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

Abstract

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 subsections 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.

Temporal cavity solitons and frequency combs via quantum interference

“…Recently, EIT resonance line shapes have been found in a variety of optical cavities [14] including microring resonators in silicon-on-insulator chips with air holes [15]. On the theoretical side, optical cavities with three-level media displaying EIT have also been studied for the onset and stability of various transverse structures, from patterns to diffractive cavity solitons [16][17][18].…”

“…where t is the slow time over several round-trips in the cavity, P is the amplitude of the input pump, θ is the cavity detuning from the input frequency, and 2C is the cooperativity parameter of the light-matter coupling that is proportional to the dipole moment of the transition between levels |1 and |3 . In [16][17][18] we focused on the transverse diffractive case, while here we investigate the anomalous group-velocity-dispersion case with a longitudinal variable τ , the fast time, defined in a reference frame moving at the group velocity of the light at the driving wavelength. Here R 13 is the density matrix element in the Lindblad master equation given by [16,21]…”