temporal pulse trains, and the FSR of frequency combs, respectively. In both chapters, the properties of the method to increase the signal energy over the level of incoherent noise propagating alongside are analyzed. The proposed method is indeed capable of redistributing the energy content of the signals of interest, producing an effect of passive amplification, thus avoiding the need for conventional active gain mechanisms (which are known to amplify both the signal and its noise content, and typically inject additional external noise contributions to the signal). Finally, Chapter 6 presents experimental examples and applications of the developed period control method to the spectra of arbitrary, aperiodic signals. In particular, two applications are reported: (i) a method for introducing reversible frequency gaps (frequency bands free of energy in the spectrum of a wave) to the spectrum of isolated optical waveforms, allowing for implementation of a novel technique for invisibility cloaking; and (ii) a method for compressing the spectra of modulated sequences of short pulses, while preserving the temporal shape of the pulses (including pulse duration), thus combining the performance advantages and robustness of short pulses for transferring and processing information with the convenience of frequency-domain multiplexing and processing operations. Considering the wide range of application of periodic temporal and spectral waveforms (e.g., trains of pulses and frequency combs), interest in the methods reported in this dissertation can be foreseen across many different fields. A particularly appealing feature of the proposed methods for pulse period/FSR control is that they offer a high flexibility and energy efficiency. Furthermore, this project could inspire the development of new applications that would take advantage of the energy redistribution strategies for the design of signal processing systems and techniques.

Type de document: Thèse Thèse
Directeur de mémoire/thèse: Azaña, José
Mots-clés libres: télécommunications
Centre: Centre Énergie Matériaux Télécommunications
Date de dépôt: 22 oct. 2020 17:15
Dernière modification: 22 oct. 2020 17:15
URI: https://espace.inrs.ca/id/eprint/10422

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