Bistability in sine-Gordon: the ideal switch

The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows to discover that sine-Gordon can work as an it ideal switch by reaching a transmissive regime with vanishing driving amplitude.Comment: Phys. Rev. E, (to be published, May 2005

Driving light pulses with light in two-level media

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

Bistable light detectors with nonlinear waveguide arrays

Bistability induced by nonlinear Kerr effect in arrays of coupled waveguides is studied and shown to be a means to conceive light detectors that switch under excitation by a weak signal. The detector is obtained by coupling two single 1D waveguide to an array of coupled waveguides with adjusted indices and coupling. The process is understood by analytical description in the conservative and continuous case and illustrated by numerical simulations of the model with attenuation.Comment: Phys. Rev. Lett., v.94, (2005, to be published

Gap soliton dynamics in an optical lattice as a parametrically driven pendulum

A long wavelength optical lattice is generated in a two-level medium by low-frequency contrapropagating beams. Then a short wave length gap soliton generated by evanescent boundary instability (supratransmission) undergoes a dynamics shown to obey the Newton equation of the parametrically driven pendulum, hence presenting extremely rich, possibly chaotic, dynamical behavior. The theory is sustained by numerical simulations and provides an efficient tool to study soliton trajectories

Nonlinear Dynamics in Double Square Well Potential

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

Bistable Transmitting Nonlinear Directional Couplers

Nonlinearity induced by intensity-dependent refractive indices (Kerr media) can be used as a means to conceive light detectors sensitive to very weak excitation. This property results from the bistability properties of the nonlinear SchrÄodinger equation submitted to boundary value data on the finite interval. The detector is obtained by coupling two single 1D waveguide to a 2D slab waveguide with adjusted indices. The resulting device then presents unusual light propagation properties and in particular may switch from almost vanishing to intense output under excitation by a weak signal

Theory of a Josephson junction parallel array detector sensitive to very weak signals

An array of coupled short junctions (Josephson junction parallel array) is shown to be able to response to ultra-weak signals when it is worked at the onset of nonlinear supratransmission in the hysteresis loop of bistability. The theory is based on the fundamental solutions of the continuous limit (the sine-Gordon equation on the finite interval submitted to Neuman boundary conditions) that result from synchronization and adaptation to the external driving. This provides the solution to a problem that dates back to 1986 [O. H. Olsen and M. R. Samulsen, Phys. Rev. B34, 3510 (1986)], namely the complete analytical understanding of the bistability in a long Josephson junction or in an array of short junctions. The property allows to conceive ultrasensitive detectors or else, by convenient modulation of the seed, efficient digital amplifiers. Numerical simulations reveal that such a bistable behavior occurs also in two-dimensional lattices where no theory is available yet

Bistable Magnetization Profiles in Magnetic Thin Films Driven in the Allowed Band

A yttrium-iron-garnet magnetic thin film, driven by means of two antennas, produces a standing wave in-plane magnetization. When the driving frequency is chosen close to the upper edge of the passing band, it is shown by rigorous asymptotic multiscale analysis that the governing model for the generated backward volume waves is the defocusing nonlinear Schrödinger equation. Although being driven inside the allowed band, the nonlinear response of the system is discovered to allow for the formation of bistable magnetization profiles for a film width comparable with the wavelength of the driving radiation