Difference between revisions of "Ridged mirror"
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===Interpretation as Zeno effect=== |
===Interpretation as Zeno effect=== |
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For narrow ridges with large period <math>L</math>, the ridges just blocks the part of the wavefront. Then, it can be interpreted in terms of the [[Fresnel diffraction]]<ref name="pra"> |
For narrow ridges with large period <math>L</math>, the ridges just blocks the part of the wavefront. Then, it can be interpreted in terms of the [[Fresnel diffraction]]<ref name="pra"> |
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| + | http://www.ils.uec.ac.jp/~dima/PAPERS/PhysRevA_72_013617.pdf<br> |
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| − | {{cite journal |
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| + | http://mizugadro.mydns.jp/PAPERS/PhysRevLett_94_013203.pdf |
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| − | | author= D.Kouznetsov | coauthors=H.Oberst |
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| + | D.Kouznetsov, H.Oberst |
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| − | | year=2005 |
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| − | + | Scattering of waves at ridged mirrors. |
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| + | Physical Review A, 2005, v. 72, issue 1, 013617; |
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| − | | url=http://www.ils.uec.ac.jp/~dima/PhysRevA_72_013617.pdf |
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| + | doi=10.1103/PhysRevA.72.013617 |
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| − | | journal=[[Physical Review A]] |
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| + | </ref><ref name="fres"> |
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| − | | volume=72 |issue=1 | pages=013617 |
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| + | http://www.ils.uec.ac.jp/~dima/PAPERS/PhysRevLett_94_013203.pdf <br> |
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| − | | doi=10.1103/PhysRevA.72.013617 |
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| + | http://mizugadro.mydns.jp/PAPERS/PhysRevLett_94_013203.pdf |
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| − | |bibcode = 2005PhRvA..72a3617K }}</ref><ref name="fres"> |
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| + | H.Oberst, D.Kouznetsov, K.Shimizu, J.Fujita, and F. Shimizu |
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| − | {{cite journal |
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| + | Fresnel Diffraction Mirror for an Atomic Wave, |
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| − | | author= H.Oberst |
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| + | [[Physical Review Letters]], 2005 |
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| − | | coauthors=D.Kouznetsov, K.Shimizu, J.Fujita, and F. Shimizu |
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| + | v. 94, issue=1, pages=013203, |
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| − | | year=2005 |
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| + | doi=10.1103/PhysRevLett.94.013203 |
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| − | | title=Fresnel Diffraction Mirror for an Atomic Wave |
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| + | </ref> |
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| − | | journal=[[Physical Review Letters]] |
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| − | | volume=94 |issue=1 | pages=013203 |
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| − | | doi=10.1103/PhysRevLett.94.013203 |
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| − | | bibcode=2005PhRvL..94a3203O |
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| − | }}</ref> of the [[de Broglie wave]], or the [[Zeno effect]];<ref name="zeno"> |
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| − | {{cite journal |
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| − | | author= D.Kouznetsov |
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| − | | coauthors= H.Oberst |
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| − | | year=2005 |
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| − | | title=Reflection of Waves from a Ridged Surface and the Zeno Effect |
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| − | | journal=[[Optical Review]] |
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| − | | volume=12 | pages=1605–1623 |
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| − | | doi=10.1007/s10043-005-0363-9 |
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| − | | issue= 5 |
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| − | | bibcode=2005OptRv..12..363K |
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| − | }}</ref> such interpretation leads to the estimate the reflectivity |
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| + | of the [[de Broglie wave]], or the [[Zeno effect]];<ref name="zeno"> |
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| − | :<math>~\displaystyle r \approx \exp\!\left(-\sqrt{8\!~K\!~L}~\theta\right)~</math>, <!--where <math> ~K~</math> is wavenumber, <math>~L~</math> is period (distance between ridges) and--> |
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| + | http://www.ils.uec.ac.jp/~dima/PAPERS/optrevri.pdf <br> |
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| + | http://mizugadro.mydns.jp/PAPERS/optrevri.pdf |
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| + | D.Kouznetsov, |
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| + | H.Oberst. |
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| + | Reflection of Waves from a Ridged Surface and the Zeno Effect. |
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| + | [[Optical Review]], 2005 |
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| + | v. 12, p.1605–1623, doi=10.1007/s10043-005-0363-9, |
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| + | issue= 5 |
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| + | </ref>. |
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| + | |||
| + | Such interpretation leads to the estimate the reflectivity |
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| + | <math>~\displaystyle r \approx \exp\!\left(-\sqrt{8\!~K\!~L}~\theta\right)~</math>, <!--where <math> ~K~</math> is wavenumber, <math>~L~</math> is period (distance between ridges) and--> |
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where the [[grazing angle]] <math>\displaystyle ~\theta~</math> is supposed to be small. This estimate predicts enhancement of the reflectivity at the '''reduction''' of period <math>~L~</math>. This estimate requires that <math>~\ell/L \ll 1~</math>. |
where the [[grazing angle]] <math>\displaystyle ~\theta~</math> is supposed to be small. This estimate predicts enhancement of the reflectivity at the '''reduction''' of period <math>~L~</math>. This estimate requires that <math>~\ell/L \ll 1~</math>. |
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===Fundamental limit=== |
===Fundamental limit=== |
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| − | For efficient ridged mirrors, both estimates above should predict high reflectivity. This implies reduction of both, width, <math>\ell</math> of the ridges and the period, <math>L</math>. The width of the ridges cannot be smaller than the size of atom; this sets the limit of performance of the ridged mirrors.<ref name=" |
+ | For efficient ridged mirrors, both estimates above should predict high reflectivity. This implies reduction of both, width, <math>\ell</math> of the ridges and the period, <math>L</math>. The width of the ridges cannot be smaller than the size of atom; this sets the limit of performance of the ridged mirrors.<ref name="nano scope"> |
| + | http://stacks.iop.org/0953-4075/39/1605 <br> |
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| − | {{cite journal |
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| + | http://mizugadro.mydns.jp/PAPERS/nanoscope.pdf<br> |
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| − | | author= D.Kouznetsov |
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| − | + | D.Kouznetsov, H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck |
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| + | Ridged atomic mirrors and atomic nano scope. |
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| − | | year=2006 |
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| + | [[Journal of Physics B]], 2006, |
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| − | | title=Ridged atomic mirrors and atomic nanoscope |
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| + | v.39, p.1605–1623, |
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| − | | journal=[[Journal of Physics B]] |
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| + | issue 7, |
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| − | | volume=39 | pages=1605–1623 |
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| − | + | doi=10.1088/0953-4075/39/7/005 |
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| + | </ref> |
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| − | | issue= 7 |
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| − | |bibcode = 2006JPhB...39.1605K }}</ref> |
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==Applications of ridged mirrors== |
==Applications of ridged mirrors== |
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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. |
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. |
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| − | In Shimizu's and Fujita's work |
+ | In Shimizu's and Fujita's work <ref name="holo"> |
| + | F.Shimizu, J.Fujita. |
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| − | {{cite journal |
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| + | Reflection-Type Hologram for Atoms. |
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| − | | author =F.Shimizu |
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| + | [[Physical Review Letters]], |
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| − | | coauthors=J.Fujita |
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| + | 2002, v. 88, issue 12, page 123201, |
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| − | | year = 2002 |
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| + | doi 10.1103/PhysRevLett.88.123201 |
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| − | | title = Reflection-Type Hologram for Atoms |
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| + | </ref>, |
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| − | | journal=[[Physical Review Letters]] |
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| − | | volume=88 | issue = 12 |page=123201 |
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| − | | doi = 10.1103/PhysRevLett.88.123201 |
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| − | | pmid=11909457 |
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| − | | bibcode=2002PhRvL..88l3201S |
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| − | }}</ref> atom holography is achieved via electrodes implanted into SiN<sub>4</sub> film over an atomic mirror, or maybe as the atomic mirror itself. |
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| + | the atom holography is achieved via electrodes implanted into SiN<sub>4</sub> film over an atomic mirror, or maybe as the atomic mirror itself. |
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| − | Ridged mirrors can also reflect [[visible light]];<ref name="nanoscope"/> 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]]). |
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| + | |||
| + | Ridged mirrors can also reflect [[visible light]] |
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| + | <ref name="nano scope"> |
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| + | http://stacks.iop.org/0953-4075/39/1605 <br> |
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| + | http://mizugadro.mydns.jp/PAPERS/nanoscope.pdf<br> |
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| + | D.Kouznetsov, H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck |
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| + | Ridged atomic mirrors and atomic nano scope. |
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| + | [[Journal of Physics B]], 2006, |
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| + | v.39, p.1605–1623, |
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| + | issue 7, |
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| + | doi=10.1088/0953-4075/39/7/005 |
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| + | </ref>. |
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| + | |||
| + | 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]]). |
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==See also== |
==See also== |
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==References== |
==References== |
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| + | <references/> |
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| − | {{reflist}} |
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The content of the article above previously appeared at http://en.wikipedia.org/wiki/Ridged_mirror |
The content of the article above previously appeared at http://en.wikipedia.org/wiki/Ridged_mirror |
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[[Category:Atomic, molecular, and optical physics]] |
[[Category:Atomic, molecular, and optical physics]] |
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| − | [[Category:Quantum mechanics]] |
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[[Category:Content from Wikipedia]] |
[[Category:Content from Wikipedia]] |
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| − | [[Category: |
+ | [[Category:English]] |
| + | [[Category:ILS]] |
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| + | [[Category:Japan]] |
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| + | [[Category:Quantum mechanics]] |
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Latest revision as of 07:04, 1 December 2018
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, characterized 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]
Reflectivity of ridged atomic mirrors
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.
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 \[\displaystyle r \approx r_0\!\left( \frac \ell L C,\!~K\sin(\theta)\right)\], 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 \(~r_0~\).
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]
of the de Broglie wave, or the Zeno effect;[4].
Such interpretation leads to the estimate the reflectivity \(~\displaystyle r \approx \exp\!\left(-\sqrt{8\!~K\!~L}~\theta\right)~\), where the grazing angle \(\displaystyle ~\theta~\) is supposed to be small. This estimate predicts enhancement of the reflectivity at the reduction of period \(~L~\). This estimate requires that \(~\ell/L \ll 1~\).
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, \(L\). The width of the ridges cannot be smaller than the size of atom; this sets the limit of performance of the ridged mirrors.[5]
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 [6],
the 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 [5].
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).
See also
References
- ↑ F.Shimizu, J. Fujita. Giant Quantum Reflection of Neon Atoms from a Ridged Silicon Surface Journal of the Physical Society of Japan 71 p.5–8 (2002)
- ↑
http://www.ils.uec.ac.jp/~dima/PAPERS/PhysRevA_72_013617.pdf
http://mizugadro.mydns.jp/PAPERS/PhysRevLett_94_013203.pdf D.Kouznetsov, H.Oberst Scattering of waves at ridged mirrors. Physical Review A, 2005, v. 72, issue 1, 013617; doi=10.1103/PhysRevA.72.013617 - ↑
http://www.ils.uec.ac.jp/~dima/PAPERS/PhysRevLett_94_013203.pdf
http://mizugadro.mydns.jp/PAPERS/PhysRevLett_94_013203.pdf H.Oberst, D.Kouznetsov, K.Shimizu, J.Fujita, and F. Shimizu Fresnel Diffraction Mirror for an Atomic Wave, Physical Review Letters, 2005 v. 94, issue=1, pages=013203, doi=10.1103/PhysRevLett.94.013203 - ↑
http://www.ils.uec.ac.jp/~dima/PAPERS/optrevri.pdf
http://mizugadro.mydns.jp/PAPERS/optrevri.pdf D.Kouznetsov, H.Oberst. Reflection of Waves from a Ridged Surface and the Zeno Effect. Optical Review, 2005 v. 12, p.1605–1623, doi=10.1007/s10043-005-0363-9, issue= 5 - ↑ 5.0 5.1
http://stacks.iop.org/0953-4075/39/1605
http://mizugadro.mydns.jp/PAPERS/nanoscope.pdf
D.Kouznetsov, H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck Ridged atomic mirrors and atomic nano scope. Journal of Physics B, 2006, v.39, p.1605–1623, issue 7, doi=10.1088/0953-4075/39/7/005 - ↑ F.Shimizu, J.Fujita. Reflection-Type Hologram for Atoms. Physical Review Letters, 2002, v. 88, issue 12, page 123201, doi 10.1103/PhysRevLett.88.123201
The content of the article above previously appeared at http://en.wikipedia.org/wiki/Ridged_mirror