Manifestation of extremely high-Q pseudo-modes in scattering of a Bessel light beam by a sphere

The exact analytical solution of Maxwell equations for a Bessel light beam scattered by a sphere is found. Scattered power, stored energy, and a generalized Q factor as a function of frequency, the sphere radius, permittivity, and the Bessel beam angle are found. On the basis of this solution, modes and pseudo-modes of a dielectric sphere are extracted by calculation of the generalized Q factor. It is shown that an appropriate choice of Bessel beam parameters can provide excitation of a single given mode and an unlimited value of the radiative Q factor of pseudo-modes.