  The dispersive resonant-state expansion, developed for an accurate
calculation of the resonant states in open optical systems with frequency
dispersion, is applied here to realistic materials, such as metallic
nanoparticles and semiconductor microspheres. The material permittivity is
determined by fitting the measured indices of refraction and absorption with a
generalized Drude-Lorentz model containing a number of poles in the complex
frequency plane. Each Drude or Lorentz pole generates an infinite series of
resonant states. Furthermore, for small nanoparticles, each of these poles
produces a distinct surface plasmon polariton mode. The evolution of these
multiple surface modes with increasing radius traces the transition from the
electrostatic limit to significant retardation and radiation. Treating the
optical phonon range in a semiconductor microsphere, a reststrahlen band
separating the resonant states is found. Considering a small energy range
around the semiconductor band gap, the transition from absorption to gain is
described by inverting the Lorentz pole weight, which results in the formation
of lasing resonant states. Interestingly, the series of resonant states
converging towards the absorption pole from the lower frequency side reshapes
for a gain pole into a clockwise loop approaching the pole from the higher
frequency side, being separated from a series spanning from low to high
frequencies and containing the lasing modes.
