Aperiodic Structures Research Articles

Self-similar transmission properties of aperiodic Cantor potentials in gapped graphene

We investigate the transmission properties of quasiperiodic or aperiodic structures based on graphene arranged according to the Cantor sequence. In particular, we have found self-similar behaviour in the transmission spectra, and most importantly, we have calculated the scalability of the spectra. To do this, we implement and propose scaling rules for each one of the fundamental parameters: generation number, height of the barriers and length of the system. With this in mind we have been able to reproduce the reference transmission spectrum, applying the appropriate scaling rule, by means of the scaled transmission spectrum. These scaling rules are valid for both normal and oblique incidence, and as far as we can see the basic ingredients to obtain self-similar characteristics are: relativistic Dirac electrons, a self-similar structure and the non-conservation of the pseudo-spin. This constitutes a reduction of the number of conditions needed to observe self-similarity in graphene-based structures, see D\'iaz-Guerrero et al. [D. S. D\'iaz-Guerrero, L. M. Gaggero-Sager, I. Rodr\'iguez-Vargas, and G. G. Naumis, arXiv:1503.03412v1, 2015].

Narrow stop band optical filter using one-dimensional regular Fibonacci/Rudin Shapiro photonic quasicrystals

One-dimensional deterministic aperiodic multilayered photonic crystals can be formed by stacking together dielectric layers of several different types according to substitutional generalized Fibonacci or Rudin Shapiro sequences. An efficient numerical technique based on calculus of transfer matrix of multiple layers is used to study the formation of optical gaps. The quasi-periodicic distribution gives some interesting optical properties and offers a multitude of adjacent pseudo-band gaps in different frequency range. The potential of photonic structure are explored by varying the structural parameters. The presence of band gaps due to long-range correlations. Further analysis shows that the central frequency of transmission band (stop band) can be changed by varying the type of distribution of two considered layers which formed the all quasi-photonic crystals cells and the order of quasiperiodic sequences. The structure is exploited to design selective optical filters with narrow band gaps and polychromatic stop band filters. These results make aperiodic photonic structures very attractive for the engineering of novel passive photonic.

Chromatic Dispersion of an Optical Fiber Based on Photonic Quasicrystals with Twelve-Fold Symmetry and its Application as Directional Coupling

Optical fibers composed by photonic quasicrystals it is based on aperiodic structures characterized by at least two different symmetrical patterns from the base matrix. In this work, an optical fiber composed by quasi-periodic and symmetric matrix was analyzed using the finite element method in conjunction with cylindrical perfectly matched layers. The structure is composed by pure silica and/or silica doped with germanium, and originated from twelve distributions of air holes symmetrically with a defect caused by the absence of the fiber central hole. The obtained results shown that the structure in analysis exhibits an ultra-flat chromatic dispersion for a range of wavelengths varying from 1.4 to 1.6 µm covering the bands E,S, C and L, with chromatic dispersion, for the silica doped with germanium, varying between 22.1 and 23.01 [ps.km-1.nm-1]. This photonic quasicrystal fiber (PQCF) was used to form a coupler with three identical horizontal cores surrounded by air holes. The signal power launched in the central core is equally divided between the two neighboring cores with 50% of the coupling ratio.

Aperiodic multilayer structures in soft X-ray optics

We review a series of studies that address the development and application of aperiodic multilayer structures (aperiodic multilayer mirrors) as soft X-ray (SXR) (- nm) optical elements. We discuss the potential of such structures for reflecting SXR radiation in a broad wavelength range, primarily at normal radiation incidence, and as polarization elements (broadband polarizer mirrors and phase shifters). The results of multiparametric optimization are presented, and experimental data for aperiodic Mo/Si ( nm) multilayer mirrors are outlined. The feasibility of advancing to the nm domain by using other materials is examined, and the capabilities of aperiodic structures as elements of attosecond SXR optics are discussed.

Kolakoski sequence as an element to radiate giant forward and backward second harmonic signals

We propose a novel type of aperiodic one-dimensional photonic crystal structures which can be used for generating giant forward and backward second harmonic signals. The studied structure is formed by stacking together the air and nonlinear layers according to the Kolakoski self-generation scheme in which each nonlinear layer contains a pair of antiparallel 180° poled LiNbO3 crystal layers. For different generation stages of the structure, conversion efficiencies of forward and backward second harmonic waves have been calculated by nonlinear transfer matrix method. Numerical simulations show that conversion efficiencies in the Kolakoski-based multilayer are larger than the perfect ones for at least one order of magnitude. Especially for 33rd and 39th generation stages, forward second harmonic wave are 42 and 19 times larger, respectively. In this paper, we validate the strong fundamental field enhancement and localization within Kolakoski-based multilayer due to periodicity breaking which consequently leads to very strong radiation of backward and forward second harmonic signals. Following the applications of analogous aperiodic structures, we expect that Kolakosi-based multilayer can play a role in optical parametric devices such as multicolor second harmonic generators with high efficiency.

Propagation Dynamics of a Light Beam in a Fractional Schrödinger Equation.

The dynamics of wave packets in the fractional Schrödinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in the fractional Schrödinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional input chirped Gaussian beams is not harmonic. In one dimension, the beam propagates along a zigzag trajectory in real space, which corresponds to a modulated anharmonic oscillation in momentum space. In two dimensions, the input Gaussian beam evolves into a breathing ring structure in both real and momentum spaces, which forms a filamented funnel-like aperiodic structure. The beams remain localized in propagation, but with increasing distance display an increasingly irregular behavior, unless both the linear chirp and the transverse displacement of the incident beam are zero.

Pressure in the Landau-Ginzburg functional: Pascal's law, nucleation in fluid mixtures, a meanfield theory of amphiphilic action, and interface wetting in glassy liquids.

We set up the problem of finding the transition state for phase nucleation in multi-component fluid mixtures, within the Landau-Ginzburg density functional. We establish an expression for the coordinate-dependent local pressure that applies to mixtures, arbitrary geometries, and certain non-equilibrium configurations. The expression allows one to explicitly evaluate the pressure in spherical geometry, à la van der Waals. Pascal's law is recovered within the Landau-Ginzburg density functional theory, formally analogously to how conservation of energy is recovered in the Lagrangian formulation of mechanics. We establish proper boundary conditions for certain singular functional forms of the bulk free energy density that allow one to obtain droplet solutions with thick walls in essentially closed form. The hydrodynamic modes responsible for mixing near the interface are explicitly identified in the treatment; the composition at the interface is found to depend only weakly on the droplet size. Next we develop a Landau-Ginzburg treatment of the effects of amphiphiles on the surface tension; the amphiphilic action is seen as a violation of Pascal's law. We explicitly obtain the binding potential for the detergent at the interface and the dependence of the down-renormalization of the surface tension on the activity of the detergent. Finally, we argue that the renormalization of the activation barrier for escape from long-lived structures in glassy liquids can be viewed as an action of uniformly seeded, randomly oriented amphiphilic molecules on the interface separating two dissimilar aperiodic structures. This renormalization is also considered as a "wetting" of the interface. The resulting conclusions are consistent with the random first order transition theory.

Irene Manton, Erwin Schrödinger and the Puzzle of Chromosome Structure

Erwin Schrödinger's 1944 publication What is Life? is a classic of twentieth century science writing. In his book, Schrödinger discussed the chromosome fibre as the seat of heredity and variation thanks to a hypothetical aperiodic structure - a suggestion that famously spurred on a generation of scientists in their pursuit of the gene as a physico-chemical entity. While historical attention has been given to physicists who were inspired by the book, little has been written about its biologist readers. This paper examines the case of the English evolutionary botanist and cytologist Irène Manton, who took an interest in What is Life? for its relevance to her own research in chromosome structure as a clue to plant phylogeny. Drawing on recently discovered correspondence between Manton and Schrödinger, the paper reconstructs Manton 's path to the book (including the role of the chemist-philosopher Michael Polanyi) and her response to it by way of throwing new light on a pivotal moment in the history of the debate on chromosome structure.

Three‐Dimensional μ‐Printing: An Enabling Technology

In this progress report the development of three‐dimensional μ‐printing and its impact as an enabling technology onto different scientific fields is reviewed. Driven by direct laser writing via two‐photon absorption, the technology has reached a level of maturity and ease of application such that 3D printing on the micrometer scale can now be considered. While the underlying technology is still developing towards higher resolution and increasing speed of fabrication, the last five years have seen new fields rising that were obviously enabled by 3D μ‐printing. Among the recent technological developments discussed in this progress report are the fields of super‐resolution lithography and spatial light modulator‐based lithography. Novel fields relying on these technological advances like aperiodic photonic structures, mechanical metamaterials, and structures for biological studies will be reviewed. A glimpse into developing research directions will also be provided.

Fibonacci quasiregular graphene-based superlattices: Quasiperiodicity and its effects on the transmission, transport and electronic structure properties

We study the transmission, transport and electronic structure properties of aperiodic Fibonacci monolayer graphene-based structures (AFGBSs). The transfer matrix method has been implemented to obtain the transmittance, linear-regime conductance and electronic structure. In particular, we have studied two types of aperiodic graphene-based structures: (1) electrostatic AFGBSs (EAFGBSs), structures formed with electrostatic potentials, and (2) substrate AFGBSs (SAFGBSs), obtained alternating substrates that can open and non-open, such as SiC and SiO2, an energy bandgap on graphene. We have found that the transmission properties can be modulated readily by changing the main parameters of the systems: well and barrier widths, energy and angle of incident electrons and the degree of aperiodicity. In the case of the linear-regime conductance turns out that it diminishes various orders of magnitude increasing the barrier width for SAFGBSs. On the contrary, Klein tunneling sustains the conductance in EAFGBSs. Calculating the electronic structure or miniband-structure formation and its fragmentation we establish a direct connection between the conductance peaks and the opening, closure and degeneration of energy minibands for both EAFGSLs and SAFGSLs.

Characterization of aperiodic domain structure in lithium niobate by spontaneous parametric down-conversion spectroscopy

We develop a technique for detailed analysis of aperiodically poled crystalline nonlinear transfer functions. The method allows precise evaluation of 1D aperiodic domain structure amplitude spectra. It also allows determining the angle of periodic poling in respect to the crystalline z axis, as well as the dispersion of both ordinary and extraordinary refractive indexes in a broad spectral range. The measurement is non-destructive, and all data can be extracted from two frequency-angular spontaneous parametric down-conversion (SPDC) spectra. The precision of the domain structure analysis for aperiodically poled lithium niobate is increased by an order of magnitude in comparison to previously reported techniques based on spontaneous parametric down-conversion.

Spatial correlations and optical properties in three-dimensional deterministic aperiodic structures.

Photonic systems have strongly varying optical properties depending on the spatial correlations present in a given realization. In photonic crystals the correlations are spatially periodic forming Bravais lattices whereas the building blocks of an amorphous medium are randomly distributed without any long-range order. In this manuscript we study the optical properties of so-called deterministic aperiodic structures which fill the gap between the aforementioned two limiting cases. Within this group we vary the spectrum of the spatial correlations from being pure-point over singularly-continuous to absolutely-continuous. The desired correlations are created in direct-laser written three-dimensional polymer structures using one construction principle which allows us to attribute the optical behaviour solely to the encoded spectrum. Infrared reflection measurements reveal the characteristic response of each spectral type verifying the successful fabrication of large deterministic aperiodic structures. To prove the presence of the correlations in all directions we perform transmission experiments parallel to the substrate by means of micro-optical mirrors placed next to the structures. Transport measurements reveal a strong dependence of the effective beam width at the output facet on the encoded lattice type. Finally, we reproduce the lattice type dependent transport behavior in numerical calculations ruling out extrinsic experimental reasons for these findings.

Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations.

Systems of particles interacting with "stealthy" pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like "pseudo" disordered equilibrium hard-sphere systems in Fourier space. The pair statistics obey certain exact integral conditions with very high accuracy. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. In the crystalline regime (low densities), there exist aperiodic structures that are part of the ground-state manifold but yet are not entropically favored. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperature limit. Our techniques may be applied to sample the zero-temperature limit of the canonical ensemble of other potentials with highly degenerate ground states.

Complex plasma in g×B configurations: Stability switching and stationary structure

In a low-pressure magneto-gravitated complex plasma, the stability state of dust gravitational drift wave is switched at a critical wavenumber and the propagating dust magneto-gravitational drift wave is transformed into an aperiodic stationary structure at a cut-off wavenumber. In this paper, two analytical formulas have been derived for the critical wavenumber of stability switching and the cut-off wavenumber of stationary structure. The critical wavenumber is equal to the ratio of ion plasma frequency to ion streaming velocity and the cut-off wavenumber is proportional to the ratio of dust plasma frequency to dust g×B drift velocity. These scaling formulas are in excellent agreement with exact numerical solutions of dispersion relations. These scenarios are expected to be observed in fully magnetized dusty plasma experiments as the next frontier for complex plasma research.

Design and Performances of Three-Dimensional Lithium-Ion Battery

High-power and high-energy densities of lithium ion batteries are required, whereas there has been much less progress in the improvement of the conventional lithium ion batteries. Three-dimensional (3D) concept of batteries has been suggested to improve performances of batteries. A number of 3D architectures, such as 3D interdigitated rods, 3D interdigitated plates, concentric tube, and 3D aperiodic sponge structures, have been proposed in order to increase the areal energy density [1]. The 3D cells showed higher energy and power compared to the conventional structure of cells; however, their energy was limited due to the limitation of the manufacturing process.[2] In this paper, the novel design and the performances of 3D lithium ion battery were suggested. First, the 3D trench cathode structure was rendered without a conducting agent or a binder. The cathode has an internal current collector for the electronic conduction and was controlled as a thick-film. Lipon and Li metal were applied as the electrolyte and the anode, respectively. Expansion buffers were located in the anode to stable the cell structure under the anode expansion during the charge. The design of the 3D cell increased the energy density considerably, depending on the dimension of the electrode.

Methane as a diagnostic tracer of changes in the Brewer–Dobson circulation of the stratosphere

Abstract. This study makes use of time series of methane (CH4) data from the Halogen Occultation Experiment (HALOE) to detect whether there were any statistically significant changes of the Brewer–Dobson circulation (BDC) within the stratosphere during 1992–2005. The HALOE CH4 profiles are in terms of mixing ratio versus pressure altitude and are binned into latitude zones within the Southern Hemisphere and the Northern Hemisphere. Their separate time series are then analyzed using multiple linear regression (MLR) techniques. The CH4 trend terms for the Northern Hemisphere are significant and positive at 10° N from 50 to 7 hPa and larger than the tropospheric CH4 trends of about 3% decade−1 from 20 to 7 hPa. At 60° N the trends are clearly negative from 20 to 7 hPa. Their combined trends indicate an acceleration of the BDC in the middle stratosphere of the Northern Hemisphere during those years, most likely due to changes from the effects of wave activity. No similar significant BDC acceleration is found for the Southern Hemisphere. Trends from HALOE H2O are analyzed for consistency. Their mutual trends with CH4 are anti-correlated qualitatively in the middle and upper stratosphere, where CH4 is chemically oxidized to H2O. Conversely, their mutual trends in the lower stratosphere are dominated by their trends upon entry to the tropical stratosphere. Time series residuals for CH4 in the lower mesosphere also exhibit structures that are anti-correlated in some instances with those of the tracer-like species HCl. Their occasional aperiodic structures indicate the effects of transport following episodic, wintertime wave activity. It is concluded that observed multi-year, zonally averaged distributions of CH4 can be used to diagnose major instances of wave-induced transport in the middle atmosphere and to detect changes in the stratospheric BDC.

A Stable and Accurate Preconditioner for Bidirectional Beam Propagation Method

A stable and accurate preconditioner based on the Denman-Beavers iteration (DBI) for the square-root operator to construct an efficient bidirectional beam propagation method (Bi-BPM) is proposed. Utilizing a branch-cut rotation technique, numerical instability from the evanescent wave in classical DBI is nearly removed. The biconjugate gradient stabilized method is applied to solve the preconditioned formulations due to its fast convergence rate. Moreover, the present preconditioner is shown to be highly efficient for dealing with the optical devices with multiple longitudinal dielectric interfaces, especially for those with aperiodic structures since it can be simultaneously obtained during the calculation of the square root of the characteristic matrix. To validate the present approach, a typical single facet waveguide structure and two kinds of multilayer coating structures are considered as the numerical examples. Results show that the present Bi-BPM has the advantages of excellent convergence, and high accuracy and stability, superior to the widely used Pade approximation.

Conception of broadband stigmatic high-resolution spectrometers for the soft X-ray range

We formulate an approach to the development of stigmatic high-resolution spectral instruments for the soft X-ray range , which is based on the combined operation of normal-incidence multilayer mirrors (including broadband aperiodic ones) and grazing-incidence reflection gratings with nonequidistant grooves (so-called VLS gratings). A concave multilayer mirror serves to produce a slightly astigmatic image of the radiation source (for instance, an entrance slit), and the diffraction grating produces a set of its dispersed stigmatic spectral images. The width of the operating spectral region is determined by the aperiodic structure of the multilayer mirror and may range up to an octave in wavelength.

Periodically distributed objects with quasicrystalline diffraction pattern

It is possible to construct fully periodically distributed objects with a diffraction pattern identical to the one obtained for quasicrystals. These objects are probability distributions of distances obtained in the statistical approach to aperiodic structures distributed periodically. The diffraction patterns have been derived by using a two-mode Fourier transform—a very powerful method not used in classical crystallography. It is shown that if scaling is present in the structure, this two-mode Fourier transform can be reduced to a regular Fourier transform with appropriately rescaled scattering vectors and added phases. Detailed case studies for model sets 1D Fibonacci chain and 2D Penrose tiling are discussed. Finally, it is shown that crystalline, quasicrystalline, and approximant structures can be treated in the same way.

Design of reflective quarter-wave plates in extreme ultraviolet

Using an optimization method of layer thicknesses based on a genetic algorithm, aperiodic multilayer structures are designed, which display excellent quarter-wave plate (QWP) characteristics for extreme ultraviolet (EUV) radiation in reflection. In addition, a broadband QWP with 3eV bandwidth in the EUV region, was also designed with the same optimization algorithm and an adapted merit function. The structural and reflective characteristics of single photon energy and broadband reflective QWPs have been explored numerically. Fabricating such optical components could allow polarization control of EUV radiations and ultrafast EUV pulses.