On absence of sources at infinity and uniqueness for waveguide solutions

This paper discusses criteria for establishing uniqueness of wave propagation problems. Causality, or passivity that implies causality, is adopted as the fundamental principle. It is stressed that radiation conditions are not applicable for waveguide modes that carry no active power. The Jones' criteria for causality in the frequency domain, which covers the convectively unstable case, are presented and analysed, the vanishing absorption principle, VAP, in particular. It is proposed to use L² for a lossy medium but a weighted L² for the lossless case.