Ridged mirror

From Wikipedia, the free encyclopedia

1 Definition
2 Reflectivity of ridged atomic mirrors
3 Aplications of ridged mirrors
4 See also
5 References

[edit] Definition

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. ^[1]

[edit] Reflectivity of ridged atomic mirrors

Various estimates for the efficiency of quantum reflection of waves from ridged mirror were discussed in the literature.

[edit] Scaling of the van der Waals force

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

where $~\ell~$ is width of the ridges, $~L~$ is distance between ridges, $\displaystyle ~\theta~$ is grazing angle, and $~K=mV/\hbar~$ is wavenumber and $~r_0(C,k)~$ is coefficient of reflection of atoms with wavenumber $~k~$ from a flat surface at the normal incidence. Such estimate predicts the enhancement of the reflectivity at the increase of period $~L~$ ; this estimate is valid at $KL\!~\theta^2\ll 1$ . See quantum reflection for the approximation (fit) of the function $~r_0~$ .

[edit] Interpretation as Zeno effect

For narrow ridges with large period $L$ , the ridges just blocks the part of the wavefront. Then, it can be interpreted in terms of the Fresnel diffraction ^[2] , ^[3] , or the the Zeno effect ^[4]; such interpretation leads to the estimate the reflectivity

where grazing ange $\displaystyle ~\theta~$ is supposed to be small. This estimate predicts enhancement of the reflectivity at the reduction of period $~L~$ . This estimate requires that $~\ell/L \ll 1~$ .

[edit] Fundamental limit

For efficient ridged mirrors, both estimates above should predict high reflectivity. This implies reduction of both, width $~\ell~$ of the ridges and the period $~\ell~$ . The width of the ridges cannot be smaller than the size of atom; this sets the fundamental limit of performance of the ridged mirrors.

[edit] Aplications of ridged mirrors

The ridged mirrors are not yet commercialized, although certain achievements can be mentioned. The reflectivity of a ridged atomic mirror can be orders of magnitude better than that of a flat surface. The use of a ridged mirror as an atomic hologram is demonstrated ^[5] .

The ridged mirror can reflect also the visible light ^[6]; however, for the light waves, the performance is not better than that of a flat surface. Ellipsoidal ridged mirror is proposed as focusing element for the atom optical system with submicron resolution (atomic nanoscope).