High-accuracy finite-difference equations for dielectric waveguide analysis II: dielectric corners

• Published in: Journal of lightwave technology Vol. 20; no. 7; pp. 1219 - 1231
• Main Author: Hadley, G.R.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2002; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Boundary conditions; Corners; Dielectric waveguides; Dielectrics; Equations; Etching; Finite difference method; Finite difference methods; Magnetic analysis; Magnetic fields; Mathematical analysis; Optical device fabrication; Optical waveguide components; Optical waveguides; Waveguides
• ISSN: 0733-8724; 1558-2213
• DOI: 10.1109/JLT.2002.800371

For part I see ibid., p. 1210, 2002. We present a discussion of the behavior of the electric and magnetic fields satisfying the two-dimensional Helmholtz equation for waveguides in the vicinity of a dielectric corner. Although certain components of the electric field have long been known to be infinite at the corner, it is shown that all components of the magnetic field are finite, and that finite-difference equations may be derived for these fields that satisfy correct boundary conditions at the corner. These finite-difference equations have been combined with those derived in the previous paper to form a full-vector waveguide solution algorithm of unprecedented accuracy. This algorithm is employed to provide highly accurate solutions for the fundamental modes of a previously studied standard rib waveguide structure.