Light localization in optically induced deterministic aperiodic Fibonacci lattices

Abstract

As light localization becomes increasingly pronounced in photonic systems with less order, we investigate optically induced two-dimensional Fibonacci structures which are supposed to be amongst the most ordered realizations of deterministic aperiodic patterns. For the generation of corresponding refractive index structures, we implement a recently developed incremental induction method using nondiffracting Bessel beams as waveguide formation entities. Even though Fibonacci structures present slightly reduced order, we show that transverse light transport is significantly hampered here in comparison with periodic lattices that account for discrete diffraction. Our experimental findings are supported by numerical simulations that additionally illustrate a development of transverse light localization for increasing propagation distance.

Anisotropic nonlinear refractive index measurement of a photorefractive crystal via spatial self-phase modulation

“…The values extracted from the experimental data are in good agreement with the theoretical value, |∆n max | = 2.32 × 10 −4 given by Eq. (6).…”

“…arrays of coupled waveguides. It has been widely used to observe various families of optical discrete solitons [3][4][5], to study wave properties of quasicrystals [6] and graphenelike structures [7,8] as well as to evidence weak or strong transverse localisation in disordered lattices [9,10]. On the other hand, in homogeneous configuration, nonlinear patterns formation dynamics [11][12][13] as well as quantum hydrodynamical features of light [14][15][16] have been investigated.…”

Quantum Walks in Periodic and Quasiperiodic Fibonacci Fibers

“…At this point, we would like to note that localization in photonic lattices of waveguides constructed with the Fibonacci sequence in distances between nearest identical waveguides, both 1D and 2D, have recently been investigated theoretically and experimentally [48,49]. Essentially, the Fibonacci arrays of waveguides considered in [48] are defined as the elements in Eq.…”

Quantum Walks in Quasi-Periodic Photonics Lattices

“…At this point, we want to stress that localization of light has been investigated theoretically and experimentally in 1D and 2D arrays of identical waveguides that are constructed with the Fibonacci sequence in distances [38,39]. The quasiperiodic arrays of waveguides considered in those works are defined as the Fibonacci elements in Figure 2; however, the waveguides A and B were defined as the two distances 1 (unit) and τ = 1.618 (golden ratio of the Fibonacci sequence) between identical SM waveguides [37,38].…”