الفهرس 
English summaryOnly 14 pages are availabe for public view
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Abstract
In this thesis, we have developed a home-built finite element bidirectional beam propagation method (FE-BiBPM) to be used in the reliable modeling and design of both plasmonic and quantum devices. In this thesis, one of the major problems facing both plasmonic and quantum devices, specially hybrid dielectric-plasmonic devices and electron based devices, is being addressed, that is the accuracy and stability problems when treating very-high-index-contrast structures with strong discontinuities in the propagation direction using existing methods. A study of the physical reasons behind the failure of these methods has been demonstrated. Moreover, we have developed a completely new BiBPM solving Maxwell’s equations by adopting Blocked Schur (BS) algorithm (BS-FE-BiBPM) to introduce an unconditionally-stable method able to efficiently treat such plasmonic structures. In addition to the computational speed of our proposed method, it overbears the instability and accuracy problems of conventional methods thanks to the proper physical treatment of surface and evanescent waves; the notorious sources of instability. Through plasmonic discontinuity problems, the superiority of BS approach has been determined numerically and explained physically. Furthermore, when the dimensions of the structures are reduced to a few nanometers/sub-nanometer, quantum effects start to appear and have to be taken into accounts while modeling such structures. So, we have extended our FE-BiBPM to solve time-independent-Schrödinger equation to be able to efficiently describe such quantum effects at nanoscale. The efficiency of BS-FE-BiBPM with quantum devices has been proven through the analysis of some modern electron-based devices such as a quantum waveguide transistor. Moreover, the analysis time is substantially reduced to only few seconds compared to multiple hours using the conventional quantum solvers.