Periodic and Quasiperiodic Structures

Albuquerque, E.L.; Cottam, M. G.

doi:10.1016/b978-044451627-5/50002-x

Cited by 49 publications

(99 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…9,13 ). For such amazing discovery, in 2011, Shechtman was awarded with the Nobel Prize in Chemistry 14 .…”

mentioning

confidence: 99%

“…It has been recognized that in addition to crystalline and amorphous materials, there exists a third intermediate class known as "deterministic aperiodic" structures, which can be generated by a substitution rule based on two or more 29 blocks that exhibit long-range order, which does not have translational symmetry. Also, it has been shown that these structures exhibit properties of self-similarity in their spectra 13 . In a general way, this new class of structures can be classified into two groups: quasicrystals and all other deterministic aperiodic structures.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Octonacci photonic quasicrystals

et al. 2015

View full text Add to dashboard Cite

We study theoretically the transmission spectra in one-dimensional photonic quasicrystals, made up of SiO 2 (A) and TiO 2 (B) materials, organized following the Octonacci sequence, where the nth-stage of the multilayer S n is given by the rule S n = S n−1 S n−2 S n−1 , for n ≥ 3 and with S 1 = A and S 2 = B. The expression for transmittance was obtained by employing a theoretical calculation based in the transfer-matrix method. To normally incident waves, we observe that, for a same generation, the transmission spectra for TE and TM waves are equal, at least qualitatively, and they present a scaling property where a self-similar behavior is obtained, as an evidence that these spectra are fractals. The spectra show regions where the omnidirectional band gaps emerges for specific generations of Octonacci photonic structure, except to TM waves. For TE waves, we note that all of them have the almost same width, for different generations. We also report the localization of modes as a consequence of the quasiperiodicity of the heterostructure.

show abstract

“…9,13 ). For such amazing discovery, in 2011, Shechtman was awarded with the Nobel Prize in Chemistry 14 .…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Octonacci photonic quasicrystals

et al. 2015

View full text Add to dashboard Cite

show abstract

“…The Fibonacci sequence is of particular importance, since it leads to the existence of two incommensurable periods in the spatial spectrum of the structure. Such behavior is typical of sequences with a so-called pure point spectrum, which makes the Fibonacci sequence truly quasiperiodic, as a consequence of the appearance of Bragg-like peaks in the spatial spectrum [5]. This property has been demonstrated to be very valuable for nonlinear optical applications, such as third harmonic generation [7].…”

Section: Introductionmentioning

confidence: 93%

Photonic Analysis of Semiconductor Fibonacci Superlattices: Properties and Applications

Rahimi¹

2014

PIER M

View full text Add to dashboard Cite

Abstract-In this paper, we theoretically study the phase treatment of reflected waves in onedimensional Fibonacci photonic quasicrystals composed of nano-scale fullerene and semiconductor layers. The dependence of the phase shift of reflected waves for TE mode and TM mode on the wavelength and incident angle is calculated by using the theoretical model based on the transfer matrix method in the infrared wavelength region. In the band gaps of supposed structures, it is found that the phase shift of reflected wave changes more slowly than within the transmission band gaps. Furthermore, the phase shift decreases with the incident angle increasing for TE mode, and increases with the incident angle increasing for TM mode. Also, for the supposed structures it is found that there is a band gap which is insensitive to the order of the Fibonacci sequence. These structures open a promising way to fabricate subwavelength tunable phase compensators, very compact wave plates and phase-sensitive interferometry for TE and TM waves.

show abstract

“…This feature properly distinguishes the BACs studied in this work from both the purely geometric on-site (i.e., t k;k 1 1, 8k) and the chemically unrealistic transfer (i.e., V k 0, 8k) models, which have been widely considered in the physical and mathematical literature during the last three decades. [4,10,[36][37][38] After Eq. (2) the wave function amplitudes can be recursively obtained from the matrix expression 0…”

Section: General Binary Aperiodic Crystals: a Unified Treatmentmentioning

confidence: 99%

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Maciá

2017

Annalen der Physik

View full text Add to dashboard Cite

A spectral classi…cation of general one-dimensional binary aperiodic crystals (BACs) based on both their di¤raction patterns and energy spectrum measures is introduced along with a systematic comparison of the zeroth-order energy spectrum main features for BACs belonging to di¤erent spectral classes, including Fibonacci-class, precious means, metallic means, mixed means and period doubling based representatives. These systems are described by means of mixed-type Hamiltonians which include both diagonal and o¤-diagonal terms aperiodically distributed. An algebraic approach highlighting chemical correlation e¤ects present in the underlying lattice is introduced.Close analytical expressions are obtained by exploiting some algebraic properties of suitable blocking schemes preserving the atomic order of the original lattice. The existence of a resonance energy which de…nes the basic anatomy of the zeroth-order energy spectra structure for the standard Fibonacci, the precious means and the Fibonacci-class quasicrystals is disclosed. This eigenstate is also found in the energy spectra of BACs belonging to other spectral classes, but for speci…c particular choices of the corresponding model parameters only. The transmission coe¢ cient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the relative strength of the chemical bonds.

show abstract

Periodic and Quasiperiodic Structures

Cited by 49 publications

References 48 publications

Octonacci photonic quasicrystals

Octonacci photonic quasicrystals

Photonic Analysis of Semiconductor Fibonacci Superlattices: Properties and Applications

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Contact Info

Product

Resources

About