Reducing Thermal Noise By Using Khalili Etalon And High-order Mode

Laser interferometer gravitational wave detector is the main means of gravitational wave detection.However,the most sensitive frequency band is limited by the thermal noise of the mirror coating in the test mass.Thermal noise can be divided into Brownian noise,thermo-elastic noise and thermo-refractive noise.Brownian noise is arise from the Brownian motion of material molecules composed of test mass substrate and coatings,which is the main component of thermal noise.Thermo-elastic noise is caused by the thermal expansion due to the fundamental thermodynamic fluctuations,while thermorefractive noise is caused by the change of refractive index due to the fundamental thermodynamic fluctuations.Thermo-elastic noise and thermo-refractive noise are collectively referred to thermo-optic noise because of the same mechanism,and they have a minus sign between each other.In order to reduce the thermal noise of coatings,Khalili etalon(KE)and high-order Laguerre-Gaussian(LG)mode and other technologies to suppress thermal noise have been developed successively.Khalili etalon device the coatings into two parts,which avoids the accumulation of thermal noise for all layers in the conventional mirror(CM)on a single surface.High-order LG modes has good axial symmetry and better convergence beyond the radius of beam spot than base mode,which can be used to reduce thermal noise.According to the fluctuation-dissipation theorem,the stochastic intensity fluctuations of the macroscopic degrees of freedom in a thermodynamic system are directly proportional to its coupling to the microscopic degrees of freedom.In this paper,we study the suppression effect of the beam of Khalili etalon and high-order LG mode for thermal noise based on the fluctuation-dissipation theorem.The main content of this article includes the following three parts:(1)We introduced the theoretical background and generation mechanism of gravitational waves and summarized the types of gravitational wave sources.We analyzed the detection principle of the laser interferometer gravitational wave detector and described the source of the noise in the laser interferometer gravitational wave detector and the corresponding solutions;(2)We analyzed the generation mechanism of thermal noise,gave the mathematical model of Brownian noise and photothermal noise.We demonstrated the quantitative calculation method by using the fluctuation-dissipation theorem.Based on the mechanism of thermal noise generation,we listed the techniques to reduce thermal noise and analyze the feasibility and application prospect for each one;(3)We calculated the coating thermal noise of Advanced LIGO(a LIGO)and Einstein telescope(ET)with the high reverse coatings corresponding to the laser with a wavelength of 1550 nm,which Khalili etalon and high-order LG beam technology are employed in a LIGO and ET.On the premise that the substrate absorption is acceptable,we obtained the thermal noise suppression effects of each technique,then we combined the two technique and got the combined effect.