Before proceeding with a more detailed description it should be emphasized that the
fact that in the time domain all the fields (Hx, Ey, Hz) are real quantities. Thus,
accounting for loss is possible only through a non-zero conductivity σ of the medium:
where
Here we have assumed that
and
corresponds to time-to-frequency domain Fourier transform. The real and imaginary
part of the permitivity can be expressed through the real and imaginary part of the
refractive index:
This makes the refractive index approach and the conductivity approach equivalent.