The thermal noise of mirror coatings for gravitational-wave detectors critically depends on the elastic properties of the constituent materials. Data analyses and theoretical models typically assume each material is homogeneous and isotropic, but isotropy has never been explicitly verified. Using Brillouin light scattering (BLS), we demonstrate that ion-beam-sputtered SiO_{2}—a material still viable for future mirror coatings—exhibits cylindrical elastic symmetry, with in-plane isotropy but a notable 6% compressive anisotropy along the film normal. This anisotropy remains unchanged after the postdeposition heat treatment currently used in ground-based detectors (500 °C, 10 h) but is nearly eliminated at 900 °C. Infrared reflectivity experiments support these findings by directly revealing heterogeneities in the distribution of bridging and nonbridging oxygen structures along the growth axis. While BLS measures the real part of the elastic constants at gigahertz frequencies, the data reveal negligible contributions from mechanical relaxations in the kilohertz to gigahertz range, making BLS a valid substitute for low-frequency properties obtained from standard anisotropy-insensitive techniques. Our results highlight that restoring isotropy through heat treatment—by softening the material, enabling more than 7% out-of-plane expansion, and smoothing out structural heterogeneities—may play a key role in reducing thermal noise. This proof-of-concept study extends beyond silica, providing critical insights for the design of future coatings.

Crystalline coatings have emerged as a promising alternative to amorphous mirror coatings for planned upgrades of second-generation detectors such as Advanced Virgo and for future 3G observatories. In this work, we investigate the structural and mechanical properties of epitaxial Cr2O3 thin films grown on c-plane sapphire by molecular beam epitaxy, with the objective of evaluating corundum-structured oxides as a new class of crystalline coating materials for gravitational wave interferometers. We report, for the first time, cryogenic mechanical loss measurements of Cr2O3 coatings and relate the measured dissipation to their crystalline quality. The structural and mechanical properties of the coatings were evaluated by XRD, RHEED, AFM, and GeNS measurements. Our findings show that the highest-quality chromia layers exhibit mechanical losses at 6 K as low as (5±1) × 10−6 rad, while poorer crystalline quality is associated with significantly higher losses. These results demonstrate the potential of corundum-structured oxides as mirror coatings for next-generation interferometers. The wide availability of corundum-structured oxides (X2O3 with X = Al, Ga, Fe, V, Cr, Ti, …) and their epitaxial compatibility with sapphire, including the possibility of forming solid solutions, further highlights the potential of this largely unexplored materials class.

Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

Amorphous tantala is an important optical material used in a number of high-precision optical applications, including gravitational wave interferometry. In this paper, we study in-situ the structural changes that occur in amorphous ion-beam sputtered coatings during an annealing treatment by means of a synchrotron radiation scattering experiment. The scattering signal is measured as a function of time on a large range of the Q-space. X-Ray diffraction and Rietveld analysis are used to study crystallization during the annealing treatment, whereas pair distribution function analysis allows to inspect the structural changes occurring during the amorphous to crystalline transition. Our findings indicate that several structural rearrangements occur in parallel, namely a first quick establishment of a backbone structure in the cationic substructure appearing on a rather extended range (up to 100 Angstrom), followed by a progressive rearrangement of the oxygen atoms environment which gradually increases the crystallinity of the structure.

Minimizing coating thermal noise is crucial for enhancing gravitational wave detector sensitivity, with a target amplitude spectral density reduction factor (henceforth ASD RF) of 0.5 relative to the coatings used currently. This study investigates the design of low-noise dielectric stacks using the double stack of doublets strategy, explored via ad hoc optimization heuristics specifically developed for efficient parametric analysis of coating performance. We analyze the performance limits of ternary coatings based on SiO2, Ti & Proportion;SiO2, and Ti & Proportion;GeO2, considering both their material and optical properties with respect to detector constraints. Optimization results suggest such coating configurations, even with a relaxed absorbance constraint (1 ppm), fall short of the target, achieving a best ASD RF of similar to 0.69. Consequently, we explore alternative ternary double stack of doublets designs incorporating higher refractive index materials. Simulations demonstrate that incorporating alternative high-index materials offers a promising pathway, potentially enabling the achievement of the project target. We discuss the optimization strategies, performance trade-offs, design robustness, and implications of using high-index, potentially higher-loss materials for next-generation optical coatings.

Coating Brownian thermal noise is a major limitation to the sensitivity of gravitational-wave detectors. To reduce it, future detectors are planned to operate at cryogenic temperatures. This implies a change of their mirror coating materials and the use of a longer laser wavelength, such as 1550 nm. A stack of amorphous silicon and silicon nitride layers has previously been proposed as a promising combination of low- and high-refractive index materials to realize low-noise highly-reflective coatings. An essential step towards such coatings is the production of both materials via ion-beam sputtering. In this paper, for the first time, we present a study of the optical properties at 1550 nm of silicon nitride thin films deposited via ion beam sputtering. The refractive index and optical absorption as a function of post-deposition heat treatment temperature are investigated using a spectrophotometer and a photo-thermal common-path interferometer. Finally, we discuss the prospect of combining this material with amorphous silicon.

Reducing coating thermal noise (CTN) in mirrors for gravitational wave (GW) interferometers is pivotal to improving sensitivity in the mid-frequency range. Current mirror coatings are heat-treated (annealed) after deposition in order to partially relax their microstructure and to improve their optical and mechanical properties. The maximum annealing temperature is an important parameter in this respect as a higher thermal energy allows the system to relax to more stable configurations, which is often beneficial for the thermal noise performances of the coatings. However, the useful temperature range is limited by the stability of the amorphous microstructure, since excessive heating eventually leads to the formation of crystalline grains which are detrimental from both the mechanical and optical viewpoints. In this work, inspired by the possibility to improve glass stability in alloys by a careful choice of mixing ratios, we studied ion-beam co-sputtered amorphous HfO2:Ta2O5 thin films with different HfO2 concentrations, so as to identify conditions that would lead to a higher glass stability in order to explore the effects of a thermal annealing over an extended temperature range. We then deposited a multilayer mirror, alternating layers of HfO2:Ta2O5 with composition providing the highest crystallization temperature and SiO2 layers. The thermal Brownian noise of the mirror coating was found to decrease with increasing heat-treatment temperatures, reaching losses comparable to the Ti-doped Ta2O5 coatings of Advanced LIGO when heated at the highest possible temperature. Our results demonstrate the critical importance of optimizing the film composition and annealing procedure in order to improve the coating performances and the sensitivity for the next generation of GW detectors.

Gravitational wave detectors (GWDs) are designed to detect the elusive signals produced by spacetime ripples, the GWs. The key to improving GWD sensitivity relies on the reduction of the thermal noise introduced by the mirrors. The high refractive index component of the high-reflectance mirrors installed in the current generation GWDs, such as Advanced LIGO and Advanced Virgo, is made of a mixture of similar to 27% TiO2 and similar to 73% Ta2O5. Such a coating plays a fundamental role in the GWD performance. The 27:73 TiO2:Ta2O5 ratio ensures high structural, optical, and mechanical performances, which allowed for the first ever detection of GWs, but might not be enough for new generation GWDs. Here, we investigate the potential of TiO2:Ta2O5 coatings, in a wider range of Ti/(Ta+Ti) cation ratio. Our research spans over the morphological and structural coating characteristics, and their correlation with optical and mechanical properties. On one hand, we unveil the profound influence of substrate selection and TiO2 content on the quality of coating morphology. On the other, we pinpoint the effect of TiO2 content on the structural properties of the coating, as increasing TiO2 content leads to lower temperature amorphous-to-crystalline transition, and we show that internal strain may arise due to the coexistence of TiO2 and Ta2O5 crystalline phases. Finally, substrate choice, TiO2 concentration, and crystallization characteristics emerge as pivotal factors in the pursuit of precision optics.

The characterization of thin film parameters derives from the measurement difference between the coated and bare substrate. This method of comparison is based on the stationarity of the substrate: the characteristics of the substrate do not depend on the presence of the film. However, the thermoelastic loss of a coated substrate depends on the thermo-mechanical parameters of the film as well, which are generally unknown. When thermoelastic loss is dominant, the coating loss measurements are completely altered. In this paper, we propose a model that helps to understand the role of each material property in the thermoelasticity of layered plates, and with this we identified three possible cases in which any coating-substrate combination could be classified. In particular, we analyzed the IBS silica film deposited on silicon. Using the model, we were able to explain the experimental results and also selected a thinner substrate for future coating loss measurements. With this choice, cryogenic loss measurements on bare substrate confirm that thermoelastic loss becomes irrelevant for temperatures below 130 K-180 K, depending on the mode.

A new generation of gravitational wave detectors is currently being designed with the likely use of a different laser wavelength compared to current instruments. The estimation of the optical losses for this new wavelength is particularly relevant to derive the detector sensitivity and also to anticipate the optical performances of future instruments. In this article, we measured the absorption and angle-resolved scattering of several mirror samples in order to compare optical losses at a wavelength of 1064 and 1550 nm. In addition, we have carried out simulations of the Einstein Telescope arm cavities at 1064 and 1550 nm taking into account losses due to surface low-spatial frequency flatness. Our results suggest that optical losses as measured at 1064 nm are about twice as large as those at 1550 nm as predicted with a simple model.

This study explores the impact of crystalline fraction on the mechanical losses of amorphous tantalum oxide (tantala, Ta2O5) thin films intended for gravitational wave detectors. We use ion beam sputtering technique to prepare a series of samples, which are then subjected to controlled thermal annealing to achieve varying degrees of crystallized fraction. The microscopic structure of the annealed samples is characterized by combining different analytical techniques. Our investigation reveals that the amorphous films comprise randomly distributed crystalline grains, whose density and average size depends on the duration of thermal treatment. To assess mechanical losses of the coatings, a gentle nodal suspension system is applied. Remarkably, a substantial reduction of approximately 20% in the coating's mechanical loss angle with respect to annealed amorphous coatings is observed for samples exhibiting a crystalline fraction of around 5%. This improvement may lead to the definition of alternative thermal treatments to improve the mechanical performances of coatings for gravitational wave detectors or other highly sensitive optical experiments. However the reduction in mechanical losses comes at the expense of an increase in optical scattering. The possibility of reducing the optical losses to the level required by gravitational interferometers by modifying the grain size distribution via appropriate annealing treatments is discussed.

Thermal annealing plays a key role in optimizing the properties of amorphous optical coatings. In the field of gravitational wave detection (GWD), however, the effects of annealing protocols on the interferometry mirror coatings have been explored primarily by ex post analysis. As a result, the dynamics of the coatings properties during annealing is still poorly known, potentially leading to suboptimal performance. Here, using real-time, in situ spectroscopic ellipsometry (SE) we have tracked the refractive index and thickness of a titania-tantala coating during controlled annealing. We have tested the material and the annealing protocol used in current GWD mirrors. The annealing cycle consisted of a heating ramp from room temperature to 500 degrees C, followed by a 10-h plateau at the same temperature and the final cooling ramp. SE measurements have been run continuously during the entire cycle. Significant variations in the thickness and refractive index, which accompany the coating structural relaxation, have been recorded during the heating ramp. These variations start around 200 degrees C, slightly above the deposition temperature, and show an increased rate in the range 250 degrees C-350 degrees C. A smaller, continuous evolution has been observed during the 10-h high-temperature plateau. The results offer suggestions to modify the current annealing protocol for titania-tantala coatings, for example by increasing the time duration of the high-temperature plateau. They also suggest an increase in the substrate temperature at deposition. The approach presented here paves the way for systematic, real-time investigations to clarify how the annealing parameters shape the properties of optical coatings, and can be leveraged to define and optimize the annealing protocol of new candidate materials for GWD mirrors.

Thermal annealing plays a key role in optimizing the properties of amorphous optical coatings. In the field of gravitational wave detection (GWD), however, the effects of annealing protocols on the interferometry mirror coatings have been explored primarily by ex post analysis. As a result, the dynamics of the coatings properties during annealing is still poorly known, potentially leading to suboptimal performance. Here, using real-time, in situ spectroscopic ellipsometry (SE) we have tracked the refractive index and thickness of a titania-tantala coating during controlled annealing. We have tested the material and the annealing protocol used in current GWD mirrors. The annealing cycle consisted of a heating ramp from room temperature to 500 ∘C, followed by a 10-h plateau at the same temperature and the final cooling ramp. SE measurements have been run continuously during the entire cycle. Significant variations in the thickness and refractive index, which accompany the coating structural relaxation, have been recorded during the heating ramp. These variations start around 200 ∘C, slightly above the deposition temperature, and show an increased rate in the range 250 ∘C–350 ∘C. A smaller, continuous evolution has been observed during the 10-h high-temperature plateau. The results offer suggestions to modify the current annealing protocol for titania-tantala coatings, for example by increasing the time duration of the high-temperature plateau. They also suggest an increase in the substrate temperature at deposition. The approach presented here paves the way for systematic, real-time investigations to clarify how the annealing parameters shape the properties of optical coatings, and can be leveraged to define and optimize the annealing protocol of new candidate materials for GWD mirrors.

Mechanical and optical thermal noises play an important role in many precise opto-mechanical experiments, in which positions of test bodies are monitored by laser beams. Much of the research in this area was driven by the physics of gravitational wave interferometers, to counteract the mirror’s multi-layered dielectric coating thermal noise. Coating thermal noise is directly related to structural dissipation inside the material through the loss angle. In view of future upgrades of gravitational wave detectors, increasing the coatings mechanical performances, by lowering the loss angle and retaining their outstanding optical and morphological properties, is fundamental. The measurement of the coating loss angle requires substrates to be stable with respect to their dissipative behavior. It has been seen that fused silica disc losses are resonant-mode shape dependent and are subject to ageing effects, compromising the accuracy of mechanical characterizations of the substrates and, consequently, of the coatings. In commercial samples, the source of this deteriorations can be related to the ground, unpolished lateral surface. In this work we show that the polishing of the sample’s edge reduces the amount of spurious losses and ageing effects. A new procedure through CO2 laser polishing of the edge surface is proposed, explained and put in place. The results of these procedures, in terms of roughness and loss behavior is shown. The loss angle measurements are compared with an edge loss model and other existing models.

Amorphous mixed titania-tantala coatings are key components of Bragg reflectors in gravitational-wave detectors (GWDs). Attaining the lowest possible values of optical absorption and mechanical losses in coatings is of paramount importance for GWDs, and this requires a complex optimization of the coating deposition and postdeposition annealing. We present here a systematic investigation of the optical properties and internal friction of amorphous mixed titania-tantala coatings grown by ion beam sputtering. We consider coatings with six different cation mixing ratios─defined as Ti/(Ti + Ta)─and we study them both in the as-deposited and annealed states. All coatings have been subject to the same annealing of 500 °C for 10 h in air, which is the postdeposition treatment adopted so far for Bragg reflectors in GWD applications. By exploiting spectroscopic ellipsometry data and modeling, along with ancillary techniques, we retrieved the dielectric function of the coatings in a wide spectral range. When varying the mixing ratio and performing the annealing, we find monotonic─in some cases, almost linear─trends for most of the aforementioned properties. Remakably, the postannealing Urbach energy displays a definite minimum for a mixing ratio around 20%, very close to the composition of the coatings showing the lowest optical absorption for GWD applications. We suggest that the observed minimum in the Urbach energy depends not only on the mixing ratio but also on the annealing parameters. On the other hand, the minimum coating loss angle was found to be weakly dependent on the considered measurement frequency and to lie within a rather broad range of Ti content (cation ratios of 21 and 44%), suggesting that the search for an absolute minimum following postdeposition annealing should be rather sought in the study of the best annealing parameters for each specific cation ratio considered. This work constitutes a reference for the optical properties of the amorphous mixed titania-tantala coatings and highlights the relevance of the Urbach energy as an additional parameter to guide the optimization process of materials for high-performing Bragg reflectors.

Gravitational wave detectors (GWDs) are designed to detect the elusive signals produced by spacetime ripples, the GWs. The key to improving GWD sensitivity relies on the reduction of the thermal noise introduced by the mirrors. The high refractive index component of the high-reflectance mirrors installed in the current generation GWDs, such as Advanced LIGO and Advanced Virgo, is made of a mixture of ∼27% TiO2 and ∼73% Ta2O5. Such a coating plays a fundamental role in the GWD performance. The 27:73 TiO2:Ta2O5 ratio ensures high structural, optical, and mechanical performances, which allowed for the first ever detection of GWs, but might not be enough for new generation GWDs. Here, we investigate the potential of TiO2:Ta2O5 coatings, in a wider range of Ti/(Ta + Ti) cation ratio. Our research spans over the morphological and structural coating characteristics, and their correlation with optical and mechanical properties. On one hand, we unveil the profound influence of substrate selection and TiO2 content on the quality of coating morphology. On the other, we pinpoint the effect of TiO2 content on the structural properties of the coating, as increasing TiO2 content leads to lower temperature amorphous-to-crystalline transition, and we show that internal strain may arise due to the coexistence of TiO2 and Ta2O5 crystalline phases. Finally, substrate choice, TiO2 concentration, and crystallization characteristics emerge as pivotal factors in the pursuit of precision optics.

The performance of optical cavities in gravitational wave detectors (GWD) is negatively affected by the growth of ice layers when operating at cryo temperatures. Loss of performance begins when the ice overlayer is only a few-nm thick. Careful planning is then required to minimize, monitor and take into account the presence of ultrathin ice on cryo-cooled optical surfaces. Here we employed spectroscopic ellipsometry (SE) to study icing on the surfaces of SiO2 and Ti:Ta2O5 thin films, two materials used in the high-reflective mirrors of current GWD. SE measurements were performed at 75 K. The data presented suggest that SE is a most convenient tool to monitor in operando the ice formation on the surfaces of GWD mirrors. Furthermore, ultrathin ice layers can affect the evaluation of the optical properties of materials at low temperatures, a valuable task for those next-generation GWD that will operate at cryogenic temperatures. The characterization of an ultrathin ice overlayer ( < 10 nm) allowed to determine for the first time the low-temperature optical properties of Ti:Ta2O5. The same approach could be applied to determine the low-temperature optical properties of other dielectric films, thus helping to screen new materials for cryo-operated GWD mirrors.

Low internal friction coatings are key components of advanced technologies such as optical atomic clocks and high-finesse optical cavity and often lie at the forefront of the most advanced experiments in Physics. Notably, increasing the sensitivity of gravitational-wave detectors depends in a very large part on developing new coatings, which entails developing more suitable methods and models to investigate their loss angle. In fact, the most sensitive region of the detection band in such detectors is limited by the coating thermal noise, which is related to the loss angle of the coating. Until now, models which describe only ideal physical properties have been adopted, wondering about the use of one or more loss angles to describe the mechanical properties of coatings. Here we show the presence of a systematic error ascribed to inhomogeneity of the sample at its edges in measuring the coating loss angle. We present a model for disk-shaped resonators, largely used in loss angle measurements, and we compare the theory with measurements showing how this systematic error impacts on the accuracy with which the loss model parameters are known.

Amorphous mixed titania-tantala coatings are key components of Bragg reflectors in the gravitational wave detectors (GWDs). Attaining the lowest possible values of optical absorption and mechanical losses in the coatings is of paramount importance for GWDs, and this requires a complex optimization of the coating deposition and post-deposition annealing. We present here a systematic investigation of the optical properties and internal friction of amorphous mixed titania-tantala coatings grown by ion beam sputtering. We consider coatings with six different cation mixing ratios and we study them both in the as-deposited and annealed state. By exploiting spectroscopic ellipsometry data and modelling, along with ancillary techniques, we retrieved the dielectric function of the coatings in a wide spectral range. When varying the mixing ratio and performing the annealing we find monotonic trends for most of the aforementioned properties. Remakably, the post-annealing Urbach energy displays a definite minimum for a mixing ratio around 20 composition of the coatings showing the lowest optical absorption for GWDs applications. We suggest that the observed minimum in the Urbach energy depends not only on the mixing ratio, but also on the annealing parameters. On the other hand, the minimum coating loss angle was found to be weakly dependent on the considered measurement frequency and to lie within a rather broad range of Ti content, suggesting that the search for an absolute minimum following post-deposition annealing should be rather sought in the study of the best annealing parameters for each specific cation ratio considered. This work constitutes a reference for the optical properties of the amorphous mixed titania-tantala coatings, and highlights the relevance of the Urbach energy in the optimization process of materials for high-performing Bragg reflectors.

Amorphous SiO2 thin films are one of the two components of the highly reflective mirror coatings of gravitational-wave detectors. For this study, layers of amorphous SiO2 on crystalline Si substrates were produced by ion-beam sputtering (IBS), using accelerated neutralized argon ions as sputtering particles, as is the case for the actual mirror coatings of gravitational-wave detectors. The aim of this study is to investigate the possible presence of various defects in the materials in order to improve the coating quality. We provide evidence that, due to the synthesis method, about 0.2 wt.% of Ar is present in the coatings, and it can be released by means of thermal treatments, starting around 400 °C. The time and temperature to obtain the total release of Ar increases with the coating thickness; for a thickness of 100 nm, all argon is released below 600 °C, while an isotherm of one hour at 900 °C is necessary for a coating 5 μm thick. Besides the Ar atoms left from the synthesis, other defects, such as Si clusters and silicon dangling bonds, are present in the coatings. The concentration of both of them is strongly reduced by thermal treatments either in vacuum or in air. The overall thickness of the coating is slightly increased after thermal treatments, as witnessed by the change of the period of interference fringes.