• beam geometry
• mesa beam
• non-Gaussian
• optimized coating
• thermal noise reduction

Thermal noise of the test masses is expected to be a limiting factor in Advanced Gravitational Waves (GW) Interferometers. Many research groups work on R&D activities finalized to improve the thermal noise performance of next generation detectors. Some research lines deal with cryogenic temperature, other with improved or new materials, other with optical beam shaping and optimization of the mirror geometry and/or coating. Non Gaussian beams have been proposed years ago to reduce a particular type of thermal noise (substrate thermoelastic).
In this thesis we provide a quantitative analysis of the impact of non-Gaussian beams on different kinds of thermal noises. We show that the mesa beam implementation could boost the Advanced LIGO sensitivity considerably: even with a rough estimation (without re-optimizing the detector for the introduction of mesa beams), the binary neutron star inspiral range increases from 175 Mpc to 225 Mpc. We illustrate the importance of uniform sampling of the mirror surface to reduce thermal noise and the limitation brought by the use of excited modes with nodes on the mirror surface.
We developed the theory of mesa beam, in view of a future implementation in advanced GW interferometers of the mesa beam idea, focusing on the analytical derivation of the quantities (beam width, divergence, M2 factor, etc...), which are chosen as ISO standard reference parameters for the characterization of an optical beam. We also analytically proved a new duality relation between optical cavities with nonspherical mirrors. This derivation provides a unique mapping between the eigenvalues and eigenvectors of two cavities whose mirrors shapes are related by a simple relation. This duality allows the direct application of beam property calculations performed in a case to geometries of the other configuration.
The interest of the GW community in this new beam technology led us to the construction and testing of a prototype mesa beam Fabry-Perot cavity with mexican-hat mirror. Part of the work of this thesis was devoted to the development of new simulation programs of optical systems. These programs provided the theoretical expected behavior of our experiment, in particular cavity’s modes structure and misalignments sensitivity to be confronted with the experimental results. We developed new simulation packages to analyze the performance of our cavity prototype with real imperfect mirrors, using the measured mirrors maps. The model developed can include uniform and non-uniform scattering and absorption losses, as well as the effects of mirror heating A particular attention has been devoted to keep theses simulation programs very easy to use and very easy to change/upgade by anyone involved in optics research. The good agreement between theory and experiment validated the mathematical tools here developed thus allowing safe extrapolation to the larger optical systems needed in GW observatories.
We also explored another complementary way of reducing the mirror thermal noise, beside the beam shaping, that is the multi-layered coating thickness optimization. We show it to be effective in reducing the coating noise and explore the possible implications for GW interferometers in terms of sensitivity.
During this analysis we developed an independent model for the coating effective elastic parameters, which is based on the well understood subject of homogenization theory.