Optical Attenuation Models

Most real-world media absorb some energy from the electromagnetic waves that pass through them, converting this energy into another form such as heat. A medium might also redirect some energy without absorbing it, a phenomenon called scattering which will be explored in a later section.

In the Geometrical Optics interface, an absorbing medium has a complex-valued refractive index of the form n − iκ., where n and κ are real numbers and κ > 0. As a ray propagates through an absorbing medium, the built-in variables that track ray intensity and power may decrease.


	There is yet another phenomenon that influences the calculation of the built-in variable for ray intensity: the convergence or divergence of the wavefront. For simplicity this is not considered here (the rays are assumed to represent plane waves) but will be revisited in a later section.

Recall that the electric field amplitude of a plane electromagnetic wave in a medium of complex-valued refractive index n − iκ is

Noting that the intensity is proportional to

, the imaginary terms in the exponents vanish, leaving only the attenuation term,

Then, using the relationship

the intensity decays exponentially according to

In the physics interface Medium Properties node, you can control how the value of κ is defined by selecting different options from the list.

Extinction Coefficient

For , enter the value of κ directly.

Attenuation Coefficient

For , enter the value or expression of the coefficient α, defined as

Thus

Internal Transmittance

The list also includes the following options:

•

The internal transmittance is the fraction of the ray intensity that is transmitted, rather than absorbed, through a sample of the given thickness d, neglecting Fresnel losses at the surfaces of the sample. Setting x = d in the previous equations,

Solving this equation for κ yields

(3-6)

This result is positive or zero because the internal transmittance cannot exceed unity.

Internal Transmittance Data and Numerical Precision

If internal transmittance data is tabulated for different glasses and different wavelengths, and all internal transmittance values are reported to the same number of digits, loss of precision may occur if the internal transmittance data for a very thin sample of a weakly absorbing glass, or a thick sample of a very strongly absorbing glass, is used.

To see this more concretely, suppose that internal transmittance data is available for 10 mm and 25 mm samples of a glass at λ0 = 600 nm, each reported to three digits. Suppose the reported values are τi,10 = 0.998 and τi,25 = 0.995. Because of roundoff, we may presume the actual value of τi,10 to be between 0.9975 and 0.9985, and similarly for τi,25 to be between 0.9945 and 0.9955. Substituting these lower and upper bounds into Equation 3-6 then gives the following results:

•

For the 10 mm sample, 7.2 × 10-9 < κ < 12.0 × 10-9

•

For the 25 mm sample, 8.6 × 10-9 < κ < 10.5 × 10-9

Therefore it would be preferable to use the data for the thicker sample if it is available.

Conversely, if the reported transmittance values were very close to zero (perhaps in the IR or UV range) it would be beneficial to use data for the thinnest sample available.

If a material uses internal transmittance data and one of the options or is selected, the transmittance data will automatically be converted to this coefficient. If two or more sets of transmittance data for different sample thicknesses are defined for the material, the default behavior is to use the data for the thicker sample unless otherwise specified.