Finite-difference time-domain simulations of metamaterials

Zhengwei Hao
Northeastern University
Northeastern University, 2012


   title={Finite-difference time-domain simulations of metamaterials},

   author={Hao, Zhengwei},



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Metamaterials are periodic structures created by many identical scattering objects which are stationary and small compared to the wavelength of electromagnetic wave applied to it so that when combined with different elements, these materials have the potential to be coupled to the applied electromagnetic wave without modifying the structure. Due to their unusual properties that are not readily available in nature, metamaterials have been drawing significant attentions in many research areas, including theoretical, experimental as well as numerical investigations. As one of the major computational electromagnetic modeling methods, finite-difference time-domain (FDTD) technique tackles problems by providing a full wave solution. FDTD, which is able to show transient evolution of interactions between electromagnetic wave and physical objects, not only has the advantage in dispersive and nonlinear material simulations, but also has the ability to model circuit elements including semiconductor devices. All these features make FDTD a competitive candidate in numerical methods of metamaterial simulations. This dissertation presents the implementation of FDTD technique to deal with three dimensional (3D) problems characterized with metamaterial structures. We endeavor to make the FDTD engine multi-functional and fast, as depicted in the following three efforts: We incorporated FDTD engine with the stable and highly efficient model for materials with dispersion, nonlinearity and gain properties. We coupled FDTD engine with SPICE, the general-purpose and powerful analog electronic circuit simulator. This makes FDTD ready to simulate complex semiconductor devices and provides a variety of possibilities for novel metamaterials. We investigated the cutting-edge area of Graphics Processing Units (GPU) computing module to speed up the FDTD engine, and implemented subgridding system to target more efficient modeling for metamaterial applications with embedded fine structures. The contribution of this work is toward the development of a powerful FDTD engine for modern metamaterial analysis. Our implementation could be used to improve the analysis of a number of electromagnetic problems.
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