where L is the optical path length between the points at which
E and
E0 are measured and
k0 is the wave number in free space. In weakly absorbing media,
N = n, K = κ, and
α = 0. If the
Use corrections for strongly absorbing media check box is selected,
N is the real part of the apparent refractive index,
K is the complex part of the apparent refractive index, and
α is the angle between the surfaces of constant amplitude and surfaces of constant phase; both of these concepts are explained in
Refraction in Strongly Absorbing Media. The ray intensity and power are both proportional to the square of the electric field norm, so these quantities change according to the relations
where c is the speed of light in the medium and
si,0 is value of one of the Stokes parameters of the ray before the effects of changes in the principal radii of curvature have been applied.
Despite requiring an extra degree of freedom per ray, the advantage of Equation 3-21 over
Equation 3-20 is that the dependent variables in
Equation 3-21 all vary linearly within a homogeneous medium. This makes
Equation 3-21 less prone to numerical stiffness; it remains more accurate when the solver takes long time steps, compared to
Equation 3-20, potentially reducing solution time and improving accuracy.