Transformation Optics Based Finite-Difference Time-Domain Simulation of Superscattering

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In this dissertation we study the Transformation Optics Finite Difference Time-Domain (TO-FDTD) method. We show how applying a coordinate transformation can be employed to map an irregular mesh to a cartesian mesh. We apply the anisotropic FDTD method to solve the transformed Maxwell's equation in the new transformed grid. To validate our claim we model the local field near the metallic nanoparticles and superscattering. The TO method achieves the same level of accuracy or more with half the grid size mesh as the standard FDTD, and the computational cost is reduced compared to the standard FDTD method.

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