LOCK ACQUISITION AND NOISE PERFORMANCE
3.1 Fabry-Pérot arm cavities
3.1.1 Length control
This is the simplest interferometric configuration that involves an optical cavity (c.f.
locking a simple Michelson interferometer which doesn’t involve any cavities). It is also the first step in locking more complex interferometer configurations like a
PRFPMI (Section3.4) - the cavity alignment is optimized using the dither alignment technique [28]. The PRM and SRM are misaligned such that they don’t form optical cavities that interact with the rest of the interferometer. Since the beam still has to pass through these optics, the power incident on the beamsplitter and exiting the AS port of the interferometer are attenuated by the PRM and SRM transmissivities of 5.637% and 9.903% respectively1.
The optical gains for PDH sensing of the arm cavity lengths are consequently reduced - however, the SNR is still sufficient to be able to suppress the residual relative length fluctuations between the PSL frequency and arm cavity’s resonant frequency to well below the cavity linewidth of ≈ 9 kHz. At the 40m, individual photodiodes are available that monitor the reflected light from each arm cavity - these are called POX11 and POY112for the X- and Y-arms respectively. Other sensors can also be used for locking each arm cavity - for example, if only one cavity is to be controlled, a photodiode at the AS port can serve as the PDH sensor once the other arm cavity is completely misaligned (to avoid contamination by signal from the unwanted arm cavity) - this is the scheme used for the measurement described in Section 3.1.4.
There is negligible contamination (< −60 dB) due to Y-arm cavity motion in the POX sensor (and similarly for X-arm cavity motion in the POY sensor), such that a single arm cavity, or both at the same time, can be locked relatively easily. A feedback loop with≈100 Hz bandwidth is closed by filtering the PDH error signals from the POX / POY photodiode by a digital servo filter, and then actuating on the position of the suspended cavity optics (the choice is made to only actuate on the ETM for each arm cavity). The PDH error signal is only linear within the cavity linewidth, whereas the cavity length can be driven by seismic disturbances over multiple FSRs. To ensure that the feedback loop only actuates on the ETM position when the PDH error signal is in the linear regime, and hence a valid readback of the cavity length,triggeringlogic is employed. The transmitted power through the arm
1One could imagine a scheme where there would be some remote actuation capability that allows us to move optics in and out of the beam path from outside the vacuum envelope, without having to vent the system to atmospheric pressure. However, such a system would be extremely complex, and the reproducibility of optical configuration to the levels necessary for precision interferometry is questionable. The suspensions are also clamped down to the optical tables for the best vibration isolation - any remote actuation system would also need to have this capability.
2It is worth explaining the naming convention of the PDH error signals, since they come up frequently in this chapter. The general notation is the catenation of the port at which the photodiode is located, the demodulation frequency (in MHz), and signal quadrature, in that order. For example, REFL11 I refers to the quadrature signal in phase with theelectricalLO signal used for demodulation, derived from a photodiode at the REFL port of the interferometer, demodulating the photocurrent at 11 MHz. TheDC signalfrom the same photodiode would be called REFLDC.
100 101 102 103 104
Frequency [Hz]
10−16 10−15 10−14 10−13 10−12 10−11 10−10 10−9 10−8 10−7 10−6
Displacementnoise[m/√ Hz]
X arm
Suspension Thermal Seismic
Dark Noise Free-running In-loop residual Arm cavity linewidth
100 101 102 103 104
Frequency [Hz]
Y arm
Figure 3.1: Noise budget of the 40m arm cavity when locked to the PSL frequency.
Only a few noise sources are budgeted and this is not meant to be a comprehensive noise budget. The "Seismic" noise is only an estimate, which is why it appears to exceed the measured noise at certain frequencies. The residual relative length fluctuation between the arm cavity’s resonant frequency and the PSL frequency under closed loop feedback is suppressed to≈ 0.1% of the cavity linewidth.
cavity is monitored. When this exceeds some threshold value (empirically chosen to be 30% of the value when the arm cavity is on resonance and well aligned), we have high confidence that the PDH error signal is in the linear regime since the intracavity buildup is large. Additionally, normalizing the PDH error signal in reflection by the transmitted power has the effect of broadening the linear regime (see, for example, Figure 8.1 of [6]). For typical seismic velocities at the 40m, the cavity spends≈500µs in the linear regime, during which time sufficient force can be applied on the ETM to bring it under control. The linewidth of the arm cavity is large enough that the arm cavities can be locked within a few seconds even during the daytime, when the seismic activity levels (particularly in the anthropogenic band of 1−10 Hz) on the campus are elevated by a factor of a few in RMS compared to their levels after 10 PM local time.
The free-running displacement noise, and in-loop residual, are summarized in Fig- ure3.1.
Ground Passive
vibration isolation Suspended
optic
Vacuum chamber
Glass viewport
Quadrant photodiode
HeNe laser Pitch
motion
Figure 3.2: Conceptual diagram (not to scale) of an optical lever. Two angular degrees of freedom are controlled using the Oplev, namely "Pitch" (rotation about the y−axis) and "Yaw" (rotation about thez−axis). A segmented photodiode (split into 4 quadrants) is used to read out the position of the beam reflected from the suspended optic, which carries information about the angular motion of the optic.