Chiang, Yen-ChungYen-ChungChiangLai, Chih-HsienChih-HsienLaiDu, Cheng-HanCheng-HanDuHUNG-CHUN CHANGYIH-PENG CHIOU2018-09-102018-09-102009-0607338724http://scholars.lib.ntu.edu.tw/handle/123456789/351891https://www.scopus.com/inward/record.uri?eid=2-s2.0-67649849594&doi=10.1109%2fJLT.2008.2006862&partnerID=40&md5=091755754b13a6953d3492de8f1c084eWith the help of an improved finite-difference (FD) formulation, we investigate the field behaviors near the corners of simple dielectric waveguides and the propagation characteristics of a slant-faceted polarization converter. The formulation is full-vectorial, and it takes into consideration discontinuities of fields and their derivatives across the abrupt interfaces. Hence, the limitations in conventional FD formulation are alleviated. In the first investigation, each corner is replaced with a tiny arc rather than a really sharp wedge, and nonuniform grids are adopted. Singularity-like behavior of the electric fields emerge as the arc becomes smaller without specific treatment such as quasi-static approximation. Convergent results are obtained in the numerical analysis as compared with results from the finite-element method. In the second investigation, field behaviors across the slanted facet are incorporated in the formulation, and hence the staircase approximation in conventional FD formulation is removed to get better modeling of the full-vectorial properties. © 2009 IEEE.Approximation methods; Converters; Corners; Data mining; Dielectric waveguides; Finite element methods; Finite-difference method (FDM); Frequency-domain analysis; Full-vectorial; Optical waveguides; Photonics; Probability density function; Singularities; Step index; Tiny arcsApproximation methods; Converters; Corners; Finite-difference method (FDM); Full-vectorial; Singularities; Step index; Tiny arcs; Approximation theory; Cavity resonators; Dielectric waveguides; Electric fields; Finite difference method; Finite element method; Frequency domain analysis; Information management; Integrated optoelectronics; Mining; Optical waveguides; Orthogonal frequency division multiplexing; Probability density functionjournal article10.1109/JLT.2008.20068622-s2.0-67649849594WOS:000267993400013