Control of the Gravitational Wave Interferometric Detector Advanced Virgo by Julia Casanueva Diaz

Author:Julia Casanueva Diaz
Language: eng
Format: epub, pdf
ISBN: 9783319960142
Publisher: Springer International Publishing

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6.2.2 PRC Stability Versus Alignment: 131 MHz

As it was anticipated in the introduction the Power Recycling cavity needs a special consideration due to its optical configuration. The conditions for an optical cavity to be stable were explained in Sect. 5.​3.​3. The PRC of Advanced Virgo is very close to the limit of stability, in particular , which is equivalent to mrad. This situation is worsened by the mirror imperfections since they scatter light from the fundamental mode to the HOMs.

The consequence of being so close to the instability region is that the frequencies of the HOMs are very close to the fundamental mode. In this case, in the presence of HOMs (due to a misalignment or to a mismatch for example) they will couple very strongly to the optical cavity, diminishing the power in the fundamental mode. Figure 6.8 shows the relationship between the HOM separation for the PRC and the Gouy phase of the cavity. On it they are marked the Advanced Virgo configuration as well as the Virgo+ one. The separation decreases with the Gouy phase, until becoming a degenerate cavity when reaching instability.

The frequency separation between HOMs has been calculated from Eq. 5.​39, and for the PRC is 11.3 kHz. When compared to its linewidth which is 210 kHz it is obvious that the coupling is going to be very important. Figure 6.9 shows the power distribution between the fundamental mode and the different HOMs on the B4 photodiode for a scan of the PRC length at the working point. Only the first four orders are shown, but it is clear that the coupling of the HOMs inside the interferometer is very important.

Fig. 6.8HOM separation in the PRC as a function of its Gouy phase. The Advanced Virgo and Virgo+ PRC configurations are shown for comparison

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