Significant suppression of radiation in 3D structured media with small refractive indices 1.4–1.6, such as glass or polymers, is a desirable feature yet to be obtained. We present here quasiperiodic structures homogeneous distribution Bragg peaks on sphere reciprocal space obtained by an overlap multiple gratings. Simulations revealed limitation emission contrasting from theoretical predictions...

The one-dimensional Fibonacci chain is a toy model central to theoretical studies of the physics electronic states in quasiperiodic structures. This review surveys state art methods study energy spectra and models, including exact solutions, renormalization group, perturbation theory, numerical analysis. Results highlight distinctive properties systems, projection from higher dimensions, nontri...

We are concerned with the persistence of frequency of invariant tori for analytic integrable Hamiltonian system with quasiperiodic perturbation. It is proved that if the unperturbed system satisfies the Rüssmann’s nondegeneracy condition and has nonzero Brouwer’s topological degree at someDiophantine frequency; the perturbed system satisfies the colinked nonresonant condition, then the invarian...

By using a theoretical formalism able to work in both real and k spaces, the physical origin of the phenomenon of extraordinary transmission of light through quasiperiodic arrays of holes is revealed. Long-range order present in a quasiperiodic array selects the wave vector(s) of the surface electromagnetic mode(s) that allows an efficient transmission of light through subwavelength holes.

A string z is quasiperiodic if there is a second string w :I z such that the occurrences of w in z cover z entirely, i.e., every position ~----ofTfalls wiUiin some occurrence ofwinz~Itisshown-here that all:--maximal quasiperiodic substrings of a string x of n symbols can be detected in time O(nlog n).

We report on the first experimental evidence of guided resonances (GRs) in photonic crystal slabs based on aperiodically ordered supercells. Using Ammann-Beenker (quasiperiodic, eightfold symmetric) tiling geometry, we present our study on the fabrication, experimental characterization, and full-wave numerical simulation of two representative structures (with different filling parameters) opera...

For more than a century Liesegang patterns – self-organized, quasiperiodic structures occurring in diffusion-limited chemical reactions with two components – have been attracting scientists. The pattern formation can be described by four basic empirical laws. In addition to many experiments, several models have been devised to understand the formation of the bands and rings. Here we review the ...

An average structure associated with a given quasilattice is a system composed of several average lattices that in reciprocal space produces strong main reflections. The average lattice of a quasicrystal is a useful concept closely related to the geometric description of the quasicrystal to crystal transformation and has been proved to be structurally significant. Here we calculate average stru...

The planar circular restricted three-body problem (PCR3BP) is a standard example of a system with two degrees of freedom that is not integrable. Despite the efforts of many great mathematicians for over the past two centuries, our understanding of the solutions of PCR3BP is still far from complete. One way to understand the behavior of such solutions is through the investigation of invariant se...