Complex modes in optical fibers and silicon waveguides

In an open optical waveguide, complex modes that are confined around the waveguide core and have a complex propagation constant may exist, even though the waveguide consists of lossless isotropic dielectric materials. However, the existing studies on complex modes are very limited. In this Letter, we consider circular fibers and silicon waveguides, study the formation mechanism of complex modes, and calculate the dispersion relations for several complex modes in each waveguide. For circular fibers, we also determine the minimum refractive-index ratio for the existence of complex modes. Our study fills a gap in optical waveguide theory and provides a basis for realizing potential applications of complex modes.