Meta-Heuristics Optimization of Mirrors for Gravitational Wave Detectors: Cryogenic Case

In this paper, we explore the behavior of several optimization methods for reducing coating Brownian noise in the mirrors of gravitational wave detectors. We will refer to cryogenic operating temperatures, where the low refractive index material has mechanical losses higher than those of the high refractive index material. This situation is the exact opposite of that which occurs at room temperature, which is already widely known. The optimal design of the dielectric mirror (without a priori assumptions on thicknesses) can be obtained through the combined multi-objective optimization of transmittance and thermal noise. In the following, we apply several multi-objective meta-heuristics to compute the Pareto front related to the optimization problem of dielectric mirror thicknesses made of two materials (binary coatings). This approach gives us more certainty about the structure of the final result. We find strong evidence that all meta-heuristics converge to the same solution. The final result can be interpreted with simple physical considerations, providing useful rules to simplify the thicknesses of the optimization algorithm.