Complex modes in optical fibers and silicon waveguides

TL;DR

This paper investigates complex guided modes in lossless optical fibers and silicon waveguides, revealing their formation, dispersion relations, and conditions for existence, thus filling a theoretical gap and enabling future applications.

Contribution

It introduces the study of complex modes in open lossless dielectric waveguides, providing dispersion relations and conditions for their existence in circular fibers and silicon waveguides.

Findings

Complex modes can exist in lossless waveguides with specific dispersion relations.

Minimum refractive-index ratio for complex modes in circular fibers is identified.

The study enhances understanding of waveguide modal structures and potential applications.

Abstract

At a fixed frequency, a general wave field in an open optical waveguide is a sum of finite number of guided modes and an integral of radiation modes. Most studies on open lossless dielectric waveguides are concerned with regular guided modes which are confined around the waveguide core, have a real propagation constant, and propagate along the waveguide axis without attenuation. However, there may be guided modes with a complex propagation constant even though the waveguide consists of lossless isotropic dielectric materials, and they are the so-called complex modes. The complex modes are proper modes confined around the waveguide core, and are different from the leaky modes which have divergent wave fields in the transverse plane. For waveguides with discontinuities and defects, the complex modes can be excited and must be included in eigenmode expansions. However, existing studies on complex modes in open lossless dielectric waveguides 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.