Quasiperiodic Structures Research Articles

Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure

In this paper, an omnidirectional photonic band gap realized by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure, which is composed of homogeneous unmagnetized plasma and two kinds of isotropic dielectric, is theoretically studied by the transfer matrix method. It has been shown that such an omnidirectional photonic band gap originates from Bragg gap in contrast to zero-n¯ gap or single negative (negative permittivity or negative permeability) gap, and it is insensitive to the incidence angle and the polarization of electromagnetic wave. From the numerical results, the frequency range and central frequency of omnidirectional photonic band gap can be tuned by the thickness and density of the plasma but cease to change with increasing Fibonacci order. The bandwidth of omnidirectional photonic band gap can be notably enlarged. Moreover, the plasma collision frequency has no effect on the bandwidth of omnidirectional photonic band gap. It is shown that such new structure Fibonacci quasiperiodic one-dimensional ternary plasma photonic crystals have a superior feature in the enhancement of frequency range of omnidirectional photonic band gap compared with the conventional ternary and conventional Fibonacci quasiperiodic ternary plasma photonic crystals.

Air‐sea interface in hurricane conditions

Improving hurricane prediction models requires better understanding of complex processes taking place at the air‐sea interface at high wind speeds. The change of the air‐sea interaction regime in hurricane conditions has been linked to the mechanism of direct disruption of the air‐sea interface by pressure fluctuations working against the surface tension force. This can be achieved through the Kelvin‐Helmholtz type instability. In order to investigate this mechanism, we have conducted a series of 3D numerical experiments using a volume of fluid multiphase model. The experiments were initialized with either a flat interface or short wavelets and wind stress applied at the upper boundary of the air layer. The direct disruption of the air‐water interface and formation of two‐phase transition layer were observed in the numerical model under hurricane force wind. The vertical profiles of density and velocity in the transition layer were consistent with the regime of marginal stability, which permitted estimation of the lower limit on the drag coefficient under hurricane conditions. This limit was appreciably lower than the wave resistance law; though, it was gradually increasing with wind speed. The numerical experiments with imposed short wavelets demonstrated the tearing of wave crests, formation of water sheets and spume ejected into the air, smoothing of the water surface, as well as quasiperiodic structures on the top of wave crests resembling the Tollmien‐Schlichting instability. This study can help in developing a framework for combining the effects of the two‐phase environment with the contribution to the drag from waves.

Switching waves and dissipative structures in a chain of spasers

We have considered the physical mechanism of optical bistability in a spaser in the field of an external optical wave. We have studied the effect of this phenomenon on the dynamics of a 1D chain of coupled spasers. It is shown that such a chain demonstrates the behaviour typical of open nonlinear systems. In particular, for high Joule losses in a spaser, a nonlinear switching autowave propagatesin the chain, thereby evolving the spasers' state from a low population inversion state into a high population inversion state or vice versa. The control parameter that determines the type ofswitching is the amplitude of the external optical wave. For low Joule losses there emerge quasi-periodic dissipative structures whose formation dynamics is of 'self-assembly' nature.

Omnidirectional photonic band gaps enlarged by Fibonacci quasi-periodic one-dimensional ternary superconductor photonic crystals

First two omnidirectional photonic band gaps (OBGs) realized by one-dimensional (1D) Fibonacci quasi-periodic structure which is composed of superconductor and two kinds of isotropic dielectric are theoretically studied by the transfer matrix method (TMM). From the numerical results, it has been shown that such OBGs are insensitive to the incident angle and the polarization of electromagnetic wave (EM wave), and the frequency ranges and central frequencies of OBGs cease to change with increasing Fibonacci order, but vary with the ambient temperature of system and the thickness of the superconductor, respectively. The bandwidths of OBGs can be notably enlarged. The damping coefficient of superconductor layers has no effect on the frequency ranges of OBGs. Those OBGs originate from a Bragg gap in contrast to zero-n˜ gap or single negative (negative permittivity or negative permeability) gap. It has been proved that Fibonacci quasi-periodic 1D ternary superconductor dielectric photonic crystals (SDPCs) have a superior feature in the enhancement of OBGs frequency ranges compared with the conventional binary dielectric photonic crystals (DPCs).

Fabrication of Au/SnO<SUB>2</SUB> Nanocomposites Based on 3D Structures of Butterfly Wing Scales and Research on Its SERS Effects

Scales from fore wings of Papilio paris was used as templates, by ringing the original fore wings in the precursor and treatment by calcinations, SnO2 (rutile) which inherited the 3D quasi-periodic structures of original wing scale was fabricated. After that, Au nanoparticles were incorporated in the system of as-prepared SnO2 to form the Au/SnO2 nanocomposites. XRD, SEM and TEM were carried out to investigate the morphologies, structures and elemental composition. For measuring Surface-enhanced Raman Scattering (SERS) effects of the Au/SnO2 substrate, R6G was used as analyte molecules. By analyzing morphologies of this nanocomposites and UV-Vis DRS spectra of different substrates, mechanisms of SERS effects for this Au/SnO2 nanocomposites substrate were analyzed. The three-dimensional nanostructures of the substrate provide large quantities of Raman 'hot spots', meanwhile, the SnO2 and Au make synergetic contribution to the enhancement effects. The satisfying SERS properties combined

Discrete solitons in azimuthally modulated Bessel lattices: An introduction to solitons in quasi-periodic structure

The investigation of discrete solitons in quasi-periodic structure, namely azimuthally modulated Bessel lattices imprinted in photorefractive crystal, is introduced. It is shown that the discrete solitons centralize more energy in the internal layers than the Bessel lattice and moreover, the effect of centralization of discrete solitons in focusing media is stronger than that in defocusing media. The discrete solitons are unstable in some propagation constant windows and they are absolutely stable when the propagation constant is large enough. The stable solitons perform long-distance and periodic oscillation of intensity and shape under the perturbation of intrinsic excitation.

Polarization-dependent femtosecond laser ablation of poly-methyl methacrylate

We show that ablation features in poly-methyl methacrylate (PMMA) induced by a single femtosecond laser pulse are imposed by light polarization. The ablation craters are elongated along the major axis of the polarization vector and become increasingly prominent as the pulse energy is increased above the threshold energy. We demonstrate ∼40% elongation for linearly and elliptically polarized light in the fluence range of 4–20 J cm−2, while circularly polarized light produced near circular ablation craters irrespective of pulse energies. We also show that irradiation with multiple pulses erases the polarization-dependent elongation of the ablation craters. However, for line ablation the orientation of the electric field vector is imprinted in the form of quasi-periodic structures inside the ablated region. Theoretically, we show that the polarization dependence of the ablation features arises from a local field enhancement during light–plasma interaction. Simulations also show that in materials with high nonlinearities such as doped PMMA, in addition to conventional explosive boiling, sub-surface multiple filamentation can also give rise to porosity.

Omnidirectional band gaps in quasiperiodic photonic crystals in the THz region

In this work we calculate the emittance spectra of the electromagnetic radiation normally and obliquely incident (s- and p-polarized modes) on a one-dimensional multilayer quasiperiodic photonic structure made up by layered system of positive (SiO2) and negative (LiTaO3) refractive index materials organized in a quasiperiodic (Fibonacci-like) fashion. We model the negative refractive index material by an effective medium, whose electric permittivity ϵ(ω) is characterized by a phonon-polariton frequency dependent dielectric function, while for the magnetic permeability μ(ω) we have a Drude-like frequency-dependent function. The emittance spectra are determined by means of a well known theoretical model based on Kirchoff’s second law, together with a transfer matrix formalism. Our results shows that the omnidirectional band gaps appear in the THz regime, in well defined frequency intervals independently of the electromagnetic radiation’s polarized modes.

Bloch-mode analysis for retrieving effective parameters of metamaterials

We introduce an approach for retrieving effective parameters of metamaterials based on the Bloch-mode analysis of quasiperiodic composite structures. We demonstrate that, in the case of single-mode propagation, a complex effective refractive index can be assigned to the structure, being restored by our method with a high accuracy. We employ both surface and volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes to determine the Bloch and wave impedances, respectively. We discuss how this method works for several characteristic examples, and demonstrate that this approach can be useful for retrieval of both material and wave effective parameters of a broad range of metamaterials.

Renormalization group approach for the wave packet dynamics in golden-mean and silver-mean labyrinth tilings

We study the quantum diffusion in quasiperiodic tight-binding models in one, two, and three dimensions. First, we investigate a class of one-dimensional quasiperiodic chains, in which the atoms are coupled by weak and strong bonds aligned according to the metallic-mean sequences. The associated generalized labyrinth tilings in d dimensions are then constructed from the direct product of d such chains, which allows us to consider rather large systems numerically. The electronic transport is studied by computing the scaling behavior of the mean-square displacement of the wave packets with respect to the time. The results reveal the occurrence of anomalous diffusion in these systems. By extending a renormalization group approach, originally proposed for the golden-mean chain, we show also for the silver-mean chain as well as for the higher-dimensional labyrinth tilings that in the regime of strong quasiperiodic modulation the wave-packet dynamics are governed by the underlying quasiperiodic structure.

Band gap properties of one-dimensional aperiodically deterministic multilayer structure containing left-handed materials

By using the transfer-matrix method and effective medium theory, we have theoretically investigated band gap properties of one-dimensional aperiodically deterministic (quasiperiodic) structure composed of left-handed material and right-handed material layers. The proposed multilayer structure is ordered according to the Fibonacci sequence constituted of two blocks A and B. It is found that this structure possesses a new type of photonic band gap which is invariant with a change of thickness scale, and sensitive to the incident angle and wave polarization. It is also found that for TE (TM) polarization, moving away from normal incidence to oblique incidence shows that the width of the band gap increases (decreases). More interestingly, our numerical results show that for angles of incidence greater than 50° the band gap for TM mode is eliminated. Moreover, for incident angles less than 50° the structure works as a tunable band edge filter.

PERFECT OPTICAL TRANSPORT AND OPTICAL BAND GAP IN QUASIPERIODIC SUPERLATTICES

A three-component quasiperiodic superlattice structures composing of both positive and negative refractive index materials are shown to display resonant transport behavior and optical band gaps. When the structure is composed of nondispersive refractive index material, the number of the resonant transmission peaks increases and the optical band gap becomes broad with the increasing of the medium generation. The band gap covers all the wavelength except for some singular wavelength points when the structure is composed of negative refractive index materials. Moreover, it is found that the spectrum shifts to low frequency for oblique incidence. And with the increasing of the optical thickness, the band gap splits and new perfect transport channels emerge. For a more realistic dispersive negative refractive index material, the transmission coefficients are characterized by a rich transmission profile without symmetry, more wide band gaps and abundance transmissive channels appear.

The DNA electronic specific heat at low temperature: The role of aperiodicity

The electronic specific heat spectra at constant volume (CV) of a long-range correlated extended ladder model, mimicking a DNA molecule, is theoretically analyzed for a stacked array of a double-stranded structure made up from the nucleotides guanine G, adenine A, cytosine C and thymine T. The role of the aperiodicity on CV is discussed, considering two different nucleotide arrangements with increasing disorder, namely the Fibonacci and the Rudin–Shapiro quasiperiodic structures. Comparisons are made for different values of the band fillings, considering also a finite segment of natural DNA, as part of the human chromosome Ch22.

Fabrication of quasiperiodic nanostructures with EUV interference lithography

We demonstrate the fabrication and analysis of well-ordered high-resolution quasiperiodic nanostructures with feature sizes down to a few tens of nanometers using extreme ultraviolet interference lithography. A well-controlled mask manufacturing process for producing high quality transmission diffraction masks enables simple and fast fabrication of highly ordered 2D quasiperiodic structures using 5- and 8-beam interference setups.

Reversed Drifting Quasi-periodic Pulsating Structure in the X1.3 Solar Flare on 30 July 2005

Based on the analysis of the microwave observations at frequency of 2.60 -- 3.80 GHz in a solar X1.3 flare event observed at Solar Broadband RadioSpectrometer in Huairou (SBRS/Huairou) on 2005 July 30, an interesting reversed drifting quasi-periodic pulsating structure (R-DPS) is confirmed. The R-DPS is mainly composed of two drifting pulsating components: one is a relatively slow very short-period pulsation (VSP) with period of about 130 -- 170 ms, the other is a relatively fast VSP with period of about 70 -- 80 ms. The R-DPS has a weak left-handed circular polarization. Based on the synthetic investigations of Reuven Ramaty High Energy Solar Spectroscopic Imaging (RHESSI) hard X-ray, Geostationary Operational Environmental Satellite (GOES) soft X-ray observation, and magnetic field extrapolation, we suggest the R-DPS possibly reflects flaring dynamic processes of the emission source regions.

Ballistic transmission through quasi-periodic shape barrier resonant tunneling structures

A theoretical model is proposed to study the ballistic electron transport for a quasi-periodic multibarrier structure where two different barrier shapes are arranged according to the Thue–Morse sequence. Important tunneling features are revealed form such arrangements. It is noted that the tunneling band spectrum could be fragmented by tailoring the shape of the barriers in the structure. Results for the transmission coefficients and the current densities are compared with the corresponding periodic and single shape barrier arrangements. The quasi-periodic structure consisting of the rectangular and triangular barrier shapes is suggested to be more suitable for the electronic and opto-electronic devices due to its high negative differential conducting effect.

Almost periodic structures and the semiconjugacy problem

The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80ʼs. Frequently, the modelling of such structures leads to different types of dynamical systems which include, depending on the concept of quasiperiodicity being considered, skew products over quasiperiodic or almost periodic base flows, mathematical quasicrystals or maps of the real line with almost periodic displacement. An important problem in this context is to know whether the considered system is semiconjugate to a rigid translation. We solve this question in a general setting that includes all the above-mentioned examples and also allows the treatment of scalar differential equations that are almost periodic both in space and time. To that end, we study a certain class of flows that preserve a one-dimensional foliation and show that a semiconjugacy to a minimal translation flow exists if and only if a boundedness condition, concerning the distance of orbits of the flow to those of the translation, holds.

Mechanism analysis of one-dimensional short groove quasicrystal structure drag-reduction

Short groove arranged in one-dimensional quasicrystal structure is designed by mechanical method in this paper and drag reduction experiments are performed by viscometer. The results show that there is a novel drag reduction effect compared with periodic structure of one-dimensional short groove, in which 12-fold quasicrystal structure of one-dimensional short groove has the best drag reduction, and has an equal effect compared with one-dimensional periodic groove structure. An two-dimensional grating model is proposed to investigate the mechanism. It is found that in comparison with two-dimensional periodic grating, the intensity spectrum of coherent wave passing through two-dimensional quasiperiodic grating has several characteristic structure factors. Corresponding to the quasicrystal structures of one-dimensional short groove, the quasiperiodic structure in spanwise direction can activate little disturbance on boundary layer and make the secondary vortex more uniform, which restrains the strong disturbance in spanwise, consequently reducing the drag.

Micro and Nanowrinkled Conductive Polymer Surfaces on Shape-memory Polymer Substrates: Tuning of Surface Microfeatures Towards Smart Biointerfaces.

ABSTRACTWith the aim of providing an easy and versatile method for realizing conductive polymer surfaces with controlled micro and nano-scale topographical cues patterning, we deposited a ultra-thin film of the conductive polymer poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) on a thermo-retractable polystyrene sheet. Biaxial and uniaxial micro and nano-wrinkles were formed with different features depending on clamping geometry during shrinking of the substrate upon heating. Homogeneous nano and micro-patterning of surface topography over large areas (several cm2) was obtained. The formed wrinkles were very robust and adhered strongly to the substrate because of their penetration into the soft substrate during the heat-shrink process. In the case of uniaxial wrinkles a very well aligned quasi-periodic structure is formed with different populations of wavelengths ranging from submicrometric to 10-20 μm, depending on PEDOT:PSS thickness. Surface topography, wrinkles amplitude and wavelength have been evaluated by means of SEM and AFM and the results have been related to sheet resistance as measured with a four point probe technique. The realized conductive surfaces can offer new opportunities in the field of cell stimulation and growth.

The transmission properties in one-dimensional piezoelectric Fibonacci-class quasi-periodical phononic crystals

The transmission properties of phononic crystals in one-dimensional piezoelectric Fibonacci quasi-periodical superlattices are studied using the transfer matrix method. The transmission coefficients in piezoelectric Fibonacci quasi-periodical superlattices are compared with those of the phononic crystals with periodical structure and with non-piezoelectric Fibonacci quasi-periodical structure. The results show that the band gap can also be found in the phononic crystals with both piezoelectric and non-piezoelectric Fibonacci quasi-periodical superlattices, and the frequency range of the gap in piezoelectric Fibonacci quasi-periodical superlattices is larger than those of periodical structure and non-piezoelectric Fibonacci quasi-periodical structure. Furthermore, the transmission coefficients are studied as a function of the properties of the material and incidence angle of the wave. The results show that the transmission coefficients in piezoelectric Fibonacci quasi-periodical superlattices are correlated with incidence angle of the wave.