Maria Inês Carvalho

Abstract
We study the dynamics as well as the interaction of stable dissipative solitons (DSs) of the cubic complex Ginzburg-Landau equation which are stabilized only by nonlinear gradient (NLG) terms. First we review stationary, periodic, quasi-periodic, and chaotic solutions. Then we investigate sudden transitions to chaotic from periodic and vice versa as a function of one parameter, as well as different outcomes, for fixed parameters, when varying the initial condition. In addition, we present a quasi-analytic approach to evaluate the separation of nearby trajectories for the case of stationary DSs as well as for periodic DSs, both stabilized by nonlinear gradient terms. In a separate section collisions between different types of DSs are reviewed. First we present a concise review of collisions of DSs without NLG terms and then the results of collisions between stationary DSs stabilized by NLG terms are summarized focusing on the influence of the nonlinear gradient term associated with the Raman effect. We point out that both, meandering oscillatory bound states as well as bound states with large amplitude oscillations appear to be specific for coupled cubic complex Ginzburg-Landau equations with a stabilizing cubic nonlinear gradient term.

Abstract
Measuring the density of tartrazine (TZ) powder allowed to develop a protocol for fast preparation of aqueous solutions with a desired concentration. The stability time of these solutions decreases exponentially with the increase of TZ concentration: solutions with TZ concentrations below 25% remain stable for more than 24 h, while the solution with 60% TZ remains stable only for 35 min. To validate the developed protocol, muscle samples were immersed in the 40% TZ solution and, as expected, the tissue transparency increased smoothly and exponentially during the whole treatment of 30 min. The diffusion time of TZ in ex vivo skeletal muscle was quantitatively determined with high accuracy as tau TZ = 5.39 +/- 0.49 min for sample thickness of 0.5 mm. By measuring the refractive index of TZ solutions during preparation, it will be easier to prepare such solutions in a fast manner for future research on tissue optical clearing.

Abstract
We studied the characteristics, regions of existence, and stability of different types of solitons for a distributed model of a mode-locked laser whose dispersion is purely quartic and normal. Among the different types of solitons, we identified three main branches that are named according to their different amplitude: low, medium, and high amplitude solitons. It was found that the first solitons are always unstable while the latter two exist and are stable in relatively large regions of the parameter space. Moreover, the stability regions of medium and high amplitude solitons overlap over a certain range of parameters, manifesting effects of bistability. The energy of high amplitude solitons increases quadratically with their width, whereas the energy of medium amplitude solitons may decrease or increase with the width depending on the parameter region. Furthermore, we have investigated the long term evolution of the continuous-wave solutions under modulational instability, showing that medium amplitude solitons can arise in this scenario. Additionally, we assessed the effects of second- and third-order dispersion on medium and high amplitude solitons and found that both remain stable in the presence of these terms.

Abstract
Computer simulations, which are performed at a single wavelength at a time, have been traditionally used to estimate the optical properties of tissues. The results of these simulations need to be interpolated. For a broadband estimation of tissue optical properties, the use of computer simulations becomes time consuming and computer demanding. When spectral measurements are available for a tissue, the use of the photon diffusion approximation can be done to perform simple and direct calculations to obtain the broadband spectra of some optical properties. The additional estimation of the reduced scattering coefficient at a small number of discrete wavelengths allows to perform further calculations to obtain the spectra of other optical properties. This study used spectral measurements from the heart muscle to explain the calculation pipeline to obtain a complete set of the spectral optical properties and to show its versatility for use with other tissues for various biophotonics applications.

Abstract
The refractive index of the pigs heart was measured at wavelengths between 255 and 850 nm to calculate the dispersion. The total transmittance and total reflectance spectra of the pig heart were measured between 200 and 1000 nm to calculate the spectral absorption coefficient. Using Kramers-Kronig relations, the dispersion of the heart was matched to experimental refractive index values.