2020
Berry, Eric A; Rumpf, Raymond C
Generating Spatially-Variant Metamaterial Lattices Designed from Spatial Transforms Journal Article
In: Progress In Electromagnetics Research M, vol. 92, pp. 103-113, 2020, ISSN: 1937-8726.
Abstract | Links | BibTeX | Tags: conformal mapping, transformation optics
@article{RN149,
title = {Generating Spatially-Variant Metamaterial Lattices Designed from Spatial Transforms},
author = {Eric A Berry and Raymond C Rumpf},
url = {https://www.jpier.org/PIERM/pierm92/10.19103004.pdf},
issn = {1937-8726},
year = {2020},
date = {2020-06-01},
journal = {Progress In Electromagnetics Research M},
volume = {92},
pages = {103-113},
abstract = {Spatial transform techniques like transformation optics and conformal mapping have arisen
as the dominant techniques for designing metamaterial devices. However, these techniques only produce
the electrical permittivity and permeability as a function of position. The manner in which these
functions are converted into physical metamaterial lattices remains elusive, except in some simple or
canonical configurations. Metamaterial lattices designed by spatial transforms are composed of elements
of different sizes, orientations, and designs. The elements must be distributed and oriented in a manner
that makes the final lattice smooth, continuous, have uniform density, be free of unintentional defects,
and have minimal distortions to the elements. Any of these would weaken or destroy the electromagnetic
properties of the lattice. This paper describes a general purpose method to generate such arbitrary
metamaterial lattices. Inputs to the algorithm are the permittivity and permeability functions as well
as the baseline metamaterials that can provide the necessary permittivity and permeability values.
In prior research, we reported a simple finite-difference technique for calculating the permittivity and
permeability functions for arbitrary shaped devices using transformation optics. The methodology
presented in this work is illustrated by generating an electromagnetic cloak of arbitrary shape that
was designed using the previously reported technique. The final metamaterial cloak is simulated using
the finite-difference time-domain method and performance compared to other cloaks reported in the
literature. },
keywords = {conformal mapping, transformation optics},
pubstate = {published},
tppubtype = {article}
}
Spatial transform techniques like transformation optics and conformal mapping have arisen
as the dominant techniques for designing metamaterial devices. However, these techniques only produce
the electrical permittivity and permeability as a function of position. The manner in which these
functions are converted into physical metamaterial lattices remains elusive, except in some simple or
canonical configurations. Metamaterial lattices designed by spatial transforms are composed of elements
of different sizes, orientations, and designs. The elements must be distributed and oriented in a manner
that makes the final lattice smooth, continuous, have uniform density, be free of unintentional defects,
and have minimal distortions to the elements. Any of these would weaken or destroy the electromagnetic
properties of the lattice. This paper describes a general purpose method to generate such arbitrary
metamaterial lattices. Inputs to the algorithm are the permittivity and permeability functions as well
as the baseline metamaterials that can provide the necessary permittivity and permeability values.
In prior research, we reported a simple finite-difference technique for calculating the permittivity and
permeability functions for arbitrary shaped devices using transformation optics. The methodology
presented in this work is illustrated by generating an electromagnetic cloak of arbitrary shape that
was designed using the previously reported technique. The final metamaterial cloak is simulated using
the finite-difference time-domain method and performance compared to other cloaks reported in the
literature.Â
as the dominant techniques for designing metamaterial devices. However, these techniques only produce
the electrical permittivity and permeability as a function of position. The manner in which these
functions are converted into physical metamaterial lattices remains elusive, except in some simple or
canonical configurations. Metamaterial lattices designed by spatial transforms are composed of elements
of different sizes, orientations, and designs. The elements must be distributed and oriented in a manner
that makes the final lattice smooth, continuous, have uniform density, be free of unintentional defects,
and have minimal distortions to the elements. Any of these would weaken or destroy the electromagnetic
properties of the lattice. This paper describes a general purpose method to generate such arbitrary
metamaterial lattices. Inputs to the algorithm are the permittivity and permeability functions as well
as the baseline metamaterials that can provide the necessary permittivity and permeability values.
In prior research, we reported a simple finite-difference technique for calculating the permittivity and
permeability functions for arbitrary shaped devices using transformation optics. The methodology
presented in this work is illustrated by generating an electromagnetic cloak of arbitrary shape that
was designed using the previously reported technique. The final metamaterial cloak is simulated using
the finite-difference time-domain method and performance compared to other cloaks reported in the
literature.Â