Proposed all optical amplification scenario is based on the properties of light propagation in two coupled subwavelength metallic slab waveguides where for particular choice of waveguide parameters two propagating (symmetric) and non-propagating (antisymmetric) eigenmodes coexist. For such a setup incident beams realize boundary conditions for forming a stationary state as a superposition of mentioned eigenmodes. It is shown both analytically and numerically that amplification rate in this completely linear mechanism diverges for small signal values.
Experiments on a chain of coupled pendula driven periodically at one end demonstrate the existence of a novel regime which produces an output frequency at an odd fraction of the driving frequency. The new stationary state is then obtained on numerical simulations and modeled with an analytical solution of the continuous sine-Gordon equation that resembles a kink-like motion back and forth in the restricted geometry of the chain. This solution differs from the expressions used to understand nonlinear bistability where the synchronization constraint was the basic assumption. As a result the short pendula chain is shown to possess tristable stationary states and to act as a frequency divider.
Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.
A two-level medium, described by the Maxwell-Bloch (MB) system, is engraved by establishing a standing cavity wave with a linearly polarized electromagnetic field that drives the medium on both ends. A light pulse, polarized along the other direction, then scatters the medium and couples to the cavity standing wave by means of the population inversion density variations. We demonstrate that control of the applied amplitudes of the grating field allows to stop the light pulse and to make it move backward (eventually to drive it freely). A simplified limit model of the MB system with variable boundary driving is obtained as a discrete nonlinear Schroedinger equation with tunable external potential. It reproduces qualitatively the dynamics of the driven light pulse.
