The Future: It’s easy being green

The primary difference between the scheme proposed below and the scheme described in8.6involves replacing step A with a version which is deterministic in nature.

The 40 m experience has demonstrated that it is not difficult to lock a 3 DOF system such as the DRMI, provided there is an appropriate selection of signals and the recycling cavities are of sufficiently low finesse, which is the case for the current Advanced LIGO design. In order to have an essentially deterministic locking scheme for Advanced LIGO, it should thus be sufficient to improve the locking time of the arm cavities, which can be accomplished with the addition of some auxiliary hardware dedicated to lock acquisition.

The basic idea is to quadruple the number of laser fields. For a primary laser (i.e., the one that will be used during interferometer operation) operating at 1064 nm, we would add

• A laser field frequency doubled from the main (PSL) laser (so at 532 nm—green).

• Two additional 532 nm lasers at the transmitted ports of the two arm cavities.

• Dichroic coatings for the ETMs (T _∼0.9 for 532 nm).

• Dichroic coatings for the ITMs (T ∼0.99 for 532 nm).

The benefits of this additional hardware include (more details in the following)

• Multiple lasers allow truly independent sensing of the two arm cavities.

• Independent velocity damping of arm cavities can be done when they are not resonant for the main carrier field.

• Green light + wedged optics allows excellent isolation of the arm cavities from other degrees of freedom, and helps to isolate the arms from each other.

With these benefits, the basic plan would be to lock the arms first using the green laser, then lock the short degrees of freedom in the same manner as is already done at the 40 m.

8.7.1.1 Envisioned lock acquisition procedure

At each end station, the green laser will be phase modulated, and the field injected into the arm cavity through the ETM. With the ITM having a highly reflective coating for green light, this system now forms a low-finesse, overcoupled cavity, and a standard PDH based length sensing and control scheme can be easily applied, with the feedback to the green laser frequency, which must be a fast actuator (a PZT). This fast actuator combined with a low-finesse cavity will make for tremendously simple lock acquisition. The feedback loop should only be limited by the range of the frequency actuator, which should be at least several tens of MHz. Such a range corresponds to many free-spectral ranges of the arm cavity.

Now the green laser is resonant in the arm cavity; the transmitted field (exiting the ITM toward the BS) can be picked off and directed to a photodetector, where it can be heterodyned with the frequency-doubled PSL light. The beat frequency is then exactly twice the difference between the resonant frequency of the arm cavity and the optical frequency of the PSL; this is exactly what we want for lock acquisition. The linear range of this signal will be limited only by the bandwidth of the photodetector used for heterodyning. The linear range, expressed as the number of wavelengthsn, should be the PD bandwidth (∆f) divided by the cavity free-spectral rangeνF SR, which of course

is much larger than the linear range of a PDH signalλ/4_F:

n= ∆f

νF SR

1

4F, (8.8)

where we are consideringF the finesse for the PSL (λ= 1064 nm) light.

With this broad linear signal, the arm length can simply be velocity damped with gentle length actuation until it is no longer fluctuating with respect to the PSL light. Once the arm is under length control, it can be held stably at a point near the carrier resonance. With the arm lengths held such that they fluctuate much less than a fringe, they will not disturb the signals for the short DOFs (MICH, PRCL, SRCL), control of which can be easily acquired using the techniques described in section8.6.

Once control of the short DOFs has been achieved, the full IFO is under control, and techniques similar to those described in Step B and onward in section 8.6 can be used to bring the IFO to the operating point. Alternatively, it may also be possible to use the green light sensing chain to control the arm cavities independently while the offset is reduced; this might be possible if the initial

lock stage is done at low laser power, thus avoiding significant radiation pressure effects. Radiation pressure effects can also be avoided by appropriately locking the SRCL away from its own nominal operating point (detuning it), and adjusting this offset in concert with the arm offsets to eliminate any optical spring in the DARM degree of freedom. Such a procedure is conceivable as the sensing scheme for the SRCL in Advanced LIGO has been designed to allow the SRC to be operable at multiple detunings, and to be able to switch between these detunings in lock.

8.7.1.2 Advantages of this technique

With an understanding of the technique, the advantages relative to the procedure in Step A of8.6

become apparent:

• Using green light: breaks the degeneracy of cavity finesse for lock acquisition and GW detection; highly reflective ITMs isolates arm cavities from flashing in the short DOFs; highly reflective ITM plus the optic wedge angle serves to isolate arm cavities from flashing in the other arm cavity.

• A secondary laser: allows the creation of a length signal with a broad linear range. This would permit effective velocity damping of the cavity, eliminating the need for actuators that can acquire lock before the cavity has swept through a single fringe. With this the concerns outlined in section 8.2can be sidestepped.

• Two secondary lasers: allow the two arms to be locked independently, both with a frequency control technique followed by velocity damping. Moreover, independent signals for the two arms allows the choice of locking to any point in the two dimensional CARM + DARM configuration space.

8.7.1.3 Alternative Technique

It is possible that this technique will be adversely affected by the green light transmitted through the ITM resonating in the short degrees of freedom. In that case, nearly the same technique can be used, by installing optical fibers that can transmit the main carrier field to the end stations. The lasers at the end station are phase locked to the PSL light, then frequency doubled. The resulting green light can then be locked to the arm cavity in the same way, with the error point of the phase-locked loop now taking the place of the frequency actuator. The feedback to the phase-locked loop error point now is the sensing signal for the arm cavity length; it can be used in the same way to velocity damp the arm cavity. In this case, all the sensing for the arm takes place at the end station, and so the high reflectivity (for green light) of the ITM will effectively isolate the arm from the short degrees of freedom. The main drawback of this scheme is the need for a 4 km optical fiber, which

can introduce substantial noise. The fiber system would thus require a setup to cancel phase noise induced by the fiber, such as the system devised in [95].

8.8

Discussion

The lock acquisition development work at the 40 m will provide significant advantages to Advanced LIGO commissioning, not only from the training of personnel, but also from the lessons learned and the techniques developed. In this chapter we have described a lock acquisition technique which differs in approach from that taken in initial LIGO, while extending it to another dimension: signal recycling.

This technique, rather than going directly from the uncontrolled state to the operating point, goes from the uncontrolled state to an acquisition point where the signals are naturally mostly diagonal, and then in a controlled process migrates to the operating point.

We have also described the steps necessary to make this technique directly applicable to Advanced LIGO, which will require additional hardware in order to reach the acquisition point. The first versions of this additional hardware will be commissioned at the 40 m in the coming year.

Chapter 9

Measurement of Laser and

Oscillator Noise Couplings in

RF/DC Readout

An experiment was performed at the Caltech 40 m prototype interferometer to study the relative merits of RF/DC readout, to gain experience with the DC readout technique, and to validate the modeling tools used in interferometer design studies. The work involved design of the output optical system (already described in chapter5), commissioning the system, and making calibrated coupling measurements for laser and oscillator noise.

9.1

DC Readout Experiment

Two sets of measurements are presented. One set of measurements, in section 9.2, were taken with the interferometer in a power-recycled Fabry-P´erot Michelson configuration. This can be done simply by radically mis-aligning the signal recycling mirror, which then just behaves as a lossy element rather than a mirror. This was done to study DC readout in preparation for Enhanced LIGO.

The second set of measurements, in section9.3, were taken with the interferometer in a detuned RSE configuration. This was to study one potential operating mode of Advanced LIGO. These measurements are all in the anti-spring configuration, because it is easier to lock (cf. section8.6.2). The purpose of the experiment is not necessarily to demonstrate that DC is unequivocally better than RF readout; what we are doing is validating our simulation and theory, and to search for unanticipated, significant problems with the technique which is planned for Advanced LIGO.

The laser amplitude noise measurements will show that DC readout appears to be worse than RF readout; this is actually the case for the 40 m with its relatively short arms. Extrapolating to a LIGO interferometer, which is 100 times longer, DC readout will have significant advantages due to the increased storage time of the carrier light in the interferometer.

The measurements below_∼100 Hz are typically not indicative of the real coupling; there is too much noise in the interferometer to get a solid measurement of the couplings at these low frequencies. In addition, some of the measurements around 1.5 and 4 kHz are similarly untrustworthy due to suspected mechanical resonances at those frequencies which create excess noise in DARM. This is unfortunate, as the RSE peak is near that frequency, and it would be good to have a clear understanding of how noises actually couple in that frequency region.