arXiv subjects

Massimo Granata

Publications and source records attributed to Massimo Granata.

15 recordsLinked to original sources

arXiv2026

Improving Beam Quality in Gravitational-Wave Interferometers Illuminated by Higher-Order Laguerre-Gaussian Modes

Higher-order Laguerre-Gaussian (LG) laser modes have been proposed to reduce test-mass thermal noise in laser interferometric gravitational-wave detectors, owing to their more homogeneous intensity profiles compared to the currently employed fundamental Gaussian beam. However, LG beams such as the LG$_{3,3}$ mode suffer significant beam quality degradation in Fabry-Perot arm cavities in GW detectors with realistic state-of-the-art mirror surface figure errors, due to scattering into degenerate modes of the same order, which are resonantly enhanced by shared cavity resonance conditions. In this work, we investigate an alternative ''donut-shaped'' LG$_{0,\ell}$-like mode, specifically the LG$_{0,6}$ mode, and demonstrate strategies to improve its performance. These include the introduction of a tailored circular mirror mask with anti-reflective coating in the central region, which selectively increases the losses of parasitic degenerate modes while minimally impacting the LG$_{0,6}$ mode due to its limited overlap with the masked area. We further assess the marginal benefits of anticipated improvements in mirror surface figure errors and the potential reduction of cavity finesse. We demonstrate that these strategies can reduce the average contrast defect by more than two orders of magnitude and lower the mode loss by nearly a factor of five, achieving performance at or below the typical values observed in current detectors. This work opens up new research and development pathways for employing LG$_{0,\ell}$-type modes that achieve significant thermal noise reduction while maintaining beam quality and optical performance comparable to current gravitational-wave interferometers.

astro-ph.IM↗

arXiv2026

In-situ total scattering investigation of crystalline ordering in amorphous ion-beam sputtered thin films for interferometric gravitational wave detectors

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.

cond-mat.mtrl-sci↗

arXiv2026

Elastic and structural anisotropy in silica thin films for gravitational-wave detectors

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 for the first time that ion-beam-sputtered SiO2 -- 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 post-deposition heat treatment currently used in ground-based detectors (500 $^\circ$C, 10 h) but is nearly eliminated at 900 $^\circ$C. Infrared reflectivity experiments support these findings by directly revealing heterogeneities in the distribution of bridging and non-bridging oxygen structures along the growth axis. While BLS measures the real part of the elastic constants at GHz frequencies, the data reveal negligible contributions from mechanical relaxations in the kHz-GHz 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.

physics.optics↗

arXiv2026

Thermal Noise Reduction in Ternary Optical Coatings: From Ti::GeO$_2$-Based Ternary Systems to High Index Materials

Minimizing coating thermal noise is crucial for enhancing gravitational wave detector sensitivity, with a target Amplitude Spectral Density Reduction Factor (ASD RF) of $0.5$ relative to standard coatings. This study investigates the design of low-noise dielectric stacks using the 'Double Stack of Doublet' 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 SiO$_2$, Ti::SiO$_2$, and Ti::GeO$_2$, considering material property uncertainties and absorption constraints. Optimization results show that this system, even with relaxed absorbance constraint (1 ppm), falls short of the target, achieving a best ASD RF of $\sim 0.69$. Consequently, we explore alternative ternary 'Double Stack of Doublet' 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.

physics.optics↗

arXiv2024

Comparison of arm cavity optical losses for the two wavelengths of the Einstein Telescope gravitational wave detector

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.

physics.optics↗

arXiv2022

A Systematic Error in the Internal Friction Measurement of Coatings for Gravitational Waves Detectors

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.

astro-ph.IM↗

arXiv2022

Effects of mixing and annealing on the optical and mechanical properties of TiO$_{2}$:Ta$_{2}$O$_{5}$ amorphous coatings

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%, very close to the 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.

physics.app-ph↗

arXiv2020

Observation of a Correlation Between Internal friction and Urbach Energy in Amorphous Oxides Thin Films

We have investigated by spectroscopic ellipsometry (SE, 190-1700 nm) the optical properties of uniform, amorphous thin films of Ta2O5 and Nb2O5 as deposited and after annealing, and after so-called "doping" with Ti atoms which leads to mixed oxides. Ta2O5 and Ti:Ta2O5 are currently used as high-index components in Bragg reflectors for Gravitational Wave Detectors. Parallel to the optical investigation, we measured the mechanical energy dissipation of the same coatings, through the so-called "loss angle" phi = Q^-1, which quantifies the energy loss in materials. By applying the well-known Cody-Lorentz model in the analysis of SE data we have been able to derive accurate information on the fundamental absorption edge through important parameters related to the electronic density of states, such as the optical gap (E_g) and the energy width of the exponential Urbach tail (the Urbach energy E_U). We have found that E_U is neatly reduced by suitable annealing as is also perceptible from direct inspection of SE data. Ti-doping also points to a minor decrease of E_U. The reduction of E_U parallels a lowering of the mechanical losses quantified by the loss angle phi. The correlation highlights that both the electronic states responsible of Urbach tail and the internal friction are sensitive to a self-correlation of defects on a medium-range scale, which is promoted by annealing and in our case, to a lesser extent, by doping. These observations may contribute to a better understanding of the relationship between structural and mechanical properties in amorphous oxides.

physics.optics↗

arXiv2019

Progress in the measurement and reduction of thermal noise in optical coatings for gravitational-wave detectors

Coating thermal noise is a fundamental limit for precision experiments based on optical and quantum transducers. In this review, after a brief overview of the techniques for coating thermal noise measurements, we present the latest world-wide research activity on low-noise coatings, with a focus on the results obtained at the Laboratoire des Mat\'{e}riaux Avanc\'{e}s. We report new updated values for the Ta$_2$O$_5$, Ta$_2$O$_5$-TiO$_2$ and SiO$_2$ coatings of the Advanced LIGO, Advanced Virgo and KAGRA detectors, and new results from sputtered Nb$_2$O$_5$, TiO$_2$-Nb$_2$O$_5$, Ta$_2$O$_5$-ZrO$_2$, MgF$_2$, AlF$_3$ and silicon nitride coatings. Amorphous silicon, crystalline coatings, high-temperature deposition, multi-material coatings and composite layers are also briefly discussed, together with the latest developments of structural analyses and models.

physics.ins-det↗

arXiv2019

Amorphous optical coatings of present gravitational-wave interferometers

We report on the results of an extensive campaign of optical and mechanical characterization of the ion-beam sputtered oxide layers (Ta$_2$O$_5$, TiO$_2$, Ta$_2$O$_5$-TiO$_2$, SiO$_2$) within the high-reflection coatings of the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors: refractive index, thickness, optical absorption, composition, density, internal friction and elastic constants have been measured; the impact of deposition rate and post-deposition annealing on coating internal friction has been assessed. For Ta$_2$O$_5$ and SiO$_2$ layers, coating internal friction increases with the deposition rate, whereas the annealing treatment either erases or largely reduces the gap between samples with different deposition history. For Ta$_2$O$_5$-TiO$_2$ layers, the reduction of internal friction due to TiO$_2$ doping becomes effective only if coupled with annealing. All measured samples showed a weak dependence of internal friction on frequency ($\phi_c(f) = af^{b}$, with $-0.208 < b < 0.140$ depending on the coating material considered). SiO$_2$ films showed a mode-dependent loss branching, likely due to spurious losses at the coated edge of the samples. The reference loss values of the Advanced LIGO and Advanced Virgo input (ITM) and end (ETM) mirror HR coatings have been updated by using our estimated value of Young's modulus of Ta$_2$O$_5$-TiO$_2$ layers (120 GPa) and are about 10\% higher than previous estimations.

physics.ins-det↗

arXiv2017

High-Reflection Coatings for Gravitational-Wave Detectors: State of The Art and Future Developments

We report on the optical, mechanical and structural characterization of the sputtered coating materials of Advanced LIGO, Advanced Virgo and KAGRA gravitational-waves detectors. We present the latest results of our research program aiming at decreasing coating thermal noise through doping, optimization of deposition parameters and post-deposition annealing. Finally, we propose sputtered Si3N4 as a candidate material for the mirrors of future detectors.

physics.ins-det↗

arXiv2017

Correlated evolution of structure and mechanical loss of a sputtered silica film

Energy dissipation in amorphous coatings severely affects high-precision optical and quantum transducers. In order to isolate the source of coating loss, we performed an extensive study of Raman scattering and mechanical loss of a thermally-treated sputtered silica coating. Our results show that loss is correlated with the population of three-membered rings of Si-O$_4$ tetrahedral units, and support the evidence that thermal treatment reduces the density of metastable states separated by a characteristic energy of about 0.5 eV, in favour of an increase of the states separated by smaller activation energies. Finally, we conclude that three-fold rings are involved in the relaxation mechanisms only if they belong to more complex chain-like structures of 10 to 100 tetrahedra.

cond-mat.mtrl-sci↗

arXiv2016

Mechanical loss in state-of-the-art amorphous optical coatings

We present the results of mechanical characterizations of many different high-quality optical coatings made of ion-beam-sputtered titania-doped tantala and silica, developed originally for interferometric gravitational-wave detectors. Our data show that in multi-layer stacks (like high-reflection Bragg mirrors, for example) the measured coating dissipation is systematically higher than the expectation and is correlated with the stress condition in the sample. This has a particular relevance for the noise budget of current advanced gravitational-wave interferometers, and, more generally, for any experiment involving thermal-noise limited optical cavities.

physics.ins-det↗

arXiv2014

Measurements of mechanical thermal noise and energy dissipation in optical dielectric coatings

In recent years an increasing number of devices and experiments are shown to be limited by mechanical thermal noise. In particular sub-Hertz laser frequency stabilization and gravitational wave detectors, that are able to measure fluctuations of 1E-18 m/rtHz or less, are being limited by thermal noise in the dielectric coatings deposited on mirrors. In this paper we present a new measurement of thermal noise in low absorption dielectric coatings deposited on micro-cantilevers and we compare it with the results obtained from the mechanical loss measurements. The coating thermal noise is measured on the widest range of frequencies with the highest signal to noise ratio ever achieved. In addition we present a novel technique to deduce the coating mechanical losses from the measurement of the mechanical quality factor which does not rely on the knowledge of the coating and substrate Young moduli. The dielectric coatings are deposited by ion beam sputtering. The results presented here give a frequency independent loss angle of (4.70 $\pm$ 0.2)x1E-4 with a Young's modulus of 118 GPa for annealed tantala from 10 Hz to 20 kHz. For as-deposited silica, a weak frequency dependence (~ f^{-0.025}) is observed in this frequency range, with a Young's modulus of 70 GPa and an internal damping of (6.0 $\pm$ 0.3)x1E-4 at 16 kHz, but this value decreases by one order of magnitude after annealing and the frequency dependence disappears.

physics.ins-det↗

arXiv2010

Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors

We report on the first experimental demonstration of higher-order Laguerre-Gauss (LGpl) mode generation and interferometry using a method scalable to the requirements of gravitational wave (GW) detection. GW detectors which use higher-order LGpl modes will be less susceptible to mirror thermal noise, which is expected to limit the sensitivity of all currently planned terrestrial detectors. We used a diffractive optic and a mode-cleaner cavity to convert a fundamental LG00 Gaussian beam into an LG33 mode with a purity of 98%. The ratio between the power of the LG00 mode of our laser and the power of the LG33 transmitted by the cavity was 36%. By measuring the transmission of our setup using the LG00, we inferred that the conversion efficiency specific to the LG33 mode was 49%. We illuminated a Michelson interferometer with the LG33 beam and achieved a visibility of 97%.

gr-qc↗