Nonlinear supratransmission in multicomponent systems

A method is proposed to solve the challenging problem of determining the supratransmission threshold (onset of instability of harmonic boundary driving inside a band gap) in multicomponent nonintegrable nonlinear systems. It is successfully applied to the degenerate three-wave resonant interaction in a birefringent quadratic medium where the process generates spatial gap solitons. No analytic expression is known for this model showing the broad applicability of the method to nonlinear systems.Comment: 4 pages, 3 figure

Scattering of slow-light gap solitons with charges in a two-level medium

The Maxwell-Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the two-level medium) as e.g. slow-light gap solitons that result from the nonlinear instability of the evanescent wave at the boundary. As nonlinearity couples the different polarizations of the electromagnetic field, the slow-light gap soliton is shown to experience effective scattering whith charges in the medium, allowing it for instance to be trapped or reflected. This scattering process is understood qualitatively as being governed by a nonlinear Schroedinger model in an external potential related to the charges (the electrostatic permanent background component of the field).Comment: RevTex, 14 pages with 5 figures, to appear in J. Phys. A: Math. Theo

Generation and dynamics of quadratic birefringent spatial gap solitons

A method is proposed to generate and study the dynamics of spatial light solitons in a birefringent medium with quadratic nonlinearity. Although no analytical expression for propagating solitons has been obtained, our numerical simulations show the existence of stable localized spatial solitons in the frequency forbidden band gap of the medium. The dynamics of these objects is quite rich and manifests for instance elastic reflections, or inelastic collisions where two solitons merge and propagate as a single solitary wave. We derive the dynamics of the slowly varying envelopes of the three fields (second harmonic pump and two-component signal) and study this new system theoretically. We show that it does present a threshold for nonlinear supratransmission that can be calculated from a series expansion approach with a very high accuracy. Specific physical implications of our theoretical predictions are illustrated on LiGaTe(2) (LGT) crystals. Once irradiated by a cw laser beam of 10 mu m wavelength, at an incidence beyond the extinction angle, such crystals will transmit light, in the form of spatial solitons generated in the nonlinear regime above the nonlinear supratransmission threshold

Association of a Hydrophobically Modified Polyelectrolyte and a Block Copolymer Followed by Fluorescence Techniques

By using absorption and fluorescence (steady-state and time-resolved) techniques, the interaction between a poly(acrylic acid) (PAA), randomly grafted with pyrene (Py) units (PAAMePy55), and a triblock copolymer of poly(ethylene oxide) and poly(propylene oxide) (EO20PO68EO20, P123) was investigated. From the fluorescence data, it is shown that upon addition of P123 a decrease of the (pyrene−pyrene, Py−Py) intramolecular association, i.e., a decrease of dynamic and static excimer formation, is observed. Time-resolved fluorescence data reveal the existence of two types of monomers (monomers that are able to form excimer, MAGRE, and isolated monomers) and two excimers. Addition of P123 causes also an increase of the amount of isolated Py monomers. The overall fluorescence data suggest that the PAAMePy55 and the P123 block copolymer associate strongly at low pH, leading to the formation of P123 micelles surrounded by one PAAMePy55 chain, where the pyrene groups are located at the PPO/PEO interface of the P123 micelles. Steady-state fluorescence results also showed that an excess of P123 micelles in solution is required for the association to occur. At high pH (pH 9 and above) the situation is less clear. The steady-state (particularly in the I1/I3 ratio) and time-resolved fluorescence results indicate a contact between the pyrene groups and PEO, which then would imply that there may be an interaction, but much weaker than at low pH