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math.AP2026
The Calderón operator for time-harmonic Maxwell's equations in closed waveguides
Martin Halla
We consider the time-harmonic Maxwell's equations in a closed, cylindrical waveguide with longitudinal invariant but heterogeneous permittivity and permeability. We consider minima…
math.AP2026
Modal bases of coaxial electromagnetic step index fibers
Martin Halla
We consider the eigenvalue problem to find the modes of an electromagnetic coaxial step index fiber. More specific, we consider a closed (meaning PEC boundary conditions) cylindric…
math.AP2026
Length-explicit stability analysis of Helmholtz problems in leaky circular waveguides
Leszek Demkowicz, Martin Halla, Jens Markus Melenk
Motivated by the study and simulation of long, coiled optical fibers we consider in this article a simplified model that is prevalent in the engineering community. Mathematically,…