ObjectiveThe thermal noise in the mirror coatings of a test mass is an important limiting noise source in high-precision measurements such as gravitational wave detection, and has become one of the main limitations of improving detection sensitivity. In order to improve the sensitivity of detection, it is necessary to adopt the thermal noise suppression technology, and even to adopt a combination of multiple non-interfering suppression techniques to reduce the thermal noise. So we combine the two suppression techniques of Khalili etalon (KE) with distributed reflective coating structure and high order Laguerre-Gaussian (LG) mode beam with wider and more uniform transverse intensity distribution compared to the base mode currently used.MethodsIn this paper, we calculated thermal noise based on the fluctuation-dissipation theorem. To calculate the thermal noise of the coating, the elastic equation of the substrate needs to be solved, and the coating thermal noise can be obtained by the boundary conditions between substrate and coatings. The boundary conditions for the substrate are determined according to the reflection of the beam in conventional mirror and KE respectively, and the beam intensity profile is expanded with the oscillation mode of test mass, which is described by the Bessel function. The strain and stress tensor and the elastic energy of substrate can be obtained from the elastic equation and boundary conditions, the three corresponding mechanical quantities of the coating are derived from deve the boundary conditions between the coatings and substrate. We add up the elastic energies of all the coatings to get the total coating thermal noise. The suppression factor is defined as the ratio of the original noise level to the noise level after suppression, and the distribution of the coating layers is determined by considering the factor and the absorption of substrate due to the reduction of the front coating layer.Results and DiscussionsCompared with the LG base mode currently used in aLIGO (Advanced laser interferometer gravitational wave observatory) and KAGRA (The Kamioka Gravitational Wave Detector), the high-order LG modes, which have a wider and more uniform light intensity distribution, can effectively average the fluctuation of the mirror surface to mitigate the influence of the Brownian motion of the mirror on the sensitivity of the detector. Since the suppression effects of the high-order mode and KE does not interfere with each other, they can be directly superimposed. We applied some high-order modes to the conventional mirror and KE while ensuring the equal diffraction loss, calculated the coating thermal noise of these modes. The suppression effect of the high-order mode on thermal noise increases as the order of the mode rises, but no mode is obviously better than other modes of same order. Considering the production efficiency of high-order modes and matching with the interferometer, we chose LG₃₃ to demonstrate the suppression effect.ConclusionsAt the wavelength 1 550 nm of the laser light utilized in the third generation of gravitational-wave-detection laser interferometer, we combine with high-order LG33 mode and KE with 5 front coating layers to effectively suppress thermal noise at room temperature. The coating thermal noise is suppressed to 1/3 of the original level, which is equal to the thermal noise level when the test mass is cooled down to 30 K.