Influence of local-field anisotropy in the description of the resonance in dielectrics and their corresponding Argand diagrams

The local field existing in an ellipsoidal cavity within a dielectric is introduced as an improvement to the classical description of resonance in a dielectric under a harmonic electric field. Considering that the ellipsoids representing polarizable molecules may have any orientation with respect to the applied field, we obtained expressions for the real and imaginary parts of the permittivity as a function of the angular frequency and form factors. A shift in frequency is observed for the maximum of the imaginary permittivity with respect to the natural angular frequencies of resonance that depends on the form factors. In the particular case that all the ellipsoids are lined up with the applied field, the shift of the angular frequency of the resonance depends in a simple way on the form factor of the ellipsoid. The Argand diagrams are shown and compared to those corresponding with different approximations of the local field.