VUV & SX Optics

Kenta Amemiya
Photon Factory, High Energy Accelerator Research Organization1

Outline

1. Mirrors
1.1. focusing & collimation
1.2. substrate materials
1.3. coating & reflectivity
2. Diffraction Gratings
2.1. principle - wavelength dispersion 2.2. energy resolution- dispersion and focus 2.3. fabrication of gratings21.1. focusing & collimation
Demagnification & Aberration

R=2(1 / r + 1 / r ' ) cos θr’ = 5 m

r = 10 m

Spot size becomes r’/r = 1/2⇒ 1:2 Demagnification* Divergence becomes 2 times larger
Elliptical mirror ⇒ perfect focus (determined by demagnification only)
Use of a cylindrical or spherical mirror ⇒ poor focus (aberration)
Larger divergence (larger illumination area) ⇒ larger aberration

Combination of focusing mirrors
r1 = 10 m

r’1 = 5 m

Spot size: r’1/r1 ・ r’2/r2 = 1/6
r’2 = 2 m

r2 = 6 m
Divergence: 6x 3

1.1. focusing & collimation
Collimationr = 10 m
r’ = ∞
Parabolic mirror ⇒ perfect collimation (spot-size limited)
Use of a cylindrical or spherical mirror ⇒ poor collimation (aberration)
Larger divergence (larger illumination area) ⇒ larger aberration

Combination of collimating mirrors
r1 = 10 m

Spot size: r’2/r1 = 1/5
r’2 = 2 m
Divergence: 5x 4

1.1. focusing & collimation

Tangential focusing

Sagittal focusing

Aberration: smaller in tangential focusing* Sagittal focusing is often adopted undulator beamlines
Radius: smaller in sagittal focusing
2 cos θ2R=ρ=
(1 / r + 1 / r ' ) cos θe.g. 88 deg (from normal)，(1 / r + 1 / r ' )r = 10 m, r’ = 5 m⇒ R = 190 m (tangential focusing)，ρ = 0.23 m (sagittal focusing)Higher precision in sagittal focusing
e.g. R = 190 m ± 3%, ρ = 0.23 m ± < 0.5 %Slope error effects: smaller in sagittal focusing51.2. substrate materials
Needs:
Easy to fabricate: precise control of the mirror shape
Low defects, pores
Hardness: small distortion
High thermal conductivity: cooling efficiency
Low thermal expansion: against a heat load
Typical materials
Si: for high heat load, with cooling
SiO2: without cooling* SiO2 is suitable for mirror current measurements61.3. coating & reflectivity
Coating layer:
High reflectivity by “total reflection”
Protection against oxidation etc.
Typical coating material in VUV-SX: Au (50-100 nm)
88 deg86 deghttp://henke.lbl.gov/optical_constants/

71.3. coating & reflectivity
Higher energy region
Critical energy for total reflection depends on incidence angle
Au: 88 deg

Au: 88.5 deg

http://henke.lbl.gov/optical_constants/
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1.3. coating & reflectivity
Higher order suppression
Si: 87 deg

55%

3.3%

http://henke.lbl.gov/optical_constants/

91.3. coating & reflectivity
Higher order suppression: coating material dependence
Ni: 84 deg

Si: 86 deg

52%

42%
3.5%

4.5%

http://henke.lbl.gov/optical_constants/

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1.3. coating & reflectivity
Higher order suppression: incidence-angle dependence
Si: 86 deg

Si: 88 deg

42%
3.5%

http://henke.lbl.gov/optical_constants/

Simultaneous rotation with energy
scan is necessary
No precise control is required11

1.3. coating & reflectivity
Higher order suppression in low energy region
Ni: 80 deg

Ni: 82 deg

43%

11%

31%
2.9%

http://henke.lbl.gov/optical_constants/

It is difficult to achieve high reduction ratio
keeping high reflectivity for fundamental lightNot effective below ~100 eV

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1.3. coating & reflectivity
Multilayer mirror[W/C]80, d = 3 nm, 75 deg

http://henke.lbl.gov/optical_constants/

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1. Mirrors
1.1. focusing & collimation
1.2. substrate materials
1.3. coating & reflectivity
2. Diffraction Gratings
2.1. principle - wavelength dispersion 2.2. energy resolution- dispersion and focus 2.3. fabrication of gratings

142.1. principle - wavelength dispersion Diffraction grating： Periodic grooves on a substrate

1 μm
10 nm

Principle： Interference between the raysreflected at different grooves
Enhanced when light path difference = mλsin α + sin β = nmλ

α
*α>0

β

n: groove density
m: diffraction order
β depends on λ ⇒ Wavelength dispersion(conversion of wavelength to angle)* α ≠|β |(if α = |β |, any λ satisfies the above condition at m = 0)15
⇒ zero-th order light2.2. energy resolution - dispersion and focus How can we monochromatize by using a diffraction grating?
Most basic mode: collimated-light illumination
dispersed

Collimated white
αlightβsin α + sin β = nmλProblem 1： SR is not a collimated light！
Problem 2: Superposition of diffracted lights⇒ difficult to be resolved

Solution 1: Collimation of diverging light with a parabolic mirror
Solution 2: Focusing of diffracted lights with another parabolic mirror
Parabolic mirror(collimation)

SourceParabolic mirror(focusing)

Plane grating(dispersion)

Exit slit(wavelengthselection)

Focused diffracted lights arewell resolved in wavelength
at the exit slit !

Dispersion and Focus
162.2. energy resolution - dispersion and focus The simplest monochromator
Exit slit(wavelengthselection)

Point source

Both the “dispersion” and“focus” are achieved bya diffraction grating only.

Concave grating(dispersion & focusing)Is that really possible?
It is impossible to obtain a perfect focus at all wavelength
But, ”perfect focus” is not necessary !
Small number of optical elements172.2. energy resolution - dispersion and focus What determines the energy resolution?
“Dispersion”: separation of lights with different wavelengths ⇒ dz/dλsin α + sin β = nmλ ⇒cos β dβ = nmdλ , dz / dλ = r ' dβ / dλ = r ' nm / cos β

Ratio between “dispersion” and “light size” determines resolution.
i.e. large dispersion & small focus ⇒ high energy resolution
Dispersion

Small dispersion

Slit

Large dispersion

SourceGrating

Focusing

Poor focus

Good focus

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2.2. energy resolution - dispersion and focus What determines the focus size?
Source size & Demagnification
Low demagnification
SourceSlit

High demagnification

Grating

Aberration

Defocus(focus shift)

Higher-orderaberrationsSlope error (figure error)
Large error

Small error

192.2. energy resolution - dispersion and focus (a) Source size & Demagnification
Source size & Demagnification
Low demagnification
SourceSlit

High demagnification

Gratings’ (lower limit) = s d/d’

d：divergence at the sourced’： divergence at the focus

How to reduce s’:
1. reduce r’ compared to r
long entrance arm & short exit arm

αr～l cosαd ～ l cosα/r

βr’～l cosβd’ ～ l cosβ/rl
2. decrease |β | compared to α
make the incidence angle more grazing⇒ High groove density(keeping the diffraction condition satisfied)large included angle (α−β)
202.2. energy resolution - dispersion and focus 3. reduce the source size (s)Must we reduce the size of the SR source itself?
Use of “pre-focusing optics” and “entrance slit”

Plane grating
SourceCylindrical Cylindrical Entrance
slit
mirrormirrorPre-focusing optics

Toroidal mirror

Plane
Exit slit
Spherical
mirrormirror
Monochromator Post-focusing optics“Entrance slit” can be regarded as a virtual source
Source size can be controlled by entrance-slit opening(at the sacrifice of intensity)
Demagnification in the pre-focusing optics is effective(* divergence increases)21

2.2. energy resolution - dispersion and focus What determines the focus size?
Source size & Demagnification
Low demagnification
SourceSlit

High demagnification

Grating

Aberration

Defocus(focus shift)

Higher-orderaberrations

Slope error (figure error)
Large error

Small error

222.2. energy resolution - dispersion and focus (b) Aberration
Caused by a deviation from the elliptical (or parabolic) shapee.g. Use of a spherical mirror instead of elliptical one
Diffraction effects should be taken into account for a diffraction grating
Aberration is usually expanded in a power series of theposition on the optical element, (w, l), using the light path function, F

For grating
Diffraction condition
Defocus(deviation from focal condition)“coma” aberration

Larger illumination area (larger w and l) ⇒ larger effects of aberration 23

2.2. energy resolution - dispersion and focus Aberration

Higher-orderaberrations

Defocus(focus shift)

How to reduce the aberration:
Defocus can be compensated by adjusting the exit-slit position
Higher-order aberrations can be canceled by a combination of mirrors (not easy)
Reduce the illumination area ⇒ small divergence (acceptance)

Examples for aberration-free or small-aberration optics
Parabolic mirror(focusing)
Parabolic mirror(collimation)

Plane grating(dispersion)

Exit slit(wavelengthselection)

No aberration

Exit slit(wavelengthselection)
Spherical grating(dispersion & focusing)“Rowland condition”
r = R cos α, r’ = R sin β24

2.2. energy resolution - dispersion and focus What determines the focus size?
Source size & Demagnification
Low demagnification
SourceSlitHigh demagnification

Grating

Aberration

Defocus(focus shift)

Higher-orderaberrations

Slope error (figure error)
Large error

Small error

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2.2. energy resolution - dispersion and focus (c) Slope errors
Errors in fabrication of optical elements (e.g. undulation of a plane mirror)
Not systematic ⇒ compensation is impossible⇒ One have to fabricate optical elements with small slope error
ordesign optics to reduce the effects of the slope errors

Demagnification is also effective to reduce the slope-error effects.
30000(d) Number of illuminated grooves
Intrinsic problem of diffraction
Resolving power (λ/Δλ) ~ N

Total Ion Yield (CPS)25000
0.1 mrad
20000
15000
10000

0.05 mrad

50000* Small divergence

399.5

400.0

400.5

401.0

401.5

Photon Energy (eV)⇒ small effects of aberration but small number of grooves 26

2.3. fabrication of gratings
1. Substrate (Plane, Cylindrical, Spherical, Toroidal,…)Same as mirror fabrication
2. Fabrication of grooves (uniform or varied line spacing)
N = N0 (1 + a1w + a2 w2 + a3 w3) (groove density)= N0= 0 for uniform line spacing(a) Mechanical ruling
All groove parameters (a1, a2,… ) can be controlled !
Relatively rough surface ⇒ causes stray light
Suitable for “Brazed” gratings27

2.3. fabrication of gratings(b) Holographic recording
Interference patterns of Laser lights
Some groove parameters might not be controlled* aspheric wavefront recording is available
Relatively smooth surface ⇒ high reflectivity & low stray light
Both the “Laminar” and “Brazed” gratings can be fabricated* some manufacturer strongly prefers the Laminar type

Collimated lights⇒ uniform line spacing

Spherical wavefronts⇒ varied line spacing(poor control)

Aspheric wavefronts⇒ varied line spacing(fine control)

T.Namikoka and M.Koike
Appl. Opt. 34 (1995) 2180

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2.3. fabrication of gratings
3. Groove shape (Laminar & Brazed)(a) Laminar typeMedium diffraction efficiency (typically 20-30%)
Higher order suppressioninterference between top and bottom parts(b) Brazed typeHigh diffraction efficiency when “on Braze”
Strong higher orders29

Thank you for your attention !

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