Modal Analysis of Homogeneous Optical Waveguides by Boundary Integral Method

The optical eld in a weakly guiding homogeneous waveguide satis es scalar Helmholtz equations in both the core and cladding, and transmission conditions on the boundary. The transverse wavenumbers of the two scalar Helmholtz equations for the core and cladding are di erent and both of them depend on the propagation constants in the longitudinal direction of the waveguide. Two di erent systems of boundary integral equations are derived for the numerical solutions of the discrete propagation constants; one of them is in the form of Fredholm integral equations of the second kind and the other is a "mixed" rst and second kind. A Nystrom algorithm is used to solve the boundary integral equations numerically. The numerical results show that the two boundary integral formulations are both very e cient in the numerical simulations of homogeneous waveguides. But the second kind is more advantageous because it controls spurious modes better.