Question

What is meant by imaginary part of complex permittivity?

Answer 1

Optics: What is the meaning of the imaginary part of the complex relative permittivity?
The complex permittivity represents the relationship between the electric and magnetic fields in a material. The imaginary part is directly related to the resistivity, while the real part tells you whether the material has a capacitative or inductive optical response. The ratio between the two corresponds to the phase lag between electric and magnetic fields.

From Ampere's Law we have,



Assuming time-harmonic fields such that ,





We can now express the complex permittivity as,



So there's a direct relationship between the conductivity of a material and the imaginary part of the permittivity.

Taking this one step further, we can see that there's a phase lag between the electric and magnetic fields given by . When the real part is positive, the phase shift is positive and the material is said to have an intrinsically capacitative (current leads voltage) optical response. When the real part is negative, the phase shift between electric and magnetic fields is negative and the material is said to have an inductive (voltage leads current) optical response. Using the same analogy, we can say that when the imaginary part is finite, the material has a resistive optical response