Third-order Nédélec curl-conforming finite element
ABSTRACT The third-order version of Nédélec's first family of curl-conforming elements over simplices is presented. Following the definition of the element given by Nédélec, the third-order vector basis functions are deduced. The elements thus ob-tained exhibit some important differences with respect to other higher-order curl-conforming elements appeared in the literature. Among other features, the proposed third-order curl-conforming finite element leads to better conditioned finite-element method matrices. Index Terms—Curl-conforming element, finite element calcula-tions, Nédélec elements, third-order element.
SourceAvailable from: citeseerx.ist.psu.edu[Show abstract] [Hide abstract]
ABSTRACT: In this dissertation; the silicon-on-insulator (SOI) technology is introduced to the design and fabrication of passive polarization rotators (PR). Efficient and accurate full-vectorial finite-element eigenmode solvers as well as propagation schemes for characterizing novel SOI PRs are developed because commercial software packages based on finite-difference techniques are inefficient in dealing with arbitrary waveguide geometries. A novel configuration with asymmetric external waveguiding layers is proposed, which is advantageous for fabrication procedure, manufacturing tolerance, single-mode region, and conversion efficiency. By etching along the crystallographic plane, the angled-facet can be perfectly fabricated. Completely removing external waveguiding layer beside the sloped sidewall not only simplifies production procedures but also enhances fabrication tolerances. To accurately and efficiently characterize asymmetric slanted-angle SOI polarization converters, adaptive mesh generation procedures are incorporated into our finite-clement method (FEM) analysis. In addition, anisotropic perfectly-matched-layer (PML) boundary condition (BC) is employed in the beam propagation method (BPM) in order to effectively suppress reflections from the edges of the computation window. For the BPM algorithm, the power conservation is strictly monitored, the non-unitarity is thoroughly analyzed, and the inherent numerical dissipation is reduced by adopting the quasi-Crank-Nicholson scheme and adaptive complex reference index. Advantages of SOI polarization rotators over III-V counterparts are studied through comprehensive research on power exchange, single-mode condition, fabrication tolerance, wavelength stability, bending characteristics, loss and coupling properties. The performance of SOI PRs is stable for wavelengths in the ITU-T C-band and L-band, making such devices quite suitable for DWDM applications. Due to the flexible cross-section of SOI polarization converters, the coupling loss to laser diodes and single mode fibers (SMF) can be designed to be very small and can be further reduced by a tapered waveguide with cross-sections always satisfying the single-mode criteria. Slanted-angle SOI polarization rotators display asymmetric bending characteristics and permit extremely small curvatures with negligible radiation loss when the angled-facet is located at the outer bend radius. Moreover, SOI polarization rotators can be manufactured with low-price processing techniques that are fully compatible with CMOS integrated circuits (IC) technology, and thus can be integrated on both photonic and electronic chips. Experimental verifications have shown good agreement with theoretical analysis and have confirmed the promising characteristics of our novel asymmetric SOI polarization converters. Similar asymmetric-outer-slab geometry has recently been employed by peer researchers to fabricate high performance III-V polarization rotators. We therefore believe that results in this dissertation will contribute much to related research fields. (Abstract shortened by UMI.)
[Show abstract] [Hide abstract]
ABSTRACT: A multi-hybrid method combining the finite element method (FEM) and several high frequency techniques (HFTs) for the efficient analysis of the radiation and scattering of electromagnetic waves on complex three-dimensional environments is presented. It makes use of FEM for the regions with small and complex features and one or several HFTs for the analysis of the electrically large objects of the structure. The hybridization is done in a fully-coupled way taking into account mutual interactions between the FEM domains and the objects analyzed with HFTs. Two main HFTs are used: physical optics (PO) and the uniform theory of diffraction (UTD) in order to take advantage of the use of distributed and point sources. Physical theory of diffraction (PTD) is also used when needed in order to improve the accuracy of POIEEE Transactions on Magnetics 05/2007; DOI:10.1109/TMAG.2007.892416 · 1.21 Impact Factor
[Show abstract] [Hide abstract]
ABSTRACT: A general fully coupled multi-hybrid method in three dimensions combining the finite element method, the method of moments, and a high-frequency asymptotic technique, namely, physical optics, is presented. Complex radiating structures are analyzed with finite element method (which easily handles complex geometries, permeable materials, anisotropy, and so on), while small- and medium-sized perfect electric conductor objects are rigorously analyzed using the method of moments; large perfect electric conductor objects can be efficiently analyzed with physical optics. Furthermore, different regions of the same object can be modeled with the method of moments and physical optics. Several numerical results are presented showing the validity of the method.Electromagnetics 03/2010; 30(1-2):3-22. DOI:10.1080/02726340903485232 · 0.77 Impact Factor