Complex structures in cavities with media displaying EIT: coexistence, defects and selection mechanism

A cavity filled with a medium displaying electromagnetically induced transparency is shown to exhibit coexistence of complex transverse structures often leading to pattern competition. Because of multi-stability of the solutions, the asymptotic state in such a cavity crucially depends on the values of the control parameters and the initial conditions. The pattern competition can result in coexisting regions of pattern structures of different geometry separated by stable or metastable fronts. Here we propose a selection technique based on external periodic modulations for directing the system to a single pattern state of choice and thus removing the separation fronts. The control technique takes the system close to sub-sections in the phase space providing the operator with the choice of the final state from different multi-stable solutions. We extend the use of the technique to stationary or drifting structures composed of regions made of a single pattern state with different orientations. In this case the regularization to a pattern with a single orientation is associated with the removal of defects. The harmonic signal technique has not been used previously to control a spatio-temporal system where the multi-stability is due to the coupling of nonlinearity and diffraction.