Spurious results of EFIE and CFIE applied to dielectric/optical waveguides

It is proven that the surface Electric Field Integral Equation (EFIE) has a non-unique solution when applied to a dielectric waveguide of arbitrary cross section. The Method of Moments (MOM) is used to numerically solve the EFIE applied to an optical fiber of arbitrary cross section. The fiber is assumed to consist of a dielectric core of arbitrary cross section surrounded by an infinite dielectric cladding. The numerical results for a circular fiber verify the existence of spurious results. On the other hand, no spurious results were observed when the surface Combined Field Integral Equation (CFIE) was used to solve the problem of an optical fiber of arbitrary cross section. However, it can be proven that spurious results may exist when CFIE is applied to a fiber with hollow core. The core may have one or more air tubes. Numerical results verified this claim when CFIE is applied to a circular coaxial dielectric waveguide that consists of a circular core with one or two circular air holes.