2016
Berry, Eric A; Gutierrez, Jesus; Rumpf, Raymond C
Design and simulation of arbitrarily-shaped transformation optic devices using a simple finite-difference method Journal Article
In: Progress In Electromagnetics Research B, vol. 68, pp. 1-16, 2016, ISSN: 1937-6472.
Abstract | Links | BibTeX | Tags: anisotropic finite-difference time-domain, spatial transforms, transformation optics
@article{RN108,
title = {Design and simulation of arbitrarily-shaped transformation optic devices using a simple finite-difference method},
author = {Eric A Berry and Jesus Gutierrez and Raymond C Rumpf},
url = {https://www.jpier.org/pierb/pier.php?paper=16012007},
doi = {doi:10.2528/PIERB16012007},
issn = {1937-6472},
year = {2016},
date = {2016-05-10},
journal = {Progress In Electromagnetics Research B},
volume = {68},
pages = {1-16},
abstract = {A fast and simple design methodology for transformation optics (TO) is described for devices having completely arbitrary geometries. An intuitive approach to the design of arbitrary devices is presented which enables possibilities not available through analytical coordinate transformations. Laplace's equation is solved using the finite-difference method to generate the arbitrary spatial transforms. Simple techniques are presented for enforcing boundary conditions and for isolating the solution of Laplace's equation to just the device itself. It is then described how to calculate the permittivity and permeability functions via TO from the numerical spatial transforms. Last, a modification is made to the standard anisotropic finite-difference frequency-domain (AFDFD) method for much faster and more efficient simulations. Several examples are given at the end to benchmark and to demonstrate the versatility of the approach. This work provides the basis for a complete set of tools to design and simulate transformation electromagnetic devices of any shape and size.},
keywords = {anisotropic finite-difference time-domain, spatial transforms, transformation optics},
pubstate = {published},
tppubtype = {article}
}
A fast and simple design methodology for transformation optics (TO) is described for devices having completely arbitrary geometries. An intuitive approach to the design of arbitrary devices is presented which enables possibilities not available through analytical coordinate transformations. Laplace's equation is solved using the finite-difference method to generate the arbitrary spatial transforms. Simple techniques are presented for enforcing boundary conditions and for isolating the solution of Laplace's equation to just the device itself. It is then described how to calculate the permittivity and permeability functions via TO from the numerical spatial transforms. Last, a modification is made to the standard anisotropic finite-difference frequency-domain (AFDFD) method for much faster and more efficient simulations. Several examples are given at the end to benchmark and to demonstrate the versatility of the approach. This work provides the basis for a complete set of tools to design and simulate transformation electromagnetic devices of any shape and size.
2015
Rumpf, Raymond C; Pazos, Javier J; Digaum, Jennefir L; Kuebler, Stephen M
Spatially variant periodic structures in electromagnetics Journal Article
In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 373, no. 2049, pp. 20140359, 2015, ISSN: 1364-503X.
Abstract | Links | BibTeX | Tags: fuctionally graded, metamaterials, metasurfaces, optics, photonic crystals, physiological optics, spatially variant, transformation optics
@article{RN102,
title = {Spatially variant periodic structures in electromagnetics},
author = {Raymond C Rumpf and Javier J Pazos and Jennefir L Digaum and Stephen M Kuebler},
url = {https://royalsocietypublishing.org/doi/full/10.1098/rsta.2014.0359},
doi = {https://doi.org/10.1098/rsta.2014.0359},
issn = {1364-503X},
year = {2015},
date = {2015-08-28},
journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences},
volume = {373},
number = {2049},
pages = {20140359},
abstract = {Spatial transforms are a popular technique for designing periodic structures that are macroscopically inhomogeneous. The structures are often required to be anisotropic, provide a magnetic response, and to have extreme values for the constitutive parameters in Maxwell's equations. Metamaterials and photonic crystals are capable of providing these, although sometimes only approximately. The problem still remains about how to generate the geometry of the final lattice when it is functionally graded, or spatially varied. This paper describes a simple numerical technique to spatially vary any periodic structure while minimizing deformations to the unit cells that would weaken or destroy the electromagnetic properties. New developments in this algorithm are disclosed that increase efficiency, improve the quality of the lattices and provide the ability to design aplanatic metasurfaces. The ability to spatially vary a lattice in this manner enables new design paradigms that are not possible using spatial transforms, three of which are discussed here. First, spatially variant self-collimating photonic crystals are shown to flow unguided waves around very tight bends using ordinary materials with low refractive index. Second, multi-mode waveguides in spatially variant band gap materials are shown to guide waves around bends without mixing power between the modes. Third, spatially variant anisotropic materials are shown to sculpt the near-field around electric components. This can be used to improve electromagnetic compatibility between components in close proximity.},
keywords = {fuctionally graded, metamaterials, metasurfaces, optics, photonic crystals, physiological optics, spatially variant, transformation optics},
pubstate = {published},
tppubtype = {article}
}
Spatial transforms are a popular technique for designing periodic structures that are macroscopically inhomogeneous. The structures are often required to be anisotropic, provide a magnetic response, and to have extreme values for the constitutive parameters in Maxwell's equations. Metamaterials and photonic crystals are capable of providing these, although sometimes only approximately. The problem still remains about how to generate the geometry of the final lattice when it is functionally graded, or spatially varied. This paper describes a simple numerical technique to spatially vary any periodic structure while minimizing deformations to the unit cells that would weaken or destroy the electromagnetic properties. New developments in this algorithm are disclosed that increase efficiency, improve the quality of the lattices and provide the ability to design aplanatic metasurfaces. The ability to spatially vary a lattice in this manner enables new design paradigms that are not possible using spatial transforms, three of which are discussed here. First, spatially variant self-collimating photonic crystals are shown to flow unguided waves around very tight bends using ordinary materials with low refractive index. Second, multi-mode waveguides in spatially variant band gap materials are shown to guide waves around bends without mixing power between the modes. Third, spatially variant anisotropic materials are shown to sculpt the near-field around electric components. This can be used to improve electromagnetic compatibility between components in close proximity.