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J. Stahn solid state polarisers
Erice, 07. 2017 0
PAUL SCHERRER INSTITUT
Jochen Stahn
Laboratory for Neutron Scattering and Imaging
Solid State Polarisers
and
Focussing Neutron Optics
Erice School Neutron Science and Instrumentation, IV course
Neutron Precession Techniques
Erice, Sicily, Italy, 01. – 08. 07. 2017
outlineJ. Stahn solid state polarisers
Erice, 07. 2017 1
basics
◦ reflectometry
◦ supermirrors
◦ polarising coatings
polarisers
◦ overview
◦ reflective coatings
◦ comparison
focusing optics
◦ refractive
◦ reflective
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 2
basics
◦ reflectometry
◦ supermirrors
◦ polarising coatings
polarisers
◦ overview
◦ reflective coatings
◦ comparison
focusing optics
◦ refractive
◦ reflective
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 3
analogy to visible light
flat surfaces partly reflect light
→ image of the boot
some media also transmit light
→ ground below the water
parallel interfaces cause interference
→ colourful soap bubbles
reflectivity of a surface
function of index of refraction n
ω ω
k0 kR
k1
n0
n1
qz = 2|k0| sinω
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 4
analogy to visible light
flat surfaces partly reflect light
→ image of the boot
some media also transmit light
→ ground below the water
parallel interfaces cause interference
→ colourful soap bubbles
reflectivity of plane parallel interfaces
interference pattern I(qz ,ni,di)
ω ω
k0 kR
k1
n0
n1
n2
n3
d1 thickness of layer 1
d2
d3
qz
reflectometryJ. Stahn solid state polarisers
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simulated reflectivity of a surface
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
qz/A−1
log10[R(q
z)]
critical edge ⇒ nsubstrate
R ∝
(q
qc
)4
for q ≫ qc
reflectometryJ. Stahn solid state polarisers
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simulated reflectivity of a thin layer
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
qz/A−1
log10[R(q
z)] amplitude ⇒ ∆nlayer,substrate
minimum ⇒ dlayer
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 7
simulated reflectivity of a thick layer
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
qz/A−1
log10[R(q
z)]
amplitude ⇒ ∆nlayer,substrate
minimum ⇒ dlayer
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 8
simulated reflectivity of a periodic stack of layers
= multilayer, ml
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
qz/A−1
log10[R(q
z)]
maxima ⇒ dbilayer
amplitudes ⇒ ∆nlayers
∆dlayers
minima ⇒ dfilm
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 9
simulated reflectivity of a stack of mls
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
qz/A−1
log10[R(q
z)]
B
A
B A
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 10
simulated reflectivity of a stack with thickness gradient
= supermirror, sm
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
qz/A−1
log10[R(q
z)]
critical edge of sm
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 11
simulated reflectivity of a sm
and of Ni
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
qz/A−1
log10[R(q
z)]
qcNi critical edge of Ni
qcsm := mqc
Ni critical edge of sm
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 12
index of refraction n :=|ki |
|k0|
≈ 1−V
2Ekin
V =2π~2
mnρb − µµµnB
︸ ︷︷ ︸
±µnB
:=2π~2
mn
(
ρb ± ρm)
ω ω
k0 kR
k1
n0
n1
qz = 2|k0| sinω
|k| = 2π/λ
reflectometryJ. Stahn solid state polarisers
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polarising sm
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
qz/A−1
log10[R(q
z)]
ρb − ρp ≈ ρsρb > ρs
ρb + ρp ≫ ρs
reflectometryJ. Stahn solid state polarisers
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polarising sm coatings
FM spacer substrate pro con
Fe89Co11 Si Si Co
Fe Si : N high transmission q|−〉
c
low activation
FeCoV Ti : N absorber q|−〉
c < 0 A−1 Co
Fe0.5Co0.5 Co
Co gets activated ⇒ avoid whenever possible!
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 15
off-specular scattering
ρ = ρ(x , z)
⇒ R(qx) 6= 0!
⇒ dilution of phase space
background
losses
ρmagnetic(x , y) 6= 0
⇒ spin flip
Ni/Ti multilayer
k0in-plane off-specularspecular
out-of-plane off-specular
qxz
qzqxyz
qz
qx0
reflectometryJ. Stahn solid state polarisers
Erice, 07. 2017 16
keep in mind:R(qz) = R(n(z),B(z))
= 1 ∀ qz < qc
= 1 . . .0.55 for qz < qsm
∝ q−4z ∀ qz ≫ qc
• typical numbers:
ρb /10−6 A−2 qc / A−1 ωc @4A
Si, Fe|−〉
2.1 0.010 0.18◦
Fe|+〉
13.9 0.026 0.47◦
Ni 9.4 0.022 0.40◦
Ti -3.4
⇒ small angles ⇒ geometrical constraints
• roughness ⇒ off-specular scattering ⇒ background & depolarisation
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
polarisersJ. Stahn solid state polarisers
Erice, 07. 2017 17
basics
◦ reflectometry
◦ supermirrors
◦ polarising coatings
polarisers
◦ overview
◦ reflective coatings
◦ comparison
focusing optics
◦ refractive
◦ reflective
polarisersJ. Stahn solid state polarisers
Erice, 07. 2017 18
overview
transmission throgh polycristalline Fe
6mm Fe: P = 33% at λ = 3.6 A
3He
→ talk by E. Babcock
Heusler alloy
crystal monochromator
thin film coatings
polarisersJ. Stahn solid state polarisers
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Heusler alloy monochromator / analyser
Cu2MnAl single crystals with Fmagnetic(111) = ±Fnuclear(111)
⇒ F(111) reflex strong for µµµn ↑↑ B
weak for µµµn ↓↑ B
• λ ∈ [0.8, 6.5] A
• ∆λ/λ ≈ 1%
• P ≈ 95%P ≈ 95%P ≈ 95%
• used for triple-axis spectrometers
P. Courtois et al: N.I.M. A 529, 157 (2004)
polarisers - based on SMJ. Stahn solid state polarisers
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Using Reflected beam
• trajectory is inclined
• high polarisation
PR ≈ 96%− 99%PR ≈ 96%− 99%PR ≈ 96%− 99%
R|+〉
R|−〉
qzω1/λ
lost intensity
- transmitted
- absorbed
PR =R
|+〉−R
|−〉
R|+〉
+R|−〉
qzω1/λ
PR ≈ 1−R
|−〉
R|+〉
SwissNeutronics
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 21
single, falt mirror switchable remanent polariser
HM ≈ 200Oe, Hg < 40Oe
-1
-0.5
0
0.5
1
-100 -50 0 50 100
magnetization
M
polarization field H/Oe
R|+〉
R|−〉
qz
R|+〉
R|−〉
qz
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M
M
Hg
Hg
HM
HM
polarisers - based on SMJ. Stahn solid state polarisers
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benderlength
width≈ 150
|−〉 |+〉 |+〉
optimum parameters-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 20 40 60 80 100 120 140-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 20 40 60 80 100 120 140-3 -2 -1 0 1 2 3
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
-1
-0.5
0
0.5
1
1.5
2
y
θ
too large δθ-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 20 40 60 80 100 120 140
garland reflections of |−〉
too high λ-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 20 40 60 80 100 120 140
polarisers - based on SMJ. Stahn solid state polarisers
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S-benderlength
width≈ 250
• almost straight trajectory
• garland-problem is solved
polarisers - based on SMJ. Stahn solid state polarisers
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application: solid-state S-bender
Si wafers (150µm) used as channel
◦ thin and short channels
◦ q|−〉
c < 0 A−1
◦ no dark regiond due to substrate
◦ higher absorption
this principle also
applies to benders
T. Krist et al.: N.I.M. 698, 94 (2013)
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 25
using Transmitted beam
• straight trajectory
• moderate polarisation
PT ≈ 60%− 80%PT ≈ 60%− 80%PT ≈ 60%− 80%
T|+〉
T|−〉
qz
PT =T
|−〉−T
|+〉
T|−〉
+T|+〉
qz
SwissNeutronics
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 26
using Transmitted beam
• straight trajectory
• high polarisation
PT ≈ 96%− 99%PT ≈ 96%− 99%PT ≈ 96%− 99%
T|+〉
T|−〉
qz
PT =T
|−〉−T
|+〉
T|−〉
+T|+〉
qz
increase of efficiency by
multiple transmission:
• both sides of substrates coated
• several substrates in sequence
⇒ reduced intensitySwissNeutronics
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 27
transmission bender + collimatorlength
width≈ 300
• straight trajectory
• dark areas due to substrates
T. Krist: solid-state transmission bender + collimator
polarisers - based on SMJ. Stahn solid state polarisers
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cavitylength
width≈ 50
|+〉 |−〉 |−〉
optimum parameters -1
-0.5
0
0.5
1
0 20 40 60 80 100
-1
-0.5
0
0.5
1
0 20 40 60 80 100-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-1
-0.5
0
0.5
1
1.5
2
y
θ
too large δθ -1
-0.5
0
0.5
1
0 20 40 60 80 100
too high mchannel -1
-0.5
0
0.5
1
0 20 40 60 80 100
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 29
cavitylength
width≈ 50
|+〉 |−〉 |−〉
optimum parameters -1
-0.5
0
0.5
1
0 20 40 60 80 100
-1
-0.5
0
0.5
1
0 20 40 60 80 100-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-1
-0.5
0
0.5
1
1.5
2
y
θ
too low λ -1
-0.5
0
0.5
1
0 20 40 60 80 100
too high λ -1
-0.5
0
0.5
1
0 20 40 60 80 100
-1
-0.5
0
0.5
1
0 20 40 60 80 100-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-1
-0.5
0
0.5
1
1.5
2
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 30
V-cavitylength
width≈ 30
• straight beam geometry
F. Mezei et al.: Physica B 180-181, 1005 (1992)
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 31
V-cavitylength
width≈ 30
• straight beam geometry phase space affected
• ∆λ/λmin ≈ 5
• P ≈ 99%P ≈ 99%P ≈ 99%
P. BoniF. Mezei et al.: Physica B 180-181, 1005 (1992)
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 32
equiangular spiral
for beams
{emerging from
focused to
}
a narrow area
• same ω for all trajectories
→ flexibility for ω, m, λ
• phase space hardly affected
y
0 xmin xmax
xαδθ
θ
prototype at PSI
J. Stahn, A. Glavic: Journal of Physics: Conference Series 862, 012007 (2017)
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 33
using Reflected and Transmitted beam
◦ split neutron guide for 2 polarised instruments (at HMI / HZB)
F. Mezei et al.: Physica B 213-214, 393 (1995)
◦ suggested analyser for Estia@ESS
A. Glavic
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 34
wide-angle analysers
stack of cavities / benders / spirals pointing towards the sample
challanges:
◦ avoid / minimise black angles
◦ provide a high magnetisation field
◦ reduce losses
example: Hyspec analyser by PSI
60◦ coverage with 1000 benders
P ≈ 95%
transmission = 10% to 45% for λ ∈ [2, 5] A
polarisers - based on SMJ. Stahn solid state polarisers
Erice, 07. 2017 35
wide-angle analysers study for MIEZE@ESS
λ > 6 A
by P. Boni
optimisation of shape using an equiangular spiral: λ ∈ [6, 48] A
2.3◦
166mm
polarisers - comparisonJ. Stahn solid state polarisers
Erice, 07. 2017 36
comparison
Heusler
3He
−− − ± + ++
P ∆λ ∆λ/λpsl/d
polarisers - comparisonJ. Stahn solid state polarisers
Erice, 07. 2017 37
comparison
Heusler
3He
−− − ± + ++
P ∆λ ∆λ/λpsl/d
f ai l
ed
focusing opticsJ. Stahn solid state polarisers
Erice, 07. 2017 38
basics
◦ reflectometry
◦ supermirrors
◦ polarising coatings
polarisers
◦ overview
◦ reflective coatings
◦ comparison
focusing optics
◦ refractive
◦ reflective
focusing opticsJ. Stahn solid state polarisers
Erice, 07. 2017 39
motivation
higher flux on small samples
no illumination of sample environment
selection of area on /within sample
control over phase space / trajectories
deal with small sources
remote footprint control
focusing opticsJ. Stahn solid state polarisers
Erice, 07. 2017 40
focusing optics
reshapes the phase space of a n-beam (an ensemble of neutrons)
to a small spatial extent at a given position
shading optics
reshapes the phase space by restricting it in space (slit)
θ
x
focusing opticsJ. Stahn solid state polarisers
Erice, 07. 2017 41
focusing optics vs. shading optics
high costs (needs high precision)
lower transmission
convenient beam manipulation
real focusing
aberration
robust
flexible
high transmission
high background
focusing optics – refractiveJ. Stahn solid state polarisers
Erice, 07. 2017 42
refractive optics
n ≈ 0.99999 . . .1 for all bulk materials
Snell’s law: n =sinαex
sinαin
⇒ αin ≈ nαex close to normal incidence
• used for SANS
αin
αex
M. R. Eskildsen et al. nature 391, 563 (1998)
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 43
reflective optics
parabolic
parallel to convergent
hyperbolic
convergent to convergent
elliptic
divergent to convergent
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 44
reflective focusing optics
elliptic
divergent to convergent
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 45
reflective focusing optics
early reflections suffer the most from coma aberration
⇒ multiple reflections
⇒ non-convergent beam behind guide exit
elliptic
divergent to convergent ?
L. Cusssen et al.: NIM A 705, 121 (2013)
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 46
reflective focusing optics
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 47
reflective focusing optics
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 49
coma aberration
. . . and its correction
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 50
coma aberration
. . . and its correction
• I(xy) is restored
• I(θ) is not!
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 51
Selene guide
point-to-point focusing
with
2 subsequent elliptical reflectors
for
horizontal and vertical direction
Selene
Selene picture:
ceiling painting in the Ny Carlsberg Glyptotek, København
focusing optics – reflectiveJ. Stahn solid state polarisers
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Selene guide
decoupling of
• spot-size
and
• divergence
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 53
condenser: parabolic deflector to generate a parallel beam
parabola axis ⇒ beam direction
focal length ⇒ beam width
beam width& spot size
⇒ divergence
no collimator needed
tunable
adaptive parabola (convex)
focal spot with 170µm reached
(PSI, early version)
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 54
astigmatic focusing: focusing to the detector by shifting the focal point
hyperbolic deflector
focusing optics – reflectiveJ. Stahn solid state polarisers
Erice, 07. 2017 55
solid-state neutron lense
T. Krist et al.: N.I.M. A 634, S104 (2011)
focusing optics - discussionJ. Stahn solid state polarisers
Erice, 07. 2017 56
focusing results in . . .
. . . no gain in brilliance
. . . a defined footprint
. . . a clean beam
homogeneous
uni-modal angular or spatial distribution
non-perfect optics
⇒ reduction of resolution / transmission
works best for small samples
weak aberration
thanks toJ. Stahn solid state polarisers
Erice, 07. 2017 57
Thomas Krist HZB
Peter Boni TUM
Uwe Filges PSI
Artur Glavic PSI
for discussions and for
contributing to these slides
PNCMI 2016 proceedings: Journal of Physics – Conference Series 862 (2017)