Maria Inês Carvalho

Abstract
We investigate the properties of time-dependent dissipative solitons for a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. The separation of initially nearby trajectories in the asymptotic limit is predominantly used to distinguish qualitatively between time-periodic behavior and chaotic localized states. These results are further corroborated by Fourier transforms and time series. Quasiperiodic behavior is obtained as well, but typically over a fairly narrow range of parameter values. For illustration, two examples of nonlinear gradient terms are examined: the Raman term and combinations of the Raman term with dispersion of the nonlinear gain. For small quintic perturbations, it turns out that the chaotic localized states are showing a transition to periodic states, stationary states, or collapse already for a small magnitude of the quintic perturbations. This result indicates that the basin of attraction for chaotic localized states is rather shallow.

Abstract
Dissipative quartic solitons have gained interest in the field of mode-locked lasers for their energy-width scaling which allows the generation of ultrashort pulses with high energies. Pursuing the characterization of such pulses, here we found soliton solutions of a distributed model for mode locked lasers in the presence of either positive or negative fourth-order dispersion (4OD). We studied the impact the laser parameters may have on the profiles, range of existence, and energy-width relation of the output pulses. The most energetic and narrowest solutions occur for negative 4OD, with the energy having an inverse cubic dependence with the width in most cases. Our simulations showed that the spectral filtering has the biggest contribution in the generation of short (widths as low as 39 fs) and very energetic (391 nJ) optical pulses.(c) 2023 Optica Publishing Group

Abstract
We study the time-dependent behavior of dissipative solitons (DSs) stabilized by nonlinear gradient terms. Two cases are investigated: first, the case of the presence of a Raman term, and second, the simultaneous presence of two nonlinear gradient terms, the Raman term and the dispersion of nonlinear gain. As possible types of time-dependence, we find a number of different possibilities including periodic behavior, quasi-periodic behavior, and also chaos. These different types of time-dependence are found to form quite frequently from a window structure of alternating behavior, for example, of periodic and quasi-periodic behaviors. To analyze the time dependence, we exploit extensively time series and Fourier transforms. We discuss in detail quantitatively the question whether all the DSs found for the cubic complex Ginzburg-Landau equation with nonlinear gradient terms are generic, meaning whether they are stable against structural perturbations, for example, to the additions of a small quintic perturbation as it arises naturally in an envelope equation framework. Finally, we examine to what extent it is possible to have different types of DSs for fixed parameter values in the equation by just varying the initial conditions, for example, by using narrow and high vs broad and low amplitudes. These results indicate an overlapping multi-basin structure in parameter space. Published under an exclusive license by AIP Publishing.

Abstract
We study the electromagnetically induced transparency (EIT) phenomenon in a hollow-core fibre filled with rubidium gas. We analyse the impact of the guiding effect and of the temperature on the properties of the EIT phenomenon. The refractive index felt by the probe laser is found to vary due to the radial dependence of the fibre mode field at the pump frequency. Several results are presented for the transmission, dispersion, and group velocity of the probe field, considering both the free propagation regime and the guided propagation along the hollow-core fibre. We note that the EIT occurring in a waveguide has a great potential for practical applications since it can be controlled by adjusting the gas and the fibre properties.

Abstract
The estimation of atmospheric turbulence parameters is of relevance for the following: (a) site evaluation and characterization; (b) prediction of the point spread function; (c) live assessment of error budgets and optimization of adaptive optics performance; (d) optimization of fringe trackers for long baseline optical interferometry. The ubiquitous deployment of Shack-Hartmann wavefront sensors in large telescopes makes them central for atmospheric turbulence parameter estimation via adaptive optics telemetry. Several methods for the estimation of the Fried parameter and outer scale have been developed, most of which are based on the fitting of Zernike polynomial coefficient variances reconstructed from the telemetry. The non-orthogonality of Zernike polynomial derivatives introduces modal cross coupling, which affects the variances. Furthermore, the finite resolution of the sensor introduces aliasing. In this article the impact of these effects on atmospheric turbulence parameter estimation is addressed with simulations. It is found that cross-coupling is the dominant bias. An iterative algorithm to overcome it is presented. Simulations are conducted for typical ranges of the outer scale (4-32 m), Fried parameter (10 cm) and noise in the variances (signal-to-noise ratio of 10 and above). It is found that, using the algorithm, both parameters are recovered with sub-per cent accuracy.