Guided-mode extracted integral equation combined with quasi-multiple medium for computer aided design of 2-dimensional waveguide

The guided-mode extracted integral equation (GMEIE) was proposed as a basic theory for the computer aided design (CAD) of a 2-dimensional waveguide (Tanaka, K. and Kojima, M., 1988). The GMEIE has some advantages: (1) it is solved by the standard method of moments; (2) it does not use a mode expansion technique; (3) it is mathematically rigorous. The disadvantage of the GMEIE is that the coefficient matrix obtained by the standard method of moments is dense. Therefore, the computational cost to solve the matrix equation is expensive, and a fast method is required to solve the huge problem and to extend it to the 3-dimensional waveguide problem. The quasi-multiple medium (QMM) method (Yu, W. et al., 2003; Yu and Wang, Z., 2003) decomposes each region into a few fictitious medium regions. Applying the method of moments, QMM generates a coefficient matrix with high sparsity. We derive a GMEIE combined with QMM, in order to reduce the computational cost. When the GMEIE combined with QMM is discretized into a matrix equation by the standard method of moments, the resultant matrix has high sparsity. The computational cost of the matrix vector multiplication is reduced when an iterative method is used to solve the sparse matrix equation.