Waveguide mode solver based on Neumann-to-Dirichlet operators and boundary integral equations

• Published in: Journal of computational physics Vol. 231; no. 4; pp. 1360 - 1371
• Main Authors: Lu, Wangtao, Lu, Ya Yan
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.02.2012; Elsevier
• Subjects: Accuracy; Boundaries; Boundary integral equation; Computational techniques; Corners; Exact sciences and technology; Integral equations; Mathematical analysis; Mathematical methods in physics; Neumann-to-Dirichlet operator; Operators; Optical waveguide; Physics; Solvers; Waveguide mode solver; Waveguides; Optical waveguide; Boundary integral equation; Neumann-to-Dirichlet operator; Waveguide mode solver; Integral operator; Second order; Refractive index; Third order; Electromagnetic fields; Calculation methods; Waveguides; Calculation; Magnetic fields; Boundary integral equations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2011.10.016

For optical waveguides with high index-contrast and sharp corners, existing full-vectorial mode solvers including those based on boundary integral equations typically have only second or third order of accuracy. In this paper, a new full-vectorial waveguide mode solver is developed based on a new formulation of boundary integral equations and the so-called Neumann-to-Dirichlet operators for sub-domains of constant refractive index. The method uses the normal derivatives of the two transverse magnetic field components as the basic unknown functions, and it offers higher order of accuracy where the order depends on a parameter used in a graded mesh for handling the corners. The method relies on a standard Nyström method for discretizing integral operators and it does not require analytic properties of the electromagnetic field (which are singular) at the corners.