Experimental Realization of Optimized Ternary Mirror Coatings

TL;DR

The paper addresses the challenge of reducing coating Brownian thermal noise while keeping optical losses low in precision optical cavities. It introduces a design-to-fabrication pipeline using a Double-Stack of Doublets (DSD) architecture and a Borg MOEA-based multi-objective optimization to balance coating noise $S_{CB}$, transmittance $\tau_c$, and absorption $\alpha_c$ at the operating wavelength of $1064$ nm. The authors validate two ternary coatings, SiN$_x$/SiO$_2$ and Ti:GeO$_2$/SiO$_2$, demonstrating agreement with predictions and achieving $S_{CB}$ reductions with ASD RF of $0.82$ and $0.81$ respectively, with sub-ppm absorption for the Ti:GeO$_2$ design and around $1.5$ ppm for the SiN$_x$ design; The Ti:GeO$_2$ design approaches the predicted limit of $S_{CB}$ corresponding to an ASD RF near $0.71$ but experimental transmittance and absorption show the need for deeper process optimization. Overall this work provides a robust design framework with potential impact on next-generation gravitational-wave detectors.

Abstract

We report on the first experimental realization of multi-material dielectric mirror coatings designed through a multi-objective optimization algorithm to simultaneously minimize thermal noise and optical losses. We validate this design strategy by fabricating and characterizing two distinct ternary systems: a SiNx -based proof-of-concept and a Ti:GeO2 -based system targeting lower optical losses. The performance of the SiN x coating shows remarkable agreement with predictions, demonstrating a noise amplitude spectral density reduction of 0.82 with respect to current reference coatings, and validating our design-to-fabrication pipeline. The Ti:GeO2 -based system achieves the crucial goal of sub-ppm absorption; its measured thermal noise, however, is higher than the theoretically predicted level of 0.71, extrapolated from single-layer material characterization. A dedicated tolerance analysis confirms that this discrepancy is not attributable to random thickness errors, emphasizing that further studies of the manufacturing process are needed to fully exploit this combination of materials. This work establishes a robust methodology for producing complex, high-performance optical coatings tailored for precision experiments.

Figures (22)

• Figure 1: Layout and predicted thermal noise performance (ASD RF) of the two optimized ternary mirror coatings realized in this work. Vacuum is on the left (the top) of the design, substrate is on the right of the figure. The bar colors correspond to the different dielectric materials. For the SiN$_x$-based design (a), the bottom stack consists of SiN$_x$ (black) and SiO$_2$ (green) both deposited in an R&D IBS facility at LMA. The top stack consists of Ti:Ta$_2$O$_5$ (blue) and SiO$_2$ (red), both deposited in the main IBS facility at LMA (the Grand Coater). For the Ti:GeO$_2$-based design (b), the bottom stack uses Ti:GeO$_2$ (black) and SiO$_2$ (red), while the top stack uses Ta$_2$O$_5$-TiO$_2$ (blue) and SiO$_2$ (red), all deposited in the LMA Grand Coater.
• Figure 2: CTN measurements of the two optimized ternary mirror coatings. (a) SiN$_x$-based design. (b) Ti:GeO$_2$-based design. The experimental noise is presented as both a raw measurement ( data) and a filtered trace ( chopped data), from which noise around the harmonics of the 60 Hz power-line frequency has been removed. The solid curve, labeled fit, represents the estimated thermal noise.
• Figure 3: Comparison of the measured (red curve) and theoretical (black curve) transmittance spectra for the two optimized ternary coatings: (a) the SiN$_x$-based design and (b) the Ti:GeO$_2$-based design. For both coatings, an excellent agreement is observed around the $1064$ nm design wavelength, especially for the SiN$_x$ based structure, validating the quasi-periodic design and the high precision of the fabrication process. The minor deviation at shorter wavelengths is expected, as the theoretical model does not account for material dispersion, assuming instead constant refractive indices based on their values at 1064 nm.
• Figure S1: (a) Transmittance ($\tau_c$) and (b) absorbance ($\alpha_c$) for a QWL multilayer stack of Silica/SiN$_x$ as a function of the number of doublets. The transmittance is shown on a logarithmic scale and decreases as more layers are added. The absorbance, measured in parts per million (ppm), increases. Both saturate at the Koppelmann Limit. The limit is $44.9$ ppm for a stack using all GC silica, and $46.8$ ppm (as shown in this plot) when using silica of the R&D deposition system for the bottom layers, corresponding to the hybrid design. Here the extinction coefficient is $\kappa_{SiN_x} = 1.5 \times 10^{-5}$.
• Figure S2: Schematic representation of the tapered layer thicknesses in the SiN$_x$/SiO$_2$ stack designed according to the Carniglia method. The high-index SiN$_x$ layers (blue) are progressively thinned towards the front of the mirror (left), while the low-index SiO$_2$ layers (red) are thickened to minimize absorption.