In this diploma work, two versions of the discrete nonlinear Schrödinger (DNLS) equation are used to model a nonlinear layered photonic crystal system; the cubic DNLS (cDNLS) equation and the saturable DNLS (sDNLS) equation. They both have site-dependent coefficients to break mirror symmetry with respect to propagation direction, as well as to describe the linear and nonlinear properties of the system. Analytical solutions taking on plane wave form are, via the backward transfer map, used to derive a transmission coefficient as well as a rectifying factor to quantify the diode effect. The effect of varying site-dependent coefficients is studied in detail. Numerical simulations of Gaussian wave packets impinging on the system, using open boundary conditions, show the breaking of parity symmetry. Evidence of a change in the wave packet dynamics occurring in the transition between the cubic and the saturable DNLS model is presented. A saturated system prevents the wave packet from getting stuck in the nonlinear lattice layers. The transmission properties were found to be very sensitive to slight changes of the system parameters.

No / The purpose of this study was to ascertain whether or not spreading depression (CSD) propagates symmetrically along the anteroposterior axis of the cortex of mice, and to determine where CSD should be elicited to achieve a uniform exposure of the cortex to this phenomenon. Experiments were performed in halothane-anesthetized mice, with three different locations aligned 1.5 mm from the midline used for either KCl elicitation of CSD or the recording of its propagation. Our results demonstrated that, at least in the mouse cortex, CSD propagated much more effectively from posterior to anterior regions than in the opposite direction. This feature was due to a different efficacy of propagation in the two opposite directions, and not to a reduced susceptibility of occipital regions to CSD elicitation. Heterogeneous CSD propagation constitutes a potential pitfall for neurochemical studies of post-CSD changes in mice, as brain tissue samples collected for this purpose should be uniformly exposed to CSD. Occipital sites for CSD induction are clearly optimal for this purpose. If CSD propagation is confirmed to be more effective from posterior to anterior regions in other species, this may be relevant to the pathophysiology of classical migraine because the most frequent aura symptoms (i.e., visual disturbances) originate in the occipital cortex.