Summary
Why do some Fourier formulations converge poorly at material boundaries?
Derives rules for factorizing Fourier coefficients of products with jump discontinuities.
Gives a mathematical basis for improved convergence, notably for TM metallic gratings.
Related modelling approaches
Relation labels come from the method guide and are editorial. Unlabelled links are conceptual connections or comparison methods; the paper does not necessarily implement them.
Commentary
Correct factorization does not eliminate basis truncation or establish near-field convergence automatically.
Modern vector FMM and differentiable implementations inherit this interface problem.
Interpretation and connections in this note, separate from the authors’ reported findings.