Abstract
The interaction of light with matter in near-to-resonant conditions opens a path for the exploration of nontrivial optical response that can play an important role in future photonics-driven technology. But as the attention shifts towards many-level atomic systems and involving multi-dimensional experimental scenarios, the complexity of the physical systems makes the analytical approach to the semiclassical model of the MaxwellBloch equations impossible without any strongly-limiting approximations. In this context, robust and highperformance computational tools are mandatory. In this work, we describe the development and implementation of a cross-platform Maxwell-Bloch numerical solver that is capable to exploit the different hardware available to tackle efficiently the problems under consideration. Moreover, it is demonstrated that this simulation tool can address a vast class of problems with considerable reduction of simulation time, featuring speedups up to 30 when running in massive parallel GPUs compared with the same codes running on a CPU, showing its potential towards addressing a large class of modern problems in photonics.

Abstract
Solitons are localized wave solutions that appear in nonlinear systems when self-focusing effects balance the usual pulse dispersion of common optical media. Their stability and particle-like behavior make them ideal candidates for applications that range from communication to optical computing, but in real world physical systems, dissipative processes makes these otherwise stable solutions unstable, and true solitons are particularly hard to observe in systems featuring non-negligible dissipation. In these cases a special type of localized stable solutions, called dissipative solitons, are still possible to obtain, if in addition to a balance between diffraction and nonlinearity, an equilibrium between gain and loss is also present. In this work we discuss theoretically how a 4-level atomic system and an incoherent pumping process can be an ideal experimental testbed for studying this interesting class of solutions, featuring tunable optical properties and controllable gain/loss dynamics that allow to study both classes of temporal and spatial dissipative optical solitons.

Abstract
As quantum-driven processes and properties start to shape the future of technology, quantum simulations appear as a crucial piece of the puzzle, acting both as building blocks and catalysts for the improvement of the understanding of unique quantum features. In essence, they can be understood as a class of prototype experiments that allow a study of quantum properties in a controllable environment. In this context, quantum fluids of light are one of the strongest candidates for this role as coherent behavior is easily accessible and not hidden by detrimental thermal noise usually present in more common quantum systems. In this work we explore the underlying theory of quantum fluids of light in propagating geometries through the hydrodynamic interpretation of light, where photons behave as interacting particles in the presence of a nonlinear medium. Exploiting the highly controllable optical properties of atomic systems and their enhanced nonlinear properties related to quantum coherence phenomena, we discuss how they can be used to set a tunable platform for quantum simulations. As examples, we demonstrate a series of quantum features of this light fluid in the form of superfluidic-like behaviors, ranging from the more common and experimentally confirmed suppressed scattering, drag-force cancellation and Bogoliubov-like dispersion relation for the elementary excitations, to other interesting phenomena yet to be explored, such as the case of persistent currents.

Abstract
Although the quantum theory of the optical response of individual atoms to coherent light with frequencies close to electronic transitions and the fluid equations for a gas are well known and understood from first principles, they are developed independently of each other and therefore cannot be applied directly to describe many of the quantum collective and transport phenomena that occur in cold atomic gases, especially in what regards their interaction with optical pulses and beams. Few attempts have been made to derive a consistent formalism and theory that are capable to model this type of systems, and those which exist rely on the adaptation of several ad-hoc hypothesis and simplifications, such as space and time dependent density operators. In this paper we provide the theoretical foundations and establish a formalism capable of paving the way for the development of new simulation tools and to explore new problems in nonlinear optics out of equilibrium.

Abstract
This paper reports the development of a numerical module for the HiLight simulation platform dedicated to the propagation of light in nonlocal nonlinear optical media and the adaptions implemented for it to be used as a numerical test-bed to evaluate the impact of new extensions of the Theory of General Relativity in the dynamics of a N-body system. The phenomenology of light in nonlocal and nonlinear media is very rich and can be described by a multitude of effective models, with different levels of detail and approximations, which coincide with few or no differences with those found in many other fields of physics. In particular, nonlocal extensions of the Generalized Nonlinear Schrodinger equation (also known as the generalized Schrodinger-Newton system) constitute a wide class of physical models that can be found in both optics and in the studies of alternative theories for gravity. Therefore, numerical solvers developed for the former can be adapted to address the later. Indeed, this paper discusses the adaptation of a numerical solver of the generalized Schrodinger-Newton system based on GPGPU supercomputing, initially developed to investigate the properties of light in exotic nonlocal media, to tackle the dynamics of large distributions of matter whose interaction is governed by extensions of the Theory of General Relativity, namely those based on non-minimal coupling between curvature and matter. This paper analysis the structure of the resulting simulation module, its performance and validation tests.

Abstract
This paper proposes the use of nematic liquid crystals as tunable setups to implement optical analogues of physical systems and phenomena that are hard or even impossible to study experimentally under controlled conditions. Optical analogues share the same physical model with the systems that they emulate and can be understood as a form of physical simulations or optical computation. However, their success relies not only on the existence of media with optical properties capable of emulating the models associated with the original system as they interact with light, but also on the possibility of being able to tune those properties in order to cover the multitude of conditions or range of parameters. In particular, the Schrodinger-Newton model is a good target for this kind of studies as it can describe a plethora of different phenomena in physics and can be implemented in the laboratory using optical analogues, usually using thermo-optical materials. However, such materials have limitations, and in this work we propose nematic liquid crystals as a more advantageous alternative. We discuss how nematic liquid crystals can be used as a tunable support medium for optical analogues of superfluids by analyzing the dispersion relation of light under specific conditions and using numerical simulations based on GPGPU supercomputing to verify our findings. Extending on this, we explore more direct manifestations of superfluid effects in nematic liquid crystals, such as drag-force cancellation in the superfluid regime and the possibility of creating a roton-minimum in the dispersion relation.