Displacement noise from back scattering and specular reflection of input optics in advanced gravitational wave detectors

The second generation of ground-based interferometric gravitational wave detectors are currently being built and installed. They are designed to be better in strain sensitivity by about a factor 10 with respect to the first generation. Light originating from the laser and following unintended paths, called stray light, has been a major problem during the commissioning of all of the first generation detectors. Indeed, stray light carries information about the phase of the emitting object. Therefore, in the next generation all the optics will be suspended in the vacuum in order to mitigate their associated stray light displacement noise. Despite this additional precaution, the challenging target sensitivity at low frequency which is partially limited by quantum radiation pressure combined with up-conversion effects, requires more detailed investigation. In this paper, we turn our attention to stray light originating from auxiliary optical benches. We use a dedicated formalism to compute the re-coupling of back-reflected and back-scattered light. We show, in particular, how much care should be taken in designing and setting requirements for the input bench optics.