Mirrors for Advanced Interferometer – substrate and coating requirements

S.Rowan

ESF workshopPerugia

20-23rd September 2005

Reminder of motivation

Consider here: technology status of some aspects of the detector mirrors and coatings

Thermal noise from mirrors and coatings forms an important limit to design sensitivities at most sensitive point in mid-frequency band

Analyse the recent developments in technologies foreseen for Advanced detectors to explore the path needed for a European 3rd generation gravitational wave detector

Coated fused silica mirror

~18cm diameter

Timescales

VIRGO/GEO/LIGO all plan ‘Advanced’ upgrades:

VIRGO (Benoit, yesterday) 2008/9 VIRGO + 2011 (?) Advanced VIRGO

LIGO 2008/9 (?) staged improvements 2010-13 Advanced LIGO

GEO 2008 ? GEO-HF – staged improvements

3rd European detector (20??)

Common theme for Advanced detectors is higher laser power (Benno) and new mirrors

What is the status of technologies related to low-thermal-noise mirrors? (Gregg will talk re: thermal loading effects)

Current mirrors

All detectors currently use fused silica substrates with coatings

formed from SiO2/Ta2O5

Optics in the detectors were installed several years ago

Design curves for GEO, LIGO,

VIRGO which we use were

based on best models for

thermal noise at that time

The same optics are still

installed but our models for the

thermal noise have changed a

lot LIGO fused silica mirror (10kg) in suspension cradle

Three significant changes

Levin: for mirrors with inhomogeneous loss we should not simply add incoherently the noise from the thermally excited modes of a mirror – loss from a volume close to the laser beam dominates

Penn et al: loss in silica may be modelled as sum of surface, thermoelastic, and frequency dependent bulk losses – the latter improving towards low frequency

Levin, (Nakagawa, Crooks, Harry et al)Dissipation from dielectric mirror coatings is at

a significant level

Substrates - Fused silica Two big vendors used – Corning (LIGO) ,

Heraeus (LIGO, VIRGO, GEO)

Each vendor makes a number of different optical grades

Empirical measurements suggest:

Heraeus fused silica has lower mechanical loss than Corning

The various Heraeus Suprasil grades have different loss from one another

Substrates – fused silica

Semi-empirical model developed by Penn et al (Phys Rev Lett,

Submitted) arXive:gr-qc/0507097

C1, C2, C3, C4 are constants fitted to existing loss

measurements, and dependent of the exact grade of silica used

ticthermoelassurfacebulkS

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Mechanical loss in fused silica

Substrates – fused silica

Penn et al point out:’’The internal friction of very pure fused silica is associated with strained Si-O-Si bonds, where the energy of the bond has minima at two different bond angles, forming an asymmetric double-well potential. Redistribution of the bond angles in response to an applied strain leads to mechanical dissipation’’

Empirically we deduce that the manufacturing and processing of the different grades of silica is affecting the distribution of bond angles

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Bulk loss Empirically it seems that Suprasil 311, 312 are the grades of silica

with the lowest loss (SV not as low ??)

Good! -We tend to choose these for our optical needs

However we don’t yet understand in detail what processing (annealing/cooling/ temps/rates geometry etc) optimises the mechanical loss (eg why is Corning silica not as good as Heraeus..?)

(Penn et al actively researching this area)

Understanding this would perhaps allow us to lower loss even further

Surface loss

Empirically, measurements are consistent with the existence

of a surface loss ‘limit’

Annealing samples allows them to approach this, but

dissipation then reaches a lower ‘limit’

The source(s) of dissipation for this surface layer are not

unambiguously determined (microcracks, polishing damage –

what about flame annealled samples??)

Substrates – fused silica

Status of current models and experiments suggest substrate

thermal noise could be ~10 times lower (or more?) than old

design sensitivities - good news!!

Maybe we can lower it even further – however….

Coatings – now are a dominant source of thermal noise

Consider an ‘Advanced LIGO-Like’ design

Coating thermal noise is expected to be the dominant noise source at

mid frequencies for advanced interferometer designs

Penn et al

Coating studies

Thermal noise from the dielectric mirror coatings applied to test masses is -essentially acceptable- for Adv. LIGO, (Adv. VIRGO ?)

However, reduction in coating noise translates directly to interferometer sensitivity

Unacceptable for any future detectors beyond Adv. LIGO

Studies carried out with coatings from number of vendors

(MLD, Waveprecision, REO, LMA Lyon)

to study the mechanical dissipation of ion-beam-sputtered dielectric

coatings via loss measurements

Focussed initially on SiO2/Ta2O5 coatings

Mechanical loss of multi-layer SiO2/Ta2O5 coatingswith varying proportions of SiO2 and Ta2O5

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

2.5E-04

3.0E-04

3.5E-04

4.0E-04

4.5E-04

5.0E-04

0 10 20 30 40 50 60 70 80

Frequency [kHz]

Loss

lambda/4 silica, lambda/4 tantalalambda/8 tantala, 3lambda/8 silica3lambda/8 tantala, lambda/8 silica

Silica and tantala mechanical loss results

Assume for each material: residual = 0 + ff

For silica: residual = (1.2± 0.2) x 10-4 + f(1.3 ± 0.5) x 10-9

For tantala: residual = (3.2 ± 0.1) x 10-4 + f(1.8 ± 0.4) x 10-9

y = 1.32E-09x + 1.16E-04

y = 1.78E-09x + 3.17E-04

0.E+00

5.E-05

1.E-04

2.E-04

2.E-04

3.E-04

3.E-04

4.E-04

4.E-04

5.E-04

5.E-04

0 10 20 30 40 50 60 70 80Frequency [kHz]

Loss

Silica residual loss

Tantala residual loss

Status

Measured losses are dominated by intrinsic loss of the

materials involved

Ta2O5 is mechanically lossier than SiO2

Studies carried out of loss of Ta2O5 doped with TiO2 -

suggestion by LMA

Doping of Ta2O5 with TiO2

Loss Angle of SiO2 /TiO2 doped Ta2O5 at 100 Hz• Clear improvement with

addition of titania

• Appears no strong

correlation with amount

of TiO2

• However exact

concentrations of TiO2

not known

• Results from Ian

MacLaren in Glasgow

now available0 10 20 30 40 50 60

1.5

2

2.5

3x 10-4

Relative Concentration

Loss

An

gle

Small CoaterLarge Coater

Doping of Ta2O5 with TiO2

Loss Angle of SiO2 /TiO2 doped Ta2O5 at 100 Hz• Mechanism by which

TiO2 reduces dissipation

not yet known

• (Helping prevent

movement of oxygen

vacancies..??)

• Recent measurements by

Black et al (Caltech)

confirm reduction in

thermal noise from

doped coatings

0 10 20 30 40 50 60

1.5

2

2.5

3x 10-4

Relative Concentration

Loss

An

gle

Small CoaterLarge Coater

Importance of material properties

NB to get previous loss results needed to know the Young’s modulus

of the individual coating materials

Previous results use ‘best estimates’ of properties (– these are typically

not well known for ion-beam-sputtered coatings)

I. Wygant et al (Stanford) measured the acoustic impedance of witness

multi-layer samples using an ultrasonic reflection technique If coating density is known then this allows Young’s modulus

to be found

However it has proved difficult to extract precise properties of the

individual materials from measurements of multi-layers

Material properties – next steps

Studies of some single layers of materials would be very

valuable

Study loss, Young’s modulus and density (may have to study

as a function of thickness)

These would then help inform our analysis of multi-layer

coatings

Necessary both to quantify our loss measurements and

thermal noise calculations

Other approaches

Pinto et al – studying algorithms to vary thickness and

periodicity of coating layers Optimise for desired reflectivity whilst minimising amount of

Ta2O5 present

Use ‘flat-topped’ laser beams to more efficiently average

coating and substrate thermal noise?

Conclusions

2nd generation of detectors will use fused silica optics

Coatings will be the limiting source of thermal noise in these

‘advanced detector’ test masses

To go to 3rd generation detectors we need better coatings – or

maybe to cool?? Results from Yamamoto et al suggest coating loss angle does

not decrease significantly with lowering T but still gain in reducing thermal noise

Where does this leave us for 3rd generation detectors?

Limited by coating thermal noise/optical noise

Possibly considering cooling to reduce the coating noise

Thermal noise is not the only issue for substrate and coating

developments

Other substrate and coating issues; Thermal loading effects can be significant – see talk by Gregg The low thermal conductivity of silica may prove to make it unattractive

for higher power operation

Necessitate switch to sapphire/silicon some other material??

Challenges for future detectors

Future detectors may require higher levels of laser power

In addition, further reductions in test mass and suspension thermal

noise are required

Possible materials meeting these requirements are sapphire or

silicon – are there others???

Mirror substrates must sustain high thermal loads and maintain optical figure

Deformation of mirror surface is proportional to /kth [Winkler et al., 1991].

= substrate expansion coefficientkth = substrate thermal conductivity

Would like a substrate material for which /kth is minimised

1.E-23

1.E-22

1.E-21

1.E-20

1.E-19

1.E-18

0 50 100 150 200 250 300

Te mpe rature (K)

Dis

plac

emen

t (m

Hz

-0.5

)

Thermoe las tic noise Intrins ic the rmal noise

Mechanical dissipation - silicon Silicon

Both thermoelastic and intrinsic thermal noise may be reduced by cooling:

Thermoelastic noise is proportional to and should vanish at T ~120 K and ~18 K where tends to zero

Intrinsic thermal noise exhibits two peaks at similar temperatures

Silicon may allow significant thermal noise improvements at low temperatures but material properties need further study

Calculated intrinsic thermal and thermoelastic noise @ 10 Hz in a single silicon test mass, sensed with a laser beam of radius ~ 6 cm

Mechanical dissipation - sapphire

Sapphire studied in the US as part of Ad

LIGO substrate downselect studied by colleagues in Japan for

LCGT

Likely to have levels of intrinsic and thermoelastic dissipation similar to silicon (slightly lower) but without the nulls in expansion coefficient

Could be interesting, particularly at higher frequencies

Sapphire piece used in spot polishing compensation demonstration; 25cm diameter sample (photo courtesy Goodrich).

Mechanical dissipation from coatings

Potential sources of loss :

Dissipation intrinsic to the coating materials (defects, vacancies etc?)

Thermoelastic damping (see Fejer et al, Phys Rev D,

Braginsky,PLA) resulting from the different thermal and elastic properties of the coating and substrate

Coating

Substrate

fs

l

x

y

z In both cases resulting thermal noise level

depends on relative thermal and elastic properties of coating and substrate

It follows that the optimum coating for a fused silica or sapphire mass may not be the ideal choice for a silicon mass

Mechanical dissipation in coatings (contd)

Diffractive coatings: To use silicon as a diffractive optic, either:

a diffraction grating can be etched on to the surface of the test mass onto which a coating is applied

(Institute for Applied Optics, University of Jena);or

the test mass can be coated, and a diffraction grating etched into the coating surface (Lawrence Livermore National Laboratories).

The mechanical dissipation associated with such coatings (room and cryo) needs investigated

3rd generation detectors - a problem of size

Test masses of >50 kg are desirable

Silicon ingots of 450kg have been manufactured, but aspect ratio is not optimal

Sapphire is available up to only ~40kg

Use composite test masses??,

Bonded interfaces

Separate masssegments

Silicon ingot in growth furnace Cradle ?Segmented design?

Pic. from D. Coyne

Conclusions cont

‘Analyse the recent developments in technologies foreseen for

Advanced detectors to explore the path needed for a European 3rd

generation gravitational wave detector’

Status of substrate/coating technology for Advanced Detectors is in

pretty good shape (silica + doped coatings)

Limited by coating thermal noise – but various approaches

discussed here may help us

For 3rd generation detectors cooling and/or a change of substrate

material is likely to be needed – really need to work hard on how to

beat coating thermal noise