1,611 research outputs found
Robust topology optimization of three-dimensional photonic-crystal band-gap structures
We perform full 3D topology optimization (in which "every voxel" of the unit
cell is a degree of freedom) of photonic-crystal structures in order to find
optimal omnidirectional band gaps for various symmetry groups, including fcc
(including diamond), bcc, and simple-cubic lattices. Even without imposing the
constraints of any fabrication process, the resulting optimal gaps are only
slightly larger than previous hand designs, suggesting that current photonic
crystals are nearly optimal in this respect. However, optimization can discover
new structures, e.g. a new fcc structure with the same symmetry but slightly
larger gap than the well known inverse opal, which may offer new degrees of
freedom to future fabrication technologies. Furthermore, our band-gap
optimization is an illustration of a computational approach to 3D dispersion
engineering which is applicable to many other problems in optics, based on a
novel semidefinite-program formulation for nonconvex eigenvalue optimization
combined with other techniques such as a simple approach to impose symmetry
constraints. We also demonstrate a technique for \emph{robust} topology
optimization, in which some uncertainty is included in each voxel and we
optimize the worst-case gap, and we show that the resulting band gaps have
increased robustness to systematic fabrication errors.Comment: 17 pages, 9 figures, submitted to Optics Expres
Extremal Spectral Gaps for Periodic Schr\"odinger Operators
The spectrum of a Schr\"odinger operator with periodic potential generally
consists of bands and gaps. In this paper, for fixed m, we consider the problem
of maximizing the gap-to-midgap ratio for the m-th spectral gap over the class
of potentials which have fixed periodicity and are pointwise bounded above and
below. We prove that the potential maximizing the m-th gap-to-midgap ratio
exists. In one dimension, we prove that the optimal potential attains the
pointwise bounds almost everywhere in the domain and is a step-function
attaining the imposed minimum and maximum values on exactly m intervals.
Optimal potentials are computed numerically using a rearrangement algorithm and
are observed to be periodic. In two dimensions, we develop an efficient
rearrangement method for this problem based on a semi-definite formulation and
apply it to study properties of extremal potentials. We show that, provided a
geometric assumption about the maximizer holds, a lattice of disks maximizes
the first gap-to-midgap ratio in the infinite contrast limit. Using an explicit
parametrization of two-dimensional Bravais lattices, we also consider how the
optimal value varies over all equal-volume lattices.Comment: 34 pages, 14 figure
'Hexagon-type' photonic crystal slabs based on SOI
In this paper we discuss the design of a novel category of photonic crystal slabs (PCS) and as an example, we consider structures based on SOI wafers. Fabrication issues related to lithographic accuracy are addressed, too. The geometry consists in a triangular lattice of hexagons having their symmetry axes rotated with respect to the lattice.We show that the mirror-symmetric 'hexagon-type' PCS with air claddings can have an absolute (i.e. polarization independent) gap in guided modes with normalized width of approximately 10%. This gap, although reduced to about 4%, is still present in an asymmetric geometry, when the under-cladding is a silicon oxide layer with deeply etched holes
Dispersive Elastodynamics of 1D Banded Materials and Structures: Design
Within periodic materials and structures, wave scattering and dispersion
occur across constituent material interfaces leading to a banded frequency
response. In an earlier paper, the elastodynamics of one-dimensional periodic
materials and finite structures comprising these materials were examined with
an emphasis on their frequency-dependent characteristics. In this work, a novel
design paradigm is presented whereby periodic unit cells are designed for
desired frequency band properties, and with appropriate scaling, these cells
are used as building blocks for forming fully periodic or partially periodic
structures with related dynamical characteristics. Through this multiscale
dispersive design methodology, which is hierarchical and integrated, structures
can be devised for effective vibration or shock isolation without needing to
employ dissipative damping mechanisms. The speed of energy propagation in a
designed structure can also be dictated through synthesis of the unit cells.
Case studies are presented to demonstrate the effectiveness of the methodology
for several applications. Results are given from sensitivity analyses that
indicate a high level of robustness to geometric variation.Comment: 33 text pages, 27 figure
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