Center for Photonic and Smart Materials (CPMS), Zewail City of Science and Technology, Sheikh Zayed District, 6th of October City, 12588 Giza, Egypt. For any photonic device simulation, the accuracy of the numerical solution not only depends on the methods being used but also on the discretization parameters used in that numerical method. The analysis of optical waveguides with strong longitudinal and transverse discontinuities remains a defiance facing numerical techniques. In this work, three innovative methods will be presented to overcome some of the problems facing the traditional methods of modeling photonic devices, especially plasmonics. A new smoothed finite element method (SFEM) is proposed to analyse time domain wave propagation in photonic devices. Moreover, to accurately analyze plasmonic structures with strong discontinuities, a stable Bidirectional Beam Propagation Method (BiBPM) based on Blocked Schur (BS) algorithm is introduced. Finally, an accurate and computationally efficient rational Chebyshev multi-domain pseudospectral method (RC-MDPSM) for modal analysis of Photonic devices is presented. The efficiency of the suggested technique stems from using rational Chebyshev basis functions to accurately represent the semi-infinite computational domain; thus, eliminating the use of PML like absorbing boundary conditions.
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