Mirror coatings

The design of these coatings presents many challenges.

• The coatings must be highly reflective for the new laser frequencies up to a reflection ratio of 99.9995%.
• Distortions in the coatings must be avoided at all costs. This means that the coatings must be perfect down to the nanometer level. Any flaw in the coating can lead to light scattering with measurement errors as a result, or make the mirror unusable.
• The mechanical loss in the coatings (which is related to the intrinsic mechanical noise) must be extremely low when applied to the crystalline silicon or sapphire.
• Mechanical stability must be maintained at the built-up optical power of up to 1 MW. All heat absorbed in the coating must be conducted to the substrate and dissipated via the crystalline silicon rods supporting the mirror.
• The coatings must follow the curvature of the mirror, which has an exceptionally long focal length of 5 km.
• Finally, the coatings must be applied to mirrors measuring up to 50 cm, 40 to 60 cm thick and weighing between 100 and 300 kg, while maintaining nanometer precision. The machinery for these coatings still needs to be developed.
• These highly reflective coatings are obtained by stacking many layers of coating materials of a few nanometers thick and using two materials with different refractive index n.
• The optical layer thickness should be a quarter of a wavelength. The higher the refractive index n, the thinner the layer should be. For example: amorphous SiO2 (n=1.45) and Ta2O5 (n=2.05)
• The light intensity decreases for each layer of the coating. To achieve a reflectivity of 99.999%, approximately 38 layers will be needed.
• Each layer requires extremely high accuracy. A single error during one of the coating runs will only extrapolate and result in unacceptable errors in the mirror. This means that the coating process must be monitored day and night. The coating is also carried out at high temperatures, which increases the risk of thermal deformations. A separate area of research is therefore the use of coating techniques at lower temperatures.

The research to find the optimal coating for the mirrors of the ET is still ongoing. A first method is to use monocrystalline coatings on crystalline silicon or sapphire. Another approach is to use polymorph SiO2 on crystalline silicon.

Initial research focuses on smaller diameter mirrors to investigate mechanical losses. The diameter of the mirror bodies is then increased to investigate how the mechanical noise scales with the larger diameter.

A second area of research is to significantly improve the Coating Thermal Noise (CTN) by lowering the operating temperature. This technique should significantly reduce the mechanical losses of the coatings, hopefully by a factor of about 10.

The high frequency part of the Einstein Telescope (also called ET-HF) will operate at room temperature. The interferometers for ET-HF are optimized for so-called shot noise (also called quantum phase noise ). The ET is so sensitive that individual photons (shots) or quantum noise can already make a difference in the measurements. The sensitivity can be increased by drastically increasing the optical power (the number of photons).

This means that powerful lasers are used and up to 1 MW of optical power is captured between the mirrors. Because a large number of photons are involved in the measurements, the impact of noise in the coatings is lower. The higher power does mean that the mirrors operate at higher temperatures, and therefore suffer more from thermal noise. The thermal noise increases at low frequencies (in the case of the ET-HF from around 30 Hz) and so the ET-HF is very sensitive to higher frequencies, but not to lower frequencies.

Optionally, the same wavelengths and substrate materials can be used as are already used in the LIGO and Virgo detectors. The challenge is to increase the diameter of the mirrors by almost a factor of two. However, the coatings must remain free of defects, which is certainly not an easy task.

The low frequency part of the Einstein Telescope (also called ET-LF) will operate at cryogenic temperatures of 10K to 20K (-263 °C to -253 °C). The interferometers for ET-LF are thus optimized for thermal noise (in the case of the ET-LF from 0.4 Hz).

After all, a higher temperature actually means that the molecules and atoms in the mirror and the mirror coating vibrate faster. This (thermal) noise is also visible in the laser light that hits the coating. By drastically lowering the temperature, this noise is reduced and the ET-LF can measure the lower frequencies.

To maintain this low temperature, the laser power levels must be kept low. As a result, every photon hitting the sensors counts. In normal operation, about 1018 photons per second will hit the detectors. Because the ET-LF is so sensitive, the accuracy of the measurement can be compromised as soon as a few photons per second are in error. These errors can come from stray light from hitting an air molecule, or from quantum noise (the aforementioned shot noise ), which becomes important especially at higher frequencies.

The ET-LF is therefore sensitive (e.g. 10-23/ ÖHz ) for low frequencies (from 0.3 Hz) and less sensitive for higher frequencies (up to 70 Hz). The ET-HF frequency band is less sensitive for low frequencies (from 15 Hz) and sensitive up to the higher frequencies (up to above 10 KHz). Together the two interferometers form a kind of xylophone that can operate over a wider bandwidth.

This does mean that especially for ET-LF new types of mirror substrates (e.g. silicon or sapphire) have to be found that can work at these low temperatures. The consequence is that new laser frequencies and mirror coatings have to be found. The research focuses on the electromagnetic spectrum and includes the use of nanolayers , multilayer coatings and crystalline coatings.

Firstly, it is expected that the new coatings can also be used for mirrors in other gravitational wave detectors. This could be for new detectors (such as LISA or the Cosmic Explorer), or for upgrading existing detectors (such as LIGO or Virgo). There could also be interest for mirrors used in optical astronomy or space applications.

The mirror coating techniques could also find their way into civil use, for example for coating windows or regular mirrors. The use of the coating techniques in, for example, microelectronics still needs to be investigated.