Analytical models for small Omega-shaped conductive particles in free
space or embedded in isotropic materials are presented and discussed.
The electromagnetic analysis is based on the antenna theory for circul
ar loop antennas and dipole wire antennas. Analytical expressions for
the polarizabilities valid in the frequency area covering the two lowe
r resonances are given. Mutual coupling between two portions of the pa
rticle: the loop and the straight wire is considered in terms of the m
utual impedance, which is analytically calculated with the use of the
induced electromotive force method. Approximate analytical expressions
are compared with numerical simulations and are seen to be in good ag
reement. The results can be used in analytical modelling of omega and
chiral composite materials and in the antenna theory.