The imaginary component of χ χ T L ( E ) is formed as the product of the imaginary component of the Lorentz oscillator model and a model developed by Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material. The real component of χ χ T L ( E ) is obtained via the Kramers-Kronig transform of its imaginary component. Mathematically, they are given by