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. The dispersion relation bears the names of Rahim Forouhi and Iris Bloomer, who created the model and interpreted the physical significance of its parameters. The model is aphysical due to its incorrect asymptotic behavior and non-Hermitian character. These shortcomings inspired modified versions of the model as well as development of  the Tauc–Lorentz model. Mathematical Formulation. 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 formula_6 for amorphous materials. The formula and complementary Kramers–Kronig integral are given by where formula_10, formula_11, and formula_12 are subject to the constraints formula_19, formula_20, formula_21, and formula_22. Evaluating the Kramers-Kronig integral, where The Forouhi–Bloomer model for crystalline materials is similar to that of amorphous materials. The formulas for formula_27 and formula_6 are given by where all  variables are defined similarly to the amorphous case, but with unique values for each value of the summation index formula_31. 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.