Electromagnetics - Modelling, Simulation, Control and Industrial Applications - Abstract
Lu, Ya Yan
Finding guided or leaky modes for optical waveguides is a classical problem that has been considered by many authors. For waveguides of current interest, including silicon waveguides, plasmonic waveguides and photonic crystal fibers, a rigorous analysis based on the full Maxwell's equations is essential. Existing numerical methods such as the finite element method have limitations in accuracy and efficiency due to field singularities at waveguide corners and/or complicated microstructures. Boundary integral equation (BIE) methods have also been used to analyze optical waveguides. For waveguides with smooth interfaces (discontinuities of the refractive index profile), full-vectorial BIE methods usually solve four functions on the interfaces. In a recent work, we developed a more efficient BIE method that solve only two unknown functions on the interfaces, but it is still limited by field singularities at waveguide corners. In another work, we developed a high order BIE method for waveguides with corners, but it requires solving four unknown functions on the interfaces. In this paper, we present two new high order BIE methods for waveguides with corners, solving two or three unknown functions on the interfaces, respectively. The required number of operations of these new methods is roughly $12.5?or $42.2?of the four-function method. The two-function method relies on a new high order scheme for discretizing a related hypersingular boundary integral operator. The three-function method is simpler to implement.