Dynamic versus Anderson wavepacket localization

We address the interplay between two fundamentally different wavepacket localization mechanisms, namely resonant dynamic localization due to collapse of quasi-energy bands in periodic media and disorder-induced Anderson localization. Specifically, we consider light propagation in periodically curved waveguide arrays on-resonance and off-resonance, and show that inclusion of disorder leads to a gradual transition from dynamic localization to Anderson localization, which eventually is found to strongly dominate. While in the absence of disorder, the degree of localization depends critically on the bending amplitude of the waveguide array, when the Anderson regime takes over the impact of resonant effects becomes negligible.Comment: 13 pages, 5 figures, to appear in Physical Review

Defect-free surface states in modulated photonic lattices

We predict that interfaces of periodically curved waveguide arrays can support a novel type of surface states which exist in a certain region of modulation parameters associated with the band flattening. Such linear surface states appear in truncated but otherwise perfect (defect-free) lattices as a direct consequence of the periodic modulation of the lattice potential. We show that the existence of these modes in different band gaps can be flexibly controlled by selecting the modulation profile, with no restrictions on Blochwave symmetries characteristic of Shockley states

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

Vector mixed-gap surface solitons

We elucidate the properties of mixed-gap vector surface solitons supported by the interface between a uniform medium and an optical lattice imprinted in a Kerr-type nonlinear media. The components of such mixed-gap solitons emerge from different gaps of lattice spectrum and their mutual trapping results in the formation of stable vector states. The unstable soliton component is stabilized by the cross-coupling with the stable component. We show that vector mixed-gap surface solitons exhibit a new combination of properties of vectorial surface waves and gap solitons.Comment: 7 pages, 4 figures, to appear in Optics Expres

Sine-Gordon breathers generation in driven long Josephson junctions

We consider a long Josephson junction excited by a suitable external ac-signal, in order to generate control and detect breathers. Studying the nonlinear supratransmission phenomenon in a nonlinear sine-Gordon chain sinusoidally driven, Geniet and Leon explored the bifurcation of the energy transmitted into the chain and calculated a threshold $A (\omega)$ for the external driving signal amplitude, at which the energy flows into the system by breathers modes. I numerically study the continuous sine-Gordon model, describing the dynamics of the phase difference in a long Josephson junction, in order to deeply investigate the "continuous limit" modifications to this threshold. Wherever the energy flows into the system due to the nonlinear supratransmission, a peculiar breather localization areas appear in a $(A, \omega)$ parameters space. The emergence of these areas depends on the damping parameter value, the bias current, and the waveform of driving external signal. The robustness of generated breathers is checked by introducing into the model a thermal noise source to mimic the environmental fluctuations. Presented results allows one to consider a cryogenic experiment for creation and detection of Josephson breathers.Comment: 8 pages, 3 figure

Slow Excitation Trapping in Quantum Transport with Long-Range Interactions

Long-range interactions slow down the excitation trapping in quantum transport processes on a one-dimensional chain with traps at both ends. This is counter intuitive and in contrast to the corresponding classical processes with long-range interactions, which lead to faster excitation trapping. We give a pertubation theoretical explanation of this effect.Comment: 4 pages, 3 figure