For example, Refs. 1 and
9 use the sign convention in
Equation 3-1, whereas Refs.
10,
12,
15,
17, and
20 use the sign convention in
Equation 3-2.
Suppose that the wave propagates in the positive x direction. Then the wave vector may be defined as
where n (dimensionless) is the refractive index of the medium, assumed to be isotropic. For an absorbing or gain medium,
n is complex valued. Using
Equation 3-1, the electric field along a plane wave in an absorbing or gain medium is
which has an exponentially decaying magnitude (absorbing medium) if the imaginary part of n is positive, and an exponentially growing magnitude (gain medium) if the imaginary part of
n is negative. In contrast, when starting from
Equation 3-2, the electric field is
So the medium is absorbing if the imaginary part of n is negative, or a gain medium if the imaginary part of
n is positive.
The Geometrical Optics interface uses the convention of Equation 3-2. Therefore the complex-valued refractive index may be written as
n − iκ, where both
n and
κ are real-valued. The variable
κ, sometimes called the extinction coefficient, should then be positive when defining an absorbing medium, for example when specifying the
Refractive index, imaginary part in the
Medium Properties node.