Full-Vectorial Matched Interface and Boundary (MIB) Method for the Modal Analysis of Dielectric Waveguides

This paper introduces the matched interface and boundary (MIB) method for the eigenmode analysis of two dimensional step-index waveguides. The MIB method distinguishes itself from other existing interface methods by avoiding the use of the Taylor series expansion and by introducing the concept of the iterative use of low-order jump conditions. The difficulty associated with other interface approaches in extending to ultrahigh order is thus bypassed in the MIB method. In solving rectangular waveguide with a single straight interface, the MIB interface treatment can be carried out systematically so that the resulting scalar approach is of arbitrarily high order, in principle. Orders up to 12 are confirmed numerically for both transverse magnetic and transverse electric modes. In dealing with rectangular waveguide with a dielectric corner, a novel full-vectorial MIB method is proposed, in which an advanced corner handling technique is applied to accommodate the singular behavior of field near the corner. Benchmark problems are employed to validate the proposed full-vectorial approach. Higher order convergence is achieved numerically.