Fresnel diffraction mirror

In atomic physics, a ridged mirror (or ridged atomic mirror, or Fresnel diffraction mirror) is a kind of atomic mirror, designed for the specular reflection of neutral particles (atoms) coming at the grazing incidence angle, characterised in the following: in order to reduce the mean attraction of particles to the surface and increase the reflectivity, this surface has narrow ridges.

Various estimates for the efficiency of quantum reflection of waves from ridged mirror were discussed in the literature. All the estimates explicitly use the de Broglie theory about wave properties of reflected atoms.

The ridges enhance the quantum reflection from the surface, reducing the effective constant ${\displaystyle ~C~}$ of the van der Waals attraction of atoms to the surface. Such interpretation leads to the estimate of the reflectivity

where ${\displaystyle ~\ell ~}$ is width of the ridges, ${\displaystyle ~L~}$ is distance between ridges, ${\displaystyle \displaystyle ~\theta ~}$ is grazing angle, and ${\displaystyle ~K=mV/\hbar ~}$ is wavenumber and ${\displaystyle ~r_{0}(C,k)~}$ is coefficient of reflection of atoms with wavenumber ${\displaystyle ~k~}$ from a flat surface at the normal incidence. Such estimate predicts the enhancement of the reflectivity at the increase of period ${\displaystyle ~L~}$; this estimate is valid at ${\displaystyle KL\!~\theta ^{2}\ll 1}$. See quantum reflection for the approximation (fit) of the function ${\displaystyle ~r_{0}~}$.

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