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Array Integral Equation-Fast Fourier Transform Solver for Simulation of Supercells and Aperiodic Penetrable Metamaterials

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A hybrid surface integral equation solver based on the hierarchical matrix, the integral equation fast Fourier transform method and the equivalent surface method is developed for simulation of (pseudo-) periodic optical metamaterial problems. The solver is typically suitable for problems with (1) large periodic supercell or aperiodic cell arrays, (2) dominance of near field interactions, (3) presence of deep subwavelength features and (4) high geometry surface to volume ratio. An integral equation accelerator is introduced which uses a four to six level block Toeplitz matrix structure which naturally maps to the pseudo-periodic structure of metamaterial array problems, eliminates the need for the correction process encountered in fast Fourier transform-based methods and leads to substantial recycling of near field matrices. Novel metamaterial designs such as a supercell metamaterials, an aperiodic metasurfaces an a surface Luneburg lens are presented and solved, verifying the efficiency and accuracy of the presented model.
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Document Type: Research Article

Publication date: October 1, 2015

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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