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:

FDTD - equation 18


FDTD - equation 18b

Here we have assumed that

FDTD - equation 18c


FDTD - equation 18d

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:

FDTD - equation 19

This makes the refractive index approach and the conductivity approach equivalent.