Advanced LIGO is a next-generation interferometer, with upgraded subsystems relative to Initial and Enhanced LIGO.
Dual-recycled configuration. The interferometer will be a power and signal-recycled Michelson
interferometer with Fabry-P´erot arms, operable in multiple signal cavity detunings (including a zero detuning).
Seismic isolation. An active system with ground motion sensors, feedback and feedforward noise reduction, and hydraulic actuators both external to the vacuum envelope and within the vacuum envelope, will isolate the optical tables housing the core optics.
Multiple pendulum suspensions. The core optics of the interferometer will be suspended from a set of triple and quadruple pendulum systems, providing additional seismic isolation. These pendulums will be actively sensed and locally damped in all degrees of freedom. They will also provide a capability for global feedback control.
High power laser. A 180 watt CW 1064 nm laser will provide the single frequency light source for the interferometer, under stringent requirements for frequency and amplitude stability.
Each of these subsystems will be integral to the success of Advanced LIGO in achieving the designed sensitivity, and each subsystem will represent the state of the art. Table 3.2 shows the Advanced LIGO optical parameters as of this writing, along with several parameters from a previous reference design. These parameters were changed in part due to lessons learned during the work described in this thesis.
Parameter Value Previous Reference Design
TIT M 0.014 0.005
TET M 5 ppm 10 ppm
TP RM 0.03 0.07
TSRM 0.20 0.07
ROCIT M 1934 m ROCET M 2245 m L (ARM) 3994.5 m
PRCL 57.656 m 8.4 m
SRCL 56.008 m 9.1 m
Schnupp asy 0.05 m .42 m
f1 9.1 MHz 9 MHz
f2 45.5 MHz 180 MHz
PRC ΦGuoy 25◦ SRC ΦGuoy 19◦
Table 3.2: The primary Advanced LIGO optical parameters.
Figure3.15shows the projected sensitivity for several operating modes of Advanced LIGO; these various modes can be achieved by changing the detuning phase and the input power. The projected noise levels due to seismic noise and mirror coating thermal noise can be inferred from this plot: the most sensitive curves below 10 Hz are limited by seismic noise, and the most sensitive curve from 30 Hz to 300 Hz is limited by thermal noise. The variation in sensitivity, which allows optimization for specific astrophysical sources, is the primary motivation for adding a signal recycling mirror.
48
101 102 103
10−24 10−23 10−22
Frequency (Hz) Strain noise (Hz−1/2 )
0) NO SRM
1a) Zero Detune, low power 1b) Zero Detune, high power 2) NS−NS Opt.
3) BH−BH 20° detune 4) BH−BH Opt.
5) High Freq
Figure 1: Proposed modes of operation for the Advanced LIGO interferometers. See text for description of the modes.
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Figure 3.15: Projected sensitivity for possible operating modes of Advanced LIGO. The blue curve shows the sensitivity with no SRM. The other curves can all be achieved by changing a combination of the detuning phase and the input power. All the curves are limited by quantum (shot) noise at high frequency. The best low frequency sensitivity curve (zero detune, low power) is limited by seismic noise at low frequency, the others are limited by quantum (radiation pressure) noise. The NS-NS optimized curve is limited in the middle frequency band (30 Hz to 300 Hz) by mirror coating thermal noise. The different modes are optimized for various astrophysical targets (black hole binaries, neutron star binaries, etc.)
In the next chapter, we will discuss the choice between two methods of gravitational wave signal extraction.
Chapter 4
Gravitational Wave Signal Extraction
The techniques described in the previous chapter centered around three principle concerns:
Shaping the gravitational wave signal frequency response using the technique of signal re- cycling/RSE.
Amplifying the GW transduction gain by using resonant cavities to increase the amplitude of the circulating laser field which samples the metric.
Reducing extraneous sources of noise by carefully employing symmetries which reduce the in- fluence of noise, especially laser noise.
These all work towards increasing the fidelity of the optical carrier phase with the strain (cf. equa- tion (3.4)), with the additional possibility of emphasizing certain frequency bands. We now have to convert this optical phase to a measurable quantity, which is the subject of this chapter.
As discussed in section 3.5.1, there are two ways to convert an optical phase to a measurable signal (current or voltage) using a photodetector: heterodyne detection and homodyne detection.
We now discuss these options in more detail as pertained to gravitational wave signal extraction, where the choice is between RF readout (heterodyne) and DC readout (homodyne), terms which refer only to the GW channel (DARM). Signal extraction for the other degrees-of-freedom (MICH, PRCL, SRCL, CARM) is by heterodyne detection, as it provides more options for non-degenerate sensing of these auxiliary DOFs [66].
For audio frequency gravitational waves incident on the interferometer, the gravitational wave signal takes the form of audio sidebands around the laser carrier light. We now need to detect these audio sidebands at the output port. The choice between RF readout and DC readout is just the choice of local oscillator used to downcovert those audio sidebands to an electronically tractable frequency.
4.1 RF Readout
In order to sense and control the length degrees-of-freedom of a complex interferometer, a sophisti- cated variant of the Pound-Drever-Hall technique (cf. section3.6.3) is employed. This involves using a set of frontal (upstream of the interferometer) phase modulation sidebands on the laser carrier field. The carrier and modulation sidebands experience different resonant conditions in different subsections of the interferometer; this is the resonance profile (more in chapter 6). By optically heterodyning the fields exiting various ports of the interferometer, we can extract non-degenerate signals about the various length degrees of freedom [43,67]. A detailed discussion of this technique for a power-recycled Fabry-P´erot Michelson interferometer is in [68]; an overview of a technique for a detuned RSE interferometer is in chapter 6. Since the length sensing and control system relies on heterodyne detection for all the auxiliary (non-DARM) degrees of freedom, it is convenient to use the same technique for DARM. This is what has been done in the first generation of detectors (LIGO, Virgo, TAMA, GEO600).
Figure 4.1shows the fields at the asymmetric port, after demodulation. The rightmost portion of the phasor diagram is basically a picture of equation (3.30a) and equation (3.31a), with the fields represented by arrows. It is worth noting that the interpretation of the I-phase and Q-phase signals is reversed here from what was mentioned in section 3.5.1 (i.e., now the Q-phase signal gives the carrier optical phase, while the I-phase signal contains the sideband imbalance); this is a common convention for the asymmetric port. The left panel shows the resultant LO-field vectors after demodulation, for the two demodulation phases; the middle panel shows both carrier field vectors reflected from the arm cavities, which ideally should sum to zero at the asymmetric port.
DARM motion counterrotates the two vectors, resulting in a vector field pointing along the horizontal axis. The third panel combines the two, showing how the I-phase signal is a combination of the carrier contrast defect (due to unequal reflectivities of the two arm cavities), while the Q-phase signal contains DARM motion.
DARM Q-phase
(carrier phase)
contrast defect I-phase
(RF sideband imbalance)
DARM signal
. =
RF sideband fields at asymmetric port
after demodulation carrier fields at asymmetric port
Figure 4.1: Phasor diagram of the asymmetric port in an RF readout scheme.
A common feature of heterodyne schemes is that the RF sidebands used as local oscillators for the DARM signal are transmitted to the asymmetric port using a Schnupp asymmetry (cf. section3.5.1),
and these sidebands do not resonate in the arm cavities. This means that the RF sidebands do not undergo any significant filtering bysc orscc, and any noise on the modulation sidebands (whether from the laser itself or the modulator) thus passes essentially unchanged to the detection port of the interferometer. Once there, amplitude and phase noise on the modulation sidebands can pollute the signal when these sidebands are used as a local oscillator (cf. equation (3.30c), also appendix C).
These noisy sidebands are the principal drawback of RF readout.