Optics and optical metrology

The optical systems are a crucial aspect of the ET.

• Several 200 kg super-polished mirrors with highly optimized coatings are located at the end of the arms. The mirrors serve as test masses for the gravitational waves.
• An ultra-stable laser provides the monochromatic laser beams used to measure the minute movements of the test masses.
• The laser beams pass through several ultra-precise photonic filters that stabilize the laser beams and filter out unwanted frequencies and noise.
• Numerous additional optical systems and sensors serve to control and stabilize the instrument so that the passage of a gravitational wave can be detected. The waves are visible as a brief ‘flicker’ in the readout of the photodetector (photodiode) that records the intensity of the recombined laser beams.

The detection of gravitational waves was demonstrated by the LIGO and Virgo observatories in their Nobel Prize winning first detections of gravitational waves (2015-2019). To achieve the impressive precision required for the Einstein Telescope (relative mirror displacements up to 10–21 m) we rely on an optimal combination and tuning of the best lasers and optical equipment on Earth.

When the laser beams are bounced back and forth between the mirrors, the optical losses must be less than 50 ppm . These very low losses are necessary to incrementally build up the many hundreds of kW of laser power in the arms (optical resonators) of the interferometer.

The total optical power between the mirrors must be able to reach 18 kW for the interferometers at low frequencies (0.1 to 10 Hz). These are the mirrors that must operate at cryogenic temperatures. For the interferometers that operate at ambient temperature and at higher frequencies (10 Hz to 10 kHz), the optical power must be able to be increased to 1 MW. The laser itself produces 700 watts continuously, but the laser beams pass back and forth between the mirrors thousands of times.

In addition, wavefront distortions and scattering of the light field in higher spatial modes must be minimized. The lasers must have extremely low amplitude and phase noise, as well as very stable pointing accuracy.

Both the LIGO and Virgo gravity detectors use ultra-pure fused silica as the substrate for their mirrors. These mirrors operate at ambient temperature, but the Einstein Telescope will have mirrors that operate at cryogenic temperatures (10K to 20K). For this reason, single-crystal silicon or sapphire mirrors must be used. The final choice depends heavily on the mechanical noise generated by the reflective mirror coatings applied to the substrates.

In addition, the noise on the mirrors also depends on the thermal noise caused by the lasers. Even though the mirrors are exceptionally reflective, they are still at risk of heating up due to the high power of the laser beams. This is even more the case when the laser light is concentrated on a small surface. Therefore, the laser beam is made relatively wide, up to a diameter of about 10 cm.

To support this wide laser beam, the (round) mirrors must have a diameter of 45 cm to 50 cm to minimize the diffraction loss on the outside of the mirror. In addition, the mirrors are made very thick, up to 40 cm or even 60 cm. This makes the mirrors very heavy (more than 200 kg), so that the optical pressure of the lasers makes the mirrors move as little as possible.

These exceptionally heavy mirrors must then be polished to a flatness of ±2 nm and an RMS roughness of less than 0.1 nm. These are purities that go down to the atomic level. An additional complexity is that some mirrors must be polished concavely with an exceptionally long focal length of five kilometers, so that the laser light is always re-centered.

This high precision is achieved by electropolishing , ion beam figuring and corrective ( multilayer ) coatings. The reflectivity of these mirrors is 99.999% and the absorption per centimeter is lower than 1 ppm . These mirrors are suspended on four fused silicon fibers with a diameter varying from a few hundred µm to a few millimeters.

Existing gravitational wave detectors operate at a continuous wave laser wavelength of 1064nm, using highly stable solid-state (NPRO) Nd:YAG lasers as a power source. However, the silicon mirrors of the Einstein Telescope are not transparent to 1064nm. Any laser light that does strike the mirror coatings would be absorbed instead of passing through the mirror and being absorbed into the vacuum towers.

This could lead to unwanted heating of the mirrors, so alternative wavelengths of 1550nm or 2090nm must be used. These longer wavelengths bring the laser frequencies closer to the infrared, to which the silicon or sapphire used is transparent.

This means that new ultra-pure lasers have to be designed. The laser light is amplified to about 700W and spatially filtered to have a very pure Gaussian profile. A series of high bandwidth control loops and stabilization circuits couple the laser frequency to the kilometer long resonators of the interferometer, so that ultimately a frequency stability of 1µHz/Hz-1/2 can be achieved.

One of the unique features of the Einstein Telescope is the use of cryogenically cooled mirrors to significantly improve the detection rate for low gravitational wave frequencies (below 20 Hz). Cryogenic operation reduces thermal noise, particularly in the mirror coatings and suspensions.

Monocrystalline silicon, a well-known material in the semiconductor industry, has unique properties. In addition to its excellent mechanical quality, silicon has a negligible thermal expansion coefficient at temperatures around 120 K and below 20 K. More importantly, silicon is an excellent thermal conductor at low temperatures. Thermal deformations of the mirror will be significantly reduced compared to fused silica mirrors.

Switching from fused silica to crystalline silicon requires a different laser wavelength so that the bulk material of the mirror remains transparent. As mentioned above, this can be achieved at wavelengths of 1550 nm and higher. The wavelength of around 2090 nm is preferred because of the optical coating. New lasers have to be developed, taking into account strict constraints on, among other things, power stability and directionality.

In addition, many new sensors need to be developed. More precisely, sensors with low noise, high efficiency and a large surface are needed for monitoring the beam and measuring the wavefronts.

As for the crystalline silicon substrate, the bulk absorption of the laser light must be kept below about 5 ppm /cm. The laser light must not heat up the substrate in order to keep the mirrors at a stable cryogenic temperature, more precisely for operation at 20 K. Since residual free carriers dominate the absorption at the target wavelengths of 1.5 to 2.0 µm, high-ohmic substrates (better than 10 kΩ cm) are required. Although float -zone drawn silicon can achieve the required high ohm value, it is technically limited to smaller diameters. Growth processes that achieve large substrate dimensions with very few impurities need to be further investigated, such as magnetically assisted Czochralsky processes.

The polishing specifications of the silicon will be similar to the very demanding requirements achieved with fused silica for the LIGO and Virgo observatories. Polishing processes that can achieve the same specifications on silicon substrates need to be investigated and their quality measured with suitable metrology, including parameters such as distortion of the transmitting wavefront and absorption.

Considering the different wavelength, and because of the cryogenic temperature conditions, completely new multilayer coatings have to be developed. This is probably one of the biggest challenges regarding the mirrors, and it is an active research area in the worldwide gravitational wave community.

Finally, the mirrors at the end of the array of vibration dampers are expected to be suspended on crystalline silicon ‘rods’ only a few millimetres thick. The advantage of using crystalline silicon rods is that they still have excellent thermal conductivity at cryogenic temperatures. In addition, there is a smaller mechanical loss (and therefore lower mechanical noise) if the same material can be used for the suspension as for the mirrors themselves.

It will be a major challenge to obtain such rods with lengths of 1 to 2 meters and with excellent mechanical quality (scratch-free surfaces) to reliably carry the mirror load of 100-200 kg. The rods will operate at about 20 percent of their breaking point when carrying the heavy mirrors. This is done to keep the natural frequency of the rods as high as possible and away from the frequency range of interest for the ET. Any impurities in the rods are a serious risk of unwanted fractures.

A list of all mirrors needed for gravitational wave measurements and other experiments and detectors has been compiled and is publicly available. This list contains mirrors of different sizes, materials and qualities. In addition to a large number of smaller mirrors, a total of about 140 high-quality silicon mirrors with masses between about 100 and 300 kg will be needed in the coming years. The first mirrors will be tested in the ETpathfinder prototype. It is expected that from about 2030 onwards many mirrors will be needed for the Einstein Telescope itself.

In particular, the large mirrors require new procedures for manufacturing, validation and testing. We are looking for companies that are willing to invest in the development of such substrates and mirrors. There is a good chance that the first company (or companies) that meets the design specifications will also be the one that receives the orders. The orders will not only come from the Einstein Telescope , but possibly also from other gravitational detectors, such as the Cosmic Explorer in the US.

Given the overlap between our specifications (mirror surface features) and key noise sources (mirror thermal deformations) and those in the nanolithography industry, we also anticipate interest from that sector.