Forouhi–Bloomer model

The Forouhi–Bloomer model is a mathematical formula for the frequency dependence of the complex-valued refractive index.

The model can be used to fit the refractive index of amorphous and crystalline semiconductor and dielectric materials at energies near and greater than their optical band gap.

[2][3][4][5][6] The dispersion relation bears the names of Rahim Forouhi and Iris Bloomer, who created the model and interpreted the physical significance of its parameters.

[1][7] The model is aphysical due to its incorrect asymptotic behavior and non-Hermitian character.

The complex refractive index is given by where 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

Evaluating the Kramers-Kronig integral, where The Forouhi–Bloomer model for crystalline materials is similar to that of amorphous materials.

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.

Forouhi–Bloomer model. The real (blue solid line) and imaginary (orange dashed line) components of complex refractive index are plotted for model with parameters 1.3 eV, 1.4910 eV, 5.2139 eV, 8.6170 eV , and 1.5256. These parameters approximate amorphous silicon. [ 1 ]