Bulk Inhomogeneity

Bulk Inhomogeneity model allows you to find the dependence of optical parameters on the thickness of a thin film. The study of the bulk inhomogeneity in the first, so-called Schroeder's approximation, allows the determination of the degree of inhomogeneity of a thin film. More exact approximations allow investigating the refractive index profile of a thin film. See more in our publications.

Char bulk

Reflectance maxima (red) are shifted upwards from the bare substrate reflectance (black). It is known from the theory that such shifts are typical for thin films featuring bulk inhomogeneity.

inhomogeneous film

inhomogeneous film

Intermediate fitting, obtained after application of Cauchy model, is not good, especially in the regions of reflectance maxima. There is nothing strange,  because the bulk inhomogeneity was not taken into account.

thin film inhomogeneity


Final fitting, obtained after application of thin film model with bulk inhomogeneity. The degree of inhomogeneity is 1.6%.


  1. A. V. Tikhonravov, M.K. Trubetskov, G. Clarke, B. T. Sullivan, J. A. Dobrowolski, Ellipsometric study of optical properties and small inhomogeneities of Nb2O5 films, Proc. SPIE. 3738, Advances in Optical Interference Coatings 183 (1999)
  2. A. V. Tikhonravov, M. K. Trubetskov, and A. V. Krasilnikova, "Spectroscopic ellipsometry of slightly inhomogeneous nonabsorbing thin films with arbitrary refractive-index profiles: theoretical study ," Appl. Opt. 37, 5902-5911 (1998)
  3. A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and J. A. Dobrowolski, "Influence of small inhomogeneities on the spectral characteristics of single thin films ," Appl. Opt. 36, 7188-9198 (1997)