Perturbations propagation in self-organized patterns

In optical cavities, self-organized patterns can emerge because of diffraction and opti-

cal nonlinearities. This phenomena can be used to induce self-organization of an atomic

cloud. Thus, this pattern can be understood as a lattice of cold atomic groups coupled by

diffraction. From this point of view, there is an analogy between this system and a lattice

of atoms in a solid. From solid-state theory, a perturbation of the position of an atom in

the lattice leads to a sound wave that propagates along the solid.

Following this idea, our aim in this work is to study the response of a self-organized

pattern to a localized perturbation at one of the pattern peaks. Since the system is highly

dissipative, we first study the dynamics of this system in order to choose a set of parameters

close to a critical point in such a way that gain can counterbalance dissipation allowing the

perturbations to propagate longer. Next, we run numerical simulations of our partial differential

equation, taking as an initial condition the perturbed pattern. From the numerical results

we extract propagation features such as the velocity, period, symmetry, etc.

Finally, we characterize the perturbation propagation theoretically, and compare the

analytical results with the numerical integration.

Supervisor: Damià Gomila

Jury: Maxi San Miguel, Emilio Hernández-García, and Damià Gomila

Conecta CSIC link: https://conectaha.csic.es/b/dam-ezx-igg-6h7