1. 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, Glasgow UK 58 th Fujihara Seminar, 28 th May 2009

2. 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

3. 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

4. Thermal noise from optics – simple picture The power spectral density of thermal noise S x (  ) of a harmonic oscillator of resonant frequency  0, mass m and temperature T can be written as: pendulum mode 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

5. 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

6. 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: V = volume S = surface area F = frequency C n = 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

7. 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

8. 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]

9. Thermal noise from optical mirror coatings Current coatings in all detectors are made of alternating layers of ion-beam- sputtered SiO 2 (low refractive index) and Ta 2 O 5 (high index) Experiments suggest: Thermal noise from mechanical loss of the dielectric mirror coatings will limit sensitivity of 2 nd 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 10 1 10 2 10 3 Frequency (Hz) 10 -24 10 -23 10 -22 Strain (1/  Hz) Ta 2 O 5 is the dominant source of dissipation in current SiO 2 /Ta 2 O 5 coatings [Penn et al CQG(2003) 20 2917] Doping the Ta 2 O 5 with TiO 2 can reduce the mechanical dissipation [Harry et al (2007) CQG 24 405] Projected Advanced LIGO sensitivity curve

10. Thermal noise from optical mirror coatings Recent studies to try to determine source of dissipation in single layers of coating materials: Ta 2 O 5 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 TiO 2 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 .

11. 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

12. 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

13. 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

14. 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 orders of magnitude compared with room temperature. From: K.Kuroda, GWADW, 14 May 2009

15. 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]

16. 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

17. Further developments in optics - silicon In Europe, cryogenic cooling of optics now being pursued in context of a future 3 rd 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

18. 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’?

19. 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 Ta 2 O 5 (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

20. 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? Si 500 nm [private communication: Brückner, IAP, Jena] first initial test: ~ 99.8%

21. Initial thermal noise comparison Contribution of different waveguide structures to the thermal noise: 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…)

22. 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.

23. 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