On optics surface imperfections and their effects on the sensitivity of speed meters

It took several decades of intense research and development and the effort of thousands of people to reach the detectors sensitivity that allowed the gravitational waves detectors Advanced LIGO and later Advanced Virgo to make the first detection of gravitational waves on September 14th 2015 (and many other after that). This event marks the birth of gravitational wave astronomy and opens a new window on the universe, giving us the ability to gather information otherwise impossible to obtain. However it is still important to further increase the sensitivity of the interferometers in order to extract more accurately the parameters of the observed gravitational wave sources, as well as to discover new classes of gravitational wave emitters. So research efforts are pursued on all fronts, trying to reduce any relevant sources of noise. One of the proposed methods for the reduction of the quantum noise is based on the concept of quantum non-demolition measurements and speed meters. In this context, a proof-of-concept experiment is underway at the University of Glasgow. The aim of the experiment is to prove that in a Sagnac interferometer, which is per se a speed meter, quantum radiation pressure noise is lower than in an equivalent Michelson at audio-band frequencies. The interferometer designed for this experiment is composed by two triangular cavities with 1 g input test masses and 100 g end test masses and a finesse of ~8000. In this way the sensitivity at low frequencies will be dominated by quantum radiation pressure noise. However these features make the interferometer very sensitive to loss and high quality surface mirrors are then indispensable. The analysis of how much the mirrors surface imperfections will affect the quantum noise in speed meters is indeed the main topic of this thesis. The work carried out can be divided in two parts. The first part consists in the derivation of the arm cavity mirrors surface requirements for the Glasgow Sagnac speed meter. Because of the high dependence of its sensitivity from optical loss, the mirror surface requirements must be very stringent and an in-depth analysis to derive them is presented here. This analysis was done performing simulations that give an estimate of the roundtrip loss generated by each kind of mirror surface imperfection. In particular most of the analyses were done using OSCAR (acronym of Optical Simulation Containing Ansys Results), a Matlab package that can simulate the behaviour of a cavity with arbitrary mirrors surface profiles. The second part of the thesis is a theoretical analysis of the backscattering effect inside a cavity and how much it affects the quantum noise. The backscattering is a mechanism that arises when the intra-cavity beam has non-zero angle of incidence on the arm cavity mirror. Due to microroughness, in fact, the beam can be scattered back in the same direction as the incident beam. It will then couple with the counter-propagating beam and this coupling causes an increment of the quantum noise. The results are applied to the case of the Glasgow Sagnac speed meter and to future large scale interferometers. It is worth noting that the analysis of this newly discovered noise coupling caused by backscattering in speed meters featuring triangular cavities can also be applied to the class of speed meters configurations using linear cavities and two different polarisations, where the coupling of the modes is caused by birefringence