properties of candidate materials for cryogenic mirrors
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Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 1
Properties of candidate materials for cryogenic mirrors
D. Heinert, R. Nawrodt, C. Schwarz, P. Seidel
Institute of Solid State Physics, University of Jena
Kyoto, 18th May 2010
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 2
I current detector parameters
outline
II improvement to 3rd generation
• challenges (thermal lensing, cooling)
• sensitivity
• possibilities of increasing sensitivity
2nd generation detectors
way to 3rd generation
• noise sources
• substrate noise contributions
III conclusion
impact on detector‘s working point
estimate resulting noise for ET
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 3
a) increase laser power
b) decrease thermal noise (substrate and coating)
Planned detector sensitivities
• steps for 2nd to 3rd generation:
2nd generation detectors
way to 3rd generation
planned sensitivities
thermal noise calculation
thermal noise spectrum
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 4
Thermal noise processes
• Brownian noise
• Thermoelastic noise
substrate coating
32222/5
222 14),(
wfC
TkTfS BITM
TE
[Braginsky 1999]
),(12
),(2
2/3Tf
Ywf
TkTfS substrate
BITMX
[Liu, Thorne 2000]
[Braginsky, Fejer et al. 2004]
)(18
),(2~
2
22
2
gC
C
w
d
f
TkTfS s
S
FSBTE
[Harry et al. 2002]
'
'2),( ||22 Y
Y
Y
Y
Yw
d
f
TkTfS B
x
2nd generation detectors
way to 3rd generation
planned sensitivities
thermal noise calculation
thermal noise spectrum
general result
TSx ~)(
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 5
Thermal noise for AdvLIGO
• thermal noise with minor influence on total sensitivity
2nd generation detectors
way to 3rd generation
planned sensitivities
thermal noise calculation
thermal noise spectrum
[R. Adhikari]
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 6
Task 1: Reducing photon shot noise
• requires increase of laser power in the interferometer
increase of optically absorbed power in the test mass
• change of refractive index variation of wave front
effect of thermal lensing of transmissive parts
• fused silica with high 161014 KdT
dn
optical instability of the interferometer
• strategies to solve the problem
decrease increase thermal conductivity
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 7
• Why not just cool fused silica test masses?
• But: remember thermal noise expressions
Decrease of thermal lensing I: decrease of beta
0,)( 00 TT
dT
dnconstTn no thermal lensing
TSx ~)(
0 50 100 150 200 250 300
1E-7
1E-6
1E-5
1E-4
1E-3
mec
hani
cal l
oss
temperature T [K]
• fused silica show increasing loss for decreasing temperature
this even overcompensates benefit due to cooling
[Naw
rod
t 2008]
explanation:- defect energy distribution in amorphous solids(jumps of oxygen in the structure)
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 8
crystalline samples
(candidates: sapphire, silicon)
Decrease of thermal lensing II: increasing thermal conductivity
• general temperature behaviour of thermal conductivity
temperature
3 zones:
a) phonon populationb) defectsc) phonon collisions
20…40 K
defects limit global maximum of thermal conductivity
• defects are
- surface of the sample- lattice defects
a)
b)
c)
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 9
[Touloukian]
Assumed numbers for thermal conductivity
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
our values (pure silicon with low defects)
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 10
• change in thermal conductivity changes position of maximum for TE losses
• alpha is high in crystalline solids
Consequences for thermoelastic noise
• Zener‘s model for thermoelastic damping change of thermoelastic noise via FDT
Ch
C
ET
2
2
22
20 ,
1~h
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
0 50 100 150 200 250 30010-3
10-2
10-1
100
101
102
f max
[Hz]
T [K]
silicon
0 50 100 150 200 250 30010-5
10-4
10-3
10-2fused silica
f max
[Hz]
T [K]
h=30 cm
[Zener, 1937]
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors
100
101
102
103
104
10-24
10-22
10-20
10-18
frequency [Hz]
the
rma
l no
ise
[m/
Hz]
bulk Brownianbulk TEcoating Browniancoating TEcoating TRtotal
100
101
102
103
104
10-24
10-22
10-20
10-18
frequency [Hz]
the
rma
l no
ise
[m/
Hz]
bulk Brownianbulk TEcoating Browniancoating TEcoating TRtotal
11
• restriction of the detector‘s working point temperature, ideal:
T=300 K T=20 K
coating Brownian dominates noise spectrum for low temperatures hope for alternative reflection concepts (gratings, Khalili etalons, …)
018 KT
Rigorous noise calculation for silicon (Ø 50 cm x 30 cm, 111)
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 12
Rigorous noise calculation for sapphire (Ø 50 cm x 30 cm, zcut)
100
101
102
103
104
10-24
10-22
10-20
10-18
frequency [Hz]
the
rma
l no
ise
[m/
Hz]
bulk Brownianbulk TEcoating Browniancoating TEcoating TRtotal
100
101
102
103
104
10-24
10-22
10-20
10-18
frequency [Hz]
the
rma
l no
ise
[m/
Hz]
bulk Brownianbulk TEcoating Browniancoating TEcoating TRtotal
T=300 K T=20 K
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
• bulk thermoelastic in the same order as coating Brownian for 20 K
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 13
Silicon vs. Sapphire
• monocrystalline silicon available in diameters up to 50 cm within the next 5 years
• change of wavelength to 1550 nm will increase Brownian coating noise moderately, but also decreases stray light by factor 4.5 )( 4
silicon is presently the best choice for substrate material
thermal noise requirements
industrial background
Silicon Sapphire
hardness machinability
optical absorption at 1064 nm
good
bad
good
good bad
good
bad medium
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 14
• measurement for crystalline silicon (Ø 76.2 mm x 75 mm)
Temperature dependene of mechanical loss of silicon
silicon maintains low losses at low temperatures
0 50 100 150 200 250 30010-9
10-8
10-7
111 100
mec
hani
cal l
oss
temperature [K]
TSx ~)(
low Brownian noise
• further information: see talk of Ch. Schwarz
2nd generation detectors
way to 3rd generation
thermal lensing
TE noise of crystals
silicon vs. sapphire
Heinert et al. 01.03.2010
Properties of candidate materials for cryogenic mirrors 15
Conclusions
• no fused silica due to high Brownian noise
• silicon as main candidate for substrate material with
- availability of large geometries- big industry behind
• to achieve 3rd generation sensitivity we have to go cryogenic
• coating Brownian noise dominates below ca. 25 K
cool detector to 20 K due to high thermoelastic noise change wavelength to 1550nm due to optical absorption
• achievable noise at 20 K: Hz
mHzSx
22101)100(
2nd generation detectors
way to 3rd generation
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