Ridged 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".cite journal
comment=6
url=http://jpsj.ipap.jp/link?JPSJ/71/5/
author= F.Shimizu
coauthors=J. Fujita
title=Giant Quantum Reflection of Neon Atoms from a Ridged Silicon Surface
journal=Journal of the Physical Society of Japan
volume=71
pages=5–8
year=2002
doi=10.1143/JPSJ.71.5]

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 hypothesis about wave properties of reflected atoms.

caling 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: $displaystyle\; r\; approx\; r\_0!left(\; frac\; ell\; L\; C,!~Ksin(\; heta)\; ight)$,where $~ell~$ is width of the ridges, $~L~$ is distance between ridges,$displaystyle\; ~\; heta~$ 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 thereflectivity at the increase of period $~L~$; this estimate is valid at $KL!~\; heta^2ll\; 1$. 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 cite journal
url=http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLRAAN000072000001013617000001&idtype=cvips&gifs=yes
free=http://www.ils.uec.ac.jp/~dima/PhysRevA_72_013617.pdf
author= D.Kouznetsov | coauthors=H.Oberst
title=Scattering of waves at ridged mirrors.
journal=PRA | volume=72 | pages=013617 | year=2005 ] cite journal
url=http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000094000001013203000001&idtype=cvips&gifs=yes
author= H.Oberst | coauthors=D.Kouznetsov, K.Shimizu, J.Fujita, and F. Shimizu
title=Fresnel Diffraction Mirror for an Atomic Wave
journal=PRL | volume=94 | pages=013203 | year=2005 ] of the de Broglie wave, or the Zeno effect cite journal
url=http://annex.jsap.or.jp/OSJ/opticalreview/TOC-Lists/vol12/12e0363tx.htm
author= D.Kouznetsov | coauthors= H.Oberst
title=Reflection of Waves from a Ridged Surface and the Zeno Effect
journal=Optical Review | volume=12 | pages=1605–1623 | year=2005
doi=10.1007/s10043-005-0363-9 ] ; such interpretation leads to the estimate the reflectivity

:$~displaystyle\; r\; approx\; exp!left(-sqrt\{8!~K!~L\}~\; heta\; ight)~$,

where the grazing angle $displaystyle\; ~\; heta~$ 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 cite journal
url=http://stacks.iop.org/0953-4075/39/1605
free=http://www.iop.org/EJ/abstract/0953-4075/39/7/005/;
author= D.Kouznetsov
coauthors=H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck
title=Ridged atomic mirrors and atomic nanoscope
journal=JOPB
volume=39
pages=1605–1623
year=2006
doi=10.1088/0953-4075/39/7/005] .

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,cite journal
title = Reflection-Type Hologram for Atoms
author =F.Shimizu
coauthors=J.Fujita
journal = PRL
volume = 88
number = 12
pages = 123201
numpages = 4
year = 2002
month = Mar
url=http://prola.aps.org/abstract/PRL/v88/i12/e123201
publisher = American Physical Society
format = subscription required] 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 cite journal
url=http://stacks.iop.org/0953-4075/39/1605
free=http://www.iop.org/EJ/abstract/0953-4075/39/7/005/;
author= D.Kouznetsov
coauthors=H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck
title=Ridged atomic mirrors and atomic nanoscope
journal=JOPB
volume=39
pages=1605–1623
year=2006
doi=10.1088/0953-4075/39/7/005] ; 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).

ee also

*atomic mirror (physics),
*quantum reflection,
*atomic nanoscope,
*Zeno effect
*de Broglie hypothesis

References