Lately, there has been an increasing interest in studying the propagation of electromagnetic waves in periodic dielectric structures (photonic crystals). Like the electron propagation in semiconductors, these structures are represented by band diagrams in which gaps can be found where the electromagnetic propagation is forbidden. Much effort is dedicated to find structures that can prohibit the propagation of light in all directions. This effect could lead to light localization. / Singapore-MIT Alliance (SMA)

Disordered photonics is the study of light in random media. In a disordered photonic medium, multiple scattering of light and coherence, together with the fundamental principle of reciprocity, produce a wide range of interesting phenomena, such as enhanced backscattering and Anderson localization of light. They are also responsible for the existence of modes in these random systems. It is known that analogous processes to Bose-Einstein condensation can occur in classical wave systems, too. Classical condensation has been studied in several contexts in photonics: pulse formation in lasers, mode-locking theory and coherent emission of disordered lasers. All these systems have the common theme of possessing a large ensemble of waves or modes, together with nonlinearity, dispersion or gain. In this work, we study light condensation and its connection with light localization in a disordered, passive dielectric medium. We develop a theory for the modes inside the disordered resonator, which combines the Feshbach projection technique with spin-glass theory and statistical physics. In particular, starting from the Maxwell’s equations, we map the system to a spherical p-spin model with p = 2. The spins are replaced by modes and the temperature is related to the fluctuations in the environment. We study the equilibrium thermodynamics of the system in a general framework and show that two distinct phases exist: a paramagnetic phase, where all the modes are randomly oscillating and a condensed phase, where the energy condensates on a single mode. The thermodynamic quantities can be explicitly interpreted and can also be computed from the disorder-averaged time domain correlation function. We launch an ab initio simulation campaign using our own code and the Shaheen supercomputer to test the theoretical predictions. We construct photonic samples of varying disorder and find computationally relevant ways to obtain the thermodynamic quantities. We observe the phase transition and also link the condensation process to the localization. Our research could be a step towards the ultimate goal: to build a ”photonic mode condenser”, which transforms a broadband spectrum to a narrow one - ideally, to a single mode - with minimal energy loss, aided solely by disorder.

<p>The objective of this dissertation work is to examine light localization in semiconductors provided by a complete photonic bandgap via three-dimensional (3D) woodpile photonic crystals. A 3D photonic crystal is a periodic nanostructure that demonstrates omni-directional Bragg reflection. These materials are anticipated to become a powerful tool for engineering light propagation and localization within subwavelength scales due to their complete photonic bandgap and the distinctive dispersion relation. </p><p>The approach of realizing microcavities in this dissertation is to combine multi-directional etching fabrication methods with mode gap design. Modulation of unit cell size along a line-defect 3D waveguide could bring a guiding mode into the mode gap region of the waveguide and form a microcavity with a resonance inside the complete photonic bandgap. The designed microcavities could be fabricated by multi-directional etching methods because they can structurally be decomposed into two sets of connected and straight dielectric rods. </p><p>Ultra-high-quality factor microcavities and sub-wavelength-scale waveguides are designed without introduction of local disorders. Monopole, dipole, and quadrupole resonant modes are demonstrated with a small modal volume. The smallest modal volumes obtained are 0.36 cubic half-wavelengths for a resonance field in vacuum, and 2.88 cubic half-wavelengths for a resonance field in a dielectric. Direct metal contacts with the microcavities do not significantly deteriorate the quality factors because the resonant fields are located inside the microcavities. Single-mode woodpile waveguides are also designed in both lateral and vertical propagation directions. </p><p>The multi-directional etching method is a simple approach to the fabrication of woodpile photonic crystals and designed optical components with a variety of crystal orientations and surfaces, including (110), (001), (100), and (010) planes. An arbitrary surface plane (mn0) is obtained with this method, where m and n are integers. Moreover, it can also produce large area woodpile photonic crystals with high precision in silicon and GaAs materials.</p><p>These optical components in woodpile photonic crystals would be building blocks of high-density, low-loss 3D integrated optics, cavity quantum electrodynamics (QED), nonlinear optics, and enable the realization of current-injection optical devices.</p> / Dissertation

O interesse na pesquisa de Lasers randômicos, meios dispersivos com alto ganho, tem crescido nos últimos anos em virtude das novas possibilidades advindas ao se trabalhar com estes sistemas, como emissões em bandas com baixo ganho, bicromaticidade, localização da luz em meios difusos e sistemas ópticos mais compactos. Nesse trabalho serão discutidos temas como espalhamento da luz por partículas, intensidade de retroespalhamento, ganho em meios desordenados e as transições energéticas do neodímio, correlacionando as emissões características obtidas nos experimentos com a teoria. Quanto aos resultados será apresentado a primeira observação de laser randômico com nanopó de Nd:YVO4 através de análise do comportamento da emissão espectral e temporal oriunda da transição 4F3/24I11/2 (1064 nm). Os resultados apresentam outra forma de analisar a cinética temporal da emissão de laser randômico, permitindo uma separação da fração de emissão estimulada e espontânea e comparação desse resultado com o estreitamento sutil da largura de linha, típico de lasers randômicos. As conversões ascendentes e saturação de ETU (conversão ascendente por transferência de energia) serão analisadas na mesma amostra, sendo todos os ajustes provenientes da literatura e de fundamental interesse, principalmente por se tratarem de um mecanismo de perda em lasers operando na região do infravermelho. Por fim, a emissão característica será avaliada pela técnica CBS (retroespalhamento coerente) para determinação da coerência do laser emitido e localização da luz neste meio difuso, com os resultados comparados aos da simulação. / In the past few years, the interest in random lasers, which refer to lasing in disordered media where strong multiple scattering plays a constructive role instead of being only a loss factor, have received considerable attention due to its unique properties and its potential applications, such as emission at new, extremely low gain lines, simultaneous emission of several very different wavelengths at the same time, strong light localization and miniaturization. Single and multiple particle light scattering, backscattering intensity, light diffusion with gain and the energy level diagram of Neodymium will be presented in this current work, alongside with a parallel from the typical emission lines obtained experimentally with theory. The demonstration of random laser action in Nd:YVO4 nanopowder, by analyzing the spectral and temporal behavior from the 4F3/24I11/2 (1064 nm) transition is presented. A method that analyzes the decay kinetics after long-pulse excitation is used to determine the laser characteristics, allowing measuring the fractional contribution of spontaneous and stimulated emission in the samples backscattering cone, with is in agreement to the smoothing linewidth narrowing as a function of pump power typical from random lasers. Also the visible emission along a method to determine quantitatively the ETU (energy-transfer upconversion) rate is presented, which is particularly interesting, as is a mechanism that introduces a loss channel for devices emitting in the infrared region. At last, the coherent laser emission and light localization will be evaluated by using the CBS (coherent backscattering) technique in this diffusive media, in which the results are compared with simulation.

O interesse na pesquisa de Lasers randômicos, meios dispersivos com alto ganho, tem crescido nos últimos anos em virtude das novas possibilidades advindas ao se trabalhar com estes sistemas, como emissões em bandas com baixo ganho, bicromaticidade, localização da luz em meios difusos e sistemas ópticos mais compactos. Nesse trabalho serão discutidos temas como espalhamento da luz por partículas, intensidade de retroespalhamento, ganho em meios desordenados e as transições energéticas do neodímio, correlacionando as emissões características obtidas nos experimentos com a teoria. Quanto aos resultados será apresentado a primeira observação de laser randômico com nanopó de Nd:YVO4 através de análise do comportamento da emissão espectral e temporal oriunda da transição 4F3/24I11/2 (1064 nm). Os resultados apresentam outra forma de analisar a cinética temporal da emissão de laser randômico, permitindo uma separação da fração de emissão estimulada e espontânea e comparação desse resultado com o estreitamento sutil da largura de linha, típico de lasers randômicos. As conversões ascendentes e saturação de ETU (conversão ascendente por transferência de energia) serão analisadas na mesma amostra, sendo todos os ajustes provenientes da literatura e de fundamental interesse, principalmente por se tratarem de um mecanismo de perda em lasers operando na região do infravermelho. Por fim, a emissão característica será avaliada pela técnica CBS (retroespalhamento coerente) para determinação da coerência do laser emitido e localização da luz neste meio difuso, com os resultados comparados aos da simulação. / In the past few years, the interest in random lasers, which refer to lasing in disordered media where strong multiple scattering plays a constructive role instead of being only a loss factor, have received considerable attention due to its unique properties and its potential applications, such as emission at new, extremely low gain lines, simultaneous emission of several very different wavelengths at the same time, strong light localization and miniaturization. Single and multiple particle light scattering, backscattering intensity, light diffusion with gain and the energy level diagram of Neodymium will be presented in this current work, alongside with a parallel from the typical emission lines obtained experimentally with theory. The demonstration of random laser action in Nd:YVO4 nanopowder, by analyzing the spectral and temporal behavior from the 4F3/24I11/2 (1064 nm) transition is presented. A method that analyzes the decay kinetics after long-pulse excitation is used to determine the laser characteristics, allowing measuring the fractional contribution of spontaneous and stimulated emission in the samples backscattering cone, with is in agreement to the smoothing linewidth narrowing as a function of pump power typical from random lasers. Also the visible emission along a method to determine quantitatively the ETU (energy-transfer upconversion) rate is presented, which is particularly interesting, as is a mechanism that introduces a loss channel for devices emitting in the infrared region. At last, the coherent laser emission and light localization will be evaluated by using the CBS (coherent backscattering) technique in this diffusive media, in which the results are compared with simulation.

Dans cette thèse, nous avons étudié l'impact considérable de désordre aléatoire sur le transport de la lumière lente dans les guides à cristaux photoniques 1D, c'est-à-dire la localisation de la lumière. Les mesures en champ proche, les simulations statistiques et le modèle théorique révèlent l'existence d'une limite inférieure de l’extension spatiale des modes localisés. Nous avons également présenté que le niveau de désordre et l’extension spatiale de mode localisé individuelle sont liés par la masse effective de photons plutôt que la vitesse de groupe considérant en général.Deuxièmement, les systèmes hybrides d'atomes froids et des guides à cristaux photoniques ont été reconnus comme un approche prometteuse pour l'ingénierie grande interaction lumière-matière au niveau des atomes et des photons individuels. Dans cette thèse, nous avons étudié la physique, à savoir le transport de la lumière dans des guides de nanophotonique périodiques couplées à des atomes à deux niveaux. Notre expression semi-analytique développée est générale et peut rapidement caractériser le couplage entre les atomes froids et les photons guidées. Pour surmonter les difficultés techniques considérables existent dans les systèmes hybrides atomique et photonique, nous avons conçu un guide nanophotonique qui supporte un mode de Bloch lente guidée avec grande queue évanescente dans l'espace libre pour les atomes froids de piégeage. Pour adapter précisément la région de fréquence de la lumière lente du mode guidé à la ligne de transition atomique, nous avons conçu la bande photonique et de la courbe de dispersion du mode guidé afin que la force de l'interaction est robuste contre imprévisible fabrication imperfection. / In this thesis, we firstly investigated the striking influence of random disorder on light transport near band edges in one dimensional photonic crystal wave guides, i.e. light localization. Near-field measurements, statistical simulations and theoretical model revealed the existence of a lower bound for the spatial extent of localized modes. We also showed that the disorder level and the spatial extent of individual localized mode is linked by the photon effective mass rather than the generally considered group velocity. Secondly, hybrid cold atoms and photonic crystal wave guides system have been recognized as a promising paradigm for engineering large light-matter interaction at single atoms and photons level. In this thesis, we studied the basic physics, i.e. light transport in periodic nanophotonic wave guides coupled to two-level atoms. Our developed general semi-analytical expression can quickly characterize the coupling between cold atoms and guided photons. Aim to overcome the significant technical challenges existed for developing hybrid atom-photonic systems, we designed a nanophotonic waveguide, which supports a slow guided Bloch mode with large evanescent tail in free space for cold atoms trapping (release the limitation imposed by Casmir Polder force and technical challenge of nanoscale manipulation of cold atoms). To match precisely the slow light region of the guided mode to the atomic transition line, we carefully engineered the photonic band and the dispersion curve (i.e.flatness) of the guided mode so that the interaction strength is robust against unpredictable fabrication imperfection.

L'augmentation de l'interaction lumière-matière aux échelles micro et nanométriques est un des fers de lance de la nanophotonique. En effet, le contrôle de la répartition spatiale de la lumière grâce à l'interaction résonante entre nanostructures et ondes électromagnétiques a conduit aux développements de nombreuses applications dans des domaines variés tels que les télécommunications,la spectroscopie et la détection d'objets. Le ralentissement de la lumière, sujet de la thèse, obtenue grâces à l'interférence d'ondes contre-propageantes dans des milieux périodiques ou le confinement sub-longueur d'onde dans des guides d'ondes plasmoniques, est associé à une compression des pulses lumineux et une forte augmentation du champ électrique, deux phénomènes clés pour la miniaturisation de composées optiques et l'augmentation de l'interaction lumière matière. / Enhancing light-matter interactions at micro and nanoscales is one of the spearheads of nanophotonics. Indeed, the control of the field distribution due to the resonant interaction of nanostructures with electromagnetic waves has prompted the development of numerous optical components for many applications in telecommunication, spectroscopy or sensing. A promising approach lies in the control of light speed in nanostructures. Light slowdown, obtained by wave interferences in periodic structures or subwavelength confinement in plasmonic waveguides, is associated to pulse compressions and large field enhancements,which are envisioned as key processes for the miniaturization of optical devices and the enhancement of light-matter interactions.The thesis studies both fundamental aspects and possible applications related to slow light in photonic and plasmonic nanostructures. In particular, we study the impact of periodic system sizes on the group velocity reduction and propose a novelfamily of resonators that implement slow light on very small spatial scales. We then investigate the role of fabrication disorder in slow periodic waveguides on light localization and demonstrate how modal properties influence the confinement of localized modes. Also we propose a new hollow-core photonic crystal waveguide that provides efficient and remote couplings between the waveguide and atoms thatare trapped away from it. Finally we demonstrate the important role played by slow plasmons on the emission of quantum emitters placed in nanogap plasmonic antennas and explain how large radiation efficiency can be achieved by overcoming quenching in the metal. Additionally, one part of the thesis is devoted to thederivation of a novel modal method to accurately describe the dynamics of plasmonic resonators under short pulse illumination.