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Designing a low-loss high reflectivity mirror for gravitational waves detectors by combining a dielectric metasurface and multilayer stack

Edith Hartmann, Michel Lequime, Jerome Degallaix, Michael Hartman, Paul Rouquette, Claude Amra, Myriam Zerrad

Abstract

Future generations of gravitational wave detectors require increased sensitivity, for which the availability of large mirrors with high reflectivity and low mechanical loss is essential. Current amorphous multilayer mirror designs present constraining limitations in terms of thermal noise. These mirrors require a large number of thin film layers to achieve near-perfect reflectivity. However, the thermal noise generated by this type of stack increases with the number of layers used. Reducing thermal noise is therefore very challenging and highlights the need for new technical solutions that can address this specific issue. Here, we provide insights into the expected performance of mirrors that combine a resonant metasurface with a multilayer stack. The suggested mirror design ensures the high reflectivity required for interferometric gravitational wave detectors, while using fewer layers of properly selected materials. It allows to reduce the total thickness of the material with the poorest thermal-noise performance, namely TiO2:Ta2O5, by a factor of more than 3, making it a promising option for potentially reducing thermal noise as well.

Designing a low-loss high reflectivity mirror for gravitational waves detectors by combining a dielectric metasurface and multilayer stack

Abstract

Future generations of gravitational wave detectors require increased sensitivity, for which the availability of large mirrors with high reflectivity and low mechanical loss is essential. Current amorphous multilayer mirror designs present constraining limitations in terms of thermal noise. These mirrors require a large number of thin film layers to achieve near-perfect reflectivity. However, the thermal noise generated by this type of stack increases with the number of layers used. Reducing thermal noise is therefore very challenging and highlights the need for new technical solutions that can address this specific issue. Here, we provide insights into the expected performance of mirrors that combine a resonant metasurface with a multilayer stack. The suggested mirror design ensures the high reflectivity required for interferometric gravitational wave detectors, while using fewer layers of properly selected materials. It allows to reduce the total thickness of the material with the poorest thermal-noise performance, namely TiO2:Ta2O5, by a factor of more than 3, making it a promising option for potentially reducing thermal noise as well.
Paper Structure (7 sections, 3 equations, 5 figures, 1 table)

This paper contains 7 sections, 3 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Metasurface design
  3. Association with a conventional multilayer Bragg mirror
  4. Optimization of the additional low-index layer
  5. Impact on the metasurface tolerances
  6. Thermal noise considerations
  7. Conclusion

Figures (5)

  • Figure 1: Schemes of the two alternative principles: (a) the configuration described by Ref. Dickmann_2018, and (b) our proposal.
  • Figure 2: (a) Definition of the metasurface geometric parameters; Metasurface reflectivity dependence on the periodicity $P$, the diameter $D$ and height $h$ of the pillars, when considering (b): a-Si:H or (c): tantala as the metasurface material. The color code remains the same for all the cases considered here. The chosen parameters are represented by the white star.
  • Figure 3: (a) Influence of the amorphous silicon extinction coefficient on the absorption of the optimized a-Si:H metasurface; (b) Metasurface transmittance when the pillars diameter slightly vary from the optimized value.
  • Figure 4: Assembly transmittance as a function of the silica spacer thickness $e$. The figure shows the simulated values (solid lines) and the values predicted by a Fabry-Perot model (dotted lines), for mirror designs combining the optimized a-Si:H metasurface with either a 5-layer or an 11-layer Bragg mirror. The selected thickness is $e=770$ nm.
  • Figure 5: Manufacturing tolerances: transmittance as a function of the metasurface geometric parameters (pillars diameter $D$ and height $h$) for either the single metasurface (a), or when combined with a TiO$_2$:Ta$_2$O$_5$/SiO$_2$ Bragg mirror of 11 layers. The white dashed lines show the area where $T<5$ ppm.