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This paper is concerned with the extractions of electromagnetic characteristic modes (CMs) for lossless dielectric bodies, for which spurious modes are prone to generate using the traditional definition of CMs based on the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) equations. It is found that the impedance matrix of PMCHWT equations cannot distinguish (i) which domain is the dielectric body and which domain is the background and (ii) from which domain the excitation source was applied. If the system is taken as a scattering problem, the spurious modes are solutions to a reverse media problem, i.e., exchanging the media of the dielectric body and the background space. However, if the system is taken as a radiation problem, no appropriate CMs that meet the specified boundary conditions are obtained. These phenomena indicate that CMs developed from scattering systems are not suitable for radiation systems. To clarify the issue, four cases with reverse media and with excitation sources in either domain are examined. The four cases are distinct in essence, but the PMCHWT equations cannot distinguish them. As a result, definitions of CMs for the four cases should be given along with their specific boundary conditions. Especially, the CMs for the radiation problems we consider here show that the excitation source inside the material object should be properly defined in order to be distinguished from scattering problems.

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