Interferometer techniques for gravitational-wave detection

Several km-scale gravitational-wave detectors have been constructed worldwide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques; however, the complex optical layouts provide a new challenge. In this review, we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we pro reader to use these examples to gain hands-on experience with the discussed optical methods.