text: The method uses scattering parameters of a material sample embedded in a waveguide, namely  and , to calculate permittivity and permeability data.  and  correspond to the cumulative reflection and transmission coefficient of the sample that are referenced to the each sample end, respectively: these parameters account for the multiple internal reflections inside the sample, which is considered to have a thickness of . The reflection coefficient of the bulk sample is:
  where
  The sign of the root for the reflection coefficient is chosen appropriately to ensure its passivity (). Similarly, the transmission coefficient of the bulk sample can be written as:
  Thus, the effective permeability () and permittivity () of the material can be written as:
  where
  and 
  * is the free-space wavelength. 
  * is the guided mode wavelength of the unfilled transmission line.
  * is the cutoff wavelength of the unfilled transmission line
  The constitutive relation for  admits an infinite number of solutions due to the branches of the complex logarithm. The ambiguity regarding its result can be resolved by taking the group delay into account.