This project aims to study the steering of light in different nonlinear systems with internal resonances. Nowadays such systems attract a great deal of attention because modern technologies allow to produce devices where internal resonant interactions between light and material excitations result in huge optical nonlinearities, providing a rich plethora of nonlinear effects at relatively low power. These huge nonlinearities and the flexibility of physical parameters make such devices very attractive for different practical applications, including guidance of light, information processing, and generation of new frequencies. In
addition, such systems constitute laboratories to study fundamental nonlinear phenomena.
This project addresses several kinds of physical systems and devices. We consider hollow-core photonic crystal fibers filled with gases of multi-level atoms whose resonant frequencies match the frequency band guided through the fiber. In these systems, the matter-light interactions are not only strong because of their resonant nature, but are also easily manageable through the control of the coupling field on the other hand. Systematic investigation of the nonlinear dynamics will be undertook, starting from the study of the propagation of the continuous radiation in simple geometries, but also looking into the dynamics of short pulses, to the formation of optical solitons, and to their mutual interactions in more sophisticated geometries, like coupled waveguides, networks of waveguides, couplers, etc.. The formation and stability of solitons, representing coupled states of light and matter, i.e. a kind of polaritons, is expected to be strongly affected by the waveguide characteristics and by the material dispersion of the media. Hence, it will be explored how the propagation of short pulses can be steered by the slowly varying quasi-continuous waves and by additional short pulses. Effective models describing linear and nonlinear effects by taking into account the quantum mechanical description of the interactions will be developed, giving special attention to the impact in the propagation of solitons of dissipation, particularly dissipation due to spontaneous emission from the excited states of the multilevel atoms, material losses and imperfect guidance of the light. When dissipation is weak enough we can speak about quasi-solitons propagating at long distances, whereas in the quantum regime, when dissipation is strong enough, we can expect manifestations of the Zeno effect. We also
investigate how the dissipation affects not only the maximum propagation distance of the solitons, but also their shapes and
stability. Technologically it is possible to manufacture a multi-core fiber filled with active gases. For these fibers, it is important to study the interaction between the pulses propagating in the neighbouring cores and find out the conditions of effective energy transference between modes. We plan to address this problem analytically and by extensive numerical simulations. We also investigate semiconductor microstructured systems, which are another important kind of the waveguiding systems produced on semiconductor chips. The main advantages of these systems are their small sizes and the possibility to pump them by external continuous sources of the light. Cavity solitons can survive in these systems until the pump is switched off. The bright and dark solitons can be controlled by the pump and by weak control signals. This type of systems can be used as optical memories and for information processing, as well as, on the generation of new frequencies. We also consider systems consisting of a semiconductor thin film which serve as planar waveguide for the light and can be pumped by a coherent light due of imperfect guidance. The resonant nonlinearity arises from stimulating excitons with resonant frequency coinciding with the cut-off frequency of the planar waveguide. Consequently, it is possible to excite quasiparticles
with very low group velocities, commonly known as polaritons and resulting from the resonant coupling of light and
mater excitations, which provides very strong nonlinearities. This allows the formation of resting or slow moving localized
optical structures at low pumping powers.
Meta-material waveguiding systems consisting of weakly nonlinear dielectric films with build in metallic nanoparticles are also considered. The nanoparticles provide polariton resonances playing a role similar to the exciton resonances. These systems will be modelled rigorously, starting from basic quantum-mechanical theory. We will investigate the dynamics of the solitons in detail using analytical and numerical methods. The possibility of controlling the solitons by weak perturbations of the pump, as well as, the resonant mutual interaction between cavity solitons and between the solitons and quasi-linear waves will also be investigated.