  We demonstrate that the electromagnetic fields scattered by particles made of
different materials can be equalized. Emphasize is placed first in metallic
nanoparticles that host localized surface plasmons and it is shown that their
electromagnetic fields can be identically reproduced with dielectric particles.
We derive the explicit formulas relating the different constitutive parameters
that yield identical electromagnetic responses. This method provides the
dielectric permittivities of spherical particles that reproduce the strong near
electric field intensities observed around metallic particles featuring
localized surface plasmon resonances in optics or near infrared frequencies. We
also demonstrate the ability of homogenous dielectric particles to host the
magnetic resonances predicted for exotic materials with negative permeability.
