  Rapid advancements in the micro and nano-technology create unlimited
opportunities for design of novel optical materials and their applications.
Recently, the possibility of the fast refractive index modulation was
demonstrated in semiconductors. In this paper we study the wave scattering by
small dispersionless particles with periodically varying refractive index in
scalar case by using the local perturbation method. The used formalism allows
us to study theoretically and numerically the scattering by objects made of
small particles of arbitrary shape and with oscillating refractive index.
  In this work, the field scattered by the cluster of the particles and its
resonance frequencies are calculated theoretically. In addition, the results of
the numerical modeling of the scattering by single cube and by cluster of cubes
with oscillating permittivity are presented. It was shown that the scattered
fields and their resonance frequencies are significantly affected by the
oscillating permittivity: existing resonances are shifting, new scattering
resonances are emerging, and deeps in the scattering spectrum are appearing.
