Light propagation in confined photonic structures: modeling and experiments

This thesis explored fundamental concepts of linear optics focusing on the modal interaction within waveguide/microresonator systems. In addition, it investigated a nonlinear process of stimulated degenerate four-wave mixing in a channel waveguide exploiting the analogy between photons and cold boson atoms. The backscattering phenomenon due to the surface wall roughness of a microresonator is addressed by adding to the usual conservative (Hermitian) coupling coefficient, a dissipative (non-Hermitian) term. This allows explaining the experimental measurements of a multimodal microresonator, which exhibits an asymmetrical resonance splitting characterized by a difference in the peak depths of the transmission spectra. It is shown theoretically, numerically and experimentally that the stochastic nature of the roughness along with the inter-modal dissipative coupling could give rise to a different exchange of energy between the co-propagating and the counter-propagating mode. The unbalanced exchange of energy between the two modes with opposite angular momenta can generate a different reflection by swapping the injection of the light between the input and the output ports. This effect lies at the heart of the realization of an unidirectional reflection device and it finds an explanation in the physics of the exceptional points. The realization of an optical setup based on a Mach-Zehnder interferometer, which exploits some particular techniques of data acquisition, allows obtaining a full knowledge of the complex electric field of a propagating mode. In this way, the spectrum of a wedge microresonator vertically coupled to a bus waveguide is explained using analysis methods based on parametric phasors and inverse complex representations. In addition, the energy exchange between the co-propagating and counter-propagating modes is studied from a temporal point of view by extrapolating a simple model based on the Green function. In particular, it is discussed the analytical temporal response of a microring resonator excited through a bus waveguide by an optical rectangular pulse. Here, it is shown theoretically and experimentally, how the temporal response leads to the characterization of the coupling regime simply from the knowledge of the electric field intensity. In this thesis, the isomorphism between the Schroedinger’s equation and the Helmholtz wave equation is analyzed in the nonlinear case. Considering a bulk nonlinear medium of the Kerr type, the complex amplitude of the optical field is a slowly varying function of space and time, which satisfies a nonlinear Schroedinger equation. The well-known nonlinear optical phenomenon of stimulated degenerate four wave mixing is reformulated in the language of the Bogoliubov theory. This parallelism between photons and cold atoms allows showing that the phase of the signal assumes a peculiar sound-like dispersion under proper assumptions.