With analytical (generalized Mie scattering) and numerical (integral-equation-based) considerations we show the existence of strong resonances in the scattering response of small spheres with lossless impedance boundary. With increasing size, these multipolar resonances are damped and shifted with respect to the magnitude of the surface impedance. The electric-type resonances are inductive and magnetic ones capacitive. Interestingly, these subwavelength resonances resemble plasmonic resonances in small negative-permittivity scatterers and dielectric resonances in small high-permittivity scatterers. The fundamental dipolar mode is also analyzed from the point of view of surface currents and the effect of the change of the shape into a non-spherical geometry.
Numerical solutions of various surface integral equation formulations in modeling resonating (lossless) closed impedance bodies are investigated. It is demonstrated that for certain values of purely imaginary surface impedances very strongly resonating field solutions can appear. Some of the considered formulations that are known to work well outside these resonances, e.g., for lossy surfaces, can lead to very poor accuracy or even diverging solutions at these resonances. Among the considered formulations only the combined source integral equations, discretized with a mixed scheme, both avoid the nonphysical spurious internal resonances and work reasonably well at the physical (impedance) resonances.
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