8 research outputs found
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
Fano Resonances in Flat Band Networks
Linear wave equations on Hamiltonian lattices with translational invariance
are characterized by an eigenvalue band structure in reciprocal space. Flat
band lattices have at least one of the bands completely dispersionless. Such
bands are coined flat bands. Flat bands occur in fine-tuned networks, and can
be protected by (e.g. chiral) symmetries. Recently a number of such systems
were realized in structured optical systems, exciton-polariton condensates, and
ultracold atomic gases. Flat band networks support compact localized modes.
Local defects couple these compact modes to dispersive states and generate Fano
resonances in the wave propagation. Disorder (i.e. a finite density of defects)
leads to a dense set of Fano defects, and to novel scaling laws in the
localization length of disordered dispersive states. Nonlinearities can
preserve the compactness of flat band modes, along with renormalizing (tuning)
their frequencies. These strictly compact nonlinear excitations induce tunable
Fano resonances in the wave propagation of a nonlinear flat band lattice
Traveling waves and pattern formation for spatially discrete bistable reaction-diffusion equations (survey)
Analysis and Stochastic