Novel finite element analysis of optical waveguide discontinuity problems

• Published in: Journal of lightwave technology Vol. 22; no. 5; pp. 1420 - 1425
• Main Author: Obayya, S.S.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2004; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Boundary conditions; Circuit properties; Discontinuity; Electric, optical and optoelectronic circuits; Electronics; Exact sciences and technology; Finite element method; Finite element methods; Integrated optics. Optical fibers and wave guides; Least squares approximation; Mathematical analysis; Mathematical models; Optical and optoelectronic circuits; Optical design; Optical waveguides; Sparse matrices; Taylor series; Transmission line matrix methods; Waveguide discontinuities; Waveguide junctions; Waveguide lasers; Finite element method; Discontinuity; laser-air facets; Approximation; Taylor series; Optical waveguide; Boundary condition; Discontinuity problems; finite-element method (FEM)
• ISSN: 0733-8724; 1558-2213
• DOI: 10.1109/JLT.2004.827671

In this paper, a novel finite-element method (FEM) to rigorously and efficiently solve the optical waveguide discontinuity problems is presented. Instead of performing the time-consuming modal solutions on both discontinuity sides, the square root of the characteristic matrix is efficiently approximated using Taylor's series expansion, and then the interface boundary conditions are enforced at the discontinuity plane to solve for the reflected and transmitted fields. The high numerical precision and effectiveness of the proposed method is demonstrated through the analysis of various discontinuity problems, and the excellent agreement of the results obtained using the present finite element method and those obtained using other rigorous approaches in the literature.