Complicated Unit Cells Research Articles

Dipole Radiation-Induced Extraordinary Optical Transmission for Silver Nanorod-Covered Silver Nanohole Arrays

A new extraordinary optical transmission (EOT) mode is discovered when a hexagonal Ag nanohole array is covered by a tilted Ag nanorod array. The resonant wavelength of this EOT mode red-shifts with respect to the normal EOT mode predicted by plasmon-grating coupling theory or dynamic scattering theory and increases linearly with the nanorod length. The structures also show strong polarization dependence; i.e., when the electric field (E-field) direction of the incident light is perpendicular to the long axis of the nanorods, only normal EOT spectrum is visible, but when the E-field is parallel to nanorod axis, the new mode appears. Our finite-difference-time-domain calculations confirm this finding and show that this new mode is due to the dipole radiation of the nanorods on top of the nanoholes. It is expected that other complicated unit cells of nanohole arrays could generate other new EOT modes and can be used to design new optical devices.

Mesoscale modeling of S-2 Glass/SC-15 epoxy composites: 3D-weave architecture

The addition of Z-yarns to an S-2 glass composite can increase the material's resistance to interlayer delamination and damage. However, the presence of the Z-yarns also complicates the resulting constitutive behavior, as multiple individual failure mechanisms (e.g. yarn/matrix delamination, yarn breakage) may occur before the overall ultimate failure of the composite is reached. A mesoscale model of a 3D-weave composite was created to provide insights into these processes. Material models for the yarns, matrix, and interfaces were previously developed for a similar plain-weave composite. These were combined with a complicated unit cell geometry that could be used to construct specimen meshes that closely matched the physical characteristics of the 3D-weave composite. Numerical simulations conducted using this model can reproduce most aspects of the load–displacement curves and the observed failure mechanisms from tension, torsion, and delamination tests.

Exploiting Mechanical Flexure as a Means of Tuning the Responses of Large-Scale Periodic Structures

We present techniques for designing large-scale, mechanically tunable periodic structures (PSs). Overlapping combined with relative movement, stretching/compression, and flexure are the three mechanical tuning techniques studied in this paper. We demonstrate that all of these mechanical movements may be used to tune the capacitance and inductance of elementary periodic structures with capacitive and inductive surface impedances over wide ranges of values. Analytic formulas for calculating the variable inductance and capacitance of these tunable PSs are also provided. These elementary PSs are the building blocks of a wide range of other PSs with more complicated unit cells and response types. One such structure—a frequency selective surface (FSS) composed of series combination of these inductive and capacitive structures—is also examined to demonstrate the application of the proposed tuning and analysis concepts. The FSS is fabricated on an accordion-like substrate that can be contracted or stretched to change its frequency of operation. The response and tuning properties of this structure are experimentally characterized using a free-space measurement system. A very good agreement between theory and experiment is obtained. This demonstrates that the behavior of such complex mechanically tunable PSs can be analyzed by examining the behavior of their constitutive inductive and capacitive elements.

Bethe–Salpeter calculation of optical-absorption spectra of In2O3 and Ga2O3

Transparent conducting oxides keep attracting strong scientific interest not only due to their promising potential for ‘transparent electronics’ applications but also due to their intriguing optical absorption characteristics. Materials such as In2O3 and Ga2O3 have complicated unit cells and, consequently, are interesting systems for studying the physics of excitons and anisotropy of optical absorption. Since currently no experimental data is available, for instance, for their dielectric functions across a large photon-energy range, we employ modern first-principles computational approaches based on many-body perturbation theory to provide theoretical-spectroscopy results. Using the Bethe–Salpeter framework, we compute dielectric functions and we compare to spectra computed without excitonic effects. We find that the electron–hole interaction strongly modifies the spectra and we discuss the anisotropy of optical absorption that we find for Ga2O3 in relation to existing theoretical and experimental data.

The effective conductivity of arrays of squares: Large random unit cells and extreme contrast ratios

An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends recent work on multi-component checkerboards at medium contrast ratios. General improvement include the simplification of a long-range preconditioner, the use of a banded solver, and a more efficient placement of quadrature points. This, together with a reduction in the number of unknowns, allows for a substantial increase in achievable accuracy as well as in tractable system size. Results, accurate to at least nine digits, are obtained for random checkerboards with over a million squares in the unit cell at contrast ratio 10 6. Furthermore, the scheme is flexible enough to handle complex valued conductivities and, using a homotopy method, purely negative contrast ratios. Examples of the accurate computation of resonant spectra are given.

Optical properties of photonic crystal slabs with an asymmetrical unit cell

Using the unitarity and reciprocity properties of the scattering matrix, we analyse the symmetry and resonant optical properties of the photonic crystal slabs (PCS) with complicated unit cell. We show that the reflectivity is not changed upon the 180deg-rotation of the sample around the normal axis, even in PCS with asymmetrical unit cell. Whereas the transmissivity becomes asymmetrical if the diffraction or absorption are present. The PCS reflectivity peaks to unity near the quasiguided mode resonance for normal light incidence in the absence of diffraction, depolarisation, and absorptive losses. For the oblique incidence the full reflectivity is reached only in symmetrical PCS.

A new method for calculation of crystal susceptibilities for X-ray diffraction at arbitrary wavelength

A novel method for the calculation of the X-ray susceptibility of a crystal in a wide range of radiation wavelengths is described. An analytical interpolation of one-electron wave functions is built to approximate the solution to Hartree-Fock equations for all atoms and ions of the periodic system of elements with high accuracy. These functions allow the calculation of the atomic form factors in the entire range of a transmitted momentum as well as the description of their anisotropy taking into account external and intracrystalline fields. Also, an analytical approximation for the force matrix of an arbitrary crystal is obtained and the microscopic calculation of the Debye-Waller factor for crystals with a complicated unit cell is presented.

A continuum model for the growth of epitaxial films

The continuum equations presented here model the growth of epitaxial films in terms of a local edge density ∼ ∇h and surface concentration (number density) of adatoms. This model is more amenable to computations than existing models that feature discrete edges and solve continuum equations on each terrace; yet it offers a more detailed picture than continuum models that treat the surface height as the only dependent variable. This latter feature is especially important if one wishes to account for several species which may react on the surface of the film or at step edges to build complicated unit cells. The model is motivated by and compared with numerical solutions of rate equations which are derived from kinetic Monte-Carlo simulations. After introducing the model in a 1+1 dimensional setting, we extend it to a 2+1 dimensional setting assuming spatial derivatives become surface gradients. We also discuss extension for the case with multiple species.

A program for calculating photonic band structures, Green's functions and transmission/reflection coefficients using a non-orthogonal FDTD method

In this paper we present an updated version of our ONYX program for calculating photonic band structures using a non-orthogonal finite difference time domain method. This new version employs the same transparent formalism as the first version with the same capabilities for calculating photonic band structures or causal Green's functions but also includes extra subroutines for the calculation of transmission and reflection coefficients. Both the electric and magnetic fields are placed onto a discrete lattice by approximating the spacial and temporal derivatives with finite differences. This results in discrete versions of Maxwell's equations which can be used to integrate the fields forwards in time. The time required for a calculation using this method scales linearly with the number of real space points used in the discretization so the technique is ideally suited to handling systems with large and complicated unit cells.

A program for calculating photonic band structures and Green's functions using a non-orthogonal FDTD method

We present a program which will calculate either the photonic band structure or the causal Green's function for photons incident on a complex dielectric structure. The method we use is a variant on the finite difference time domain (FDTD) method familiar to the electric engineering community, also known as the order(N) method. However, we employ a new transparent formalism which simplifies the stability analysis and identification of conserved quantities, as well as allowing the use of non-orthogonal coordinate systems without the usual computational overheads. Both the electric and magnetic fields are placed onto a discrete lattice by approximating the spacial and temporal derivatives with finite differences. This results in discrete versions of Maxwell's equations which can be used to integrate the fields forwards in time. The time required for a calculation using this method scales linearly with the number of real space points used in the discretisation so the technique is ideally suited to handling systems with large and complicated unit cells.

Order and Disorder in Boron Phases

The complicated rhombohedral unit cell of crystalline 03B2-boron containing 105 atoms is a good approximant structure for a quasicrystal. Thus one may wonder if between the amorphous and the crystalline phases of boron, a non-metallic quasi-crystalline phase could exist. In order to examine this possibility and to characterize order and disorder in boron phases, we have performed high resolution electron microscopy (HREM) and electron energy loss spectroscopy (EELS) measurements. In the crystalline phase, the creation of large number of microtwins and stacking faults is the way that nature chooses to disorder boron. The presence of these microtwins seems to be the major obstacle towards the formation of a quasicrystal. A comparison between energy loss near edge structures and electronic density of states for different boron compounds has allowed us to identify the signature of the icosahedra in EELS measurements. In the amorphous phase, a special processing of HREM images proposed by Fan and Cowley has been applied in order to estimate the extent of local order in amorphous boron. Both techniques (HREM and EELS) have confirmed the presence of icosahedral units in the amorphous phase. This raises the question of the existence of a quasi-crystalline phase.

Erratum: X-ray crystal-truncation-rod analysis of untwinned YBa2Cu3O7- delta single crystals: The growth-termination plane

Crystal truncation rods (CTR's), or x-ray scattering from a terminated surface of a three-dimensional single crystal, were measured for untwinned single crystals of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$. An expression for the intensity along the CTR's, which may be directly applied to a structure with a complicated unit cell, was derived from a Bloch wave expansion of the electron density. Data analysis using this expression indicates that the most probable metal-containing layer at the terminating surface of a flux-grown ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystal is the Y layer.

X-ray crystal-truncation-rod analysis of untwinned YBa2Cu3O7- delta single crystals: The growth-termination plane.

Crystal truncation rods (CTR's), or x-ray scattering from a terminated surface of a three-dimensional single crystal, were measured for untwinned single crystals of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$. An expression for the intensity along the CTR's, which may be directly applied to a structure with a complicated unit cell, was derived from a Bloch wave expansion of the electron density. Data analysis using this expression indicates that the most probable metal-containing layer at the terminating surface of a flux-grown ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystal is the Y layer.

Internal strain and lattice deformation of molecular-beam-epitaxy-grown GaInAsSb on GaAs substrate

The X-ray double-crystal diffraction technique has been applied to a study of the internal strain and lattice deformation of GaInAsSb epitaxial layers grown on GaAs substrate by molecular beam epitaxy. The results reveal a more complicated unit cell geometry of the GaInAsSb film which is different from the usually assumed tetragonal deformation plus an external tilt of the epilayer unit cell. Theoretical values of lattice mismatch Δa/avs. Ga1−xInxAs1−ySby epitaxial layer composition y at various lasing wavelengths are presented and compared with the experimental results. It is found that for a given lasing wavelength, e.g. 2.6 μm, Δa/a exhibits a minimum value over the entire composition range, thus expecting GaInAsSb to have the minimum internal strain at this critical point, which may be used as a guide to achieve the best-structure device design. Misorientation between the GaInAsSb epitaxial layer and GaAs substrate was observed and has been characterized more precisely with the presented X-ray double-crystal diffraction formalism.

The 6-A crystal structure of delta 5-3-ketosteroid isomerase. Architecture and location of the active center.

The crystal structure of the dimeric steroid metabolizing enzyme, delta 5-3-ketosteroid isomerase (EC 5.3.3.1), has been solved to 6-A resolution by multiple isomorphous replacement, augmented by real space direct methods. The unit cell is hexagonal (space group P6122) with dimensions a = b = 65.4 A, c = 504 A, and contains four identical 13,400-dalton protomers in each of its 12 asymmetric units. The 504-A c axis required double focusing mirrors (Franks optics) to resolve the reflections. The complexity of the combined local and lattice symmetry necessitated direct methods to establish the positions of heavy atoms in even the simplest of the isomorphous derivatives. The electron density map clearly showed both (a) the elaborate packing scheme of protomers, which accounts for this large and complicated unit cell, and (b) the coarse features of the functional dimer. The steroid-binding site has been established by imaging the bound inhibitor, 4-acetoxymercuriestradiol, in a difference Fourier map. Each of the dimer's two steroid-binding sites lies completely within one subunit but close enough to the opposing subunit that functional interactions may be possible.

Electronic properties of strained-layer superlattices

The electronic properties of semiconductor superlattices can be intentionally varied by changing their quantum well structures, i.e., by changing their layer thicknesses and their layer alloy compositions. New flexibility in varying superlattice electronic properties occurs in strained-layer superlattices, since lattice-mismatched materials can be used for the individual layers. The flexible choice of layer materials and layer thicknesses in strained-layer superlattices makes possible the tailoring of various superlattice electronic properties to desired values. Calculated values for several adjustable material properties in ternary strained-layer superlattices are presented to illustrate this tailorability. The potential advantages of new types of superlattices with more complicated unit cells are also discussed.

Eigenenergies of linear systems with periodic structures

Using a new technique of amplitude analysis, the eigenvalues and eigenenergies are analyzed for finite and infinite linear harmonic chains with any periodic structures of two species. A new phase function which is "additive" for each unit cell can be constructed. In terms of this phase function, the eigenvalue equation is reduced to a low-order algebraic equation specified completely by the unit cell. Symmetry properties among the "cyclicly" permuted unit cells, analytic properties, vertex classification, diagram expansions, leading behavior, and reduction constraints (relating structure of more complicated unit cell to less complicated ones) are developed. For infinite systems, the density of states can be expressed in closed form as a single term. Eigenvectors also demonstrate collective behavior throughout the whole system.

Determination of the self-consistent band structure of CrCl3, CrBr3, NiCl2, and NiBr2by the intersecting-spheres model

It has been proven previously that the intersecting-spheres model is capable of providing accurate band structures for Si and Ge. In order to compute the electronic structure of solids with a complicated unit cell, the intersecting-spheres model has been simply modified to neglect the core states in the secular equations without significant loss of accuracy. The model formulated in this way has been used to determine the self-consistent band structure of Cr${\mathrm{Cl}}_{3}$, Cr${\mathrm{Br}}_{3}$, Ni${\mathrm{Cl}}_{2}$, and Ni${\mathrm{Br}}_{2}$; the electronic structures of all these materials turned out to be essentially similar. For Ni${\mathrm{Cl}}_{2}$ and Ni${\mathrm{Br}}_{2}$, our results were compared with existing photoemission data, and satisfactory agreement between calculated and observed structures was found. For all the crystals investigated, a comparison was also made with ultraviolet optical and thermoreflectance data; through this comparison it seems possible to attempt a unique interpretation of the observed spectra in terms of transitions occurring between the occupied halogen $p$ bands and the unoccupied metal $s$ and $p$ bands.