Localized Floquet modes in arrays of out-of-phase curved waveguides with a quasiperiodic modulation

Abstract

We study light propagation in an array of periodically curved waveguides consisting of pairs of waveguides with out-of-phase oscillations of waveguide centers. We compute the corresponding Floquet propagation constants and find pseudocollapses where the Floquet bands shrink and, respectively, light diffraction is significantly inhibited. When, in addition, the refractive index of the waveguides in the array have quasiperiodic modulation in the transverse direction, we establish the existence of Floquet modes localized in the transverse direction and periodic in the longitudinal direction. With increase of the depth of quasiperiodic modulation of the refractive index in the array, the localized Floquet modes emerge near the pseudocollapse points of the periodic array. In array with sufficiently high frequencies of waveguide oscillations, the localized Floquet modes can exist even for weak quasiperiodic modulation which is situated below the localization transition in the array of straight waveguides.

arXiv comment9 pages, 8 figures; to appear in Phys. Rev. A

References in corpus (20)

• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Atomic quantum gases in periodically driven optical lattices
• Light propagation and localization in modulated photonic lattices and waveguides
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Observation of dynamic localization in periodically-curved waveguide arrays
• Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Observation of anomalous π modes in photonic Floquet engineering
• Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains
• Nondifractive Propagation of Light in Photonic Crystals
• Inhibition of light tunneling in waveguide arrays
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Light tunneling inhibition and anisotropic diffraction engineering in two-dimensional waveguide arrays
• Observation of $\pi$ solitons in oscillating waveguide arrays
• Nonlinearity-induced broadening of resonances in dynamically modulated couplers
• Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices
• Bloch-Landau-Zener oscillations in a quasi-periodic potential