Hybrid Trefftz Finite-Element Method for Analyzing the Eigenmodes of Optical Fibers

• Published in: Journal of lightwave technology Vol. 37; no. 3; pp. 1029 - 1036
• Main Authors: Sato, Shingo, Hasegawa, Koji, Mizukami, Naoya, Tsushima, Yasuo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Boundary conditions; Eigenvalues; Fiber nonlinear optics; Finite element analysis; Finite element method; Hybrid Trefftz finite-element method; nonlinear eigenvalue problem; Nonlinear programming; Numerical methods; optical fiber; Optical fibers; Sakurai–Sugiura method; Waveguides
• ISSN: 0733-8724; 1558-2213
• DOI: 10.1109/JLT.2018.2885311

We present a hybrid Trefftz finite-element method (HTFEM) for analyzing the eigenmodes of optical fibers. Using this method, waveguide problems that include open regions can be analyzed without requiring absorbing boundary conditions or utilizing artificial absorbers to enclose the region under analysis because the open region is treated as a special "Trefftz element." In addition, using a Trefftz element for the homogeneous core region and utilizing the Sakurai-Sugiura method to solve the nonlinear eigenvalue problems resulting from the HTFEM, we are able to obtain the degenerate effective indices of waveguides accurately without imposing symmetry conditions. We examine the convergence behavior of the effective indices of optical fibers computed using the HTFEM and compare the results with those obtained from analytic solutions or other numerical methods. Numerical examples demonstrate the validity of the formulation and the usefulness of eigenmode analyses using the HTFEM.