Invisible surface defects in a tight-binding lattice

Abstract

Surface Tamm states arise in one-dimensional lattices from some defects at the lattice edge and their energy generally falls in a gap of the crystal. The defects at the surface change rather generally the phase of propagative Bloch waves scattered off at the lattice edge, so that an observer, far from the surface, can detect the existence of edge defects from e.g. time-of-flight measurements as a delay or an advancement of a Bloch wave packet. Here we show that a special class of defects can sustain surface Tamm states which are invisible, in a sense that reflected waves acquire the same phase as in a fully homogeneous lattice with no surface state. Surface states have an energy embedded into the tight-binding lattice band and show a lower than exponential (algebraic) localization. Like most of bound states in the continuum of von Neumann - Wigner type, such states are fragile and decay into resonance surface states in presence of perturbations or lattice disorder. The impact of structural lattice imperfections and disorder on the invisibility of the defects is investigated by numerical simulations.

arXiv comment7 pages, 5 figures

References in corpus (12)

• Surface bound states in the continuum
• Enhanced transmission and beaming of light via photonic crystal surface modes
• Observation of surface gap solitons in semi-infinite waveguide arrays
• "Embedded solitons": solitary waves in resonance with the linear spectrum
• Observation of surface states with algebraic localization
• Invisibility in non-Hermitian tight-binding lattices
• Bound states in the continuum in PT-symmetric optical lattices
• Floquet bound states in the continuum
• Optical lattices with exceptional points in the continuum
• Invisible defects in complex crystals
• Discrete embedded solitons
• Moving embedded lattice solitons

Cited by in corpus (1)

• Floquet-surface bound states in the continuum in a resonantly driven 1D tilted defect-free lattice