Higher-order Laguerre-Gauss interferometry for gravitational-wave detectors with in situ mirror defects compensation

The use of higher-order Laguerre-Gauss modes has been proposed to decrease the influence of thermal noise in future generation gravitational-wave interferometric detectors. The main obstacle for their implementation is the degeneracy of modes with same order, which highly increases the requirements on the mirror defects, beyond the state-of-the-art polishing and coating techniques. In order to increase the mirror surface quality, it is also possible to act in situ, using a thermal source, sent on the mirrors after a proper shaping. In this paper we present the results obtained on a tabletop Fabry-Pérot Michelson interferometer illuminated with a LG_(3,3) mode. We show how an incoherent light source can reduce the astigmatism of one of the mirrors, increasing the quality of the beam in one of the Fabry-Pérot cavities and then the contrast of the interferometer. The system has the potential to reduce more complex defects and also to be used in future gravitational-wave detectors using conventional Gaussian beams