properties of candidate materials for cryogenic mirrors

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



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



a) increase laser power

b) decrease thermal noise (substrate and coating)

Planned detector sensitivities

• steps for 2nd to 3rd generation:



planned sensitivities

thermal noise calculation

thermal noise spectrum



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






general result

TSx ~)(



Thermal noise for AdvLIGO

• thermal noise with minor influence on total sensitivity






[R. Adhikari]



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



thermal lensing

TE noise of crystals

silicon vs. sapphire



• 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)



thermal lensing





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)



thermal lensing





[Touloukian]

Assumed numbers for thermal conductivity



thermal lensing



our values (pure silicon with low defects)



• 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



thermal lensing



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]


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]


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)



thermal lensing





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]


100

101

102

103

104

10-24

10-22

10-20

10-18

frequency [Hz]

the

rma

l no

ise

[m/

Hz]


T=300 K T=20 K



thermal lensing



• bulk thermoelastic in the same order as coating Brownian for 20 K



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



thermal lensing





• 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



thermal lensing





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(



properties of candidate materials for cryogenic mirrors

Documents