1,595 research outputs found
Isotropic properties of the photonic band gap in quasicrystals with low-index contrast
We report on the formation and development of the photonic band gap in
two-dimensional 8-, 10- and 12-fold symmetry quasicrystalline lattices of low
index contrast. Finite size structures made of dielectric cylindrical rods were
studied and measured in the microwave region, and their properties compared
with a conventional hexagonal crystal. Band gap characteristics were
investigated by changing the direction of propagation of the incident beam
inside the crystal. Various angles of incidence from 0 \degree to 30\degree
were used in order to investigate the isotropic nature of the band gap. The
arbitrarily high rotational symmetry of aperiodically ordered structures could
be practically exploited to manufacture isotropic band gap materials, which are
perfectly suitable for hosting waveguides or cavities.Comment: 16 pages, 7 figures, submitted to PR
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
Numerical Methods for Quasicrystals
Quasicrystals are one kind of space-filling structures. The traditional
crystalline approximant method utilizes periodic structures to approximate
quasicrystals. The errors of this approach come from two parts: the numerical
discretization, and the approximate error of Simultaneous Diophantine
Approximation which also determines the size of the domain necessary for
accurate solution. As the approximate error decreases, the computational
complexity grows rapidly, and moreover, the approximate error always exits
unless the computational region is the full space. In this work we focus on the
development of numerical method to compute quasicrystals with high accuracy.
With the help of higher-dimensional reciprocal space, a new projection method
is developed to compute quasicrystals. The approach enables us to calculate
quasicrystals rather than crystalline approximants. Compared with the
crystalline approximant method, the projection method overcomes the
restrictions of the Simultaneous Diophantine Approximation, and can also use
periodic boundary conditions conveniently. Meanwhile, the proposed method
efficiently reduces the computational complexity through implementing in a unit
cell and using pseudospectral method. For illustrative purpose we work with the
Lifshitz-Petrich model, though our present algorithm will apply to more general
systems including quasicrystals. We find that the projection method can
maintain the rotational symmetry accurately. More significantly, the algorithm
can calculate the free energy density to high precision.Comment: 27 pages, 8 figures, 6 table
Design of crystal-like aperiodic solids with selective disorder--phonon coupling
Functional materials design normally focuses on structurally-ordered systems
because disorder is considered detrimental to many important physical
properties. Here we challenge this paradigm by showing that particular types of
strongly-correlated disorder can give rise to useful characteristics that are
inaccessible to ordered states. A judicious combination of low-symmetry
building unit and high-symmetry topological template leads to aperiodic
"procrystalline" solids that harbour this type of topological disorder. We
identify key classes of procrystalline states together with their
characteristic diffraction behaviour, and establish a variety of mappings onto
known and target materials. Crucially, the strongly-correlated disorder we
consider is associated with specific sets of modulation periodicities
distributed throughout the Brillouin zone. Lattice dynamical calculations
reveal selective disorder-phonon coupling to lattice vibrations characterised
by these same periodicities. The principal effect on the phonon spectrum is to
bring about dispersion in energy rather than wave-vector, as in the
poorly-understood "waterfall" effect observed in relaxor ferroelectrics. This
property of procrystalline solids suggests a mechanism by which
strongly-correlated topological disorder might allow new and useful
functionalities, including independently-optimised thermal and electronic
transport behaviour as required for high-performance thermoelectrics.Comment: 4 figure
Computation and visualization of photonic quasicrystal spectra via Blochs theorem
Previous methods for determining photonic quasicrystal (PQC) spectra have
relied on the use of large supercells to compute the eigenfrequencies and/or
local density of states (LDOS). In this manuscript, we present a method by
which the energy spectrum and the eigenstates of a PQC can be obtained by
solving Maxwells equations in higher dimensions for any PQC defined by the
standard cut-and-project construction, to which a generalization of Blochs
theorem applies. In addition, we demonstrate how one can compute band
structures with defect states in the higher-dimensional superspace with no
additional computational cost. As a proof of concept, these general ideas are
demonstrated for the simple case of one-dimensional quasicrystals, which can
also be solved by simple transfer-matrix techniques.Comment: Published in Physical Review B, 77 104201, 200
Local symmetries and perfect transmission in aperiodic photonic multilayers
We develop a classification of perfectly transmitting resonances occuring in
effectively one-dimensional optical media which are decomposable into locally
reflection symmetric parts. The local symmetries of the medium are shown to
yield piecewise translation-invariant quantities, which are used to distinguish
resonances with arbitrary field profile from resonances following the medium
symmetries. Focusing on light scattering in aperiodic multilayer structures, we
demonstrate this classification for representative setups, providing insight
into the origin of perfect transmission. We further show how local symmetries
can be utilized for the design of optical devices with perfect transmission at
prescribed energies. Providing a link between resonant scattering and local
symmetries of the underlying medium, the proposed approach may contribute to
the understanding of optical response in complex systems.Comment: 8 pages, 4 figure
Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra
The paper investigates how correlations can completely specify a uniformly
discrete point process. The setting is that of uniformly discrete point sets in
real space for which the corresponding dynamical hull is ergodic. The first
result is that all of the essential physical information in such a system is
derivable from its -point correlations, . If the system is
pure point diffractive an upper bound on the number of correlations required
can be derived from the cycle structure of a graph formed from the dynamical
and Bragg spectra. In particular, if the diffraction has no extinctions, then
the 2 and 3 point correlations contain all the relevant information.Comment: 16 page
Hybrid photonic-bandgap accelerating cavities
In a recent investigation, we studied two-dimensional point-defected photonic
bandgap cavities composed of dielectric rods arranged according to various
representative periodic and aperiodic lattices, with special emphasis on
possible applications to particle acceleration (along the longitudinal axis).
In this paper, we present a new study aimed at highlighting the possible
advantages of using hybrid structures based on the above dielectric
configurations, but featuring metallic rods in the outermost regions, for the
design of extremely-high quality factor, bandgap-based, accelerating
resonators. In this framework, we consider diverse configurations, with
different (periodic and aperiodic) lattice geometries, sizes, and
dielectric/metal fractions. Moreover, we also explore possible improvements
attainable via the use of superconducting plates to confine the electromagnetic
field in the longitudinal direction. Results from our comparative studies,
based on numerical full-wave simulations backed by experimental validations (at
room and cryogenic temperatures) in the microwave region, identify the
candidate parametric configurations capable of yielding the highest quality
factor.Comment: 13 pages, 5 figures, 3 tables. One figure and one reference added;
minor changes in the tex
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