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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
Grazing

Grazing generally describes a type of predation in which a herbivore feeds on plants , or more broadly on a multicellular autotrophs . Grazing differs from true predation because the organism being eaten is not death, and it differs from parasitism as the two organisms do not symbiosis, nor is the grazer necessarily so limited in what it can...
 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.
ous estimates for the efficiency of quantum reflection
Quantum reflection

Quantum reflection is a physical phenomenon involving the reflection of a matter wave from an attractive potential. In classical physics, such a phenomenon is not possible; for instance when one magnet is pulled toward another, you do not expect one of the magnets to suddenly turn around and retreat in the opposite direction....
 of waves from ridged mirror were discussed in the literature.






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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
Grazing

Grazing generally describes a type of predation in which a herbivore feeds on plants , or more broadly on a multicellular autotrophs . Grazing differs from true predation because the organism being eaten is not death, and it differs from parasitism as the two organisms do not symbiosis, nor is the grazer necessarily so limited in what it can...
 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.

Reflectivity of ridged atomic mirrors

Image Ridged Mirror Figureb
Various estimates for the efficiency of quantum reflection
Quantum reflection

Quantum reflection is a physical phenomenon involving the reflection of a matter wave from an attractive potential. In classical physics, such a phenomenon is not possible; for instance when one magnet is pulled toward another, you do not expect one of the magnets to suddenly turn around and retreat in the opposite direction....
 of waves from ridged mirror were discussed in the literature. All the estimates explicitly use the de Broglie hypothesis
De Broglie hypothesis

In physics, the matter wave, aka de Broglie wave , is the wave-like nature of all matter . The de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle and that the frequency is directly proportional to the particle's kinetic energy....
 about wave properties of reflected atoms.

Scaling of the van der Waals force
Van der Waals force

In physical chemistry, the van der Waals force , named after The Netherlands scientist Johannes Diderik van der Waals, is the attractive or repulsive force between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral molecules....
 

The ridges enhance the quantum reflection
Quantum reflection

Quantum reflection is a physical phenomenon involving the reflection of a matter wave from an attractive potential. In classical physics, such a phenomenon is not possible; for instance when one magnet is pulled toward another, you do not expect one of the magnets to suddenly turn around and retreat in the opposite direction....
 from the surface, reducing the effective constant of the van der Waals
Van der Waals force

In physical chemistry, the van der Waals force , named after The Netherlands scientist Johannes Diderik van der Waals, is the attractive or repulsive force between molecules other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral molecules....
 attraction of atoms to the surface. Such interpretation leads to the estimate of the reflectivity
,
where is width of the ridges, is distance between ridges, is grazing angle, and is wavenumber and is coefficient of reflection of atoms with wavenumber from a flat surface at the normal incidence. Such estimate predicts the enhancement of the reflectivity at the increase of period ; this estimate is valid at . See quantum reflection
Quantum reflection

Quantum reflection is a physical phenomenon involving the reflection of a matter wave from an attractive potential. In classical physics, such a phenomenon is not possible; for instance when one magnet is pulled toward another, you do not expect one of the magnets to suddenly turn around and retreat in the opposite direction....
 for the approximation (fit) of the function .

Interpretation as Zeno effect

For narrow ridges with large period , the ridges just blocks the part of the wavefront. Then, it can be interpreted in terms of the Fresnel diffraction
Fresnel diffraction

In optics, Fresnel diffraction or near-field diffraction is a process of diffraction which occurs when a wave passes through an aperture and diffracts in the near field, causing any diffraction pattern observed to differ in size and shape, depending on the distance between the aperture and the projection....


of the de Broglie wave
De Broglie hypothesis

In physics, the matter wave, aka de Broglie wave , is the wave-like nature of all matter . The de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle and that the frequency is directly proportional to the particle's kinetic energy....
, or the Zeno effect ; such interpretation leads to the estimate the reflectivity

,

where the grazing angle is supposed to be small. This estimate predicts enhancement of the reflectivity at the reduction of period . This estimate requires that .

Fundamental limit

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

Applications of ridged mirrors

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 has been demonstrated. In Shimizu's and Fujita's work, atom holography is achieved via electrodes implanted into SiN4 film over an atomic mirror, or maybe as the atomic mirror itself.

Ridged mirrors can also reflect visible light ; however, for light waves, the performance is not better than that of a flat surface. An ellipsoidal ridged mirror is proposed as the focusing element for an atomic optical system with submicrometre resolution (atomic nanoscope
Atomic nanoscope

The atomic de Broglie microscope is an imaging system which is expected to provide resolution at the nanometer scale....
).

See also

  • Atomic mirror
  • Quantum reflection
    Quantum reflection

    Quantum reflection is a physical phenomenon involving the reflection of a matter wave from an attractive potential. In classical physics, such a phenomenon is not possible; for instance when one magnet is pulled toward another, you do not expect one of the magnets to suddenly turn around and retreat in the opposite direction....
  • Atomic nanoscope
    Atomic nanoscope

    The atomic de Broglie microscope is an imaging system which is expected to provide resolution at the nanometer scale....
  • Zeno effect
  • De Broglie hypothesis
    De Broglie hypothesis

    In physics, the matter wave, aka de Broglie wave , is the wave-like nature of all matter . The de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle and that the frequency is directly proportional to the particle's kinetic energy....