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On the Physical Meaning of the Spectral Decomposition

In the analysis of open planar structures, it is widely accepted that the spectral decomposition of the fields excited by a given source into its continuous and discrete spectrum components has an apparent physical meaning. The continuous spectrum is associated with radiation and/or reactive effects whereas the discrete spectrum corresponds to the bound fields guided by the structure. Although this interpretation is usually correct, the present work will show that it is not general. In particular it will be shown that a lossy grounded dielectric waveguide near the cutoff frequencies of its higher-order surface-wave modes is a simple and interesting counterexample in which the continuous and the discrete spectrum fail to bear their intended physical meaning. A careful analysis of the modal cutoff mechanism provides numerical results that fully support the above assertion.