In this chapter we derive the responses of different detectors to a given gravitational wave described in a TT coordinate system related to the solar system barycenter by wave polarization functions h+ and h×. We start in Section 5.1 by enumerating existing Earth-based gravitational-wave detectors, both laser interferometers and resonant bars. We give their geographical location and orientation with respect to local geographical directions.
In Section 5.2 we obtain a general response of a detector without assuming that the size of the detector is small compared to the wavelength of the gravitational wave. Such an approximation is considered in Section 5.3. In Section 5.4 we specialize our general formulae to the case of currently operating ground-based detectors and to the planned spaceborne detector LISA.
Detectors of gravitational waves
There are two main methods of detecting gravitational waves that have been implemented in the currently working instruments. One method is to measure changes induced by gravitational waves on the distances between freely moving test masses using coherent trains of electromagnetic waves. The other method is to measure the deformation of large masses at their resonance frequencies induced by gravitational waves. The first idea is realized in laser interferometric detectors and Doppler tracking experiments [169, 170, 171, 172], whereas the second idea is implemented in resonant mass detectors [173, 174, 175].
Currently networks of resonant detectors and laser interferometric detectors are working around the globe and collecting data. In Table 5.1 geographical positions and orientations of Earth-based laser interferometric gravitational-wave detectors are given whereas in Table 5.2 resonant detectors are listed.