Optics related research for interferometric gravitational wave detectors

S. Rowan for the Optics working group of the LIGO Scientific Collaboration

SUPA, Institute for Gravitational Research, University of Glasgow, GlasgowUK

58th Fujihara Seminar, 28th May 2009

Optics for gravitational wave detectors The suspended mirrors form

the heart of interferometric gravitational wave detectors

Key requirements: Low optical loss of

substrate material Low mechanical loss of

substrate material Low optical and mechanical

loss of mirror coating materials

Scatter, optical homogeneity, availability in suitable sizes..

GEO, LIGO, Virgo, TAMA: All use optics of synthetic

fused silica

The current generation of optics

Fused silica - chosen from a mix of its optical and mechanical properties

Very low absorption achievable at 1064nm (~0.1ppm/cm)

Critical for supporting high laser powers (many kW)

Available in large pieces (10s of kg) Crucially, also has low mechanical

loss low thermal noise Thermal noise from the optics

(substrates and coatings) will limit future detector sensitivities in their most sensitive frequency range Fused silica mirror ~18cm in

diameter

Thermal noise from optics – simple picture

The power spectral density of thermal noise Sx() of a harmonic oscillator of resonant frequency 0, mass m and temperature T can be written as:

pendulummode

internal mode

Frequency

Thermal

Detection band

displacement

where is the mechanical dissipation of the resonator, = 1/Q, at a resonant mode, with

Thermal noise predictions rely on knowing loss - – determined through experimental measurements

Mechanical loss in silica

Considerable progress in understanding level and origins of mechanical loss in silica in last 5 to 10 years

For many years typical level of loss in bulk samples taken as ~10 -7, no dependence on frequency

Origin of room temperature loss was not understood Key experimental observations:

Frequency dependence of loss in fused silica – improving towards lower frequencies

Heat treatment systematically improved levels of measured loss [Numata et al (2002) CQG 19 1697, Penn et al, (2006) PLA, 352, others]

Key in leading to currently accepted model for origin of loss in fused silica at room temperature

Mechanical loss in silica Loss in silica may be modelled as sum of surface, thermo-elastic, and

frequency dependent bulk losses –the latter improving towards low frequency:

thC

elasticthermobulksurface

CfCSVC

SVf

42

1

13

,

V = volumeS = surface areaF = frequencyCn= constants empirically

determined from loss measurements and dependent on grade of silica

Penn et al: “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

Mechanical loss in silica

Status of current models and experiments suggest substrate loss at frequencies of interest for GW detection could be ~100 times better than previously thought

Substrate thermal noise limit in silica optics could be ~10 times lower (or more) than originally thought

Ongoing work on heat-treatment of silica and study of silica surfaces to quantify how much we really can reduce loss (and thermal noise) in silica optics

However…. Mirror coatings applied to the optics now are a dominant

source of thermal noise

Thermal noise from optics

For mirrors with spatially inhomogeneous mechanical 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. [Levin (1998) PRD 57 659 ]

Finite element analysis is an extremely useful approach to calculating the thermal noise in optics having spatially inhomogeneous mechanical loss (ie all –real- optics) [Yamamoto, (2000) “Study of the thermal noise caused by inhomogeneously distributed loss”, Ph.D. thesis, Dept. of Physics, University of Tokyo]

Thermal noise from optical mirror coatings Current coatings in all detectors are made of alternating layers of ion-

beam-sputtered SiO2 (low refractive index) and Ta2O5 (high index)

Experiments suggest: Thermal noise from mechanical loss of the dielectric mirror coatings

will limit sensitivity of 2nd generation interferometric gravitational wave detectors [Crooks et al (2002) CQG 883; Harry et al (2002) CQG 897]

Coating thermal noise will limit

sensitivity between ~ 40 and 200 Hz

101 102 103

Frequency (Hz)

10-24

10-23

10-22

Stra

in (1

/H

z)

Ta2O5 is the dominant source of dissipation in current SiO2/Ta2O5 coatings [Penn et al CQG(2003) 20 2917]

Doping the Ta2O5 with TiO2 can reduce the mechanical dissipation [Harry et al (2007) CQG 24 405]

Projected Advanced LIGO sensitivity curve

Thermal noise from optical mirror coatings Recent studies to try to determine

source of dissipation in single layers of coating materials: Ta2O5

Low temperature dissipation peak seen – similar to bulk fused silica behaviour

Oxygen atoms believed to undergo thermally activated transitions between two stable bond orientations represented by an asymmetric double-well potential

TiO2 doping shifts the peak in the barrier distribution to a higher barrier height[Martin et al, submitted, CQG]

Other methods of altering the bond angle distribution of interest – perhaps heat treatment? (known to alter dissipation levels in silica)[Martin et al, in preparation] Schematic diagram of an asymmetric double

well potential, with a potential barrier V and an asymmetry .

Optimized Coatings

• Optimized Coating Design: [Agresti et al, (2006) Advances in Thin-Film Coatings for Optical Applications III, 628608]- Silica low-index, tantala high-index

layers- Thickness of tantala layers

reduced, thickness of silica layers increased

- Pairs of layers still have /2 optical thickness

• Measured at Thermal Noise Interferometer, Caltech :- 16% reduction in coating loss-angle

• New Optimized Coating:- Silica low-index, titania-doped

tantala high-index layers- Design is nearly finalized- Thermal noise will be measured at

the TNI in the coming months

Standard Coating

Optimized Coating

A. Villar, E. Black, I. Pinto, R. DeSalvo

Techniques for reducing thermal noise of optics - cooling

Cryogenic cooling:

Fused silica not suitable as a cooled optic: large broad loss peak exists centred around 40-60K

However sapphire is an excellent candidate for cooled optics:

Low mechanical loss at room T [Mitrofavov et al Kristallografiya (1979) 24, S. Rowan (2000) Phys. Lett. A]

Loss decreases at low temperatures [Braginsky, (1981) “Systems with small dissipation”]

Approach successfully pioneered for many years in Japan

fTfSx ,

Cooling technique of cryogenic mirror (1)

Heat produced by the absorption inside the Substrate is extracted through heat flow along the suspension fibers. The heat flow was large enough to be applicable to the practical high power laser interferometer.

Simulation of the heat flow through sapphire fiber

From: K.Kuroda, GWADW, 14 May 2009

Cooling technique of cryogenic mirror (2)

Thermal noise is proportional to mechanical Q / temperature T

Every sapphire sample showed better mechanical Q at cryogenic temperature.

Improvement by cooling was 2 ordersof magnitude compared with room temperature.

From: K.Kuroda, GWADW, 14 May 2009

Effect of cooling on mirror coating loss/noise Very important to understand the effect of cooling on the

loss of a multi-layer coating: Results from

Yamamoto et al show no significant increase in loss as coating is cooled to <20K

Expect gains in thermal noise proportional to √T

Cooling should allow improvements in coating-noise-limited sensitivity [Yamamoto et al, (2006) PRD 74, 022002]

CLIO - LCGT

As discussed in Prof Kuroda’s talk, this research on the use of cryogenic sapphire optics has progressed through

Single prototype developments at ICRR Suspended-mirror interferometers at CLIO

Unique set of studies have been carried out on cryogenic sapphire optics showing practical approaches to building a long baseline ‘Advanced’ cryogenic gravitational telescope of high sensitivity

Further developments in optics - silicon In Europe, cryogenic cooling of optics now being pursued in context of

a future 3rd generation instrument the Einstein Telescope – see talk by Michele Punturo

Alternative substrate material - silicon Like sapphire – mechanical loss improves on cooling, however has

other interesting properties Thermoelastic

thermal noise is proportional to expansion coefficient and should vanish at T ~120 K and ~18 K[Rowan, et al., Proceedings of SPIE 292 (2003) 4856]

Intrinsic thermal noise exhibits two peaks at similar temperatures

Could be of significant interest but material properties need further study - ongoing

Silicon – further current topics in optics Non-transmissive at 1064nm –

use diffractive optical coatings? Benefits exist from thermal loading points of view [Winkler et al Phys. Rev. A (1991) 44 7022]

Considerable work in this area – see talk by Peter Beyersdorf

Alternative approaches Switch wavelength to 1550

nm where silicon is transmissive?

Use waveguide coatings? Micro-structured surfaces to

form ‘coating-less mirrors’?

Resonant Waveguide Concept Optical idea

Advantages from the thermal noise point of view (thinner tantala layer)

Lower coating absorption due to thinner layers?

[Brückner et al (2009) Optics Express 17 163]

[Brückner et al (2009) Optics Express 17 163] “ In this article, we report on the fabrication and characterization of a resonant waveguide grating based high-reflection mirror. The mirror substrate was sodalime glass and carried a single layer grating of Ta2O5 (Tantala) with a thickness of 400 nm, and was used as a cavity coupler of a high-finesse standing wave cavity. From the cavity finesse we were able to deduce a reflectivity of (99.08 ± 0.05)% at the laser wavelength of 1064 nm.”

High index layer

Low index substrate

Monolithic Resonant Waveguide Concept Optical idea

No tantala layer needed (expected low mechanical loss?) Monocrystalline structure high thermal conductivity Small absorption at 1550 nm ?

[Brückner et al Optics Letters 33 (2008) 264]

How realistic are these structures?

Si500 nm

[private communication: Brückner, IAP, Jena] 1.45 1.50 1.55 1.60 1.65

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

Reflektivität in Abhängigkeit der Wellenlänge

Wellenlänge [µm]

Ref

lekt

ivitä

t

= 0°, TM-Pol. sim. = 0°, TM-Pol., o=298.5nm

first initial test: ~ 99.8%

Initial thermal noise comparison Contribution of different waveguide structures to the thermal

noise:

100

101

102

103

10410

-26

10-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]

Brownian bulkmonolithic waveguidethin tantala waveguidedielectric multilayer

100

101

102

103

10410

-28

10-26

10-24

10-22

10-20

frequency [Hz]st

rain

sen

sitiv

ity [1

/ H

z]

ET sensitivitymultilayerthin tantala waveguidemonolithic waveguide

3×10-9

1×10-4

Advanced LIGO mirror geometry assumed, T = 18K.Open questions:

Optical absorption @ 1550 nm and low T? Increased surface area of silicon surface loss analysis needed (poster @ Amaldi from R. Nawrodt) How to attach the optical layer (bond loss…)

Summary The field of optics for gravitational wave detectors is a

very active area of research

Cryogenic optics and associated novel techniques are being pursued in Japan and elsewhere with strong potential for creating new gravitational wave instruments of improved sensitivity.

Questions resonant frequency

>> 100 kHz ANSYS calculation + pictures follow

lateral movement = phaseshift (as in gratings) no coupling in and out of the waveguide has different

sign -> compensation

polarisation dependence grating direction = polarisation underetched hole structure would be isotropic