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Zone plates for gas-jet focusing Zone plates for gas-jet focusing

Zone plates for gas-jet focusing - PowerPoint Presentation

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Zone plates for gas-jet focusing - PPT Presentation

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

040 zone sieve size zone 040 size sieve plate holes focal focusing zones 20e rings1449 gaussian 10e hole 030

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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