Eigenwaves in Waveguides with Dielectric Inclusions: Completeness

TL;DR

This paper establishes the mathematical completeness of eigenwaves in waveguides with dielectric inclusions, providing a rigorous foundation for their analysis and highlighting limitations in basis properties.

Contribution

It introduces a formal definition of eigenwaves in nonhomogeneous waveguides and proves their double completeness, including the transversal components, with detailed mathematical properties.

Findings

Proves double completeness of eigenwaves and associated waves

Shows the system is generally not a Schauder basis

Establishes minimality of the eigenwaves system

Abstract

We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a defect. Then we prove the completeness of the system of transversal components of eigenwaves and associated waves as well as the `minimality' of this system and show that this system is generally not a Schauder basis.