Existence result for Maxwell’s equations in half-waveguides
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Date
2025-02-19
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Abstract
Maxwell’s equations are considered in a half-waveguide Ω+ := R+ × S ⊂ R3
where S ⊂ R2 is a bounded Lipschitz domain in R2. The electric permittivity ε and
the magnetic permeability μ are assumed to be strictly positive and periodic outside
a compact set. A standard radiation condition accompanies the equations. We give
a result on existence and uniqueness in the form of a Fredholm alternative: When
there is no bound state, i.e., no non-trivial solution of the homogeneous problem,
then there is a unique solution for every right-hand side.
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Keywords
Maxwell’s equations, half-waveguides, time-harmonic