Extinction coefficient

The parameter used to describe the interaction of electromagnetic radiation with matter is the complex index of refraction, ñ, which is a combination of a real part and an imaginary part.

$\tilde{n}=n-ik$

Here, n is also called 'index of refraction' which sometime leads to confusion, and k is called the 'extinction coefficient'. In a dielectric material such as glass, none of the light is absorbed and therefore k = 0.

Before a more detail definition of the extinction coefficient k is considered, let us first look at the absorption coefficient α. In a medium absorbing light, the decrease in intensiry $I$ per unit lenght $z$ is proportional to the value of $I$ . In mathematical form this means:

$\frac{dI\left( z \right)}{dz}={-\alpha I\left(z\right)}$

where α is the absorption coefficient.

This can be integrated as:

${I\left(z \right)}={I_0 e^{-\alpha z}}$

where

I 0

is the value of the intensity at the surface of the absorbing medium.

The extinction coefficient k is then defined as

$k={\frac{\lambda}{4\pi}}\alpha$

where λ is the vacuum wavelength

Categories: Physics | Optics