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25 April 2006 A novel finite element method for the modeling of multiple reflections in photonic integrated circuits
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The complex transverse waveguide geometries of integrated photonic devices warrant the application of intricate Numerical Methods when modelling these types of Planar Lightwave Circuits (PLC). To aggravate the problem, difficulties also arise when dealing with back-reflections at interfaces, counter-propagating signals and other associated losses. Routines such as the Finite Element Method (FEM) and Finite Difference Method (FDM) are utilised in simulating the propagation of light through the core waveguide structures of these PLCs. In this paper a novel FEM reliant upon device cross-sectional symmetry is proposed, developed and discussed in regards to its advantages in precision over other procedures. Upon completion of this analysis, the propagation constant and effective refractive indices are known and extensions may be employed to accurately model propagation through the device and outline any reflections or losses that may ensue. A clear and concise review of some of the foremost available schemes is also presented here. These techniques, such as the Bidirectional Eigenmode Propagation Method (BEP) and the Beam Propagation Method (BPM) will be discussed and an effective and precise 3-dimensional model is presented. Due to the myriad of available techniques and algorithms, a comparative study is drawn, listing the advantages and failures of the major methods while suggesting improvements to their application. Necessary considerations such as simulation time and the trade-off between computer memory requirements and accuracy of the solution are also acknowledged.
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John A. Ging and Ronan O'Dowd "A novel finite element method for the modeling of multiple reflections in photonic integrated circuits", Proc. SPIE 6187, Photon Management II, 61870P (25 April 2006);

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