Study of scattered light in the main arms of the Einstein Telescope gravitational wave detector

We present an estimation of the noise induced by scattered light inside the main arms of the Einstein Telescope (ET) gravitational wave detector. Both ET configurations for high- and low-frequency interferometers are considered, for which we propose baffle layouts. The level of scattered light and the ET laser beam clipping losses are intimately related to the baffle inner aperture. We discuss how this translates into minimum requirements on the vacuum pipe radius, a critical parameter in the ET design. The noise estimations are computed using analytical calculations complemented with numerical tools and depend on a number of baseline parameters we use as input in the calculations. We conclude that the scattered light noise can be maintained at acceptable levels such that it does not compromise the ET performance, provided some requirements are met.

Figure 1

Beam profile as a function of the position in the arm $z$ at different levels of clipping losses $L_c$ for (a) ET-HF and (b) ET-LF interferometers.

Figure 2

Simplified diagram showing the area of the ET main arm close to the mirror and the geometry and parameters determining the position and shape of the conical baffles (see body of the text).

Figure 3

Number of baffles per arm in ET-HF as a function of the baffle inner aperture for a vacuum tube radius of 0.5 or 0.6 m. The vertical lines indicate the corresponding inner apertures. Results are provided for both the minimal configuration and after taking into consideration baffles at the end of vacuum pipe sections with a baffle-to-baffle separation of 50 m (see body of the text).

Figure 4

Number of baffles per arm in ET-LF as a function of the baffle inner aperture for a vacuum tube radius of 0.5 m. The vertical line indicates the corresponding inner aperture. Results are provided for both the minimal configuration and after taking into consideration baffles at the end of vacuum pipe sections with a baffle-to-baffle separation of 50 m (see body of the text).

Figure 5

Left: position of the baffles along the $z$ axis. Right: the separation between consecutive baffles $\mathrm{\Delta }z$ for ET-HF (solid lines) and ET-LF (dashed lines) as a function of the baffle number. Results are provided for both the minimal configuration and after taking into consideration baffles at the end of vacuum pipe sections with a baffle-to-baffle separation of 50 m (see body of the text).

Figure 6

Left: one-dimensional PSDs of Virgo O3 and the projected values for O5 mirror maps. Vertical dashed lines correspond to the spatial frequencies associated with $z=L$ and $z=L/2$ having assumed $\lambda =1064\mathrm{nm}$. Middle: height of the deviation from a perfect surface in meters for the north end arm of Virgo during O3. Right: height of the deviation from a perfect surface in meters projected for O5.

Figure 7

Simulated BRDF, as computed using SIS and using the Virgo mirror maps foreseen for O5 as input, for both the ET-HF and ET-LF. The results are presented at a distance $z=10\mathrm{km}$ (solid lines) and $z=5\mathrm{km}$ (dashed lines) from the input mirror. The latter corresponds to the middle of the vacuum cavity.

Figure 8

Original seismic noise for the Euregio and Sardegna sites and the up-converted ones for $\lambda =1064$ and $\lambda =1550\mathrm{nm}$.

Figure 9

Scheme showing the FP cavity simulated and the power distribution at the FP mirrors and at the position of a baffle at $z=8000\mathrm{m}$.

Figure 10

Stray light noise due to diffraction effects as a function of frequency. The results for unserrated (red lines) and randomly serrated (blue lines) baffle edges are compared to the anticipated ET sensitivity (black lines) and the corresponding $1/10$ safety margin (dashed lines). The results are presented separately for (left) ET-HF and (right) ET-LF configurations. The seismic noise data from the Euregio site are used.

Figure 11

The $K^i$ values as a function of baffle position $z_i$ as computed for the different baffles at the far end of the tube, using the analytical BRDF and the numerical simulations (see body of the text) for (left) ET-HF and (right) ET-LF.

Figure 12

Stray light noise due to backscattering effects as a function of frequency. The results are computed using the seismic noise data from the Euregio (red lines) and the Sardegna (blue lines) sites and are compared to the anticipated ET sensitivity (black lines) and the corresponding $1/10$ safety margin (dashed lines). The results are presented separately for (left) ET-HF and (right) ET-LF configurations.

Figure 13

Stray light noise due to diffraction effects (cyan lines), backscattering effects (red lines), and the total noise (blue lines) as a function of frequency compared to the anticipated (top) ET-HF and (bottom) ET-LF sensitivity curves (black lines) and the corresponding $1/10$ safety margin (dashed lines). The results are computed using the seismic noise data from (left) the Sardegna site and (right) the Euregio site.

Figure 14

The $K^i$ values as a function of baffle position $z_i$ as computed for the different baffles at the far end of the tube using the analytical model of the BRDF and the numerical simulations (see body of the text) for ET-HF and a vacuum tube radius of 0.6 m.

Figure 15

Stray light noise due to diffraction effects (cyan lines), backscattering effects (red lines), and the total noise (blue lines) for 0.6 m vacuum tube radius as a function of frequency. The results are compared to the anticipated ET-HF sensitivity curve (black line) and the corresponding $1/10$ safety margin (dashed line). The results are computed using the seismic noise data from the Euregio site.

Figure 16

The $K^i$ values as a function of baffle position $z_i$ as computed for the different baffles at the far end of the tube using numerical simulations (see body of the text) for ET-LF and considering larger mirrors.

Figure 17

Stray light noise due to diffraction effects (cyan lines), backscattering effects (red lines), and the total noise (blue lines) for a larger mirror size with 31 cm radius as a function of frequency. The results are compared to the anticipated ET-LF sensitivity curve (black line) and the corresponding $1/10$ safety margin (dashed line). The results are computed using the seismic noise data from the Euregio site.