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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2016-05-10
Design and Simulation of Arbitrarily-Shaped Transformation Optic Devices Using a Simple Finite-Difference Method
By
Eric A. Berry,

    Dr. Eric A. Berry

    W. M. Keck Center for 3D Innovation

    University of Texas at El Paso

    USA

    Homepage

Jesus Gutierrez,

    Dr. Jesus Gutierrez

    EM Lab, W. M. Keck Center for 3D Innovation

    University of Texas at El Paso

    USA

    Homepage

Raymond C. Rumpf

    Dr. Raymond C. Rumpf

    Kraetonics LLC

    USA

    Homepage

Progress In Electromagnetics Research B, Vol. 68, 1-16, 2016
doi:10.2528/PIERB16012007 | Google Scholar

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.
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Citation
Eric A. Berry, Jesus Gutierrez, and Raymond C. Rumpf, "Design and Simulation of Arbitrarily-Shaped Transformation Optic Devices Using a Simple Finite-Difference Method," Progress In Electromagnetics Research B, Vol. 68, 1-16, 2016.
doi:10.2528/PIERB16012007
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