We present our recent theoretical and experimental advancements in studying complex multiple nonlinear interactions of coherent solitary wave structures on unstable background -- breathers. We use the focusing one-dimensional nonlinear Schrödinger equation (NLSE) as a theoretical model. First, we describe the nonlinear mutual interactions between a pair of co-propagative breathers called breather molecules. Then with the novel approach of breather interaction management, we adjust the initial positions and phases of several breathers to observe various desired wave states at controllable moments of evolution. Our experiments carried out on a light wave platform with a nearly conservative optical fiber system accurately reproduce the predicted dynamics. In addition, we consider generalizations of the scalar breathers theory to the vector two-component NLSE describing polarized light and show examples of resonance vector breathers transformations.

We deploy a neural network to predict the spectro-temporal evolution of simple sinusoidal temporal modulations upon propagation in a nonlinear dispersive fibre. Thanks to the speed of the neural network, we can efficiently scan the input parameter space for the generation of on-demand frequency combs or the occurrence of substantial spectral/temporal focusing.

A nonlinear interaction of waves in a dispersive medium manifests itself in a four-wave mixing process that can be described as an evolution of waves’ parameters on a phase plane in a form of closed orbits. Here we propose a method to control these trajectories and to switch from one state to another in an optimal manner by implementing an abrupt change of the average power. The method is confirmed experimentally by the reconstruction of a fundamental four-wave mixing dynamics in an idealized model using iterative propagation in a short segment of fiber.

We present in this work a study of 4-field symmetry breakings in two photonic molecule structures consisting of two identical microresonators with distinct coupling arrangements. Mediated by the Kerr-interaction, the systems also display different 2-field symmetry breakings, periodic switching and chaos. The wide range of nonlinear optical dynamics makes the system ideal for all-optical switching, optical memories, telecommunication systems, polarization controllers and integrated photonic sensors.

We have implemented of a light pulse atom interferometer based on the diffraction of free-falling atoms of Rubidium by a picosecond frequency-comb laser. We have studied the impact of the pulses' length as well as of the interrogation time on the contrast of the fringes. Our data are well reproduce by a theoretical model based on the effective coupling which depend on the overlap between the pulses and the atoms. This technique, which we demonstrated in the visible spectrum on Rb atoms, paves the way for extending light-pulse interferometry to other spectral regions (deep-UV to X-UV) and therefore to new species, since one can benefit from the high peak intensity of the ultrashort pulses which makes nonlinear frequency conversion in crystals and gas targets more efficient.

This study investigates the use of Zinc Telluride (ZnTe) as a second-order nonlinear coating to enhance THz wave generation in silica nanofibers. Numerical simulations show that ZnTe coatings can significantly improve THz wave generation efficiency due to their large second-order nonlinear susceptibility and high transparency in the THz frequency range. Specifically, we observe a 2000-fold increase in THz wave generation efficiency with a 100nm thickness ZnTe coating compared to an uncoated silica nanofiber.