Adam Jeff May 2013 Particles or Waves Davison amp Germer 1927 Particles are found to produce interference fringes as if they were waves DeBroglie Wavelength λ hp It works even if only 1 particle passes at a time ID: 529557
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Slide1
Zone plates for gas-jet focusing
Adam JeffMay 2013Slide2
Particles or Waves?
Davison &
Germer
1927
Particles are found to produce interference fringes as if they were waves
DeBroglie
Wavelength λ=h/pIt works even if only 1 particle passes at a timeHas been tested with molecules up to Buckminsterfullerene (C60)Slide3
Decoherence
C.
Jonsson, “Elektroneninterferenzen an mehreren künstlich hergestellten Feinspalten“, Zeitschrift fur Physik 161, 4 (1961)
Typically with wave-particle duality only one behaviour can be observed at one time
If we place a (non-destructive) detector at one slit, we ‘force’ the particle to choose one slit. The interference pattern then disappears!
This will affect the gas jet – if the atoms interact anywhere between the source and the focus they will cease to act as waves – Quantum
Decoherence
So we have to keep the pressure low to avoid collisions between atoms
Various papers suggest 10-6 mbar as an upper limit – still OK for our case Slide4
What is a Fresnel Zone Plate?
The path difference between each successive light ring is equal to 1 wavelength (at the focal point) constructive interference.
Each zone is equal in area
Focal spot size is roughly the width of the narrowest (outer) zone
Compared to traditional lens: no spherical aberration, large chromatic aberration
Two main types:
Transmission – alternate zones are blocked – 50% of light lost
Phase – alternate zones have π phase shiftBoth can be binary or smoothSlide5
Matter-wave Fresnel Zone Plate
Smallest zone 100 nm
DeBroglie
wavelength
≈
0.05 nm
for room temperature Helium
Focal length of zone plateResolution ≈ width of smallest zone
radius of outer zone
width of outer zone
T.
Reisinger
, S. Eder, M.M.
Greve
, H.I. Smith, B. Holst
, “Free-standing silicon nitride
zoneplates
for neutral-helium microscopy”, Microelectronic Engineering
87
(
2010
)Slide6
Zemax simulationsSlide7
Figures of Merit
Peak Intensity in the focal spot
. Ultimately, signal strength will depend on this.Transmitted power. A measure of how ‘open’ the plate is. The higher the better.FWHM of focal spot. As small as possible for resolution. However, all the designs produce spots which are plenty small enough. In reality this will be dominated by chromatic effects (not investigated yet).
% encircled in 10
μ
m or 100
μm. Maybe the most important – shows what fraction is spread out into higher order and ‘zeroth order’ diffraction.I calculate the following figures for each design in order to compare them:Slide8
Photon Sieves
Underlying geometry is the same as the zone plate
The ‘clear’ zones are replaced by a series of holes
Lower transmission but less higher-order diffraction
Easier to manufacture?Slide9
Antiholes
If the hole is a bit larger than the underlying zone, it can still have an overall focusing effect. In fact the optimum may be found around d/w =1.35.
Above a certain size the hole covers more of the neighbouring zones than its own zone, so it has a negative focusing effect.
So it’s positive if
centered
on a dark zone: an
antihole
.
L. Kipp et al
, “Sharper images by focusing soft X-rays with photon sieves”, Nature
414
(
2001
)Slide10
Equal-Hole Sieve
All the holes are the same size, for easy manufacture.
Hole
center
is switched between ‘light’ and ‘dark’ zones depending on focusing contribution.Slide11
Apodised Photon Sieve
We can try to make up for the lack of an infinitely large zone plate by smoothing the transmission towards zero at the edges
Also tried:
Composite Sieve
Fractal Sieve
Fibonacci Sieve …Slide12
Results
Design Description
Peak irradiance
Transmitted power
FWHM of focal spot
% in 0.01mm
% in 0.1mm
micrometers
Sieve, size 1, first zone 1, 10 rings
75
5.60E-04
0.35
59
97
Sieve, size 1.35, first zone 1, 10 rings
77.6
7.50E-04
0.35
50
97
Sieve, size 1.5, first zone 1, 10 rings
71
8.40E-04
0.35
48
98
Random Angle Sieve, size 1, first zone 1, 10 rings
51
4.70E-04
0.35
56
97
Random Angle Sieve, size1.35, first zone 1, 10 rings
49
6.00E-04
0.35
48
97
Random Angle Sieve, size 1.5, first zone 1, 10 rings
43
6.80E-04
0.35
48
98
Sieve, size 3.5 holes, first zone 3, 6 rings
8.7
1.10E-03
0.3
30
99
Sieve, size 3.5 holes, first zone 2, 6 rings
9.4
1.20E-03
0.35
27
99
Sieve, size 3.5 holes, first zone 1, 5 rings
6.9
9.80E-04
0.4
6.6
99
Apodised Sieve, size 1, first zone 1, Gaussian 0.8,15,0
83
5.90E-04
0.35
57
97
Apodised Sieve, size 1, first zone 1, Gaussian 0.8,15,8
195
9.20E-04
0.35
64
96
Apodised Sieve, size 1, first zone 2, Gaussian 0.8,15,8
1808.80E-040.356496Apodised Sieve, size 1, first zone 1, Gaussian 0.8,8,0222.90E-040.554798Equal holes sieve, 1 micron, 16 rings612.20E-030.32297Equal holes sieve, 2 micron, 10 rings102.50E-030.32798Equal Holes sieve, 5 micron, 6 rings1.32.50E-0355099Zone Plate, first zone 0, 6 rings1449.20E-040.56499Zone Plate, first zone 0.5, 6 rings1449.10E-040.56299Zone Plate, first zone 1, 6 rings1449.10E-040.45699Zone Plate, first zone 1.5, 6 rings1449.10E-040.45399Zone Plate, first zone 2, 6 rings1449.20E-040.45399Slide13
Linear Zone Plate
Linear Zone Plate is equivalent to a cylindrical lens
Focuses in one plane only
Makes a line at the focal plane
Equivalent to a screen if the focal length is large