Related Experiment Video
Updated: Jun 19, 2026

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material
Published on: May 20, 2013
Bilinear transformed reflectance of materials with a spatially changing refractive index
Abstract:
New approximate analytical expressions in integral form for the reflectance of materials with graded refractive-index profiles are presented. The reflectance of material containing a buried Gaussian refractive-index profile is simulated by these analytical expressions and compared with the reflectance computed by the matrix method. The two methods agree to within 0.7% in the root-mean-square sense. The analytical expressions, however, are 1 to 2 orders of magnitude faster to compute. The reflectance of a buried parabolic refractive-index profile is also investigated, and results from the proposed theory are compared with those from the WKB approximation. Also, in this instance it is shown that the integral formulation is superior to the WKB approximation at long wavelengths. As a practical example, the measured reflectance of semi-insulating GaAs implanted with protons is compared with theoretical calculations by use of the proposed formulas.
Related Concept Videos
Attenuated Total Reflectance (ATR) Infrared Spectroscopy: Overview
The ATR process begins by directing a beam...
Influence of Earth's Curvature and Atmospheric Refraction on Leveling
UV–Vis Spectroscopy: Beer–Lambert Law
Deformations in a Transverse Cross Section
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
Total Internal Reflection Fluorescence Microscopy
Propagation of Waves
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...

