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Physical Review A

Complex structures in media displaying electromagnetically induced transparency: Pattern multistability and competition

Mansour Eslami, Reza Kheradmand, Duncan McArthur, Gian‐Luca Oppo

Published Aug 21, 2014• 12 citations
Publisher

Abstract

Spatially periodic and localized structures in the transverse plane of a medium displaying electromagnetically induced transparency in an optical cavity and under the action of two pumps are investigated. The system supports a multitude of different complex spatial structures depending on the chosen initial condition. We explore regimes of multistable patterns, filaments, stable defects, scrolling structures, nested patterns, fronts, and the spontaneous occurrence of multiple cavity solitons. To simulate realistic conditions of operation, we replace periodic boundary conditions with pumps of finite size. Many of the multistable features are recovered apart from the scrolling of patterns with defects.

DOI
10.1103/physreva.90.023840

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Spatially periodic and localized structures in the transverse plane of a medium displaying electromagnetically induced transparency in an optical cavity and under the action of two pumps are investigated. The system supports a multitude of different complex spatial structures depending on the chosen initial condition. We explore regimes of multistable patterns, filaments, stable defects, scrolling structures, nested patterns, fronts, and the spontaneous occurrence of multiple cavity solitons. To simulate realistic conditions of operation, we replace periodic boundary conditions with pumps of finite size. Many of the multistable features are recovered apart from the scrolling of patterns with defects.
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 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.
Optical solitons in gaseous atomic media display many striking features under electromagnetically induced transparency (EIT). Study of theoretical model, which describes these features of optical solitons, has important meaning in optical informational process and propagation. Two-dimensional saturated nonlinear Schrdinger equation, which describes the spatial soliton evolution in the three-level gaseous atomic EIT media, is transformed into the Hamilton system with the symplectic structure. The Hamilton system is discretizated by the symplectic method. The corresponding symplectic scheme is obtained. Evolution behaviors of two and four spatial solitons with the same amplitude in a three-level, gaseous atomic EIT media are simulated by the symplectic scheme. Numerical results further show that the phase difference and the direction of the entering gauss beams have an obvious effect on the interaction of multi-solitons. The entering Gauss beam can form the stable optical solitons in a gaseous atomic media.
Two-dimensional (2D) ``chaotic'' localized structures are observed in the transverse profile of light with a delay model of a ring cavity with strongly dispersive two-level atoms. Near nascent optical bistability, the 2D homogeneous solution undergoes a subcritical transition to a spatiotemporal chaos. The inhomogeneous pattern coexisting with the homogeneous solution is filled with large-intensity peaks, oscillating with time. In the subcritical domain, localized structures are observed, with isolated peaks more stable and more coherent than the ones in the filled structure. The order is easily recovered by a filtering procedure that reduces the wave-vector bandwidth.