Sapphire mirror for the KAGRA gravitational wave detector

KAGRA, the Japanese interferometric gravitational wave detector currently under construction, will employ sapphire test masses for its cryogenic operation. Sapphire has an advantage in its higher thermal conductivity near the operating temperature 20 K compared to fused silica used in other gravitational wave detectors, but there are some uncertain properties for the application such as hardness, optical absorption, and birefringence. We introduce an optical design of the test masses and our recent R&D results to address the above properties. Test polish of sapphire substrate has especially proven that specifications on the surface are sufficiently met. Recent measurements of absorption and inhomogeneity of the refractive index of the sapphire substrate indicate that the other properties are also acceptable to use sapphire crystal as test masses.

Figure 1

Field propagation between two mirrors with aberration in a cavity. From $z=z^{\prime }$ to $z=z^{\prime }+\mathrm{\Delta }z$, fast Fourier transform (FFT) technique is used, and phase change due to the arm length $\mathrm{\Delta }z$, curvature, and surface aberration is taken care of later.

Figure 2

Distribution of loss calculated by SIS due to randomly generated surfaces’ aberration with a certain rms. In each rms, 100 pairs of surfaces were generated to make a Fabry-Perot cavity for the calculation.

Figure 3

Accumulated fraction of loss for each rms in Fig. 2. This shows what fraction of the population is below a certain loss. For $\mathrm{rms}=0.5\mathrm{nm}$, 98% of the calculated results are below 50 ppm.

Figure 4

Phase map of figure error (low spatial frequency) measured at Zygo EPO (200 mm sapphire). The aperture size is 180 mm here. rms is 0.48 nm over the diameter and 0.24 nm over 140 mm. Figure measurements done at Caltech using a different Fizeau interferometer showed almost the same results.

Figure 5

Phase maps of HSF error measured at Zygo EPO (100 mm sapphire) using PMM. The left is the result by 2.5x while the right is one by 50x. The size of the map shown here is $4.9\mathrm{mm}\times 4.9\mathrm{mm}$ (left) and $0.5\mathrm{mm}\times 0.5\mathrm{mm}$ (right), respectively.

Figure 6

PSD plot of both 200 mm and 100 mm sapphire substrates. The Zygo report for 200 mm substrate is a composite plot of three measurements, figure, PMM2.5x, and PMM50x, while 100 mm substrate is one from only two PMM measurements only. For low spatial frequency part (figure), two independent measurements done at Zygo and Caltech agree fairly well. For comparison, fused silica data is in the plot, which is one of advanced LIGO’s test mass data. We did not find disadvantages in terms of PSD. A model that gives 0.27 nm in rms when integrating from $0.01{\mathrm{mm}}^{-1}$ to $1{\mathrm{mm}}^{-1}$ is above our results.

Figure 7

Absorption of 100 mm sapphire substrate in ppm/cm. The aperture size is 50 mm and the interaction point is 2 mm from the surface. There is a line where absorption is higher than the other regions.

Figure 8

Distribution of absorption in FIG. 7. The mean is $43.4\mathrm{ppm}/\mathrm{cm}$ and the standard deviation is $8.0\mathrm{ppm}/\mathrm{cm}$.

Figure 9

Phase map of homogeneity of refractive index. The unit is nm since data is product $dn\times \text{thickness}$. We measured three wavefront data, side 1, side 2, and side 2 through side 1. The last one contains information of refractive index of the bulk, and carefully subtracted information of both side 1 and side 2. Then, terms up to power term were subtracted to bring the inhomogeneity to light. This is what will be left even if we have a spherical backsurface profile to compensate the inhomogeneity and the level is about $8\times {10}^{-8}$ after dividing by the thickness.