(ed.). Gravitational waves (IOP, 2001)(422s).

The physics of interferometers 31Drever and independently by Schilling. Normally, interferometers workon a ‘dark fringe’, that is they are arranged so that the light reachingthe photodetector is zero if there is no gravitational wave. Then, asshown in figure 3.1(a), the whole of the input light must emerge from theinterferometer travelling towards the laser. If one places another mirror,correctly positioned, between the laser and the beam splitter (figure 3.1(c)),it will reflect this wasted light back into the interferometer in such a way thatit adds coherently in phase with light emerging from the laser. In this way,light can be recycled and the required power levels in the arms achieved.Of course, there will be a maximum recycling gain, which is set by mirrorlosses. Light power builds up until the laser merely re-supplies the losses atthe mirrors, due to scattering and absorption. The maximum power gain isP =11 − R 2where 1 − R 2 is the total loss summed over all the optical surfaces. For thevery high-quality mirrors used in these projects, 1−R 2 ∼ 10 −5 . This reducesthe power requirement for the laser by the same factor, down to about 6 W.This is attainable with modern laser technology.• Ground vibration and mechanical vibrations are another source of noisethat must be screened out. Typical seismic vibration spectra fall sharplywith frequency, so this is a problem primarily below 100 Hz. Pendulumsuspensions are excellent mechanical filters above the pendulum frequency:it is a familiar elementary-physics demonstration that one can wiggle thesuspension point of a pendulum vigorously at a high frequency and thependulum itself remains undisturbed. Suspension designs typically involvemultiple pendula, each with a frequency around 1 Hz. These provide veryfat roll-off of the noise above 1 Hz. Interferometer spectra normally showa steep low-frequency noise ‘wall’: this is the expected vibrational noiseamplitude.In addition, there are noise sources that are not dominant in the presentinterferometers but will become important as sensitivity increases.• Quantum effects: uncertainty principle noise. Shot noise is a quantum noise,but in addition there are other effects similar to those that bar detectorsface, as described below: zero-point vibrations of suspensions and mirrorsurfaces, and back-action of light pressure fluctuations on the mirrors. Theseare small compared to present operating limits of detectors, but they maybecome important in five years or so. Practical schemes to reduce this noisehave already been demonstrated in principle, but they need to be improvedconsiderably. This is the subject of considerable theoretical work at themoment.• Gravity gradient noise. Gravitational-wave detectors respond to any changesin the gradients (tidal forces) of the local gravitational field, not just