Interferometer design of the KAGRA gravitational wave detector

KAGRA is a cryogenic interferometric gravitational-wave detector being constructed at the underground site of Kamioka mine in Gifu prefecture, Japan. We performed an optimization of the interferomter design, to achieve the best sensitivity and a stable operation, with boundary conditions of classical noises and under various practical constraints, such as the size of the tunnel or the mirror cooling capacity. Length and alignment sensing schemes for the robust control of the interferometer are developed. In this paper, we describe the detailed design of the KAGRA interferometer as well as the reasoning behind design choices.

Figure 1

Schematic of the KAGRA interferometer. Names of the mirrors as well as the signal detection ports are shown.

Figure 2

Estimated noises of KAGRA. The total noise is the quadratic sum of all the noises.

Figure 3

Inspiral range with different finesse and signal-recycling mirror reflectivity.

Figure 4

Resonant conditions of the carrier and the RF sidebands. Each field is represented by lines of a distinct style. A field is resonant in the parts of the interferometer in which the corresponding lines are drawn.

Figure 5

Ratio of the RF sideband reflection phases by the arm cavities. We want to set it to $8/3$, which is indicated by the green line.

Figure 6

Loop noise couplings.

Figure 7

Loop noise couplings with feed-forward.

Figure 8

HOM power in the arm cavity relative to the TEM00 power. The mode number is $n+m$ for TEMnm modes.

Figure 9

The maximum HOM power ratio in the arm cavity as a function of the test mass ROC error. The ROC is swept by $\pm 1\%$ around the nominal value.

Figure 10

Positions of the RF SBs and the HOMs in an FSR of the arm cavities. The colorful sharp peaks represent the resonant curves of the HOMs. The mode numbers are printed at the top of each resonance. The vertical lines are the positions of the RF SBs. The “$+$” and “$-$” signs indicate upper and lower sidebands, respectively.

Figure 11

Higher-order mode resonance map of the PRC.

Figure 12

Higher-order mode resonance scan of the SRC for $({\eta }_{\mathrm{p}},{\eta }_{\mathrm{s}})=(16.5°,17.5°)$.

Figure 13

Higher-order mode resonance scan of the SRC for $({\eta }_{\mathrm{p}},{\eta }_{\mathrm{s}})=(5.5°,8°)$.

Figure 14

Schematic view of the folded power-recycling cavity. The BS is omitted in this figure and the ITMs are combined into a single effective ITM.

Figure 15

The mode mismatch and the Gouy-phase error as functions of the ROC errors of the PR2 and the PR3.

Figure 16

The mode mismatch and the Gouy-phase error as functions of $l_{\mathrm{p}2}$. The curves show when ROC errors of 10 mm are added to the PR2 and the PR3. The signs of the introduced errors are indicated in the legend.

Figure 17

Contributions of WFS shot noises to the strain sensitivity. The PRC and the SRC consist of three mirrors each. Therefore, the curves labeled PRC and SRC are the quadratic sums of the noises from the three mirrors.

Figure 18

Contributions of WFS shot noises to the strain sensitivity when the SR2 is not controlled by WFS.