This Thesis is devoted to the study of topological phases of matter in optical platforms, focusing on non-Hermitian systems with gain and losses involving nonreciprocal elements, and fractional quantum Hall liquids where strong interactions play a central role.In the first part we investigated nonlinear Taiji micro-ring resonators in passive and active silicon photonics setups. Such resonators establish a unidirectional coupling between the two whispering-gallery modes circulating in their perimeter. We started by demonstrating that a single nonlinear Taiji resonator coupled to a bus waveguide breaks Lorentz reciprocity. When a saturable gain is added to a single Taiji resonator, a sufficiently strong unidirectional coupling rules out the possibility of lasing in one of the whispering-gallery modes with independence of the type of optical nonlinearity and gain saturation displayed by the material. This can be regarded as a dynamical time-reversal symmetry breaking. This effect is further enhanced by an optical Kerr nonlinearity. We showed that both ring and Taiji resonators can work as optical isolators over a broad frequency band in realistic operating conditions. Our proposal relies on the presence of a strong pump in a single direction: as a consequence four-wave mixing can only couple the pump with small intensity signals propagating in the same direction. The resulting nonreciprocal devices circumvent the restrictions imposed by dynamic reciprocity. We then studied two-dimensional arrays of ring and Taiji resonators realizing quantum spin-Hall topological insulator lasers. The strong unidirectional coupling present in Taiji resonator lattices promotes lasing with a well-defined chirality while considerably improving the slope efficiency and reducing the lasing threshold. Finally, we demonstrated that lasing in a single helical mode can be obtained in quantum spin-Hall lasers of Taiji resonators by exploiting the optical nonlinearity of the material. In the second part of this Thesis we dived into more speculative waters and explored fractional quantum Hall liquids of cold atoms and photons. We proposed strategies to experimentally access the fractional charge and anyonic statistics of the quasihole excitations arising in the bulk of such systems. Heavy impurities introduced inside a fractional quantum Hall droplet will bind quasiholes, forming composite objects that we label as anyonic molecules. Restricting ourselves to molecules formed by one quasihole and a single impurity, we find that the bound quasihole gives a finite contribution to the impurity mass, that we are able to ascertain by considering the first-order correction to the Born-Oppenheimer approximation. The effective charge and statistical parameter of the molecule are given by the sum of those of the impurity and the quasihole, respectively. While the mass and charge of such objects can be directly assessed by imaging the cyclotron orbit described by a single molecule, the anyonic statistics manifest as a rigid shift of the interference fringes in the differential scattering cross section describing a collision between two molecules.

Les isolateurs optiques sont des composants non-réciproques très important dans les systèmes de télécommunication optique. Actuellement les composants commercialisés sont tous discrets, à cause de la difficulté d’intégration des matériaux magnéto-optiques avec les technologies de l’optique intégrée. L’objectif de ma thèse était d’ouvrir une nouvelle voie technologique pour aboutir à une telle intégration. Pour cela nous avons développé une approche basée sur l’utilisation d’un matériau magnéto-optique composite complètement compatible avec la technologie d’échange d’ions sur verre. Ce matériau est élaboré par la voie sol-gel organique-inorganique et dopé par des nanoparticules magnétiques de ferrite de Cobalt (CoFe204). Il a montré des potentialités très prometteuses, illustré par une rotation Faraday spécifique de 420°/cm (@1550nm). Ce composite est déposé par la méthode dip-coating sur un guide fait par échange ionique d’Ar+/Na+, avec des extrémités enterrées par la méthode d’enterrage sélective pour faciliter le couplage-découplage de la lumière dans la structure hybride. Enfin, un traitement thermique (<100°C) et un traitement UV compatibles avec le procédé d’échange d’ions sur verre sont appliqués sur le dispositif pour finaliser la couche magnéto-optique. La caractérisation optique de notre dispositif a montré une bonne distribution de la lumière entre la couche magnéto-optique et le guide fait par échange d’ions (un bon confinement latéral). De plus, l’application d’un champ magnétique longitudinal au composant a permis de démontrer une valeur de conversion de mode TE-TM qui correspond bien à la quantité de la lumière confinée dans la couche magnéto-optique et la biréfringence modale de la structure. Donc, le but principal de la thèse est atteint, et ces résultats montrent la faisabilité d’un convertisseur de mode TE-TM compatible avec la technologie d’optique intégrée sur verre / Optical isolators are essential nonreciprocal devices used in optical communication systems. Currently, these components are commercially available but only in bulk form, due to the difficulties to embed magneto-optical materials with integrated classical technologies. To overcome this problem, our group has developed a new approach based on composite magneto-optical matrix that is fully compatible with ion-exchanged glass waveguide technology. This material is developed by organic inorganic sol-gel process and doped by magnetic nanoparticles (CoFe2O4). Such a magneto-optical composite matrix has shown promising potentialities illustrated by a specific Faraday rotation of 420°/cm (@1550nm). Using dip-coating technique, a composite layer was coated on a glass substrate containing straight channel waveguide made by a silver/sodium ion exchange. The extremities of the guides were previously buried using selective buried method in order to facilitate coupling-decoupling of light in hybrid structure. Last, a soft annealing (<100°C) and UV treatment, both compatible with the ion-exchanged process, have been implemented to finalize the magneto-optical film. Optical characterization demonstrated a good distribution of light between the magneto-optical thin film and the ion-exchanged waveguide (good lateral confinement). Furthermore TE to TM mode conversion has been observed when a longitudinal magnetic field is applied to the device. The amount of this conversion is in good agreement with the distribution of light between the layer and the guide obtained by numerical calculations, and the modal birefringence of the structure. So, the aim of my thesis is achieved and the results demonstrate the feasibility of TE to TM mode converter fully compatible with glass integrated optics