The complex refractive index is given by
where
- is the real component of the complex refractive index, commonly called the refractive index,
- is the imaginary component of the complex refractive index, commonly called the extinction coefficient,
- is the photon energy (related to the angular frequency by ).
The real and imaginary components of the refractive index are related to one another through the Kramers-Kronig relations. Forouhi and Bloomer derived a formula for for amorphous materials. The formula and complementary Kramers–Kronig integral are given by[1]
where
- is the bandgap of the material,
- , , , and are fitting parameters,
- denotes the Cauchy principal value,
- .
, , and are subject to the constraints , , , and . Evaluating the Kramers-Kronig integral,
where
- ,
- ,
- .
The Forouhi–Bloomer model for crystalline materials is similar to that of amorphous materials. The formulas for and are given by[7]
- .
- .
where all variables are defined similarly to the amorphous case, but with unique values for each value of the summation index . Thus, the model for amorphous materials is a special case of the model for crystalline materials when the sum is over a single term only.