Resonant scattering by dielectric cylinders

A dielectric cylinder immersed in an incident E- or H-wave scatters particularly strongly at certain (resonant) frequencies. The resonant peaks increase in sharpness as N, the index of refraction, increases. In the paper, the resonant modes are analysed within the limit of a very high, but finite, N. Suitable orthogonality properties are derived, and the field patterns, resonant frequencies and quality factors of the modes are determined. Particular attention is given to the monopole E-resonance, which behaves quite differently from the other resonances. Finally, a modal expansion is utilised to determine the scattered field and the scattering cross-section at resonance. The dielectric cylinder is allowed to be slightly lossy.