  We derive the electromagnetic medium equivalent to a cluster of
all-dielectric nanoparticles (i.e. enjoying high refractive indices),
distributed periodically in a smooth domain $\Omega$, while excited at nearly
resonating dielectric incident frequencies (i.e. subwavelength Mie-resonant
frequencies). This effective medium is an alteration of the permeability that
keeps the permittivity unchanged. We provide regimes under which the effective
permeability can be positive or negative valued. In addition, if the incident
frequency is close to any of the subwavelength all-dielectric resonances, then
the distributed cluster behaves as an extended quasi-static plasmonic
resonator. Therefore, exciting the cluster of all-dielectric nanoresonators
with nearly resonating incident frequencies, we can generate an extended
quasi-static plasmonic resonator which creates giant electromagnetic fields in
its surrounding.
