Optimal Light Beams and Mirror Shapes for Future LIGO Interferometers

Abstract

We report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the shape of mirrors, while fixing the mirror radius and maintaining a low diffractional loss. The result of this minimization is a beam with thermal noise a factor of 2.32 (in power) lower than previously considered Mesa Beams and a factor of 5.45 (in power) lower than the Gaussian beams employed in the current baseline design. Mirrors that confine these beams have been found to be roughly conical in shape, with an average slope approximately equal to the mirror radius divided by arm length, and with mild corrections varying at the Fresnel scale. Such a mirror system, if built, would impact the sensitivity of LIGO, increasing the event rate of observing gravitational waves in the frequency range of maximum sensitivity roughly by a factor of three compared to an Advanced LIGO using Mesa beams (assuming all other noises remain unchanged). We discuss the resulting beam and mirror properties and study requirements on mirror tilt, displacement and figure error, in order for this beam to be used in LIGO detectors.

9 pages, 11 figures

References in corpus (3)

• Entanglement of macroscopic test masses and the Standard Quantum Limit in laser interferometry
• The implications of Mexican-hat mirrors: calculations of thermoelastic noise and interferometer sensitivity to perturbation for the Mexican-hat-mirror proposal for advanced LIGO
• Finite Mirror Effects in Advanced Interferometric Gravitational Wave Detectors