Mathematical Descriptions of Opacity - AC Conductivity

AC Conductivity

Another way to incorporate attenuation is through the conductivity, as follows.

One of the equations governing electromagnetic wave propagation is the Maxwell-Ampere law:

(SI) (cgs)

where D is the displacement field. Plugging in Ohm's law and the definition of (real) permittivity

(SI) (cgs)

where is the (real, but frequency-dependent) conductivity, called AC conductivity. With sinusoidal time dependence on all quantities, i.e. and, the result is

(SI) (cgs)

If the current J was not included explicitly (through Ohm's law), but only implicitly (through a complex permittivity), the quantity in parentheses would be simply the complex permittivity. Therefore,

(SI) (cgs).

Comparing to the previous section, the AC conductivity satisfies

(SI) (cgs).