Maryland model in optical waveguide lattices

Abstract

The Maryland model was introduced more than 30 years ago as an integrable model of localization by aperiodic order. Even though quite popular and rich of fascinating mathematical properties, this model has so far remained quite artificial, as compared to other models displaying dynamical localization like the periodically-kicked quantum rotator or the Aubry-Andre${}^{\prime }$ model. Here we suggest that light propagation in a polygonal optical waveguide lattice provides a photonic realization of the Maryland model and enables to observe a main prediction of this model, namely fragility of wave localization in the commensurate potential limit.

5 pages, 6 figures, highlighted as an Editor's Pick by Optics Letters

References in corpus (11)

• Topological States and Adiabatic Pumping in Quasicrystals
• On-Chip Random Spectrometer
• Localization and delocalization of light in photonic moire lattices
• Anderson localization of entangled photons in an integrated quantum walk
• Light propagation and localization in modulated photonic lattices and waveguides
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Photonic Topological Anderson Insulators
• Experimental observation of Anderson localization in laser-kicked molecular rotors
• Topological Anderson phase in quasi-periodic waveguide lattices
• Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point
• Discrete diffraction and shape-invariant beams in optical waveguide arrays

Cited by in corpus (6)

• Anomalous mobility edges in one-dimensional quasiperiodic models
• Non-Hermitian Maryland Model
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Delocalization of light in photonic lattices with unbounded potentials
• Arithmetic Phase Transitions For Mosaic Maryland Model
• Fractal Quasicondensation in One Dimension