acase@tulane.edu / I review my three papers on ray stretching statistics, hot spot formation, and universality in motion through weak random media. In the first paper, we study the connection between stretching exponents and ray densities in weak ray scattering through a random medium. The stretching exponent is a quantitative measure that describes the degree of exponential convergence or divergence among nearby ray trajectories. In the context of non-relativistic particle motion through a correlated random potential, we show how particle densities are strongly related to the stretching exponents, where the `hot spots' in the intensity profile correspond to minima in the stretching exponents. This strong connection is expected to be valid for different random potential distributions, and is also expected to apply to other physical contexts, such as deep ocean waves. The surprising minimum in the average stretching exponent is of great interest due to the associated appearance of the first generation of hot spots, and a detailed discussion will be found in the third paper. In the second paper, we study the stretching statistics of weak ray scattering in various physical contexts and for different types of correlated disorder. The stretching exponent is mathematically linked to the monodromy matrix that evolves the phase space vector over time. From this point of view, we demonstrate analytically and numerically that the stretching statistics along the forward direction follow universal scaling relationships for different dispersion relations and in disorders of differing correlation structures. Predictions about the location of first caustics can be made using the universal evolution pattern of stretching exponents. Furthermore, we observe that the distribution of stretching exponents in 2D ray dynamics with small angular spread is equivalent to the same distribution in a simple 1D kicked model, which allows us to further explore the relation between stretching statistics and the form of the disorder. Finally, the third paper focuses on the 1D kicked model with stretching statistics that resemble 2D small-angle ray scattering. While the long time behavior of the stretching exponent displays a simple linear growth, the behavior on the scale of the Lyapunov time is mathematically nontrivial. From an analysis of the evolving monodromy matrices, we demonstrate how the stretching exponent depends on the statistics of the second derivative of the random disorder, especially the mean and standard deviation. Furthermore, the maximal Lyapunov exponent or the Lyapunov length can be expressed as nontrivial functions of the mean and standard deviation of the kicks. Lastly, we show that the higher moments of the second derivative of the disorder have small or negligible effect on the evolution of the stretching exponents or the maximal Lyapunov exponents. / 1 / SicongChen

O estudo de caminhadas aleatórias em meios desordenados e um assunto bastante explorado e pode modelar uma grande variedade de problemas, como por exemplo, problemas de transporte (difusão). O estudo de caminhadas determinísticas em meios desordenados é um assunto pouco explorado. Em uma paisagem composta de N sítios distribuídos aleatoriamente no espaço, um caminhante ("turista") visita estes sítios seguindo a seguinte regra determinística: ir para o sítio vizinho mais próximo que não tenha sido visitado nos últimos passos. De cada sítio inicial, a trajetória obtida com esta dinâmica determinística apresenta inicialmente um tempo de transiente t, onde novos sítios são visitados, e no final um atrator de período p, onde os mesmos sítios são sempre revisitados. Apesar da simplicidade do modelo, a dinâmica e complexa e os resultados não são triviais. Para dimensionalidades d = 2, a distribuição de atratores de período p, obtida numericamente, pode ser descrita por uma lei de potência com um corte exponencial. Os modelos de ligações aleatórias simétricas (que representa o limite de alta dimensionalidade d = 1 do modelo proposto) e assimétricas indicam que o corte exponencial se torna menos importante à medida que N aumenta. O expoente da lei de potência independe da memória tau, sendo portanto uma distribuição robusta. A dinâmica do turista pode ser aplicada a problemas mais abstratos, onde apenas relações de ordem entre vizinhos são dados. O estudo (por amostragem) da estrutura de um dicionário de sinônimos e um exemplo que foi considerado. Mostrou-se que as palavras podem ser embebidas em um espaço Euclidiano de baixa dimensionalidade.Este resultado concorda com um recente estudo exaustivo realizado e questiona o modelo de análise semântica latente. Com a finalidade de entender a transição entre uma caminhada determinística e uma caminhada aleatória, generalizou-se o problema com memória nula designando uma distribuição de probabilidades para o turista visitar os diversos sítios. Esta distribuição e parametrizada por uma variável externa T (temperatura) de modo que para T = 0 têm-se a caminhada do turista como caso limite e para T tendendo para infinito todos os sítios são visitados com igual probabilidade. Resultados analíticos (d = 1) e numéricos mostram a existência de uma região bem delimitada de transição entre os regimes não-ergódico (baixa temperatura) e ergódico (alta temperatura). Uma analogia é estabelecida com o modelo de vidros de Bouchaud. A eficiência da caminhada com relação aos novos sítios visitados, foi estudada e ela e máxima na borda da aleatoriedade, ou seja, ao redor da temperatura de transição. / The study of random walks in disordered media is one well-developed subject and it can model a great variety of problems, for instance, problems of transport (diffusion). The study of deterministic walks in disordered media is a subject not too explored. In a landscape composed of N sites randomly distributed in of, a walker ("tourist") visits these sites following the deterministic rule: going to the nearest site that has not been visited in the last tau steps. From each initial site, the trajectory, obtained with this deterministic dynamics, presents initially a time transient t, where new sites are visited, and, in the end, a p-period attractor, where the same sites are always revisited. In spite of the simplicity of the model, the dynamics is complex and the results are not trivial. For dimensionalities d = 2, the distribution of p-period obtained numerically can be described by a power law with an exponential cut. The models of symmetrical random connections (that represents the limit of high dimensionality d = 1 of the proposed model) and asymmetrical random connections indicate that the exponential cut turns out to be less important as N increases. The exponent law of the power law does not depend on the memory tau, being therefore a robust distribution. The tourist dynamics can be applied to more abstract problems, where just relationships of neighbor order are given. The study (by sampling) of the structure of a dictionary of synonyms has been considered. It has been shown that the words can be embedded in an Euclidean space of low dimensionality. This result agrees with a recent exhaustive study accomplished and it challenges the model of latent semantic analysis. With the purpose of understanding the transition between a deterministic and a random walk a generalization of the problem, with null memory has been performed by designating a distribution of probabilities for the tourist to visit the several sites. This distribution has the external variable T (temperature) as a parameter so that, when T = 0 it has the tourist walk as a limiting case and for T tending to infinity all of the sites are visited ith equal probability. Analytical numerical results (d = 1) show the existence of well delimited transition between non-ergodic (low temperature) and ergodic (high temperature) regime. An analogy is established Bouchaud glass model. The walk efficiency, regarding the new visited sites to trajectory length, has been studied and it is maximum at the edge of stochasticity, in other words, around the temperature of transition.

O estudo de caminhadas aleatórias em meios desordenados e um assunto bastante explorado e pode modelar uma grande variedade de problemas, como por exemplo, problemas de transporte (difusão). O estudo de caminhadas determinísticas em meios desordenados é um assunto pouco explorado. Em uma paisagem composta de N sítios distribuídos aleatoriamente no espaço, um caminhante ("turista") visita estes sítios seguindo a seguinte regra determinística: ir para o sítio vizinho mais próximo que não tenha sido visitado nos últimos passos. De cada sítio inicial, a trajetória obtida com esta dinâmica determinística apresenta inicialmente um tempo de transiente t, onde novos sítios são visitados, e no final um atrator de período p, onde os mesmos sítios são sempre revisitados. Apesar da simplicidade do modelo, a dinâmica e complexa e os resultados não são triviais. Para dimensionalidades d = 2, a distribuição de atratores de período p, obtida numericamente, pode ser descrita por uma lei de potência com um corte exponencial. Os modelos de ligações aleatórias simétricas (que representa o limite de alta dimensionalidade d = 1 do modelo proposto) e assimétricas indicam que o corte exponencial se torna menos importante à medida que N aumenta. O expoente da lei de potência independe da memória tau, sendo portanto uma distribuição robusta. A dinâmica do turista pode ser aplicada a problemas mais abstratos, onde apenas relações de ordem entre vizinhos são dados. O estudo (por amostragem) da estrutura de um dicionário de sinônimos e um exemplo que foi considerado. Mostrou-se que as palavras podem ser embebidas em um espaço Euclidiano de baixa dimensionalidade.Este resultado concorda com um recente estudo exaustivo realizado e questiona o modelo de análise semântica latente. Com a finalidade de entender a transição entre uma caminhada determinística e uma caminhada aleatória, generalizou-se o problema com memória nula designando uma distribuição de probabilidades para o turista visitar os diversos sítios. Esta distribuição e parametrizada por uma variável externa T (temperatura) de modo que para T = 0 têm-se a caminhada do turista como caso limite e para T tendendo para infinito todos os sítios são visitados com igual probabilidade. Resultados analíticos (d = 1) e numéricos mostram a existência de uma região bem delimitada de transição entre os regimes não-ergódico (baixa temperatura) e ergódico (alta temperatura). Uma analogia é estabelecida com o modelo de vidros de Bouchaud. A eficiência da caminhada com relação aos novos sítios visitados, foi estudada e ela e máxima na borda da aleatoriedade, ou seja, ao redor da temperatura de transição. / The study of random walks in disordered media is one well-developed subject and it can model a great variety of problems, for instance, problems of transport (diffusion). The study of deterministic walks in disordered media is a subject not too explored. In a landscape composed of N sites randomly distributed in of, a walker ("tourist") visits these sites following the deterministic rule: going to the nearest site that has not been visited in the last tau steps. From each initial site, the trajectory, obtained with this deterministic dynamics, presents initially a time transient t, where new sites are visited, and, in the end, a p-period attractor, where the same sites are always revisited. In spite of the simplicity of the model, the dynamics is complex and the results are not trivial. For dimensionalities d = 2, the distribution of p-period obtained numerically can be described by a power law with an exponential cut. The models of symmetrical random connections (that represents the limit of high dimensionality d = 1 of the proposed model) and asymmetrical random connections indicate that the exponential cut turns out to be less important as N increases. The exponent law of the power law does not depend on the memory tau, being therefore a robust distribution. The tourist dynamics can be applied to more abstract problems, where just relationships of neighbor order are given. The study (by sampling) of the structure of a dictionary of synonyms has been considered. It has been shown that the words can be embedded in an Euclidean space of low dimensionality. This result agrees with a recent exhaustive study accomplished and it challenges the model of latent semantic analysis. With the purpose of understanding the transition between a deterministic and a random walk a generalization of the problem, with null memory has been performed by designating a distribution of probabilities for the tourist to visit the several sites. This distribution has the external variable T (temperature) as a parameter so that, when T = 0 it has the tourist walk as a limiting case and for T tending to infinity all of the sites are visited ith equal probability. Analytical numerical results (d = 1) show the existence of well delimited transition between non-ergodic (low temperature) and ergodic (high temperature) regime. An analogy is established Bouchaud glass model. The walk efficiency, regarding the new visited sites to trajectory length, has been studied and it is maximum at the edge of stochasticity, in other words, around the temperature of transition.

Un défi actuel dans le domaine de l'optique est de mieux comprendre les effets de champ proches optiques des systèmes et de pouvoir agir dessus. C'est dans ce contexte que j'explore tout au long de cette thèse ces notions appliquées aux milieux 3D diélectriques désordonnés et aux films désordonnés métal-diélectriques. Pour les milieux 3D, nous avons choisi une approche par un montage de microscopie de champ proche pour faire la mesure du champ proche optique. Nous avons pour cela dû faire un travail en amont sur la préparation des échantillons pour éviter les artefacts de mesure. Ces mesures ont révélés des structures intéressantes. Nous avons ensuite étudié les modes optiques sur les films métal-diélectriques et montré qu'il existe des modes étendus pour certaine valeurs de la faction surfacique de métal déposée. Nous avons quantifié leur extension par la mesure de la longueur d'interaction et mesuré des valeurs de l'ordre de la dizaine de microns, suffisant pour être contrôlé depuis le champ lointain. Ces mesures ont ouvert la voie au contrôle du front d'onde du faisceau incident dans l'objectif de la focalisation en champ proche de la lumière. Ceci a pu être réalisé grâce à l'utilisation d'un modulateur spatial de lumière pour le contrôle du front d'onde et à un signal non-linéaire de luminescence à deux photons pour la mesure du champ proche optique. Nous obtenons la focalisation en champ proche de l'énergie d'un facteur supérieur à dix. Enfin, la technique de microscopie de champ proche a pu être implémentée et couplée au contrôle de front d'onde et une première optimisation a pu être obtenue. Cela reste néanmoins un travail préliminaire. / One important challenge to address in the optical field is a better understanding of the optical near field of systems and how we can interact with them from the far-field. It is in this regard that I studied and controlled of the near field of both 3D disordered dielectric media and metal-dielectric disordered films. For 3D media, we used a near-field microscope to measure the optical field on their surface. To reach a free-artefact measure, we had to carefully prepare the sample by minimising the rugosity. In a second part, we studied optical modes on metal-dielectric films et we showed that it exists extended modes for some specific values of metal filling fraction of the sample. Extension of the modes has been quantified by measuring the interaction length and has been found in the order of 10 $\mu$m, enough to allow a far field control of the modes. These measurements opened the way for wavefront control of the incident beam in order to focus light in the near field of the sample. We use a spatial light modulator to control the incident wavefront and a non-linear signal (two photons luminescence - TPL) for the near-field measurement of the optical field. We could reach focusing of the energy by a factor more than ten. Finally, the SNOM technique has been coupled to the wavefront shaping system and we get preliminary measurements of optimisation in the near-field by this technique.

Les plasmons de surface (SP) sont des excitations mêlant électrons et photons localisées aux surfaceset interfaces métalliques. On peut les voir classiquement comme les modes électromagnétiquespropres d’un ensemble constitué d’un métal et d’un diélectrique. Cette thèse se base sur la capacitéofferte par les techniques de spectroscopie utilisant des électrons rapides disponibles dans un microscopeélectronique à balayage en transmission (STEM), de cartographier, dans une large gammespectrale et avec une résolution spatiale nanométrique, les modes propres SP. Une telle capacitéa été démontrée séparément, durant ces dernières années, par des expériences de spectroscopie depertes d’énergie d’électrons (EELS), qui mesurent l’énergie perdue par des électrons rapides intéragissantavec un échantillon, et de cathodoluminescence (CL), qui mesurent l’énergie réémisepar l’échantillon par l’intermédiaire de photons, toutes deux résolues spatialement. Dans le cas del’EELS, ces résultats expérimentaux sont aujourd’hui interprétables à l’aide d’analyses théoriquesconvaincantes tendant à prouver que la quantité mesurée dans une telle expérience peut être interprétéede façon sûre en terme de modes propres de surface de l’échantillon. Afin d’élargir une telleinterprétation aux techniques de spectroscopies utilisant des électrons rapides en général, j’ai effectuédes expériences combinées d’EELS et de CL résolues spatialement sur une nanoparticle uniquesimple (un nanoprisme d’or). J’ai montré que les résultats offerts par ces deux techniques présententde fortes similitudes mais également de légères différences, ce qui est confirmé par des simulationsnumériques. J’ai étendu l’analyse théorique du signal EELS au signal CL, et ai montré que la CLcartographie, tout comme l’EELS, les modes de surface radiatifs du sytème, mais avec des propriétésspectrales légèrement différentes. Ce travail constitue une preuve de principe clarifiant les quantitésmesurées en EELS et CL sur des systèmes métal-dielectriques. Ces dernières sont démontrées êtrerespectivement des équivalents nanométriques des spectroscopies d’extinction et de diffusion de lalumière. Basé sur cette interprétation, j’ai utilisé l’EELS pour dévoiler les modes propres SP demilieux métalliques aléatoires (dans notre cas, des films semicontinus métalliques avant le seuil depercolation). Ces modes propres constituent une problématique de longue date dans le domainede la nanooptique. J’ai directement identifié ces modes par des mesures et le traitement de leursrésultats. J’ai complètement caractérisé ces modes propres via les variations spatiales de l’intensitéliée à leur champ électrique, une énergie propre et un taux de relaxation. Ce faisant, j’ai montré quela géométrie fractale du milieu, dont la prédominance croit au fur et à mesure que l’on s’approchede la percolation, est responsable de l’existence de modes propres de type aléatoire à basse énergie. / Surface Plasmons (SP) are elementary excitations mixing electrons and photons at metal surfaces,which can be seen in a classical electrodynamics framework as electromagnetic surface eigenmodesof a metal-dielectric system. The present work bases on the ability of mapping SP eigenmodes withnanometric spatial resolution over a broad spectral range using spatially resolved fast electron basedspectroscopies in a Scanning Transmission Electron Microscope (STEM). Such an ability has beenseparately demonstrated during the last few years by many spatially resolved experiments of ElectronEnergy Loss Spectroscopy (EELS), which measures the energy lost by fast electrons interactingwith the sample, and CathodoLuminescence (CL), which measures the energy released by subsequentlyemitted photons. In the case of EELS, the experimental results are today well accountedfor by strong theory elements which tend to show that the quantity measured in an experiment canbe safely interpreted in terms of the surface eigenmodes of the sample. In order to broaden thisinterpretation to fast electron based spectroscopies in general, I have performed combined spatiallyresolved EELS and CL experiments on a simple single nanoparticle (a gold nanoprism). I have shownthat EELS and CL results bear strong similarities but also slight differences, which is confirmed bynumerical simulations. I have extended the theoretical analysis of EELS to CL to show that CLmaps equally well than EELS the radiative surface eigenmodes, yet with slightly different spectralfeatures. This work is a proof of principle clarifiying the quantities measured in EELS and CL,which are shown to be respectively some nanometric equivalent of extinction and scattering spectroscopieswhen applied to metal-dielectric systems. Based on this interpretation, I have applied EELSto reveal the SP eigenmodes of random metallic media (in our case, semicontinuous metal films beforethe percolation threshold). These SP eigenmodes constitute a long standing issue in nanooptics.I have directly identified the eigenmodes from measurements and data processing. I havefully characterized these eigenmodes experimentally through an electric field intensity pattern, aneigenenergy and a relaxation rate. Doing so, I have shown that the fractal geometry of the medium,which grows towards the percolation, induces random-like eigenmodes in the system at low energies.Keywords: Surface plasmons, fast electron based spectroscopies, scanning transmission electronmicroscopy, disordered media

Surface Plasmons (SP) are elementary excitations mixing electrons and photons at metal surfaces,which can be seen in a classical electrodynamics framework as electromagnetic surface eigenmodesof a metal-dielectric system. The present work bases on the ability of mapping SP eigenmodes withnanometric spatial resolution over a broad spectral range using spatially resolved fast electron basedspectroscopies in a Scanning Transmission Electron Microscope (STEM). Such an ability has beenseparately demonstrated during the last few years by many spatially resolved experiments of ElectronEnergy Loss Spectroscopy (EELS), which measures the energy lost by fast electrons interactingwith the sample, and CathodoLuminescence (CL), which measures the energy released by subsequentlyemitted photons. In the case of EELS, the experimental results are today well accountedfor by strong theory elements which tend to show that the quantity measured in an experiment canbe safely interpreted in terms of the surface eigenmodes of the sample. In order to broaden thisinterpretation to fast electron based spectroscopies in general, I have performed combined spatiallyresolved EELS and CL experiments on a simple single nanoparticle (a gold nanoprism). I have shownthat EELS and CL results bear strong similarities but also slight differences, which is confirmed bynumerical simulations. I have extended the theoretical analysis of EELS to CL to show that CLmaps equally well than EELS the radiative surface eigenmodes, yet with slightly different spectralfeatures. This work is a proof of principle clarifiying the quantities measured in EELS and CL,which are shown to be respectively some nanometric equivalent of extinction and scattering spectroscopieswhen applied to metal-dielectric systems. Based on this interpretation, I have applied EELSto reveal the SP eigenmodes of random metallic media (in our case, semicontinuous metal films beforethe percolation threshold). These SP eigenmodes constitute a long standing issue in nanooptics.I have directly identified the eigenmodes from measurements and data processing. I havefully characterized these eigenmodes experimentally through an electric field intensity pattern, aneigenenergy and a relaxation rate. Doing so, I have shown that the fractal geometry of the medium,which grows towards the percolation, induces random-like eigenmodes in the system at low energies.Keywords: Surface plasmons, fast electron based spectroscopies, scanning transmission electronmicroscopy, disordered media

The heterogeneous structure of fractured media can lead to complex spatiotemporal fluid invasion dynamics. It thus brings forward challenging fundamental questions in the context of out-of-equilibrium dynamical systems, but also relevant to many processes of interest. The goal of the Thesis is to study the spatio-temporal dynamics of the oil-air interface between displaced air and invading oil, in imbibition through a model open fracture. The research combines exhaustive experimental work with accurate data analysis based on methods of nonlinear statistical physics. The mean postion of the interface h(t) is studied in capillary rise experiments, giving rise to a new analytical solution for h(t). The fluctuations of the interface in forced-flow experiments are analysed in the context of kinetic roughening, characterizing a super-rough scaling scenario. Finally, the burst-like dynamics is studied by analysing the local and global velocities of the front, which are widely distributed and display complex spatio-temporal correlations. We define local and global avalanches whose sizes and durations are also widely distributed, with cutoffs that diverge with the capillary number. Intermittentcy of the global signal is quantified. The ensemble of results presented in this Thesis supports a very general picture of the nonequilibrium dynamics of slowly-driven fronts in open fractures: the lateral propagation of interfacial fluctuations is controlled by local mass conservation, through the lateral correlation length; and the advancement of the interface in the direction of propagation is controlled by the characteristic extent of the disorder d and by the mean front velocity.

Quand un fluide mouillant visqueux (comme une huile) pénètre un milieu hétérogène tel qu’une fracture, l’interface (entre l’air déplacé et l’huile) développe des corrélations à longue portée menant à une dynamique spatio-temporelle complexe. Dans cette Thèse, nous avons étudié expérimentalement et théoriquement ce processus de transport d’un fluide, appelé imbibition, dans un modèle de fracture ouverte, pertinent dans diverses situations. Notre travail a combiné une étude expérimentale détaillée, avec une analyse précise des données, basées sur des méthodes de physique statistique et non-linéaire. D’abord, la position moyenne de l'interface h(t) est étudiée lors d’expériences de montée capillaire donnant lieu à une nouvelle solution analytique pour h(t). Nous avons ensuite étudié les propriétés d’invariance d’échelle de l’interface et en particulier leur évolution pour des processus d’imbibition forcées, caractérisée par un scénario dit «super-rugueux». Enfin, nous avons étudié et quantifié la dynamique intermittente par avalanches des fronts d’imbibition à partir de l’analyse multi-échelle (spatiales et temporelles) de leurs vitesses. L'ensemble des résultats présentés dans cette Thèse propose une image très générale de la dynamique hors équilibre des fronts d’imbibition se propageant lentement dans des fractures ouvertes. La propagation latérale des fluctuations interfaciales est contrôlée par conservation de la masse locale. L'avancement de l'interface dans la direction de propagation est contrôlé par l’échelle caractéristique du désordre et la vitesse moyenne du front. / The heterogeneous structure of fractured media can lead to complex spatiotemporal fluid invasion dynamics. It thus brings forward challenging fundamental questions in the context of out-of-equilibrium dynamical systems, but also relevant to many processes of interest. The goal of the Thesis is to study the spatio-temporal dynamics of the oil-air interface between displaced air and invading oil, in imbibition through a model open fracture. The research combines exhaustive experimental work with accurate data analysis based on methods of nonlinear statistical physics. The mean postion of the interface h(t) is studied in capillary rise experiments, giving rise to a new analytical solution for h(t). The fluctuations of the interface in forced-flow experiments are analysed in the context of kinetic roughening, characterizing a super-rough scaling scenario. Finally, the burst-like dynamics is studied by analysing the local and global velocities of the front, which are widely distributed and display complex spatio-temporal correlations. We define local and global avalanches whose sizes and durations are also widely distributed, with cutoffs that diverge with the capillary number. Intermittentcy of the global signal is quantified. The ensemble of results presented in this Thesis supports a very general picture of the nonequilibrium dynamics of slowly-driven fronts in open fractures: the lateral propagation of interfacial fluctuations is controlled by local mass conservation, through the lateral correlation length; and the advancement of the interface in the direction of propagation is controlled by the characteristic extent of the disorder d and by the mean front velocity.

Le déplacement cohérent dirigé au sein de troupeaux, d’essaims, de nuées, prend place à toutes les échelles du vivant. En cherchant à rationaliser l’émergence de tels mouvements collectifs, les physiciens ont décrit ces assemblées comme des matériaux actifs. Ces matériaux sont formés de constituants auto-propulsés qui se déplacent spontanément dans une direction commune. Cette thèse expérimentale s’appuie sur la réalisation de troupeaux synthétiques pour explorer les propriétés de la matière active polaire dans des situations défavorables à son auto-organisation : leur dynamique en milieux désordonnés et leur réponse à des perturbations externes. Des rouleurs colloïdaux aux interactions d’alignement sont confinés au sein de dispositifs microfluidiques. Au-delà d’une densité seuil, ils forment un troupeau caractérisé par l’émergence d’un ordre en orientation de longue portée. Ces troupeaux colloïdaux font office de prototypes de la matière active polaire. Nous avons étudié la réponse d’un liquide actif polaire assemblé à partir de rouleurs colloïdaux. Nous avons montré que face à une perturbation longitudinale leur réponse est hystérétique. Nous avons expliqué théoriquement ce comportement non-linéaire et l’avons exploité pour réaliser des oscillateurs microfluidiques autonomes. Nous avons également étudié la dynamique de troupeaux colloïdaux qui se propagent dans des environnements hétérogènes. La présence d’obstacles distribués aléatoirement focalise les troupeaux le long de chemins privilégiés qui forment un réseau épars et tortueux. Augmenter le désordre conduit à la destruction du troupeau. Nous avons démontré que la suppression du mouvement collectif consiste en une transition discontinue, générique à tous les matériaux actifs polaires. / Directed collected motion within herds, swarms and flocks, is a phenomenon that takes place at all scales in living systems. Physicists have rationalized the emergence of such collective behavior. They have described these systems as active materials. These materials are assembled from self-propelled units that spontaneously move in the same direction. By experimentally studying synthetic flocks, this work uncovers some properties of polar active materials in situations that disfavor their self-organization: their dynamics in disordered environments and their response to external perturbations. Colloidal rollers with alignment interactions are confined within microfluidic devices. At high density, they spontaneously form a flock which is characterized by the emergence of orientational long-ranged order. These colloidal flocks are prototypical realizations of polar active matter. We have studied the response of a polar active liquid assembled from colloidal rollers. We have shown that they display a hysteretic response to longitudinal perturbations. We have theoretically accounted for this non-linear behavior. We have used this behavior to realize autonomous microfluidic oscillators. We have also studied the dynamics of colloidal flocks that propagate through heterogeneous environments. Randomly positioned obstacles focalize flocks along favored channels that form a sparse and tortuous network. Increasing disorder leads to the destruction of flocks. We have demonstrated that the suppression of collective motion is a discontinuous transition generic to all polar active materials.

<p>Dipole-dipole interactions are ubiquitous fundamental physical phenomena that govern physical effects such as Casimir Forces, van der Waals forces, collective Lamb shifts, cooperative decay, and resonance energy transfer. These interactions are associated with real and virtual photon exchange between the interacting emitters. Such interactions are crucial in realizing quantum memories, novel super-radiant light sources, and light-harvesting devices. Owing to this, the control and modification of dipole-dipole interactions have been a longstanding theme. The electromagnetic environment plays a crucial role in enhancing the range and strength of the interactions. This work focuses on modifying the nanophotonic environment near interacting emitters to enhance dipole-dipole interactions instead of spontaneous emission. To this end, we focus on engineering the nanophotonic environment to enhance the strength and range of dipole-dipole interactions between an ensemble of emitters. We explore ordered and disordered nanophotonic structures. We experimentally demonstrate long-range dipole-dipole interactions mediated by surface lattice resonances in a periodic plasmonic nanoparticle lattice. Further, the modified electromagnetic environment reduces the apparent dimensionality of the interacting system compared to non-resonant in-homogeneous and homogeneous environments. We also develop a spectral domain inverse design technique for the accelerated discovery of disordered metamaterials with unique spectral features. </p> <p>Further, we explore the novel regimes of light localization at near-zero-index in such disordered media. The disordered near-zero-index medium reveals enhanced localization and near-field chirality. This work paves the way to engineer the electromagnetic nanophotonic environment to realize enhanced long-range dipole-dipole interactions.</p>