Optical and mechanical properties of ion-beam-sputtered Nb_2O_5 and TiO_2-Nb_2O_5 thin films for gravitational-wave interferometers
N. Demos, M. Granata, S. Gras, A. Amato, G. Cagnoli, B. Sassolas, J. Degallaix, D. Forest, C. Michel, L. Pinard, M. Evans, A. Di Michele, M. Canepa
OOptical and mechanical properties of ion-beam-sputtered Nb O and TiO -Nb O thinfilms for gravitational-wave interferometers A. Amato, G. Cagnoli
Universit´e de Lyon, Universit´e Claude Bernard Lyon 1,CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France
M. Granata, ∗ B. Sassolas, J. Degallaix, D. Forest, C. Michel, and L. Pinard
Laboratoire des Mat´eriaux Avanc´es, Institut de Physique des 2 Infinis de Lyon, CNRS/IN2P3,Universit´e de Lyon, Universit´e Claude Bernard Lyon 1, F-69622 Villeurbanne, France
N. Demos, † S. Gras, and M. Evans
Massachusetts Institute of Technology, 185 Albany Street NW22-295, Massachusetts 02139, Cambridge, USA
A. Di Michele
Universit`a degli Studi di Perugia, Dipartimento di Fisica e Geologia, Via Pascoli, 06123 Perugia, Italy
M. Canepa
OPTMATLAB, Dipartimento di Fisica, Universit`a di Genova, Via Dodecaneso 33, 16146 Genova, Italy andINFN, Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy (Dated: January 8, 2021)Brownian thermal noise associated with highly-reflective mirror coatings is a fundamental limitfor several precision experiments, including gravitational-wave detectors. Recently, there has been aworldwide effort to find mirror coatings with improved thermal noise properties that also fulfill strictoptical requirements such as low absorption and scatter. We report on the optical and mechanicalproperties of ion-beam-sputtered niobia and titania-niobia thin films, and we discuss application ofsuch coatings in current and future gravitational-wave detectors. We also report an updated directcoating thermal noise measurement of the HR coatings used in Advanced LIGO and AdvancedVirgo.
Energy dissipation in amorphous coatings is a fun-damental limitation for precision experiments such asinterferometric gravitational-wave detectors (GWDs)[1], optomechanical resonators [2], frequency standards[3], and quantum supercomputers [4]. In these de-vices, thermally-driven random structural relaxationsdistribute the thermal energy of the normal modes ofvibration across a wide frequency range, giving rise toBrownian coating thermal noise (CTN) [5, 6]. The powerspectral density of such thermally induced surface fluc-tuations is determined by the rate of energy dissipationin the coating material, as stated by the fluctuation-dissipation theorem [7]. The CTN power spectral density S CTN , as measured with an optical beam, can be writtenin the simplified form [8] S CTN ∝ k B T πf dω ϕ c ( f ) , (1)where k B is the Boltzmann constant, f is the frequency, T is the temperature, d is the coating thickness, ω isthe laser beam radius where intensity drops by 1/e , and ϕ c ( f ) is the loss angle associated with energy dissipationin the coating. The loss angle quantifies the internal ∗ [email protected] † [email protected] mechanical friction in the coating material and is definedas the ratio of the imaginary to real parts of the elasticmodulus, ϕ c ( f ) ≡ tan − [Im( Y c ) / Re( Y c )].Thermally induced surface fluctuations can be reducedby increasing the beam radius ω , decreasing the tempera-ture T , or by choosing coating materials which minimize dϕ c . Increases in ω are limited by both the difficultiesin uniformly coating larger substrates and by arm cavitycontrol stability, while decreases in T , such as operat-ing in the cryogenic regime, are limited by experimentalcomplexity issues [9–11] and by the narrow selection ofmaterials which are known to have favorable propertiesat cryogenic temperatures.High-reflection (HR) optical coatings are usually Braggreflectors of alternating layers of low- and high-refractive-index materials, where the number of low/high indexpairs determines the coating transmissivity. However,for the same transmissivity, the number of pairs can varydepending on the refractive index contrast C = n H /n L ,where n H and n L are the high and low refractive indices,respectively: the higher the C , the lower the coatingthickness d and hence the CTN. The high index mate-rial is usually the most dissipative one [19–21]. Ideally,for a given n L , the high index material should have thehighest n H possible in order to maximize C and reduceits physical thickness.The HR coatings of the Advanced LIGO [12], Ad-vanced Virgo [13] and KAGRA [9] GWDs are thickness- a r X i v : . [ phy s i c s . i n s - d e t ] J a n optimized stacks [14] of ion-beam-sputtered (IBS) layersof tantalum pentoxide (Ta O , also known as tantala ,high index) and silicon dioxide (SiO , silica , low index),produced by the Laboratoire des Mat´eriaux Avanc´es(LMA) [15, 16]. Following a procedure developed by theLMA [17] for the LIGO Scientific Collaboration [18] inorder to reduce their optical absorption and lower theirloss angle, the high-index layers of Advanced LIGO andAdvanced Virgo are a uniform mixture of co-sputteredtantala and titanium dioxide (TiO , titania ) [19].Despite their superb optical and mechanical properties[15, 19], the CTN of current HR coatings remains a severelimitation for further sensitivity improvement in GWDs.In the last two decades, a considerable research effort hasbeen committed to finding an alternative high-index ma-terial featuring both low mechanical loss and low opticalloss (absorption, scattering) [22].In this paper we report on the optical and mechani-cal properties of IBS niobium pentoxide (Nb O , niobia )and titania-niobia (TiO -Nb O ) thin films, and we dis-cuss application of niobia-based coatings in current andfuture GWDs. As we wanted to compare the CTN ofthose newly-developed coatings against that of currentHR coatings of GWDs, we also improved our direct CTNmeasurement method and are able to report an updatedCTN of the HR coatings used in Advanced LIGO andAdvanced Virgo. I. METHODS
Single thin layers (470 to 490 nm thick) of IBS Nb O and TiO -Nb O coatings were deposited on siliconwafers ( ∅ ∅
50 mm, 1 mmthick) to measure their mechanical properties. In or-der to fully test an alternative design for current GWDs,HR stacks for operation at 1064 nm were deposited onfused-silica witness samples ( ∅ − mbar. Argon (12 sccm) was fed into the ion-beamsource while oxygen (20 sccm) was fed into the chamber,for a total pressure of the order of 10 − mbar inside thechamber. Energy and current of the sputtering Ar ionswere 1.0 keV and 0.2 A, respectively. The source-targetand target-substrate angles were set to 45 ◦ . During de-position, the sputtered coating particles (co-sputtered,in the case of titania-niobia coatings) impinged on sub-strates heated up to about 100 ◦ C.After deposition, the coated samples were annealed inair for 10 hours at T a = 400 ◦ C. Annealing is a standardprocedure to decrease the internal stress, the optical ab-sorption and the internal friction of coatings [19, 23]. Themaximum annealing temperature T a is limited by the on- set of crystallization, which makes the amorphous coat-ings undergo a phase change and become poly-crystalline. A. Optical characterization
We used two J. A. Woollam spectroscopic ellipsometersto measure optical properties and thickness of the single-layer coatings, covering complementary spectral regions:a VASE for the 190-1100 nm range and a M-2000 forthe 245-1680 nm range. The wide range swept with bothinstruments allowed us to extend the analysis from ultra-violet to near infrared (0.7 - 6.5 eV). The coated siliconwafers (with only one-side polished to suppress spuriousreflections from the rear surface) were measured in re-flection. The optical properties were obtained by mea-suring the amplitude ratio Ψ and phase difference ∆ ofthe p- and s-polarized reflected light [24]. To maximizethe response of the instruments, the (Ψ, ∆) spectra wereacquired for three different incidence angles ( θ = 50 ◦ ,55 ◦ , 60 ◦ ), chosen to be close to the Brewster angle of thecoatings. Coating refractive index and thickness werederived by fitting the experimental data with the well-known Cody-Lorentz [25] and Tauc-Lorentz [26] opticalmodels, the optical response of the bare wafers were char-acterized with prior dedicated measurements. By way ofexample, Fig. 1 shows the (Ψ, ∆) spectra of the annealedniobia and titania-niobia coatings. Fig. 2 shows the re-constructed dispersion laws. Further details about ourellipsometric analysis are available elsewhere [27, 28].To measure scattering and optical absorption of theHR stacks at λ = 1064 nm (the operational wavelength ofcurrent GWDs), we characterized the coated fused-silicawitness samples with a commercial CASI scatterometerand a custom-developed setup [29] based on the photo-thermal deflection principle [30], respectively. B. Mechanical characterization
Before and after each treatment (coating deposition,annealing), we measured the mass of the disks with ananalytical balance and used the measured coating thick-ness values to calculate the coating density ρ c .We used the ring-down method [31] to measure thefrequency f and ring-down time τ of the first vibrationalmodes of each disk, before and after the coating deposi-tion, and calculated the coating loss angle ϕ c = ϕ + ( D − ϕ D , (2)where ϕ = ( πf τ ) − is the measured loss angle of thebare substrate, ϕ = ( πf τ ) − is the measured loss an-gle of the coated disk, and D is the frequency-dependentmeasured dilution factor [32]. We measured up to eightmodes, from ∼ ∼
33 kHz, in a frequency band whichpartially overlaps with the detection band of ground-based GWDs (10-10 Hz). In order to avoid systematic Ψ [ d e g ] Nb O datafit − ∆ [ d e g ] Nb O datafit Ψ [ d e g ] TiO -Nb O datafit − ∆ [ d e g ] TiO -Nb O datafit FIG. 1. Ellipsometric spectra of annealed Nb O (top row) and TiO -Nb O (bottom row) films, acquired at an incidenceangle θ = 60 ◦ . damping from suspension and residual gas pressure, weused a clamp-free in-vacuum Gentle Nodal Suspension(GeNS) system [33]. This system is currently the pre-ferred solution of the Virgo and LIGO Collaborations forperforming internal friction measurements [19, 34].The coating Young modulus Y c and Poisson ratio ν c were estimated by fitting finite-element simulations tomeasured dilution factors via least-squares numerical re-gression [19]. Fig. 4 shows the results of this analysis.Further details about our GeNS system, finite-elementsimulations and data analysis are available elsewhere[19, 35]. C. Thermal noise
The direct CTN measurements were conducted witha multi-mode technique [36, 37] using a folded standing-wave Fabry-Perot cavity, where the folding mirror wasthe coating sample. Each of the co-resonating second-order orthogonal transverse modes, TEM02 and TEM20,act as a cavity length sensor for a different region ofthe coating surface. Any noise common to both TEMscancels out on the beat frequency between these modes, whereas noise from thermally induced vibrations in sepa-rate regions of the coating adds in quadrature. The beatfrequency, usually ∼ ∼
30 Hz to ∼ D. Composition
We used a Zeiss LEO 1525 field-emission scanning elec-tron microscope (SEM) and a Bruker Quantax systemequipped with a Peltier-cooled XFlash 410-M silicon driftdetector to analyze the surface and elemental composi-tion of the as-deposited titania-niobia coatings. Semi-quantitative (standardless) results were based on a peak-to-background evaluation method of atomic number, self-absorption and fluorescence effects (P/B-ZAF correction)and a series fit deconvolution model provided by theBruker Esprit 1.9 software. Using the self-calibratingP/B-ZAF standard-based analysis, no system calibrationhad to be performed.The SEM beam was set to 15 keV for the surfacesurvey. We performed multiple energy-dispersive X-ray(EDX) analyses on different coating sample spots andwith different magnifications (from 100 × to 5000 × ), fora total scanned surface of ∼ . II. RESULTSA. Single layers
Several niobia samples were analyzed by spectroscopicellipsometry, all yielding consistent results, together witha single titania-niobia sample. Fig. 1 shows exemplary(Ψ , ∆) spectra for both sets of annealed samples, ac-quired at θ = 60 ◦ . All spectra showed a degradationof the signal to noise ratio above 5.3 eV, caused bystrong absorption. Above 6 eV, the signal to noise ratiowas drastically reduced and data was discarded since nolonger useful for fitting purposes. Our models fit all themeasured spectra with the same accuracy. Figures 2 and3 show the dispersion laws and the extinction coefficientderived from our analysis, respectively.On Fig. 1, the interference features (due to multiplereflections in the transparency region) stop quite sharplyat the fundamental absorption threshold. By approach-ing this threshold, in the visible region, the oscillationamplitude gradually decreases. Within the boundaries ofthe measurement uncertainty, the energy gap is the samefor niobia and titania-niobia coatings, E g = 3 . ± . E g = 3 . ± .
05 eV, i.e. verysimilar to that of niobia coatings. However, the refractiveindex of titania-niobia coatings increased substantially inthe infrared region with respect to that of niobia coat-ings. At 1064 nm, we found n = 2 . ± .
01 for niobia and n = 2 . ± .
01 for titania-niobia coatings, before anneal-ing. Our results for niobia coatings are consistent withvalues found in the literature for IBS coatings depositedwith various sputtering settings [38–40]. For compari-son, the refractive index at 1064 nm of our IBS titaniacoatings is n = 2 . ± .
05 before annealing [19].For the mechanical properties, we characterized twodisks coated with niobia films and a disk coated withtitania-niobia films. Fig. 4 shows measured dilution fac-tors of a sample from each coating set. Our finite-elementsimulations fitted the data of all samples with similar ac-curacy. Fig 5 shows the measured coating loss angles,calculated using Eq.(2).For the as-deposited niobia films, we found ρ c =4 . ± . , Y c = 100 ± ν c = 0 . ± . ρ c = 4 .
50 g/cm , a reduced Young modulusof 118 GPa and ν c = 0 .
22. Concerning the elastic con-stants, our values are substantially different from whatcan be found in the literature. This discrepancy mightbe explained by the different sputtering settings used toproduce the samples, as observed for other high-index ox-ide coatings [19], and by the different methods used forthe measurement. For the Young modulus in particular,C¸ etin¨org¨u et al. used nanoindentation, which producesresults that may vary depending on the substrate usedfor the coating deposition [19] and on the model used forthe analysis. Unlike nanoindentation, our method yieldsconsistent results for the same coating on different sub-strates [19] and does not rely on any specific assumptionabout the model to be used for data analysis and on theactual value of ν c .According to our EDX analyses, the titania-niobia coatings feature an average atomic cation ratioNb/(Ti+Nb) = 0 . ± .
01. Compared to niobia coat-ings, the co-sputtering induced a moderate decrease ofthe coating loss angle and significantly increased the coat-ing Young modulus.The maximum annealing temperature T a , limited bythe onset of crystallization, was 400 ◦ C for both niobiaand titania-niobia coatings. For comparison, 300 < T a < ◦ C for IBS titania [41, 42]. We observed that an-nealing increased the coating thickness by 2 −
3% andslightly reduced the refractive index by about 1% in thetransparency region, whereas it did not change the energygap. Further analysis of the (Ψ, ∆) spectra also foundfor both niobia and titania-niobia coatings the same ef-fect already observed in IBS tantala and tantala-titaniacoatings, that is, a reduction of the Urbach tails [23]. Re-markably, annealing decreased the coating loss angle ofa factor 1 . − ∼ n is given for the wavelength of operationof current GWDs, λ = 1064 nm (corresponding to a pho-ton energy E of 1.17 eV), as well as for the alternativewavelength λ = 1550 nm ( E = 0 .
80 eV) of future GWDssuch as Einstein Telescope [10]. . . . n . . . . n Nb O Nb O ◦ CTiO -Nb O TiO -Nb O ◦ C FIG. 2. Refractive index n of Nb O and TiO -Nb O thin films, before and after in-air annealing at 400 ◦ C for 10 hours. Theright plot is a zoom on the region of interest for present and future GWDs ( λ = 1064 nm corresponds to a photon energy E of1.17 eV, λ = 1550 nm to E = 0 .
80 eV).TABLE I. Optical and mechanical properties of IBS Nb O and TiO -Nb O coatings, before and after 400 ◦ C annealing:refractive index n at 1064 and 1550 nm, energy gap E g , density ρ c , loss angle ϕ c at ∼ Y c and Poisson ratio ν c . Loss angle extracted from CTN measurements assumelow-index material loss angle 2.3 × − rad [19]. Values of Ta O -TiO layers of Advanced LIGO and Advanced Virgo are alsolisted, for comparison [19, 27]. n n E g [eV] ρ c [g/cm ] ϕ c [10 − rad] ϕ CTN c [10 − rad] Y c [GPa] ν c Nb O ± ± ± ± ± ± ± O ◦ C 2.22 ± ± ± ± ± ± ± ± -Nb O ± ± ± ± ± ± ± -Nb O ◦ C 2.28 ± ± ± ± ± ± ± ± ± O -TiO ◦ C 2.09 ± ± ± ± ± ± ± ± . . k Nb O Nb O ◦ CTiO -Nb O TiO -Nb O ◦ C FIG. 3. Extinction coefficient k of Nb O and TiO -Nb O thin films, before and after in-air annealing at 400 ◦ C for 10hours.
B. HR stacks
We produced three different Bragg reflectors with thefollowing materials and designs for operation at 1064 nm:(i) niobia and silica layers of quarter-wavelength ( λ/ λ/ d H and d L are the cumulative thicknesses of high- and low-indexlayers, respectively, the optimization allowed to reducethe thickness ratio ξ ≡ d H /d L down to 38% in sample(iii), compared to ∼
60% of samples (i) and (ii).All HR samples were designed to yield 5 parts permillion (ppm) transmissivity, as in the current HR coat-ings of the end test masses (ETMs) of Advanced LIGOand Advanced Virgo [19]. Their design specifications aresummarized in Table II, where they are also compared tocurrent ETM coatings: all our alternative stacks are thin-ner, thanks to their higher index contrast C , and sample(iii) features the lowest ratio ξ and hence the smallestcontent of dissipative material. However, because of thetransmissivity requirement, the optimization of sample(iii) came with the cost of an increased thickness.We characterized the optical properties of our HR sam-ples after they were annealed at 400 ◦ C for 10 hours inair. For each sample, we measured 4.3 ppm transmissionand 0.3 ppm absorption. This is the same value of ab-sorption as measured in current ETMs and represents afactor 7 improvement over our previous niobia coatings[43]. Cavity response measurements (see Section I C) givecomparable results for sample (i) and a factor of 2 and 4higher for samples (ii) and (iii), respectively. Sample (iii)was measured in two different spot locations, while sam- . .
91 Frequency [Hz] D × − Nb O data fit . D × − annealed Nb O data fit . . . D × − TiO -Nb O data fit . . . D × − annealed TiO -Nb O data fit FIG. 4. Dilution factor D of Nb O and TiO -Nb O films, before and after in-air annealing at 400 ◦ C for 10 hours. · − Frequency [Hz] ϕ c [ r a d ] Nb O TiO -Nb O Nb O ◦ CTiO -Nb O ◦ C FIG. 5. Mechanical loss ϕ c of Nb O and TiO -Nb O films, before and after in-air annealing at 400 ◦ C for 10 hours (differentmarkers indicate distinct samples). ples (i) and (ii) were measured at only one spot. TableIII lists the measured optical properties.After annealing, bubble-like defects of different num-ber and size, detected with an optical microscope, ap-peared at variable depth in the coatings. We observedno trace of such defects in the annealed single layers, in-dicating that this phenomenon only occurs when layersare stacked. These defects might be caused by cluster-ing of incorporated argon atoms which, according to ourEDX analyses, amounts to an atomic concentration of0 . ± . µ m, on each ofthe three samples. An amplitude spectral density (ASD)measurement was repeated at least three times in eachlocation. For each sample, the variation in ASD betweenthe two locations was less than 3%, thus we treated thesemeasurements as statistically identical and report theirvariance weighted mean values in Table III. Fig. 6 showsan exemplary ASD measurement of the stack containingniobia. Although the direct CTN measurement is moresensitive to individual defects, because the beam spot sizeused in the measurement is small, we found no evidencethat our measurement was contaminated by the presenceof bubble-like defects. Using these measurements we ex-tracted the CTN amplitude ( N CT N ) at 100 Hz as well asthe CTN frequency dependence (slope), N CT N ( f ) = amplitude × (cid:18)
100 Hz f (cid:19) slope (3)using least-squares and Monte Carlo fitting. We foundthat the CTN of sample (i) was 4% larger, sample (ii) was2% lower, and sample (iii) was 2% larger than the CTNof current ETMs. The CTN amplitude frequency depen-dence of sample (i) matched that of the ETM samples( f − . ± . ), while the frequency dependence of samples(ii) and (iii) was more shallow ( f − . ± . ).The loss angle ϕ c of the high-index material used ineach coating, ϕ c ( f ) = ϕ c × (cid:18) f
100 Hz (cid:19) (1 − × slope) , (4)is extracted from the measurements using the ASD at 100Hz, the coating structure, a loss angle of 2.3 × − radfor the low-index material [19], and an analytic expres-sion for the CTN [44]. Results are reported in Table III.We find, in general, ϕ c values higher than found with the ring-down method (see Table I). Although the 100Hz amplitude is similar among the three samples, thereis significantly less of the high-index material in the opti-mized sample; since we kept the low-index loss angle fixedfor our fit, the extracted high-index loss angle increased. C. Updated Advanced LIGO ETM CTN
Finally, we present an updated value for the frequency-dependent CTN amplitude of the current ETMs used inAdvanced LIGO:(6 . ± . × (cid:18)
100 Hz f (cid:19) . ± . × −
21 m √ Hz . (5)This is obtained by scaling our measured CTN in TableIII to the CTN of a 6.2 cm beam on an Advanced LIGOETM using the methods outlined in in [36]. This newvalue is slightly lower than the previously reported value[36], as we are now accounting for the noise contributionof cavity couplers to the measured ASD (see Fig. 6). III. DISCUSSION
We developed a set of niobia- and titania-based thinfilms in order to test in depth their application to thecoatings of present and future GWDs, through the mea-surement of their optical and mechanical properties andthermal noise.We chose niobia and titania because of their high re-fractive index, with the aim of minimizing d in Eq.(1).By co-sputtering these two materials, we achieved a 9%higher refractive index than in tantala-titania layers ofcurrent GWDs [19]. Thus, compared to present GWDs,the higher index allowed us to realize thinner HR coatingswith comparable optical properties. Eventually, how-ever, all our newly-developed HR coatings unexpectedlyshowed a very similar CTN level, very close to that ofETMs of Advanced LIGO and Advanced Virgo. Thismay be explained by the fact that ϕ c of niobia andtitania-niobia layers turned out to be higher than intantala-titania layers [19], thus canceling out any im-provement derived from having reduced d .There is a significant difference between the loss valuesof niobia and titania-niobia layers provided by ring-downmeasurements and direct CTN measurements. Note thatthe ring-down method used single-layer samples, whereasthermal noise measurement where conducted on HR coat-ings where many layers are stacked.The observed discrepancy might come from the silicaloss angle used in the analysis of CTN data, which we as-sumed to be 2.3 × − rad as measured for silica annealedat 500 ◦ C [19]. As a reminder, the annealing tempera-ture of our newly-developed HR coatings was limited to400 ◦ C because of crystallization. Indeed, as shown inTable I, the discrepancy between ring-down and CTN
TABLE II. Nominal specifications (layers, design, number of layers N , thickness of high-index layers d H , thickness of low-indexlayers d L , thickness ratio ξ = d H /d L , total thickness d = d H + d L ) and measured properties (optical absorption α from photo-thermal deflection and CTN measurements, scattering α s ) of HR coatings for 5 ppm reflectivity. Coatings were measured afterannealing (400 ◦ C for 10 hours, in air). Values of Ta O -TiO /SiO ETM coatings of Advanced LIGO and Advanced Virgo[16, 19, 36] are also listed, for comparison. CTN absorption values are relative to α = 0 .
27 for the ETM coatings.design
N d H [nm] d L [nm] ξ d [nm] α [ppm] α CTN [ppm] α s [ppm]Nb O /SiO λ/ ± ± -Nb O /SiO λ/ ± ± -Nb O /SiO optimized 34 1545 4090 0.38 5635 0.30 ± ± ± ± µ m beam size (amplitude, ratio with respect to ETMwitness sample, power index of frequency dependence) and loss angle ϕ c of high-index material of HR coatings for 5 ppmtransmission. Loss angle calculation assume low-index material loss angle 2.3 × − rad [19]. Coatings have been measuredafter annealing (400 ◦ C for 10 hours, in air). Values of Ta O -TiO /SiO ETM coatings of Advanced LIGO and AdvancedVirgo [16, 19, 36] are also listed, for comparison.design amplitude [10 − m/ √ Hz] ratio to ETM slope ϕ c [10 − rad]Nb O /SiO λ/ ± ± ± -Nb O /SiO λ/ ± ± ± -Nb O /SiO optimized 13.2 ± ± ± ± ± ± values is about 30% for samples annealed at 400 ◦ C andabout 17% for samples annealed at 500 ◦ C. In addition,the discrepancy seems to increase with the total thick-ness of the low-index material, d L , suggesting that theassumed silica loss angle value could be underestimated.However, to make the results match, the silica loss anglewould need to be 1.8 × − rad and 1.1 × − rad for thesamples annealed at 400 ◦ C and 500 ◦ C respectively, afactor of 3-8 larger than previously measured [19, 20, 35].An alternative explanation for the observed discrep-ancy could be the presence of an excess loss in HR stacks,as observed previously on several HR stacks with differentdesigns [35] and especially with the current HR coatingsof Advanced LIGO and Advanced Virgo [19]. Althoughalready well-known, the observed excess loss remainedunexplained to date and will be the object of further in-vestigation.In order to be used in future GWDs, ϕ c of niobia andtitania-niobia coatings will have to be reduced. Thiscould be achieved with higher annealing temperatures.For titania-niobia layers, the crystallization might befrustrated either by varying the composition, i.e. the cation ratio Nb/(Ti+Nb), or by adopting a nano-layeredstructure [45].Also, further development will be needed to avoid thepresence of defects after annealing, which is a severe ob-stacle to implementation in GWDs. Argon trapped in thecoating is very likely the cause of such defects [46, 47];we are currently working to verify this hypothesis, andto find appropriate solutions. ACKNOWLEDGMENTS
This work has been promoted by the Laboratoire desMat´eriaux Avanc´es and partially supported by the VirgoCoating Research and Development (VCR&D) Collabo-ration. The authors would like to acknowledge the un-failing support and recognition of the LIGO ScientificCollaboration’s optics working group without which thiswork would not have been possible. The authors alsoacknowledge the support of the National Science Foun-dation under awards PHY-1705940 and PHY-0555406.We are also very grateful for the computing support pro-vided by The MathWorks, Inc. This work has documentnumber LIGO-P2000496. [1] R. X. Adhikari,
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