differt.em.slab_coefficients

slab_coefficients(n_r, cos_theta_i, thickness, wavelength)

Compute the Fresnel reflection and transmission coefficients of a finite-thickness dielectric slab.

Unlike fresnel_coefficients, which assumes a single interface between two infinite half-spaces, this function accounts for the coherent sum of all internal multiple reflections inside a slab of the given thickness (e.g., a wall), following [15, eq. 43-44]:

\[\begin{split}q &= \frac{2\pi d}{\lambda}\sqrt{n_r^2 - \sin^2\theta_i},\\ R &= r\frac{1 - e^{-2jq}}{1 - r^2e^{-2jq}},\\ T &= (1 - r^2)\frac{e^{-jq}}{1 - r^2e^{-2jq}},\end{split}\]

where \(r\) is the (single-interface) Fresnel reflection coefficient returned by reflection_coefficients, \(d\) is the thickness, and \(\lambda\) is the wavelength. The same formula is used independently for the s and p polarizations.

This matches the transmission and (dielectric wedge face) diffraction models used in Sionna RT’s RadioMaterial.

Parameters:

• n_r (Inexact[ArrayLike, "*#batch"]) –

  The relative refractive index.

  This is the ratio of the refractive index of the slab over the refractive index of the surrounding medium.

• cos_theta_i (Float[ArrayLike, "*#batch"]) – The (cosine of the) angle of incidence.

• thickness (Float[ArrayLike, "*#batch"]) – The thickness of the slab.

• wavelength (Float[ArrayLike, "*#batch"]) – The wavelength, in the same unit as thickness.

Return type:

tuple[tuple[Complex[Array, "*batch"], Complex[Array, "*batch"]], tuple[Complex[Array, "*batch"], Complex[Array, "*batch"]]]

Returns:

The reflection and transmission coefficients for s and p polarizations.

See also

fresnel_coefficients