  We study the generic interaction of a monochromatic electromagnetic field
with bi-isotropic nanoparticles. Such an interaction is described by
dipole-coupling terms associated with the breaking of dual, P- and
T-symmetries, including the chirality and the nonreciprocal magnetoelectric
effect. We calculate absorption rates, radiation forces, and radiation torques
for the nanoparticles and introduce novel characteristics of the field
quantifying the transfer of energy, momentum, and angular-momentum in these
interactions. In particular, we put forward the concept of 'magnetoelectric
energy density', quantifying the local PT-symmetry of the field. Akin to the
'super-chiral' light suggested recently for sensitive local probing of
molecular chirality [Phys. Rev. Lett. 104, 163901 (2010); Science 332, 333
(2011)], here we describe a complex field for sensitive probing of the
nonreciprocal magnetoelectric effect in nanoparticles or molecules.
