Dual-Recycled Michelson

4.4 Experimental Process

4.4.2 Dual-Recycled Michelson

The phases for <I>+ and

c/J-

need to be changed when going from the Fabry-Perot Michelson to RSE. Finding these new phase settings is most easily done with the dual-recycled Michelson (DRM), in which the arms are internally blocked. Also, locking the dual-recycled Michelson gives a measure for the power levels expected in the various sidebands for the RSE experiment, which are measured by the optical spectrum analyzer at the power and signal cavity pickoffs. Last, measurement of the 3 x 3 matrix of discriminants is a useful characterization of the interferometer at this point, since the coupling of the minor degrees of freedom can more clearly be determined without the overwhelming contribution from the arm cavity signals (most notably in the 81 MHz demodulation signal ports).

The procedure to acquire lock begins with the arm cavities internally blocked, and the power and signal mirror grossly misaligned. The Michelson,

c/J-,

is aligned and locked with very low gain, and the SM1 mirror is swept through several fringes as the

PRM is manually brought into alignment. Low gain means the servo bandwidth is also low, and if the cavity is swept through resonance over a time scale faster than the inverse of the servo bandwidth, the

<P-

servo remains relatively unperturbed by the power recycling cavity resonance. Both the camera and the DC power are monitored at the pickoff in the power recycling cavity. As the PRM is brought into alignment, the trace of the DC power on the oscilloscope shows the resonance peaks, and the modes resonating in the cavity clearly flash in the camera output. Good alignment is achieved when the peaks in the oscilloscope trace are clean, and the mode flashing in the camera is centered and has a good mode shape (no lobes).

Three signal ports are monitored in this sweep: the reflected 81 MHz, and both the reflected and pickoff 54 MHz. The phases of the 54 MHz signals are varied slightly to give the nice, bipolar signals expected from this sweep, and offsets are adjusted slightly to give the appropriate zero crossings. Ideally, the 54 MHz demodulation phases wouldn't have to be changed at all from the setting obtained in the Fabry- Perot Michelson; however, imperfect lengths of the power and signal cavities, even on the order of 1 em, cause the zero-signal demodulation phase to shift by a few degrees from their settings in the FPM. The shifts in demodulation phase, as well as in offsets, were usually quite small.

The power recycled Michelson is then locked. ¢+ is initially locked using the reflected 81 MHz signal port, while

<P-

uses the pickoff 81 MHz, both with fairly low gain as before. The signal cavity slow piezo, SM6, is swept over several fringes as the signal cavity mirror is manually brought into alignment. Alignment is primarily done by looking at the mode shape seen by the camera at the signal cavity pickoff, and aligning for best mode shape. Looking at the various DC powers, for example at the dark port, is only mildly helpful due to the stronger effect of the signal cavity resonance on the ¢+ and

<P-

degrees of freedom. The pickoff 54 MHz signal is likewise monitored during the sweep, and its shape is also seen to be consistent with what is expected.

Lock is acquired in somewhat of a bootstrapping method. The power and signal cavity servos, using the reflected 54 and pickoff 54 signal ports respectively, are turned

on with minimal gain and using the fast path only, while the Michelson servo is turned off. The Michelson itself is tuned to a carrier dark fringe by hand using the bias of the slow HV PZT drivers. The optical spectrum analyzer output from the signal cavity pickoff (SEC OSA) clearly shows the carrier dark fringe. The power and signal cavities are brought into lock by hand, by tuning the slow power and signal mirrors, again using the bias knob of the slow HV PZT drivers. The guide for finding the right lock is the output of the SEC OSA. It's expected from modeling that no carrier should be seen in the SEC OSA, and the lower RF sideband should be around 5 x larger than the upper RF sideband. When this condition is met, the ¢+ and c/Js servos are turned all the way on, that is the slow path is engaged with its integrator and the overall gain is increased. The Michelson signal port, however, has a large offset, which is expected due to improper demodulation phase. While maintaining the dark fringe condition for the Michelson by hand, the demodulation phase for the pickoff 81 signal port is varied until its output is at 0 volts. The

c/J-

servo is then turned on, and the demodulation phase is fine tuned to best enforce the carrier darkness at the dark port as measured by the SEC OSA. The relative strengths of the carrier and the 81 MHz sidebands in the two OSA outputs is noted and compared with the model in order to give confidence that the interferometer is locked in the right place. The results are tabulated in Table 4.5. This particular metric, however, is only modestly reliable. The OSA response is quite sensitive to the alignment of the beam into it. Misalignment of the cavity, and the effect that has on the mode structure and alignment of every individual RF sideband would conspire to make the uncertainties in this measurement quite difficult to analyze.

The last task before going on to lock the RSE interferometer is to set the phase for the <I>+ signal, which is the reflected 81 signal port. It's assumed that setting the phase of the reflected 81 signal port doesn't change in going from the dual-recycled Michelson to RSE, and so this is simply done by changing the phase such that the offset voltage in this signal port is 0. The <I>_ phase doesn't need to be changed, since there is no offset generated for the dark port signals at 81 MHz due to the lack of carrier.

II

^Pickoff

I

^Signal

I

-81 MHz 1 1

1 1

-27 MHz 1.1 0.02 1.3 0.01

Carrier 3.0 0

2.9 0 +81 MHz 2.9 0.16

3.6 0.17

Table 4.5: Powers in dual-recycled Michelson as measured by the OSA. Experimental numbers are in normal text, Twiddle numbers are in bold text. This is a relative measurement, since the OSA output is not reliably calibrated. Hence, all modeled and measured powers are scaled to the -81 MHz RF sideband.

The following table summarizes the measured change in demodulation phase pre- dicted by the Twiddle model between the DRM and FPM experiments. Given the un-

I

Signal Port

II

Measured phase change

I

Model prediction

I

Reflected 81 MHz (~+) +18.5° +140

Pickoff 81 MHz (¢_) ^{-720 -730}

Reflected 54 MHz ( ¢+) ^-50

oo

Pickoff 54 MHz (<l>s) +20 -40

Table 4.6: Demodulation phase changes for the dual-recycled Michelson experiment, relative to the Fabry-Perot Michelson experiment.

certainties in proper demodulation phase setting of roughly 10° due to cross-coupling offsets, these numbers agree with the model quite well.

4.4.3 RSE

Once the PRM and DRM have been locked, some confidence has been gained that the interferometer is aligned, demodulation phases are set, and that servo gains are somewhat appropriate for locking. Certainly, the gain for the ~ + and ~ _ servos in RSE will increase compared to the FPM due to power recycling, and so appropriate adjustments are made to allow for this.

Lock acquisition occurred by turning on the fast path feedback for all servos except

for the

c/J-

servo, hand tuning the

cp_

for a carrier dark fringe, and hand tuning the¢+

and

c/Js

slow piezos until the RF sideband powers in the SEC OSA looked about right.

Beyond this, there was nothing particularly rigorous about the procedure. Typically, some cavity, or the Michelson, would be slowly tuned using the slow HV PZT bias until the interferometer locked. Usually lock would be acquired in a few minutes, which was noted by seeing the power in the arms increase simultaneously. All slow paths, integrators, and the boosts used would be quickly turned on (except for the

cp_

servo, still), and then the

cp_

slow HV PZT bias would be carefully tuned to make sure the

cp_

servo was close to its lock point before it would be turned on as well.

Lock was usually robust, once acquired. Unless disturbed by a measurement, a particularly vigorous door slamming, or by construction which was occurring inside or outside the building, the interferometer would remain locked for anywhere from 5 minutes to an hour.

Offsets

Without any offsets added to signals, it was clear that the interferometer was not locked in the same place as in the dual-recycled Michelson. This was clear due to the difference in the RF sideband powers in the power and signal cavity compared to the DRM experiment, as measured by the OSA at these pickoffs. During lock acquisition it could be seen that the same powers for the RF sidebands as in the DRM could be attained using a modest offset (about 15 mV) added to the pickoff 54 MHz

(cps)

signal port. The source of this offset was never completely understood. Knowledge of the cross-coupling of the RF electronics, along with the fact that there would now be a significant amount of power at 81 MHz in the pickoff signal port, conspired to make this scenario not inconsistent. Even though the RF and LO inputs for the 54 MHz mixers were fairly well band-passed, there was still some power at 81 MHz present in each. It's not known if this alone would have been enough to generate this amount of offset.

Power

The RF sideband powers in the power and signal cavities were consistent with what they should be, compared to the DRM, where there was good confidence that that sub-configuration was properly locked. The carrier power, on the other hand, typically seemed to be about 15-20% low. The "dither/2!" test was applied to test whether the arms were locked at the center of their fringes. This involved driving the piezos at some frequency above unity gain and looking at the power fluctuations on an oscilloscope. If the cavity is locked in the center of the fringe, the fluctuations will occur at twice the driving frequency, with equal excursions to each side of the fringe.

In general, the arms were locked fairly close to the fringe center.

Attempts at increasing the power by alignment weren't successful, mostly because the interferometer seemed to be very sensitive to alignment, and adjustments too far one way or another to the alignment piezos tended to cause the interferometer to lose lock. The reason for this isn't well understood, since other disturbances (for example, the dither/2! test or transfer function measurements) were seemingly much more violent.

Excess power at the reflected photodiode was measured, so it was accepted that there was some combination of mode-matching and misalignment which contributed to the decrease in the expected carrier power in the interferometer. This is subse- quently modeled as a coupling factor less than unity for the carrier.