On the existence of ‘supercavity modes’ in sub-wavelength dielectric resonators and their relation to bound states in the continuum

It is shown in this letter related to the paper by M V Rybin and M F Limonov [Physics–Uspekhi 62 (8) (2019)] that in dielectric sub-wavelength resonators of equal volume but different shape no eigen-modes exist that would be qualitatively different from those in dielectric spheres. In particular, there are no ‘supercavity modes’ in dielectric cylinders whose Q-factor would exceed that of similar modes in dielectric spheres of the same volume.